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misc. TGD-Physics Questions and Answers
by Dr. Matti Pitkänen
TGD
Postal address:
Köydenpunojankatu 2 D 11
10940, Hanko, Finland
E-mail: [email protected]
URL-address: http://tgdtheory.com
(former address: http://www.helsinki.fi/~matpitka )
"Blog" forum: http://matpitka.blogspot.com/
From: Matti Pitkänen [[email protected]]
To: [email protected]
Sent: Wednesday, May 16, 2012 10:23 AM
Subject: re. the search for the 'correct' formula
> From your response to Hamed in "A Universe From Nothing" blog:
>
>> "I believe that the correct guideline is that the mathematics that one learns or perhaps
even creates must naturally emerge from applications to real world problems (in my case,
Physics). When I was younger, I used to make visits to math library and walk between
bookshelves with the idea that I might find some miraculous cure to my mathematical
problems with TGD. I left the library in a rather depressed mood!;-)."
>
> Didn't Einstein struggle with a mathematical description of General Relativity? If I
recall, it was his mathematician friend Grossman who searched the libraries (for 2 years?)
before stumbling upon Riemann's forgotten "Foundations of Geometry" lecture (1854?)
that gave the correct formula for GR.
>
> And wasn't string theory discovered by physicist Gabriele Veneziano who searched for a
year for a formula that could describe the strong nuclear force when he came upon an
almost obsolete Euler formula that was the answer?
>
> Apparently you tried the same thing by searching libraries. But how did these guys
know when they had the "correct" formula? Do you try to match up experimental data
with each-and-every formula that you come across? Or do you build hypothetical
1
mathematical models and then try to see if a more robust theorem already exists? Maybe it
doesn't; maybe the hypothetical model will come before the more formal theorem.
Yes. Einstein had to learn a lot of mathematics in the technical sense and in this
process lost his ability for great visions.
It took more than 5 years to accept that path integral formalism then and still in fashion
simply does not make sense in TGD. Same about canonical quantization. Finally I
realized that Einstein's geometrization program must be generalized. Geometrize quantum
physics by geometrizing the World of Classical Worlds (WCW) and obtain quantum
physics as physics for classical spinor fields in this space. "No quantization" as Wheeler
would say. The next question was how to identify this geometry.
After this, it took 5 years to end up with the realization that the geometry defines what
is usually called "classical physics" as Bohr orbitology.
The idea of p-adic physics emerged without any rational motivation and it took a long
time to realize that real and p-adic physics must be fused together by generalizing the
notion of geometry.
I did not fit any formulas simply because it was impossible (and is still to a high degree
impossible). All breakthroughs in TGD have been discoveries of principles just as
Einstein's key discoveries were principles rather than formulas.
-- Matti
From: Edward Halerewicz, Jr. [[email protected]]
To: McWilliams, Mark L
Sent: Thursday, May 17, 2012 3:39 AM
For the case with Einstein, the fundamental postulates about Nature come first. This is
a rare thing to do. Most discover laws or mathematics from observation. But people like
Einstein do it with their mind. Einstein thought up the Equivalence Principle (acceleration
~ gravitation) since acceleration can appear to bend light, so gravitation can bend "space".
When Einstein tried to describe such a space, it differed wildly from rigid classical
Euclidean space due to curvature and so he was left without a valid mathematical model to
describe bent space and make predictions until Grossman pointed out that Riemann had
already done so. The dilemma that Einstein faced was that his bet was the space was bent.
But at the time he did not have the vocabulary to describe bent space, what does bent space
look like, and how does it behave. No easy task to answer without a prior background and
that's why mathematicians have a special place in history. My guess is that Matti means
that he has the first principles in mind for his model but lacks the proper math to describe it
in full and make proper testable predictions.
I am not sure how to make a computer-engineering analogy. But without the right
mathematics, there are just some things you can't describe. It would be like using algebra
to solve a differential equation without knowing anything about calculus, a process that
2
could take decades or centuries and that's without getting into the physics. You know you
have the right formula when it satisfies rigorous mathematical proofs and you are able to
apply those proofs to known problems and spit out the correct solutions. I think you have
to keep in mind that chemistry makes uses of known numbers systems, natural numbers,
engineering makes use of known physics.
It's a bit like expecting to derive the Periodic Table of elements in say N-dimensional
space. Can't do that with standard chemistry because there is no language for it. You need
to create a new language to describe N-dimensional chemistry. You could probably do it
eventually but it's a time-consuming process and by default it would force you to become a
mathematician and likely years of study to obtain any tangible results. But the task
becomes trivial if you can find somebody who has already written about N-dimensional
space in a library.
Edward Halerewicz, Jr.
Independent Researcher
BSc Geography & Env Res, ASc Physics
http://da_theoretical1.tripod.com
From: Matti Pitkänen [[email protected]]
To: McWilliams, Mark L
Sent: Thursday, May 17, 2012 7:27 AM
Much of the new mathematics exists potentially. Some examples:
A. The notion of Super Kac-Moody algebra generalizes since instead of 2-D complex
space one has 3-D light-like surface. Algebra extends dramatically. Kac-Moody
algebras are based on finite Lie algebras. Now finite Lie algebra is replaced with
certain infinite-D symplectic algebra. A further generalization is extension to
multilocal algebra generalizing the notion of Yangian. All this would require a
legion of mathematicians to work out the formulas.
B. Geometry of WCW as a union of symmetric spaces would require precise mathematical
formulation and again mathematicians would be needed. The basic structure is
understood and even formulas for the metric tensor are known to high degree. But
this is far from enough.
C. The fusion of p-adic and real mathematics to larger coherent whole would require a lot
of work by mathematicians. Typically both physicists and mathematicians work with
models limited to single prime p. I learned only recently that top mathematicians
(including Grothendieck) have been working the last decades with various
mathematical problems related to p-adic physics (p-adic integration is one example).
D. Hyper-finite factors of type II1 represent existing mathematics developing all the time.
But there is a huge communication gulf between mathematicians and physicists
(including me). Bourbaki should be translated to the language of physicists.
E. The formulation for the hierarchy of Planck constants would also require a lot of
mathematical work.
3
These are just some examples. Big ideas require a new mathematical language.
-- Matti
http://matpitka.blogspot.com/2013/07/about-naturality-fine-tuning-and-recent.html#comments
topic: "About naturality, fine tuning, and the recent ego catastrophe in Theoretical Physics"
1. At 5:55 AM, Ulla said...
On Julian Barbours wikipedia page are 3 links:
● Anderson, Edward (2004) "Geometrodynamics: Spacetime or space?" Ph.D. thesis,
University of London. http://arxiv.org/abs/gr-qc/0409123
● (2007) "On the recovery of Geometrodynamics from two different sets of first principles,"
Stud. Hist. Philos. Mod. Phys. 38: 15. http://arxiv.org/abs/gr-qc/0511070
● Baierlein, R. F., D. H. Sharp, and John A. Wheeler (1962) "Three dimensional geometry as
the carrier of information about time," Phys. Rev. 126: 1864-1865. (Tthis I cannot find
for free on net).
“Why do some people get caught by an idea that takes over your life? I don’t know, but I do
know that as long as it doesn’t drive you crazy, it is a blessing,” Barbour says gently. “When I
started out on this 40 years ago, I said to my family that I know what I want to do and it will take me
the rest of my life to do it.
And that is the way it has worked out.”
http://rspa.royalsocietypublishing.org/content/382/1783/295 from 1982
Maximum
negentropy
principle
http://www.fluid.tuwien.ac.at/news?action=AttachFile&do=get&target=Einladung%26AbstractProf.Mahulikar.pdf
http://www.lawofmaximumentropyproduction.com/CSF08.pdf here is the text
2. At 9:24 PM, Matti Pitkanen said...
The basic problem of Wheeler's GeometroDynamics is that basic objects are 3-dimensional. One
should be able to get out 4-D space-time from this approach. Barboux is quite right in saying that
Time is lost in General Relativity based on Wheeler's GeometroDynamics.
Wheeler's
GeometroDynamics also has profound mathematical difficulties. For instance, it is difficult to get
fermions out of it and the geometry of super-space is poorly defined.
But why should Nature obey Wheeler's GeometroDynamics? Wheeler's notion of super space
must be modified so that it exists mathematically and is consistent with the basic space-time
symmetries (Poincare group) and geometric description of gravitation.
TGD's "World of Classical Worlds" allows us to achieve this elegantly. The news is that after
more than 2 decades this is still news!
Thank you for links. They allow to clarify the relationship of TGD to other theories.
4
The Negentropy Principle introduced by Mahulikar brings in mind Negentropy Maximization
Principle.
The abstract does not give much idea about what is involved but thermodynamics is claimed to
give NP. I find it difficult to take this seriously, at least if one talks about conscious information.
Thermodynamical definition of negentropy allows one to consider only entropy gradients and
claim that the flow of entropy out of space-time volume corresponds to flow of information into it.
But I cannot take this seriously. One should speak about absolute information rather than changes of
information. With this criterion, the best thermodynamics can give is that there is zero entropy (and
also zero negentropy).
Negentropy maximization and entropy maximization (Second Law) are apparently contradictory.
Conflict disappears when one realizes that number theoretic entanglement negentropy characterizes
a decomposition of system to 2 parts. Hence 2-particle property is in question. This notion is not
thermodynamical but purely quantal. Thermal entropy in turn characterizes average member of
ensemble of identical systems and is single-particle property.
As a matter of fact, NMP implies the Second Law and entropy maximisation for ensemble for
ordinary matter. In dark matter sector where negentropic entanglement is possible, the situation
remains unclear.
There is, however, a very close correspondence between entanglement negentropy and
thermodynamical entropy. A system having n degenerate states (corresponding to sheets of nmultifurcation of space-time sheets and heff=n*h) is highly entropic as single particle system. One
does not know at what sheet the particle is.
By entangling 2 systems of this kind by nxn unit matrix, one obtains negentropically-entangled
system stable under NMP. Living systems are this kind of system and the multi-sheetedness
provides them with high representative powers. Highly entropic systems (in sense of having large
heff) are buildings blocks of highly negentropic systems.
One can argue that these kind of entangled systems are highly critical ("in the intersection of
reality and p-adicity") and unstable. Here standard measurement theory (that is basic law of Nature)
comes in rescue. It predicts that state function reduction leads to states which are characterized by
nxn unit matrices for them so that number theoretic negentropy is positive and NMP does not force
further state function reduction.
3. At 11:14 AM, Stephen said...
Ulla, I busted the knowledge outta jail. You can find it @ http://vixra.freeforums.org/threedimensional-geometry-as-carrier-of-information-t86.html
4. At 8:53 PM, Matti Pitkanen said...
To Stephen:
Imbedding is also now needed to obtain Time. To 4-manifold which solves Einstein's equations
rather than fixed 8-D imbedding space M4xCP2.
5
They imbed 3-geometries as sub-manifolds of 4-manifolds which are solutions of Einstein's
equations. In this manner they can imbed two 3-manifolds as time=constant cross-sections of 4manifold and say which was earlier and also calculate temporal distance between them.
This works of 3-geometries that happen to be space-like intersections of the same solution of
Einstein's equations but not otherwise. In TGD this works for all 3-surfaces.
Another problem is that there is infinity of space-times containing a given 3-geometry as cross
section so that in practice one cannot apply the procedure. One would also like holography: moreor-less unique space-time as analog of Bohr orbit. But this one does not obtain.
The further problem is related to the Classical conservation laws since Noether's theorem-based
conservation laws are lost since symmetries are lost.
5. At 11:27 AM, Anonymous said...
On the sidenote, here's so far best introduction to fractional 10-adic or "reversimal" arithmetics
I've seen, touching also very deep issues like Euler's doubly infinite identity, and that the
computation on the "reversimal" side is actually much simpler than on the decimal side:
http://www.youtube.com/watch?v=XXRwlo_MHnI
PS: googeling "doubly infinite identity" gives quite a lot of results which may be of interest for
those developing arithmetics and algebra between p-adics and reals.
More good stuff, problems of theory of real numbers:
http://www.youtube.com/watch?v=tXhtYsljEvY
http://www.youtube.com/watch?v=ScLgc_98XxM
So it seems that the Original Sin of Metaphysics (aka the Fall of Physics) creeped into natural
philosophy in the theory of real numbers based on axiom of choice - which is the current standard
belief, according to which most do also physics.
On pi as "metanumber".
http://www.youtube.com/watch?v=lcIbCZR0HbU
(Finnish difference between 'numero' and 'luku' sound very important but difficult to translate
into English.)
6. At 6:48 PM, Matti Pitkanen said...
Thanks to Anonymous:
The link gives excellent intro to p-adic numbers. p-Adic numbers are indeed in many respects
much simpler than reals. Basic challenge is to understand the correspondence with Reality! How
reals and p-adics correspond to each other. The notion of p-adic manifold that I have discussed here
comes in help.
In p-adic context, pi(π) is indeed metanumber in the sense that for finite-D extensions (and
algebraic extensions in general), one can have only roots of unity. Only cosines and sines of 2* π /n
but not 2* π /n itself. One can allow infinite-D extension (not algebraic anymore) bringing in all
powers of π. But somehow I do not like it all.
6
7. At 3:42 AM, Anonymous said...
Sines and cosines etc. of current standard trigonometry based on radius and length have never
made sense to me. So I very much like good professors approach to trigonometry (and its
implications) which he calls "universal hyperbolic geometry". Here's the introduction to subsequent
lectures:
http://www.youtube.com/watch?v=EvP8VtyhzXs
This approach has much to contribute to learning TGD and perhaps TGD can also benefit from
universal hyperbolic geometry and other ideas and views of this good professors such as centrality of
rationals in all number theory, etc.
One question and idea that first came to mind was proof of "metanumber" or "metarational"
Euler's Identity of relation of π, e and i in universal hyperbolic geometry instead of standard
trigonometry.
Some discussion on 'Is there p-adic 2πi and where to look':
http://sbseminar.wordpress.com/2009/02/18/there-is-no-p-adic-2-pi-i/
The deep structure of rationals:
http://www.youtube.com/watch?v=gATEJ3f3FBM
This touches also the questions in the OP as this lecture presents simply and beautifully the
natural fractality and holonomy of the deep structure of rational numbers.
And as hinted before, the Fall of Physics can be perhaps most informatively originated to sloppy
metaphysical approach to reals with the purely metaphysical axiom of choice. Trying to run before
learning to walk. The intuition that "reals" can make sense only with "doubly infinite identity" with
p-adics rises naturally.
8. At 5:32 AM, Matti Pitkanen said...
In the link it is said that there might be a manner to define p-adic 2π i but certainly the usual
definition fails. If this definition exists, it should be also physically meaningful. Cosines and sines
however exist for roots of unity and this leads automatically to finite measurement resolution for
phases giving a hierarchy of phase/angle resolutions.
π and also other transcendentals appear in the scattering amplitudes of QFTs. The assumption
that they are absent from amplitudes poses very strong conditions on the p-adic counterparts of
scattering amplitudes and also real scattering amplitudes.
Bringing 2 πi and its powers via infinite-dimensional non-algebraic extension of p-adics might
lead to inconsistencies. exp(i2π/n) defined as power series should be equivalent with its counterpart
introduced as root of unit via algebraic extensions. All roots of unity would actually follow as a
consequence of introducing 2πi via non-algebraic extension. Is the introduction of 2πi equivalent
with the infinite-dimensional abelian extension containing all roots of unity?
And what about the numbers exp(i2 π*x/n) where x is p-adic integer containing infinite pinary
digits and therefore infinite as real integer? Can one define x modulo n for any integer to make the
formula sensibl>. Or could one define x by giving x mod n for all n?
7
9. At 2:22 AM, Anonymous said...
Does the theory of complex reals do anything worth doing that complex rationals and rational
transcendentals can't do?
If I'm not mistaken, with e^iπ you can plot each point of circle with precise number theoretical
meaning just as well and even better on complex rational plane than on complex real plane when you
treat also e and π (etc.) as "whole (meta)numbers" also giving rational relations or rational numbers.
Here's the Euler's doubly infinite identity, from the introduction to p-adics linked above: ... + x3
+ x2 + x + 1 + 1/x + 1/x2 + 1/x3 + ... = 0
Again if I'm not mistaken, it states that e.g. p-adic π is simply -π. The sum of real π and p-adic π
is zero.
10. At 3:07 AM, Matti Pitkanen said...
The problem with Euler identity deriving from 1/(1+x) +1/(1-1/x) -1 = 0 by using formal
geometric series expansions is that 1/(1-x) converges for |x|<1 only and 1//1-1/x) for |x|>1 only. For
x=1 both give infinity.
In p-adic case, N_p(x)<1 is necessary for converge for 1/(1-x) and N_p(x)>1 for the
convergences of 1/(1-1/x).
Therefore it is difficult to make any conclusions from the identity.
11. At 11:47 AM, Anonymous said...
… … Number theory is the language that equations and other algorithms use, not vice versa.
And just like forest and language of forest is not dependent from a house in forest and language of
house but a house is dependent from the larger inclusive forest, any set of of equations or more
generally an algorithm is sentence in the language of number theory which it implicates as larger
inclusive whole and from which it depends from. And thus reductionism looks only at single trees
and does not see the forest, the purest math of number theory.
So hopefully these metaphors make it even more clear than before why reductionism does not
and cannot work and why at the level of a respectful TOE of mathematical physics the only
meaningful description can be the whole of number theory. And that natural philosophy aka
mathematical physics requires only naturalization of number theory, cleaning out unnatural
metaphysical assumptions from number theory.
12. At 3:08 AM, Matti Pitkanen said...
To Anonymous:
I believe that number theory has a lot to give for Physics. Number theoretical universality for
scattering amplitudes is a very powerful constraint. Classical number fields appear in TGD
framework and allow one to understand Standard Model symmetries. The notion of infinite prime
has direct physical interpretation too.
13. At 9:48 AM, Ulla said...
http://arxiv.org/pdf/1308.0249v1.pdf Dark mass problem (solved?). Using Newton?
8
14. At 7:16 PM, Matti Pitkanen said...
To Ulla,
The "solution" just adds additional ad hoc term to Newton's equation. Nothing is said about
what happens relativity.
MOND is similar ad hoc approach to dark matter.
15. At 7:55 PM, Matti Pitkanen said...
To Anonymous:
Your arguments have been very interesting. I am sorry that I have not had time to enough to
participate in full.
I am not a mathematician in the technical sense and cannot take any strong views about
fundamentals of Mathematics. I am mathematically just an infant becoming conscious about ideas
in my own primitives manner; I am not a builder of axiomatic cathedrals. I would like to call myself
a "quantum Platonist" who tries to include also mathematician into his world view by postulating
that quantum states as purely mathematical objects representing objective existences and quantum
jumps between them define conscious information. Which is basically about these mathematical
ideas but also represented as our sensory experiences and cognition and to which we usually do not
assign anything mathematical. My views differ from those of Max Tegmark in that he does not
include consciousness in this Platonia explicitly.
TGD Platonia is also subject to evolution. Every quantum jump recreates the quantum state
describing existing potentially conscious information about mathematics (e.g., quantum Akashic
records that I have discussed in some postings). In mathematics this means endless updating of
axioms. New axioms emerge by discoveries taking place in quantum jumps. These discoveries are
not deductions from axioms but new axioms.
In this framework the basic goal is to understand the geography if Platonia - that is physics. The
2 visions behind TGD are physics as infinite-D geometry unique from its mere existence and physics
as generalized number theory (generalization means many things).
● For instance, the introduction of the notion of infinite prime as a process analogous to second
quantization applied repeatedly. Physics as a hierarchy second, third, ... quantizer ordinary
number theories would sound rather sexy;-)! I am not sure whether these 2 approaches are
equivalent or whether both are needed.
● For physicists, real continuum (and for me also p-adic continua) are fundamental since
continuum is needed for calculus and one cannot do much physics without calculus. This
leads to the vision of generalization of the notion of number by gluing real and p-adic
number fields and their algebraic extensions together along rationals (and possibly also
common algebraics). One would obtain a book-like structure and this structure would be
correlate for the sensory world and cognition.
To formulate this precisely is a huge challenge. In particular, how the quantum
physics in different number fields is related is a fascinating challenge and number theoretical
9
universality meaning kind of algebraic continuation between number fields, would pose very
strong constraints.
For instance, the notion of plane wave fundamental for physicist as something periodic does not
have p-adic counterpart. The analogs of trigonometric functions exist but are not periodic. This
forces the introduction of algebraic extensions and roots of unity defining them. In this manner the
notion of finite angular resolution emerges. Only the trigonometric functions of angles would exist
mathematically in the extension -- not angles themselves except by introducing infinite-D nonalgebraic extension generated by powers of π. Evolution would be emergence of more and more
complex algebraic extensions in quantum jumps. Mathematics would evolve like Living
organisms.
Going from reals to p-adic means algebraization. For instance, a circle is defined by its algebraic
representation x2+y2=R2 as set of discrete p-adic points satisfying this condition. The definition of
the length of circumference of circle is very difficult since the notion of definite integral does not
exist in any obvious sense in p-adic context. This reflects the fact that angle as a notion does not
exist geometrically in p-adic context.
Also the transfer of notions of real topology central for the TGD-based notion of particle to padic context is a fundamental challenge. The notion of p-adic manifold in which p-adic manifolds
has real chart maps and vice versa gives excellent hopes of solving these problems and makes finite
measurement resolution (i.e., central notion in Physics) a fundamental notion. For the old-fashioned
Platonist accepting that our knowledge is always only partial and can be also erratic is certainly
something new.
I am not only a child of my time. I am a mathematical infant so that TGD certainly involves
unnecessary and unnatural metaphysical assumptions about Mathematics. I have done met best to
eliminate such assumptions about Physics. TGD is basically a story of getting rid of unnecessary
and very probably wrong assumptions which have plagued the approach to fundamental physics for
last 4 decades: reductionistic dogma, GUT approach to particle spectrum, SUSY in standard form,
belief that only 2-D string world sheets allow conformal invariance, neglect of the fact that GRT
does not allow definition of standard conservation laws in Noetherian sense, etc.
I really see myself as innocent child. Real mathematicians are needed to find the minimal
language formulating these ideas precisely (assuming such language exists at all;-)).
http://matpitka.blogspot.com/2012/02/progress-in-number-theoretic-vision.html#comments
topic: "Progress in number theoretic vision about TGD"
At 10:00 PM, [email protected] said...
Wheeler's Geometrodynamics cannot be identified with General Relativity. The infinite-D space
of 3-metrics is the basic object and the dream is to quantize gravitation in this geometric framework
generalizing Einstein's geometrization program. This is one of the deep ideas of Wheeler.
At least 2 basic problems plague this approach.
The first problem is that one loses time. Space-times are what we want. How to make 3-D of
GeometroDynamics to 4-D of General Relativity. Semi-classical approximation to postulated path
integral over 4-geometries is the obvious approach but has formidable mathematical difficulties.
10
[The mathematical non-existence of the path integral is a quite general problem. QFT colleagues
have done their best to forget this. Pretend that there is no problem when problem is too difficult.
This has been the strategy of modern mainstream theoretical physics and guaranteed that nothing
new has emerged for 4 decades;-).]
The second problem is that one does not obtain fermions. Fermions are the problem of Classical
General Relativity too. Space-time need not allow spin structure at all so that one cannot talk about
spinor fields. This problem is much more general and also plagues string models and M-theory,
would have been excellent hint that space-times must be replaced with 4-surfaces and spinor
structure with induced spinor structure, has been put under the rug.
3-metrics are replaced with 3-surfaces in TGD framework. This solves both basic problems of
GeometroDynamics. WCW assigns to 3-surfaces space-time surfaces as analogs of Bohr orbits and
Classical Physics becomes part of Quantum Physics. The problems with fermions and spin are
circumvented via induced spinor structure. One fruit of labor is the geometrization of fermionic
statistics in terms of spinors of WCW.
Observer participancy is another very deep idea of Wheeler. The delayed choice experiment in
which one changes Geometric-Past is inspired by this idea.
The skeptic would react by saying that before we can talk about observer participancy, we must
have a physical definition for observer. We do not. The optimistic skeptic might try to imagine
what this definition might be on basis of existing and maybe some new ideas. The notion of self is
the TGD-inspired attempt to meet the challenge.
Evolution as a sequence of quantum jumps recreating the Universe repeatedly would
realize observer-participancy in the TGD Universe.
Most of us speak about cognitive, social, and cultural developments as something self evident.
But the theoretical physicist does not use these words. Very many words of Biology and
Neuroscience are absent from his vocabulary. Behavior, function, goal, homeostasis, punishments
and rewards, evolution -- everything relating to intentionality, goal directedness, values is absent.
The brutal reason is that the existing mathematical tools do not allow even attempt to define these
notions. New mathematics and new concepts are needed.
There is of course an easy way out. Self-deception which is as easy as cheating the innocent
laymen. Just say that "all that is" is nothing but a dance of quarks and consciousness is illusion and
life is nothing but complexity!
This is why I am talking about Physics as generalized number theory, p-adic physics, infinite
primes, hierarchy of Planck constants, etc. I am an observer wanting to participate the expansion of
our understanding about the white regions of the map;-).
http://matpitka.blogspot.com/2012/01/proposal-for-twistorial-description-of.html#comments
topic: "Proposal for a Twistorial description of generalized Feynman graphs"
1. At 12:37 PM, ThePeSla said...
So Matti,
11
You insist on quantum descriptions. But what then is original beyond Dirac's four spinors? I
mean that something is generalized is these work (but only so well for these decades since him) as
your last post that wants to make sense out of 4 waves. This 4- or5-fold pattern in Nature (recall
Einstein tried 5 dimensions for one rather cylindrical unified field.)
And these can be reduced to 2+1 formulism from the 3+1, much like Feynman diagram so
reduced and see as a general matrix to be expanded again into your 2x2 view (a debate of exclusion.)
Now in the quantum formulation, we have different ways to view things that amount to almost the
same thing. In its way it explains why we wind up with 3 dimensional space and 2 types of particles.
Mass in not in the equations -- that is what some are looking for as well the nature of gravity. To
base things on mass-less is merely to interpret Dirac's "nilpotent" algebra rather than "indempotent"
forms of models.
If you cut a knot (as if a string), does it have more than 2 end points? If twistors are only
complex duplications and numbers so to justify the 2 or 4 formulisms (of which in one form Dirac
uses 5...) it is not enough. Quantum Mechanics is not enough.
Now, the Mersenne primes as you use them may be enough. But that is a wide field to explore
(but it is to me an original approach).
I understand someone independent of the Academia being creative and free to read and
speculate. But I see no reason to make a great deal over idols of the day like Nima Arkani-Hamed
which all the bloggers seems to have done even when in disagreement. His is another near idea
along the way like some of Hawking's.
There are other ways to explain quantization than that from Dirac in that differences in space and
time and matter and charge are those of that great foundational difference between the continuous
and the discontinuous in the search for some measure.
Maybe the old Egyptians had it right. We should not always rationalize our fractions. We
simplify but lose information and the lost information is not clearly lost nor does it prove anything.
2. At 7:42 PM, [email protected] said...
Dear Pesla,
Some comments. First about twistors and related things.
(A) Why I appreciate Nima is that he is a theoretician with a tight contact with Reality. Also
clarity of thinking, enthusiasm, and courage and ability to imagine belong to his virtues.
Before knowing, one must imagine.
(B) The second point is that the work with twistors lead to the realization of Yangian invariance
and discovery of an infinite hierarchy of them. Their generalization emerges naturally in
TGD framework. N=4 SYM is the most useful toy model ever discovered. If I want to
formulate TGD as concrete rules someday, I must use all the wisdom that already exists.
(C) The idea that all massive states have massless building bricks is extremely powerful. Much
much more than "nilpotent Dirac algebra". Generalization of Yangian invariance, twistors,
new view about Feynman diagrams as twistor diagrams implied by Zero Energy Ontology,
12
... Together with Zero Energy Ontology, this identification might resolve also the basic
problems of twistor approach. How to get rid of infrared divergences; how massive states
emerge and can be described; how to describe non-planar diagrams; how to understand
renormalization group and coupling constant evolution; etc.
Some comments about Dirac spinors.
(1) I (and I think all theoreticians nowadays) use the term "Dirac spinor" in a more general sense
than Dirac. This may or not be regarded "original". Physics means to me much more than
"originality". Some things have been understood and the mathematical description of
"spin" is one of them. It is waste of time to try to invent ad hoc descriptions of spin.
The same applies to electroweak quantum numbers. The attempts to reduce them to, for
example, knot or braid topology is simply waste of time. There is huge data basis of
empirical facts demonstrating that group theory is behind electroweak symmetries. Braids
are also an extremely interesting part of TGD. But in the case of elementary particles (1 or 2
braids only), they do not bring in anything interesting.
The interesting new things emerge at the level of anyonic physics involving braids with
more than 2 strands. They define new kind of entities not identifiable as elementary particles
since the propagators from these states do not behave like they should behave for elementary
particles.
(2) Dirac spinors in TGD framework are 8+8-component spinors of M4xCP2 and describe
electroweak isospin besides spin and give automatically rise to quarks and leptons with
correct electroweak quantum numbers. At the level of "World of Classical Worlds"
(WCW), the counterparts of Dirac spinors are fermionic Fock states and spinor fields in
WCW describe all quantum states. Fermi statistics finds a geometrization in terms of
WCW gamma matrices expressible as combinations of fermionic oscillator operators.
Quite a leap conceptually but mathematically very natural.
(3) Mersenne primes are only specific p-adic primes which are of special importance in p-adic
physics. What is important are the p-adic topologies as the natural topologies for the
correlates of cognition. They have also deep connection with particle physics and number
theoretical universality realized in terms of quantum arithmetics becomes the deep
principle posing constraints on quantum physics. These specific primes give only grasp to
the reality via applications. The twistorial approach allows one to imagine how the number
theoretically universal amplitudes should be constructed using quantum arithmetics.
And few words about 4-wave interaction.
4-wave interaction is nonlinear interaction of laser waves. As such it is not something that
unified theorists is usually interested in. Modulation is second non-linear interaction involving 2
waves familiar from first-year courses in Physics.
Why I am talking about this kind of basic things is that the linear superposition of fields
corresponds in TGD only to the superposition of their effects. Particle has topological sum
contacts to the 2-or-more space-time sheets and experiences the sum of the fields carried by
them.
13
This is a profound difference at the basic ontological level. It is more than interesting to see
whether it really works. Can one describe effects like amplitude modulation and 4-wave
interaction in this framework?
One can!
3. At 8:41 PM, hamed said...
Dear Matti,
I don’t understand difference between 3-surface and topological field quantum in a well form.
They both are many sheeted. Are they the same?
Does Earth have 2 space-time sheets, one for outer surface and one for inner surface? And we
glue to outer surface?
“Elementary particles interpreted as CP2 type extremals topologically-condensed
simultaneously to the 2 space-time sheets involved.” Then electrons in atom topologically
condensed between 2 sheets, one for atom and other?
4. At 6:16 PM, [email protected] said...
To Hamed:
I mean by space-time surface any 4-surface.
*It could be "massless extremal" having 4-D M4 projection and would correspond to our ideas
about physics QFT in M4. This topological light ray would be example of topological field quantum
and would provide space-time correlate for say laser beam. It could carry topologically condensed
particles. Massless extremal would be more like a Macroscopic correlate for EM and other gauge
fields and also for gravitational radiation.
Also, magnetic and electric flux quanta or space-time sheets carrying magnetic and electric fields
simultaneously would be examples of topological field quanta. They have 4-D M4 projection so that
they also correspond to physics QFT in M4 intuition. Why I call them quanta is that they typically
have a finite size. For instance, an attempt to imbed constant magnetic field as induced gauge fields
give rise to a flux tube (say) with finite radius. Space-time ends at certain radius for these
imbeddings. The induced metric becomes singular and a good guess is that the boundary is lightlike and four metric is degenerate (effectively 3-D) at it. This kind of surface can also act as
wormhole throat at which region of space-time with Euclidian signature of induced metric begins.
This is quite a general phenomenon since 4-D CP2 is compact whereas the space of the values of
EM gauge potentials at given point is non-compact (essentially M4). This implies that the
representation of arbitrary gauge potential of M4 as a space-time sheet (map from M4 to CP2) cannot
be global. Boundaries are generated. This leads to the quantization of classical fields in the sense of
the splitting of the space-time surface to pieces.
Preferred extremal property also corresponds to Bohr quantization for fields. In fact, it seems
that space-time sheet very generally decomposes to regions having interpretation as massless quanta.
This would not allow superposition. Here the idea that parallel space-time sheets to which charged
particles have simultaneous topological sum contacts gives rise to a linear superposition of the
effects of Classical fields although Classical fields not superpose as in ordinary gauge theories.
14
Space-time surface could also be CP2-type vacuum extremal with 1-D light-like random curve as
M4 projection. Free elementary particles would be like this and the randomness of the light-like
curve would basically relate to massivation since motion with finite length scale resolution would be
sub-luminal. The roles of M4 and CP2 have changed and one has more like QFT with M4 valued
field in CP2.
There are also string like objects X2xY2 subset M4xCP2. X2 is string orbit (minimal surface) and
Y2 is complex surface of CP2. These would correspond to string model type description. QFT
picture would not make sense for their deformations and one would have something analogous to
field theory in X2xY2.
The Earth has a magnetic field and it is topologically quantized. The magnetic field decomposes
to topological flux quanta. They can be flux tubes or flux sheets (say spherical shells with finite and
varying thickness). One can clearly say that Earth possesses a magnetic body (and field body). In
Maxwellian theory, this kind of "personal field body" does not make sense. Dipole field splices to
flux tubes and flux walls is a good visual image.
Second question about electrons as deformations of CP2-type vacuum extremals.
Free electron when seen at CP2-length scale corresponds to space-time surface of this kind can
indeed touch several space-time sheets simultaneously because the distance between them is of order
CP2-length scale. The analogy is 2-or-more thin membranes which are parallel and extremely near
to each other.
You could assign these membranes to the Earth, Sun, Galaxy, etc. You could visualize electron
as an extremely tiny object between them having size of the order of their distance between themCP2 scale. Electron cannot avoid touching them.
When one enters to elementary particle mass scales which are much longer, one has some
delicacies. The wormhole throat associated with electrons own space-time sheet carries Kahler
magnetic charge which must be neutralized. Also the weak isospin must be neutralized above weak
scale about 10-17 meters. The second wormhole throat carrying opposite Kahler magnetic charge and
pair of neutrino and anti-neutrino could achieve this. Magnetic flux tube connects the 2 throats that
electron in the scales looks like string-like object and second end makes itself visible via the
screening of weak interaction.
Should the length of the flux tube be Compton length of electron or weak length scale? I am not
sure. Weak gauge bosons themselves are similar objects and might be enough for weak screening.
Could it be enough that the length of string is Compton length?
4. At 1:53 AM, Ulla said...
8+8 component spinors left me with? Dirac spinors acting on a field?
Is this a good text? http://www.math.sunysb.edu/rtg/Images/07.04.30.14.30.RTGSpin.pdf .
Note the Massive and massless representations in the middle of text.
In the massless case, we cannot go to the rest frame as this would require boosting up to Warp-1.
We can, however, always rotate to the frame in which the massless state of energy E is traveling in
the positive z-direction.
15
As the representation is supposed to be irreducible, it must be one-dimensional. In this case, the
eigenvalue of Sz (again half-integer) called the helicity and there are only two of them. The
massless state is making either a left-handed corkscrew around its axis of propagation or a righthanded one.
Note that helicity is a good quantum number in the massless case because we cannot change the
handedness of the screw unless we boost past the state.
...the 2-component spinors are the left- and right-handed parts of the original Dirac spinor.
5. At 6:23 PM, [email protected] said...
To Ulla:
Yes, the text looks okay although I still wonder what "warp" has to do with representations of
Poincare group.
The notion of left and right handedness mentioned in the text appears in 4-D case. In massless
theories, the numbers of left- and right-handed fermions are separately conserved.
Handedness generalizes in 8-D case to 8-D chirality which is conserved in TGD and gives rise to
separate conservation of baryon and lepton numbers. M4 handedness is not conserved anymore.
This is a direct indication for unavoidable massivation of the observed particles as opposed to the
fundamental building bricks of them.
6. At 10:31 PM, Ulla said...
Thanks, I have much to learn.
Here is a little delicate question. What is behind c as a "force" or constant/inertia, thinking of the
very broad result it is giving in the EM-radiation? And gauge forces? Holography? Mach?
Jack Sarfatti says it may not be real numbers and a square. Maybe many roots?
http://stardrive.org/index.php?option=com_myblog&show=debate-with-jim-woodward-on-hismach-starship-engine-theory-1-15-12-v2.html&Itemid=56
7. At 9:04 AM, ThePeSla said...
" People like us ... know that the distinction between Past, Present, and Future is only a
stubbornly persistent illusion."
-Albert
Einstein
Matti,
How much of other physics values can be like this concept? Chirality? Charge? Space and
Mass? Gravity?
16
What is time that we can be said to waste it with knots and braiding theory or waste it doing
endless diagonalization of matrices? (or we open the oyster to find the pearl through the p-adic,
adelic ,cracks?
If we go deep enough into the depths, will we at last find a stable world encompassing
everything explaining all variations and anomalies? Do we want this for our grounding that our
consciousness is a screen of bare charges made of shifting sand?
Hammed, quantum theory cannot yet explain why separate sheets take charges or how tape
pulled apart emits x-rays or how bits of ice build up lightening. How might such things fit in the
TGD framework?
The PeSla who had nothing to post today but wondering about someone a few years ago in the
science chat rooms who once looked at quasics and said "I hope you are not just wasting your time
diagonalizing matrices."
8. At 11:47 PM, [email protected] said...
In my opinion, Einstein is imprecise in this statement. Einstein speaks about Geometric-Time
and what he says applies to it but not to Experienced-Time. Einstein, however, identifies
Subjective/Experience-Time and Geometric-Time. This was also a mistake in the debate with Bohr.
One must distinguish between Past, Present, and Future in the case of Experienced/Subjective-Time.
Knots and braids are certainly not waste of time in my opinion. I have myself used and will use
a lot of time to them. I see them as basic objects. The attempt to artificially reduce elementary
particle quantum numbers to knot invariants is however a waste of time. A little amount of
knowledge about group theory would prevent this kind of waste of time.
http://matpitka.blogspot.com/2012/01/number-theoretical-universality-and.html#comments
topic: " Number theoretical universality and quantum arithmetics, renormalization, and
relation of TGD to N=4 SYM"
1. At 6:05 PM, hamed said...
Dear Matti,
So thanks for taking your time for answering my questions.
misunderstanding about 3 and 4 topological condensation.
I think I have some
When a space-time surface is topologically condensed in larger space-time surface (sheet) with
topological sum, this is 4-dimensional topological condensation. But if a 3-surface is topologically
condensed in larger 3-surface with topological sum, this is 3-dimensional topological condensation.
What are partons and partonic 2surfaces in a simple form?
2. At 11:40 PM, [email protected] said...
Yes, the dimension of topological condensation can vary. Usually I have in mind 3-D
topological condensation. When it is very short lasting, one cannot distinguish it 4-D topological
condensation in the sense of topological sum.
17
Partonic 2-surfaces emerged in the following manner.
● General Coordinate Invariance in strong form requires that either space-like 3-surfaces at the
ends of space-time sheet at light-like boundaries of CD or light-like 3-surfaces provide
equivalent descriptions.
● This implies that their intersections which are 2-D surfaces plus the 4-D tangent spaces of 4surfaces at them are enough. One has effective 2-dimensionality since one cannot forget
the tangent space data.
● In principle, partonic 2-surfaces are unions of 2-surfaces at the delta M4xCP2. Contributions
come from both Future and Past ends of the causal diamond (CD) in Zero Energy
Ontology. This is also important to notice. ZEO therefore means non-locality and Yangian
symmetry which is nonlocal and is therefore very natural.
● A very simple special case about partonic 2-surfaces would be holomorphic 2-surfaces of CP2.
The assumption is that partonic 2-surfaces associated with elementary particles carrying
fermion number are Kahler magnetically charged and thus correspond to non-contractible
(homologically non-trivial 2-surfaces in CP2).
http://matpitka.blogspot.com/2012/01/does-2-adic-quantum-arithmetics-explain.html#comments
topic: "Does 2-adic quantum arithmetics explain p-adic length scale hypothesis"
1. At 7:15 AM, hamed said...
Every time I see a new understanding takes place for you from your weblog (Especially
recently!), I become really happy. I have best wishes for the evolution of TGD.
Now I am struggling with Zero Energy Ontology. For first, I started with causal diamond (CD).
Suppose an object, I can imagine a causal diamond between time t1 and t2 for it. So every time
we speak about a CD, we should identify a temporal interval?
I imagine for the boundary of causal diamond of the object there is 4 pieces. Two of them are a
piece of Future light cone of the object at t1 and a piece of Past light cone of the object at t2. They
are light like 3-surfaces and intersect together at edges of causal diamond.
Other pieces are 2 snapshots of the object at t1 and t2 that are space light 3- surfaces.
I think my understanding of the causal diamond is very weaker than yours. Please guide me
more.
Is
transactional
interpretation
of
QM
by
Cramer
(at
http://en.wikipedia.org/wiki/Transactional_interpretation) like Zero Energy Ontology in some
aspects?
“The basic element of the transactional interpretation is an emitter-absorber transaction through
the exchange of advanced and retarded waves as first described by Wheeler and Feynman (1945,
1949). Advanced waves have characteristic eigenvalues of negative energy and frequency and they
propagate in the negative time direction. The advanced wave solutions of the electromagnetic wave
equation are usually ignored as unphysical because they seem to have no counterpart in Nature.”
18
2. At 6:46 PM, [email protected] said...
Dear Hammed:
Thank you for your questions. I think your confusion is due to the fact that you identify the
snapshot at t1 as 3-D surface with constant value of M4 time. This interpretation is wrong.
(A) Usually one would think that 3-D objects are at M4 time= constant snapshot. Now they are
at the boundary of light-cone (lower boundary of CD).
(B) 3-D object at t1 means object at the light-like boundary of CDxCP2 with tip at t1. If it were a
surface in M4, it would be light-like. It is however surface in M4x CP2so that only its M4 projection
is light-like. The full metric is space-like due to the CP2 contribution in it.
What might also cause confusion is that there CD boundaries are 7-D light-like objects in
imbedding space and light-like 3-surfaces X^3_l 3-D ones at space-time surface X4.
(1) Causal diamond has the tips of the intersecting light cones as special (singular) points. Note
that CD is assumed to include the CP2 as Cartesian factor so that it is 7-D. It would be
boring to write it again-and-again so I chose a little bit of loose language.
(2) The temporal interval is the proper time distance T in the metric of M4 between the points of
CD. One can perform Lorentz boosts for CD but T is of course invariant under the boosts.
(3) Causal diamond as 7-D object of M4xCP2 has just 2 pieces given by 0<r=ct<cT and 0<r =
c(T-t)< cT at the tips. r is radial distance in M4.
(4) The light-like 3 surfaces X^3_l are (or by general coordinate invariance can be chosen to bewormhole throats) sub-manifolds of 4-D space-time surface at which the signature of the
induced metric changes so that 4-metric has a vanishing determinant. It intersects the CD
boundary at partonic 2-surfaces.
There is asymmetry since for space-time ends only their M4 projections are light-like. You
might wonder why the treatment of space-like and light-like 3-surfaces in so asymmetric. The
justification for the asymmetric treatment of space-like and light-like is the following:
(A) Metric 2-dimensionality of light-like 3-surfaces gives rise to huge generalized conformal
symmetry.
(B) If light-like 3-surfaces are equivalent with space-like 3-surfaces at the ends of space-time,
the latter must allow similar symmetry. They allow and this symmetry and it comes from
the metric 2-dimensionality of M4 light-cone boundary. It is just light-like 3-surface in M4.
(C) This conformal equivalence is realized as the condition that one has so-called coset
representation of conformal symmetries. The differences of the super conformal generators
associated with these 2 conformal symmetries annihilate the physical states.
19
(D) The interpretation is as a generalization of the Equivalent Principle. Inertial conformal
quantum numbers associated with CD boundary are equal to gravitational conformal
quantum numbers associated with light-like 3-surfaces. In special case "quantum numbers"
would read "masses".
(E) Which conformal algebra contains which? One can say that Kac-Moody type conformal
algebra associated with light-like 3-surface X^3_l and its partonic ends defines a subalgebra of the symmetries assignable to the delta M4xCP_2 _2.
(F) I have asked whether these 2 symmetry algebra extend to single 4-D symmetry algebra could
be realized in terms of Yangian defined at 4-D space-time surface.
Thank you for an excellent question.
interpretation really means.
It forced me to try to understand what Cramera's
I think that there is something common. What you say obviously also applies in TGD
framework. I am not familiar enough with Cramer's interpretation. I must be honest, I have never
really understood it;-) . What I do not understand is how the flow of Subjective-Time is possible in
this framework.
Wikipedia tells that Cramer uses advanced and retarded solutions of wave equations. The basic
idea is that the waves generated by the absorber and sender interfere to zero in the Future of
absorbed and the Ppast of sender. My criticism follows:
(1) I am not all sure whether this allows to reproduce experimental facts about state function
reduction. Advanced waves do not make sense for Schrodinger equation. In general
Hamiltonian quantization, one has idPsi/dt=HPsi so that the notion of advance wave makes
no sense.
(2) Only if the scattering process can be described in terms of relativistic fields and if it makes
sense to speak about quantized fields which vanish in the Future of absorbed and Past of
sender does this picture might make sense. For Classical relativistic fields, however,
probability conservation is replaced by charge conservation and unitarity is lost. One
obtains negative probabilities. In order to solve the problem, one must second quantize.
But is it possible to formulate absorber-emitter theory in this framework?
(3) I do not understand whether Cramer obtains a realistic scattering matrix in this framework.
Wikipedia talks about stochasticity and Born rule. But what Born rule means now? How
Cramer would calculate probability for a given pair of initial and final states to appear in an
ensemble of identical emitter-absorber pairs? One should be able to reproduce the
predictions of Quantum Field Theory and therefore second quantization would be the first
step. Born rule would require inner product for 4-D evolutions of emitter-absorber
quantum fields formulated in terms of the interaction term. Does one obtain Feynman
diagrammatics?
(4) It would seem that one must introduce statistical ensemble of identical absorber-emitter pars
to representing different kinds of initial-final state pairs resulting in state preparation
followed by state function reduction. By taking square root of this thermodynamics, one
would end up with Zero Energy Ontology and the time-like entanglement coefficients of
zero energy state would give the scattering amplitudes.
20
(5) This framework does not say anything about what Time is. One just assumes that the
Time=constant snapshot representing observe moves towards the Geometric-Future.
TGD view differs in several aspects from Cramer's view:
(A) Zero energy states are pairs of positive and negative energy states. One can use state basis
for which either positive or negative energy part of the state is prepared (well-defined
particle numbers etc. just as in particle physics experiment before the scattering).
Depending on which end of CD is prepared, one has analog of retarded/advanced wave.
● The arrow of Geometric-Time is different for these 2 kinds of zero energy states and I
think that this is the correct signature.
● It seems that states tend to have same arrow of Geometric-Time. This could be seen as a
kind of phase transition analogous to magnetization in which spins tend to be parallel.
● Phase conjugate laser beams would be a physical analog of advanced waves. Also
processes like self-assembly in Biology could has non-standard arrow of GeometricTime.
(B) In TGD framework, there is no intention to get rid of state function reduction. Quantum
jump is the basic notion of the TGD-inspired theory of Consciousness. Cramer's world
would be a single solution of field equations as he understand them. TGD Universe
quantum superposition of all solutions replaced by a new one in each quantum jump.
There is continual recreation of zero energy states consistency with conservation laws
because by zero energy property.
(C) Zero energy state defines the M-matrix as time-like entanglement coefficients and Mmatrices form orthogonal rows of U-matrix so that the notion of S-matrix is generalized.
M-matrix is product of S-matrix and Hermitian square-root of density matrix so that one
has square-root of Thermodynamics. In Cramer's approach, one does not have anything
like this.
3. At 7:49 PM, hamed said...
Thank you very much. They were useful for me. But in the case of the causal diamond(CD)
although I understand more than before from your answering, it takes time to understand algebraic
meaning of it precisely and needs some algebraic tools.
Something that makes TGD harder to learn is that topics are very entangling together! And
perhaps for me it’s better to read all topics several times and in each time I read more accurate than
before.
4. At 8:04 PM, [email protected] said...
Dear Hamed,
21
I tend to avoid formulas. I have some kind of formula allergy. Often a simple drawing would be
worth of a page of text. But I hate drawing programs intensely;-). Gratis drawing programs drive
me to the border of madness.
This probably makes it more difficult to understand what I am saying. In my opinion, you have
been learning very fast. I enjoy answering to questions which force me to learn myself!
5. At 12:50 AM, Ulla said...
The complexity problem is well known and it makes TGD so difficult when everything entangles
into a mess. I don't know if there is a way out because everything IS entangled :) As it of course
must be.
I myself like figures and pictures and many times they are more clear than a page of text. But I
hate math formulas intensely too. YES. They destroy a good paper effectively. And I suspect they
make people think they know something which may not be the case. Just gibberish? I hunt the
principles behind the math.
Today I got an interesting statement as an example. The momentum is often conserved, so it is
more fundamental than energy. Energy change (tensors). Light is delivering momentum to Earth.
Momentum is the product of the mass and velocity of an object (a vector) says Wikipedia. So, a
delivery of velocity, vectors? Gravity is a vector. In relativistic mechanics, in order to be conserved
the momentum of an object must be defined as the Lorentz factor mass velocity of the object. Gives
(c2 p)/E or a reversal of Einsteins formula? This relativistic energy-momentum relationship holds
even for massless particles such as photons. Relativistic momentum is related to the de Broglie
wavelength λ by
p = h/\lambda\,, where h is the Planck constant. Ye, of course :)
Relativistic four-momentum as proposed by Albert Einstein arises from the invariance of fourvectors under Lorentzian translation. Momentum is a result of the equivalence principle?
6. At 6:31 PM, [email protected] said...
Dear Ulla,
Four-momentum conservation is a key implication of Special Relativity used routinely in the
analysis of particle physics experiments. For instance, the discovery of neutrino as missing energy
and momentum was forced by this law.
In General Relativity, things become intricate.
● One can have Poincare invariance only as an approximate tangent space symmetry (imagine
replacing the surroundings of a point of sphere with plane as we usually do when we
approximately think that Earth is flat). But what one means with this?
● One could argue that general coordinate invariance is extension of Poincare invariance. But
this would mean that Poincare transformations are like gauge transformations and fourmomentum would identically vanish.
22
The densities for Noether currents for four-momentum indeed vanish by Einstein' s
equations and four-momenta cannot be integrated as conserved charges since this procedure is
not general coordinate invariant.
● One must invent all kinds of tricky definitions of mass (one should identify also momentum
and angular nomentum) and one loses Poincare Lie algebra which is what is needed.
Things work only if one assume that space-time is a small deformation of Minkowski
space by the smallness of gravitational interaction (but what about black-holes?) and one must
restrict the consideration to asymptotic regions of space-time. Nima Arkani-Hamed has
emphasized this aspect and it could be seen as a one motivation for the notion of holography.
These mathematical and conceptual difficulties led to TGD where Poincare symmetry remains
exact symmetry and the Equivalence Principle generalizes. One can assign the Equivalence Princple
to not only gravitational and inertial mass, to not only gravitational and inertial Poincare charges, but
also to entire infinite-dimensional conformal super-algebras which could be called gravitational and
inertial (Super-symplectic algebra at light-like boundaries of CD and Super Kac-Moody at light-like
3-surfaces).
7. At 9:07 PM, Anonymous said...
Matti:
"TGD Universe quantum superposition of all solutions replaced by a new one in each quantum
jump."
So this dynamical recreation of the universe in each quantum jump at each and every time/length
scales would resonate with the notion of Plato's Cave. "Reality" is a fractal, relative projection.
If you would, examine any possible parallels with TGD.
The nature of light is to give to all other lights so that giving may give again (perpetual motion).
All lights in the Universe are connected to each other. Light is not traveling from distant stars and
galaxies. It is already here and has always been here because our star has been connected to all other
stars in the Universe ever since its birth. What we call the travel of light is actually the time that it
takes for "electrically simulated light" to reproduce itself wave-field to wave-field once light is
emitted from a source.
The light of our Sun gives to all other Suns in the Universe. And this giving is instantaneous
along the electrical torsion spirals (magnetic flux tubes) which connect all lights in our Universe.
We are not looking at stars or galaxies as they appeared millions of billions of years ago as taught by
quacks in academic theory. These connected, spiraling electrical streams of torsion between all stars
are pulsing their positions along the torsion waves which create the appearance of light at speeds
which increase by the square of their distance.
The very furthest stars are therefore pulsing their lights along these torsion waves, at speeds in
extreme excess to the limiting academic "velocity of light" and all other motions as well as theorized
by Einstein and still taught in our schools as academic truth.
23
8. At 1:23 AM, [email protected] said...
To Anonymous:
There are several parallels. Zero Energy Ontology implies time-like entanglement between
positive and negative energy parts of zero energy state which could now correspond photon at source
and photon at receiver. Also quantum entanglement in astrophysical scales is possible if one accepts
the hierarchy of Planck constants. The Universe would be a gigantic living organism.
Velocity of light has, however, an upper bound when one speaks about Classical signals. The
instantaneous changes of even space-time surfaces are possible but would not be due to superluminal signaling but due to the behavior of these space-time sheets as particle-like objects.
Could one test this picture in Living systems? Could 2 parts of the biological body show
correlations requiring super-luminal signal velocities if due to classical signals between them? For
1-meter scale, this would give a time scale of the order of nanosecond.
9. At 4:49 AM, hamed said...
Dear Matti,
Do I understand correctly? : TGD wants to say there are 2 types of entropy. One is related to
causal diamond as a whole (in each quantum jump, a new causal diamond replaced with before and
the dynamics governed by NMP). But another entropy is related to an ensemble of particles at a
snapshot (t=constant) of causal diamond (the second definition is common and for TGD the first is
important!). Then how do the 2 definitions relate together?
At “required ensemble of entropy is ensemble of strictly deterministic regions of space-time” is
the entropy the same as my understanding of first definition of entropy as before?
How do you define Macrostates and microstates of them? (and then entropy as logarithm of the
number of different microstates that correspond to a given Macrostate)
10. At 12:01 AM, [email protected] said...
Dear Hamed,
Thank you for an interesting question. There are 2 kind of entropies.
(1) Entanglement entropy assigned usually to two entangled systems.
(2) A purely statistical entropy associated with ensemble of identical systems but in different
states in general.
In case (1), entanglement probabilities str identified as eigenvalues of the density matrix
characterizing entanglement correspond to probabilities of state pairs in the eigenbasis of the density
matrix for either system. NMP states that in state function reduction this density matrix is measured
so that its eigenstates is the outcome. This state is of course pure.
In case (2), probabilities for states in ensemble are just these probabilities if the ensemble results
in quantum measurement of the density matrix for a large number of identical copies of system
entangled in the same manner with the external world.
24
One can say that entanglement probabilities for a member of ensemble become ensemble
probabilities in state function reduction.
Ensemble could be interpreted as ensemble of sub-CDs for a given bigger CD ("observer").
Each sub-CD would define a system entangled with the bigger CD and quantum measurement of the
density matrix would reduce this entanglement.
What I have said applies to ordinary entanglement entropy making sense for real numbers. For
rational or algebraic entanglement number, theoretic entanglement entropy makes sense and the
situation is more delicate.
You asked also about micro- and Macro states. I have been speaking only about various
entanglement probabilities. In Classical Thermodynamics, one speaks about microstates and
Macrostates and entropy in this sense measures the number of microstates which correspond to a
given Macrostate.
I can only try to formulate this problem in TGD framework assuming hyper-finite factors of type
II1. Let us try to count microstates at quantum level first.
(A) Macrostates are obviously equivalence classes of microstates by finite measurement
resolution. In TGD framework, measurement resolution is described in terms of inclusions N subset
M of hyper-finite factors of type II1.
(B) The included algebra N would generate the microstates defining the same Macrostate and
one should count the number of the states generated by this algebra from given state.
The problem is that the algebraic dimension of this algebra is infinite in case of hyper-finite
factors! Could one argue in the following manner?
(i) The trace of infinite-D unit matrix associated with total algebra M is by definition equal to
one. Usually it would be the infinite dimension of Hilbert space. Now we have however
hyper-finite factor of type II1 for which infinite-D unit matrix has trace and thus also
dimension equal to one.
The trick is to redefine the dimension of subspace as trace of the projector to that subspace and replace ordinary trace with what could be called quantum trace. This characterized
by quantum phase q. For identity matrix, this trace can be taken equal to one (convention).
(b) The total algebra M is tensor product of the included algebra N and the factor algebra M/N.
The dimension of M/N is the index of the inclusion which for Jones inclusions is algebraic
number in the range 1 to 4. This is not the most general case.
(c) This gives that the dimension is the inverse of the index of the inclusion and in the range 1 to
1/4 in this case.
(d) The number of microstates associated with a given Macrostate should be the inverse of the
index for the inclusion which is algebraic number and defines fractal quantum dimension of
M/N.
(e) In the general case, one would obtain a product of the inverses of the indices for different
inclusions (assuming that one replaces M by its tensor power and N by a tensor product N_i:s).
25
What about the counting of microstates at the Classical level?
(a) Quantum-Classical correspondence states that Macrostates correspond to braids at space-time
level and microstates to light-like 3 surfaces. Light-like 3-surface is effectively replaced by
a braid with strands carrying fermion number.
b) At the level of braids, one should somehow count the number of partonic 2-surfaces
corresponding to same braid end configuration. Kind of volume measure in WCW would
be needed.
(c) Could this volume be a p-adic number which can be infinite as real number? Canonical
identification defined in terms of quantum arithmetics for which quantum phase q is
characterized by p-adic prime p would map it to a finite real number. Note that quantum
phases also characterize Jones inclusions. Quantum arithmetics would however restrict
them to integers or quantum arithmetics must be generalize to allow expansions in powers
of integer n such that factors are quantum integers containing no factor if n. Maybe there is
internal consistency!
(d) If there is consistency, the Quantum counting by traces and the Classical counting by
integration over WCW should give identical results. The Classical count could be also
defined to be equal to the Quantum count!
Still about your question concerning micro- and Macro-states. First of all, the argument does not
apply to Classical thermodynamic where the measurement accuracy is really huge. One considers
just variables like pressure, temperature, etc.
Secondly, I noticed a stupid mistake in the guesswork argument for entropy. Entropy should be
additive in tensor product. My guess is multiplicative.
The first guess is that one takes just a logarithm of what I obtained. One could try to justify this
in the following manner:
(a) In thermal equilibrium for given energy, all microstates are equally probable. For a D-state
quantum system, the probability of microstate is 1/D. Shannon entropy is -\sum p(n)log(pn)=
log(D).
(b) For the factor space M/N obtained by smoothing out details away, D is fractal dimension
having values
d= 4cos2(π/n), n=3,4,....
ranging from 1 to 4. Larger fractal dimensions are also possible. If I do remember correctly,
there is no upper bound for the dimension. This formula holds true only for the simplest
situation. By taking tensor products of copies of M and N, one obtains products of these
dimensions.
One would have S(M/N) =log(d) for M/N by a formal generalization of the formula for
integer dimension.
26
(c) Now one is interested on the entropy of the N factor corresponding to the microscopic unseen
degrees-of-freedom. One can argue that the entropy for M in thermal equilibrium is just
log(d)=0 since the trace d of unit operator equals to d=1. Therefore one would have from
S(M)= S(M/N) + S(N) = 0 . S(N) = -S(M/N) = -log(d).
(d) This entropy is negative!! Could this mean that the hidden degrees-of-freedom in question
carry information instead of entropy? Could this information be regarded as conscious
information? Could one assign it with negentropic entanglement?
Something could be wrong, of course, with the argument. Maybe the naive generalization to
fractal dimension fails.
http://matpitka.blogspot.com/2012/01/mark-mcwilliams-requested-some-kind-of.html
topic: "How it(TGD) went(evolved)?"
1. At 12:31 AM, Anonymous said...
Matti:
Your work with p-adic numbers has me intrigued. Would it be possible to calculate fractals
(or fractal turning points) for a given price function using p-adic/adelic numbers?
2. At 7:18 PM, [email protected] said...
Difficult to say.
Suppose one asks for extrema -- say maxima -- for the p-adic counterpart of a cost function.
In purely p-adic context, the notion of extremum does not make sense since p-adic numbers are
not well ordered. One can only compare their norms and this variational principle is very rough
too (rough to my opinion).
One can transform the problem to a purely algebraic one just by studying the p-adic
counterparts of, say, partial differential equations associated with a real variational problem. In
TGD framework, this makes sense. (The general vision is that p-adic physics is algebraic
physics: real physics is about magnitudes.)
On could consider the p-adic analog of differentiable cost function and map it to its real
counterpart by canonical identification (I) which is a continuous map. This function would be
non-differentiable but continuous a function of its p-adic argument.
One could also map reals to p-adics by the inverse of I. The inverse would be 2-valued for
integers with finite number of pinary digits (the analog for the nonuniqueness of decimal
expansion: 1=.999999....). But one could choose branch with finite number of digits so that padic image would be unique. Altogether, one would have
R→Qp by the inverse of canonical identification. Qp→Qp by p-adic cost function and from
Qp to R by canonical identification.
I have represented some p-adic fractals at my homepage at http://tgdtheory.com/figu.html .
27
3. At 9:05 PM, Anonymous said...
Matti:
http://tgdtheory.com/square.GIF is the most relevant representation of what I am looking
for.
From what I understand, there is a need to construct some type of mapping from p-adic
numbers to real numbers. This will then yield results that can be compared with the price
dynamics. Is a supercomputer needed for the mapping?
4. At 1:24 AM, [email protected] said...
Dear Anonymous,
Let us try to figure out what should one do.
(A) One must construct modules for p-adic arithmetics. Sum, product, difference, division. I
constructed them myself using MATLAB but they are rather slow and primes must be
rather small.
Mathematica very probably has a packet for p-adic arithmetics. Probably this kind
of packet gives the expression of p-adic number as the analog of decimal expansion x=
\sum xn pn .
(B) The canonical identification is defines as the map \sum xn pn → \sumn xn-n . Canonical
identification should be coded since it is certainly not in Mathematica.
(C) In the construction of p-adic fractals, I used the inverse of the canonical identification to
map reals to p-adics. The form of inverse is the same.
This was about p-adics and reals and canonical identification. Quantum rationals require more.
(1) One should be able to construct quantum rationals rq = mq/nq from rationals =m/n interpreted
as ratios of p-adic integers.
(2) One can write r = ps*(m/n). p-Adic integers m and n have pinary expansions
m= SUM mkpk and n =SUM nk pk . mk and nk are not divisible by p and are smaller
than p.
(3) One must replace mk (nk) by the quantum counterpart by decomposing it into a product of
powers of primes pi and by replacing these prime factors by their quantum counterparts pi
→ sin(2π pi/p) / sin(2πi/p) .
(4) After this, one must map the resulting p-adic quantum rational to real quantum rational by
canonical identification taking p→ 1/p for both m and n.
Calculations require of course cutoff in the highest power of p. When I did computations almost
2 decades ago, the personal computer posed strong restrictions on the number of pinary digits and
only small p:s could be considered. Probably one can do more now. One must just try and see.
28
4. At 5:22 PM, Anonymous said...
Matti:
Along with your replies, I have consulted this source to aid in my understanding:
http://arxiv.org/ftp/arxiv/papers/1102/1102.2515.pdf .
Unfortunately, mathematics isn't my persuasion so I'm afraid a lot of this is beyond me.
After reading your replies (of which I am gracious for) and doing further research on my
own, I have come to the conclusion that I would not be able to program an indicator that
interpolates p-adic fractals onto a price chart. Assuming it's even possible to create what I am
looking for, it is obvious I do not possess the skillset for such an endeavor.
This sounds quite familiar: http://www.mdpi.com/2075-1729/2/1/1/
5. At 7:35 PM, [email protected] said...
To Anonymous:
While wandering in the Internet yesterday, I saw an article telling about the work of
Andrulis,who has written the article in the link.
Our visions are very similar. For instance, we both realize that Life and its origin are real
and profound problems. Not just dance of quarks as one skeptic Finnish colleague has been
telling with a great success in his popular books. Even representatives of the Church have
hastened to tell that they fully agree!
We seem also to share the vision that Life and Consciousness appear in all scales. The
difference is that our emphasis are very different. Andrulis is a biologist and I am a physicist.
During another Web wandering, I saw a popular article (New Scientist or some other journal)
about the evidence for the Evolutionary ladder. It might sound surprising that Evolutionary
ladder would have been challenged. Most laymen have the feeling that Darwin's theory of
Evolution postulates it and that it has been very successful.
However, this is not the case. In a materialistic approach, the Evolutionary arrow is in
principle forbidden. Goal-directed Evolution would be Intelligent Design. Even the local
direction of Evolution is at odds with the Second Law of Thermodynamics as we want to
understand it.
Therefore, Evolution would be only apparent for a good skeptic and materialist. An
Evolutionary ladder would be illusion. We only tend to put ourselves to the top and to order
lifeforms as lower ones near to us if they resemble us (say, have language facility). Random
change followed by choice selects as success makers those lifeforms which best suit to the
existing environment.
There is no Evolutionary ladder.
Only more-or-less random
environmental history faithfully reflected by the bioshpere. Suddenly the arrogant skeptic has
become infinitely humble and are forced to claim that they are at the same level as simple
monocellulars (heh heh ;-))!
Stephen Jay Gould's Wonderful Life (I also had it but I loaned it;-)) discusses so called
Burgess Shale fauna as a support for the illusionary character of evolutionary ladder.
Precambrian Explosion led to a burst of what (according to the usual standards) look like highly29
developed lifeforms, most of which then disappeared.
conform with this mass extinction.
The Evolutionary ladder does not
[StealthSkater note: The Amazon book description of The Richness of Life: The Essential
Stephen Jay Gould (http://www.amazon.com/Richness-Life-Essential-StephenGould/dp/0393064980/ref=pd_vtp_b_2) is: "The most entertaining and enlightening
writings by the beloved paleontologist, evolutionary biologist, and celebrant of the
wonder of Life. Upon his death in 2002, Stephen Jay Gould stood at the pinnacle
among observers of the natural world, recognized by Congress as a 'living legend'.
His prodigious legacy -- 16 best-selling and prize-winning books, dozens of scientific
papers, an unbroken series of 300 essays in Natural History -- combined to make
Gould the most widely read science writer of our time. This indispensable collection
of 48 pieces from his brilliant oeuvre includes selections from classics such as Ever
Since Darwin and The Mismeasure of Man plus articles and speeches never before
published in book form."]
The view in favor of real evolution is however to me quite convincing. Formation of multicellulars or animals able to communicate with language and behave socially is not to me a
random adaptation to changing environment. We differ from monocellulars in some decisive
manner. But I must be also able to explain the Cambrian explosion.
In TGD framework, one can indeed find this kind of explanation. The basic vision is that in
quantum cosmology, Cosmological Evolution takes place as relatively fast expansions between
steady situations without any cosmic expansion. This is also true for Earth. This explains the
strange finding which is much stronger than that of Wegener. If the radius of Earth were 1/2 of
its recent value, the continents would fit nicely together to form a single super-continent
covering the entire surface of Earth. The theory allows to get rid of the so-called snowball Earth
theory developed to explain ancient climate at Earth and having several difficulties. See
http://tgdtheory.com/public_html/genememe/genememe.html#expearth .
The Expanding Earth theory assumes that the Life developed in the womb of Mother Gaia
(being sheltered from meteorites and cosmic rays) in underground lakes. When the radius of
Earth grew by a factor of 2 around the Cambrian explosion, Life bursted to the surface from
under surface lakes and started to fight for survival. This explains Gould's realization without
forcing to give up the Evolutionary ladder.
This requires that the counterpart of photosynthetic machinery storing the energy of photons
of visible light to metabolic energy already existed in underground lakes before the Great Event.
It is a good home exercise to develop a theory for how this machinery might have worked;-).
6. At 11:20 PM, Ulla said...
I cannot hold back a small comment :)
It is a very hard-melted truth for these very intelligent scientists that they in fact is made
mostly of bacterias with bacterial consciousness (proto-consciousness). The human add to it is
maybe minor? We only COLLECT it from our cells which in most cases are bacterias. So, we
can say we are a colony of bacterias with superimposed fields. A superorganism.
My professor at school used to say we were a project of mitochondrias which is a symbiotic
bacteria de facto. This view is only different, not any more wrong than our usual one.
30
I just thought of Lubos when I read that :) His intelligence as a result of bacterial minds. But
so, he is also very humble :)
Yesterday I heard a great program at radio about the Finnish physicist Rauno Lauhokangas
and whale language. Whales use pictures transferred with voice and they even have personal
names. This requires memory and consciousness. One picture can be so dense with information
that it is all black, he said.
http://www.interspecies.com/pdf%20and%20styles/whale%20language.pdf 5 -160 Hz says
this:
"It cannot be overstated that these echoes are not precisely “pictures” but
something unique, closer to holograms displaying 3-dimensional, X-ray, and
kinetic information. Because the original echoes are almost inconceivably dense
with information and because the same echolocation “images” may be altered by
such attenuating factors as current, tide, and spatial distance, the actual
communication of social echoes may not consist of simply mimicking the original
sonar. One plausible idea is that whales encode the dense, overlapping beats of
social echolocation, not within phonemes but within the similarly dense,
overlapping pulses of the harmonic progression."
Remember, light is also holographic. It just gives another kind of picture.
They also used the voice as tool in hunting, like bats. Ultrasound can go through almost 1
meter of soil or rock, so they see the animal in there. The can navigate by sound. I read about a
blind boy that also had learned the skill some year ago.
How different is not their world from ours. We often forget that we use a small area of the
EM-spectrum to sense our world and it can be very different at other levels. The sensed world
can even disappear totally.
We know it is there although all signals goes straight through. But if we would be at the
other place in spectrum, would our science look like it does today? Certainly not.
7. At 9:13 PM, [email protected] said...
Thank you, Ulla.
A very interesting article. Maybe someone manages to invent code allowing humans to
understand something about whale talk. First of all, one should be able to guess about what
whales would be talking about. Problems of everyday life, family problems, business affairs,..?;)
Very probably, the pioneers have already done all kinds of things to whale talk. For instance,
when human speech is slowed down, it consists of sounds with pitch going down (somewhat like
whale song). What happens if whale talk is fastened: how would we hear it? Could it sound
more like human speech?
One old idea what comes into mind is that the Genetic Code could be the deep molecular
structure behind speech so that phonemes would be analogs of aminoacids.
31
● The coding should be extremely flexible at "phenotype level" but fixed at the level of
hardware. Somewhat like high-level computer language which is flexible but reduces
to assembly language at the bit level.
This is possible since arbitrary sequences of associations from symbol to its
representation at molecular level is possible. One-one correspondence would however
pose conditions on the number of phoneme-like basic symbols.
● The distributions of codons in intronic portions of DNA are claimed to resemble
distributions of phonemes in language (Zipf's law).
● If computers learn to understand natural language by pattern recognition, one might
consider this option seriously.
● The notion of phoneme is questioned in the article. Phoneme can be replaced with more
general symbol. In the article, coding based on rhythmic patterns is proposed.
The idea about sound hologram does not look attractive and is criticized in the article. The
whole point of language is to replace huge formation packets with simple symbols representing
classes of objects. A hologram-like representation would be like visual representation and carry
huge amount of unnecessary bits when creating a simple generating the desired association
would be enough.
http://matpitka.blogspot.com/2012/01/quantum-p-adic-deformations-of-space.html
topic: "Quantum p-adic deformations of space-time surfaces as a representation of finite
measurement resolution?"
1. At 12:25 PM, hamed said...
Dear Matti,
So thanks for last reply, for understanding more about definition of index M:N. I read pieces of
some books about subfactors and at end I am perplexed :(. I am thankful if it is possible for
you to guide me about some questions:
at M:N =dimN(L2(M)) = TrŃ (idL2(M)), I know trace of an operator A as Tr(A). But what does
it means when we add a space(or an algebra)B to corner of it as TrB(A) ? And a similar
question for dimB(A) ?
Why does TrŃ (idL2(M)) related to dimension of that space?
2. At 11:47 PM, [email protected] said...
Dear hamed,
My mathematical understanding of inclusions is rudimentary. I do not understand how Jones
arrives at his result about spectrum of the dimensions for inclusion. I just accept the results aa a
pragmatic physicists (what else can I do;-)? It would be a good challenge to translate the results
of Jones to language that simple physicists can understand.
32
I cannot guarantee whether I have understood correctly your questions. To do so, I would need
links to the texts where these notations appear.
One should learn what various notations and definitions mean. I collected some examples to
refresh my own memories. My understanding is not of a practicing mathematician but of a
physicist who tries to understand these notions physically. My guiding line is the notion of finite
measurement resolution and somehow a loose notion of "factor" space M/N with fractional
dimension.
A. What does one mean with factor?
The commutator algebra N' of algebra N appears in the definition of factors. By
definition, factors are such that N''=N holds true. This means that the only operator of N
commuting with all operators of N is unit operator in B(H). This is known as irreducibility in
representation theory. For instance, finite-D sub-algebras N of entire B(H) fail to satisfy this
condition since the commmutator of sub-algebra is infinite-D and its commutator contains
also the projector to it besides N.
B. What does one mean with factor of type I and II?
Algebra can be represented in terms of its projectors. In Quantum Theory, one typically
decomposes the operators representing observables to direct sums of projectors multiplied by
eigen values. A factor of type I has minimal projectors- projectors into 1-D sub-spaces. Spin
eigenstate would correspond to minimal projector.
Factors of type II1 have no minimal projectors. All projectors are infinite-dimensional in
an algebraic sense. The projectors finite-D with dimension not larger than 1 when one uses
TR instead of Tr to define the dimension of projector. This is definitely something new.
State function reduction would always give projection to infinite-D subspace of state space
rather than 1-D ray. The interpretation would be in terms of finite measurement resolution.
The complex ray would be replaced with N-ray and one would have non-commutative state
space.
C. What does one mean with L2(M)?
L2(M) is Hilbert space in which M acts as sub algebra of bounded operators of H acts. I
identify L2(M) as the space of elements x which are expressionable as sum of projectors of M
in such a manner that xx^dagger has finite trace so that they have also interpretation as
elements of M.
See pages 10 and 42 of http://tgdtheory.com/public_html/pdfpool/vNeumann.pdf .
D. What TrB(A) means? I would guess that it means dimension of the space formed by B-orbits
(B-rays) in algebra A. |MN|= dim_N(L2M) would be the dimension for the space of Norbits of L2M. I have talked loosely about N-orbits of elements of M.
E. What does one mean with inclusion?
How does inclusion differ from homomorphism respecting product and sum of
operators? The difference is due to the presence of beta= |M:N| as normalization factor in
the inclusion x--(x,x)/beta so that the product of images is by a factor 1/beta smaller than
33
the image of product. In standard representation for the inclusion sequence on starts from
tensor powers of algebra which could correspond to Clifford algebra for infinitedimensional space representable as infinite tensor power for Clifford algebra for n-D space.
Note that factors of type II are algebraic fractals in very precise sense.
Concrete representation: One has N=nxn matrices, M= n2 x n2 matrices, M1= n4 x n4
matrices, and so on... nxn matrices x that is N are included to M as diag(x,x)/beta. n=2
gives the simplest represention. In this case, one starts from 2-x2 matrices.
This formula is a good manner to memorize what one means with inclusion. The
inclusion is homomorphism for beta=1 that is for the minimum value n=3 of n. For
n→infinity, the normalization factor approaches 1/beta=1/4.
In TGD framework, one can identify tensor product as tensor product of finitedimensional fermionic oscillator operator algebras.
F. What does one mean with (quantum) trace?
I denote the definition of trace implying unit trace for unit matrix by TR and ordinary
trace by Tr. TR(Id)=1 for M is achieved by defining the trace as TR(x)==Tr(x) / Tr(Id).
For PN interpreted as element of N included in M in the above discussed manner, one
obtains TR(P)= 1/beta.
From this, one can define the effective dimension of M/N to be beta = |M:N| by using
the fact that trace for effective tensor product M=N x M/N is product of traces and
Tr(IdM)=1.
G. What does one mean with Trace in commutator algebra N' (..)?
N' is commutator algebra of N and M can be expressed as product of N and N'. The trace
for unit operator of M equals to 1 and is the product of TR(PN) and TR(PN') and this fixes
TR(PN') to be |M:N|. I interpret your question as a question about where this formula comes
from.
%%%%%%%%%%%%%%%%%% '
The
text
in
the
following
pages
of
http://tgdtheory.com/public_html/pdfpool/vNeumann.pdf might help (or confuse even more;)).
● "Basic definitions" -- page 10
● "Basic results about sub-factors " -- page 16
● "The fundamental construction and Temperley Lieb algebras" -- page 22.
● Basic definitions about factors can be found at page 42 -- "Basic facts about factors".
3. At 9:58 AM, Gary said...
I find "Ultimate L interesting".
http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-andbeyond.html
34
Gary Ehlenberger
Now studying Woodin's papers.
4. At 6:52 PM, [email protected] said...
Dear Gary,
Nice to hear about you. I read also this article and wrote even a new chapter "Physics as
Generalized
Number
Theory"
comparing
different
views
about
infinity.
http://tgdtheory.com/public_html/tgdnumber/tgdnumber.html#infsur
5. At 9:53 PM, hamed said...
Dear Matti,
Thank you very much. :) I listed some questions. Don’t rush to answer (in particular, third), if
they took a long time for you. So Thanks.
1. Which is correct? I didn’t understand it from your answer of my question about entropy:
“The dimension of M/N is equal with index of inclusion which for Jones inclusions is
algebraic number in the range 1 to 4” or “dimension of M/N is the inverse of index of
the inclusion in the range 1 to 1/4 ”?
Then dim(M)=dim(M/N)+dim(N)? (it is interesting for me that dimension of M and N are
infinite and dimension of M/N is finite!)
2. “At the topological condensation of space-time sheet to a larger space-time sheet, N would
correspond to the condensing space-time sheet and M to the system consisting of both
space-time sheets”.
Is it correctly? N is a von Neumann algebra and generated by all observables (operators)
which can be measured within a condensing space-time sheet and in a similar way for M? Or
operators of M/N are observables which can be measured within a condensing space-time
sheet? If it is not correct, then what do operators of N and M or M/N characterize?
3. Can one distinguish between 3 kinds of infinite dimensional space? :
(a) State space (or the "associated Hilbert space" of the system) in standard Quantum
Mechanics and in TGD correspond to infinite dimensional space of 3-surfaces of
M4xCP2 (?) (vectors of Hilbert space is correspond to the 3-sufaces). Psi function is
superposition of eigen states. But psi function replaced with M-matrix in TGD, then M
matrix is superposition of 3-sufaces! Certainly not!??
(b) In QFT, we can correspond to each vector of the state space. Creation and annihilation
operators that create or annihilate them from or to vacuum. Space of creation and
annihilation operators, for a fermion field, is infinite-dimensional. In TGD, it is
infinite-dimensional Clifford algebra. At “The space M/N would correspond to the
operators creating physical states modulo measurement resolution”, your purpose of the
operators creating physical states is like creation operators in QFT?
(c) In standard Quantum Mechanics, one can correspond to each observable an operator and
space of all operators are infinite dimensional. What is the correspondence of them in
TGD?
35
How are the 3 kinds of infinite dimensional space very entangling together in TGD? In other
words, what is relation between them?
6. At 2:59 AM, [email protected] said...
Thank you for excellent questions. I will try to answer the first 2 questions.
1. Which is correct?
I didn’t understand it from your answer of my question about entropy: “The dimension of
M/N is equal with index of inclusion which for Jones inclusions is algebraic number in the
range 1 to 4” or “dimension of M/N is the inverse of index of the inclusion in the range 1 to
1/4 ”
Then dim(M)=dim(M/N)+dim(N)? (it is interesting for me that dimension of M and N are
infinite and dimension of M/N is finite!)
I am terribly sorry. I see that there is a stupid typo!! dim(M)=dim(M/N)*dim(N)!!!
This is the correct formula. + appears for direct sum and not tensor product (obtained by
replacing matrix elements with matrices).
This is a formal identification of dimension based on the idea that for ordinary tensor
product, dimension is product of dimensions and one can generalize definition of dimension by
defining it as trace replaced with "quantum trace" which equals ti 1 for M! M is in this sense 1dimensional and N has dimension smaller than 1!!
2. At the topological condensation of space-time sheet to a larger space-time sheet, N would
correspond to the condensing space-time sheet and M to the system consisting of both
space-time sheets”.
Is it correctly? N is a von Neumann algebra and generated by all observables (operators)
which can be measured within a condensing space-time sheet and in a similar way for M? Or
operators of M/N are observables which can be measured within a condensing space-time
sheet? If it is not correct, then what do operators of N and M or M/N characterize?
This is one possible interpretation for measurement resolution. Note that I do not mention
anything about Zero Energy Ontology (ZEO) so that it must be a very early interpretation. The
idea is that the condensed space-time sheet is regarded as a point-like particle so that all its
degrees of freedom relating to its shape are below measurement resolution. M would correspond
to degrees-of-freedom associated with both space-time sheets. I will also discuss different
interpretation terms of CDs and sub-CDs.
Your third question consists of 3 parts and I organize my answer in the same way.
3. Can one distinguish between 3 kinds of infinite dimensional space? :
36
(a) "State space (or the "associated Hilbert space" of the system) in standard Quantum
Mechanics and in TGD correspond to infinite dimensional space of 3-surfaces of
M4xCP2 (?) (vectors of Hilbert space is correspond to the 3-sufaces). Psi function is
superposition of eigen states. But psi function replaced with M-matrix in TGD, then M
matrix is superposition of 3-sufaces! Certainly not!??"
As mathematical objects, Hilbert space is just Hilbert space possibly having additional
structures (separable or non-separable is one attribute). Physically, Hilbert space property is not
enough. For instance, one has usually preferred state basis -- eigenstates of measurement
observables often belonging to symmetry algebra and of Hamiltonian.
Hilbert space emerges in TGD in many manners.
(i) The space of 3-surfaces is infinite-D Kähler manifold. As a manifold and consists of
pieces which are Hilbert spaces but not in a Quantum Mechanical sense!
This kind of local piece correspond to the tangent space at one particular point (now 3surface) providing for the World of Classical Worlds (WCW) a local coordinatization (just
like plane gives coordinatization for Earth's surface locally) is Hilbert space. WCW
Kähler metric defines inner product and Hermitian conjugation and can be regarded as
Hilbert space. In the same spirit, the tangent space of 2-D manifold is 1-D complex
Hilbert space.
(ii) Ordinary3-D wave function can be formally regarded as super-positiion of points of 3space representing completely localized states. In the same spirit, M-matrix can indeed
be regarded as analog of wave function in the space of 3-surfaces formed by disjoint
unions of 3-surfaces defined by ends of space-time surfaces at light-like boundaries of
the causal diamond (CD).
The formal basis would consist of wave functions localized to single 3-surface of this
kind and is of course quite too singular.
(iii) More precisely, M-matrix can be regarded as the WCW spinor field with components of
infinite-D WCW spinor consisting of fermionic Fock states localizable at partonic 2surface by effective 2-dimensionality.
Again, finite-D analogy helps. The analog of M-matrix would consist of products of
spinor fields with arguments localized at the boundaries of CD. These would be
obtained by making 3-surfaces point like so that only cm degrees-of-freedom would
remain.
The basic rule is simple. To get from TGD to "wave mechanics", replace 3-surfaces
with point-like objects and many-fermion states with components of Dirac spinor.
(b). "In QFT, we can correspond to each vector of the state space, Creation and annihilation
operators that create or annihilate them from or to vacuum. Space of creation and
annihilation operators, for a fermion field, is infinite-dimensional. In TGD it is infinitedimensional Clifford algebra. “The space M/N would correspond to the operators
37
creating physical states modulo measurement resolution” your purpose of the operators
creating physical states is like creation operators in QFT?"
Finite measurement resolution for distance measurement means "dropping" away all
operators which create states with very high momenta.
(i) One cannot detect excitations which are too "wiggly". They are eliminated from theory
and express their presence only via the dependence of effective couplings constants on
the resolution space. This kind of momentum cutoff is necessary in interacting QFTs
not only in order to get rid of UV divergences but also because we simply have finite
measurement resolution. Already weak length scale 10-17 meters as resolution scale
requires LHC!
One does not actually drop these invisible degrees-of-freedom away but "integrates
over them" in path integral so that their actual presence is seen in the dependence of the
couplings of the resulting effective QFT on cutoff scale.
The Casimir Effect is one example about the physical effect coming from degrees-offreedom not manifestly visible (vacuum quantum fluctuations of EM field).
(ii) In Zero Energy Ontology, all states have vanishing total quantum numbers. The
Uncertainty Principle suggests how one should do translate length scale cutoff to ZEO.
One can i add to zero energy state associated with given CD details: obviously they
correspond to sub-CDs. Add to the state zero energy states associated with sub-CDs
corresponding to various scales down to CP2 scale. This is like adding to a field pattern
wiggles in various scales. A very fractal procedure.
(iii) Algebraically this means that one operates with operators in N to the zero energy state.
Momentum cutoff means "integrating out" over all sub-CDs below some minimal size
scale. This procedure corresponds to the replacement of M with M/N and should yield
in good approximation a finite-D Hilbert space but having a fractal dimension given by
|M:N|. A Fractal dimension would be able to tell about the actual presence of the
otherwise invisible fluctuations. I actually discussed this adding of details procedure in
twistor context some time ago.
(c) "In standard Quantum Mechanics, one can correspond to each observable an operator and
space of all operators are infinite dimensional. What is the correspondence of them in
TGD? In other words, what is relation between them?"
The following would be a concise answer to your question about the relation.
Spinor fields solving Dirac equation for hydrogen atom (or harmonic oscillator potential
to make the analogy even better) are replaced in TGD by WCW spinor fields. They are also
completely Classical at the WCW level. Fermionic second quantization at the space-time
level provides gamma matrix algebra at WCW level! M corresponds to the WCW spinor
fields allowing all sub-CD:s within CD. N corresponds to WCW spinor fields with all sub38
CD size up to size defining smallest sub-CD size. M/N is obtained by "integrating" over all
sub-CD sizes associated with N.
I hope that the addition of details is not confusing.
(i) In TGD framework, the simple rules of Wave Mechanics fail. Canonical quantization
fails completely for Kähler action and also path integral approach. The basic reason is
that canonical momentum densities and time derivatives for imbedding space
coordinates are not in 1-to-1 correspondence. (This actually leads to the interpretation
of what hierarchy of Planck constants means.)
(ii) The correspondence between TGD and Wave Mechanics comes from the analogy with
harmonic oscillator in 3-D. There are 3 oscillator operators and all states are created by
using them. In the infinite-D case, there is an infinite number of different harmonic
oscillators just as in free Quantum Field Theory where they are labeled by 3- momenta .
They correspond to a bosonic Kac-Moody type algebras creating physical states and
acting as complexified vector fields of WCW defining its isometries (partial derivatives
are replaced with covariant ones). Bosonic operators generate the analogs of partial
waves of ordinary spinor field in WCW orbital degrees-of-freedom.
(iii) Spinors in 3-D case are replaced with WCW spinor fields in TGD. WCW Spinor at
given point of WCW (3-surface) is created by fermionic oscillator operators. WCW
spinor field by acting on vacuum state by bosonic KAc-Moody type algebra generators.
(iv) Structure is very similar to super-string model where bosonic oscillator operators are in
rough sense in 1-to-1 correspondence with the 10-D target space coordinates for the
string world sheet and fermionic oscillator with "Gamma field" which correspond to
second quantized Majorana spinor in superstring models. In TGD, Gamma field
corresponds to WCW gamma matrices expressible in terms of fermionic oscillator
operators so that fermion statistics has a purely geometric interpretation.
(v) This picture as mathematical justification in the theory of factors. There is a theorem in
the theory of factors stating there exists vacuum ("cyclic vector") from which a dense
set of states of Hilbert space can be generated. To me, this says that quantum states can
be created by using oscillator operators. *Bosonic "oscillator operators would
correspond to Kac-Moody type algebra generators of Super-Kac-Moody type algebra.
7. At 6:18 AM, Anonymous said...
I had a friend tell me that we are forced (if we consider it) to define reality in terms of
information flows. Is this "true"? --Stephen C.
8. At 8:32 AM, [email protected] said...
Depends on what one means with "define". In any case, Information and Consciousness are
at a different ontological level than matter because they are "about. Matter and quantum states
are not about anything. Very simple but extremely profound difference. (Noticing this in time
would save us from very very many useless papers;-).
Maybe "Information is about but Matter not" should be brainwashed in the brains of innocent
children already in elementary school;-).
39
9. At 8:43 PM, hamed said...
Dear Matti,
Thanks a lot. You explained all that I needed to know for the questions. But please explain
more about
“M corresponds to the WCW spinor fields allowing all sub-CD:s within CD. N
corresponds to WCW spinor fields with all sub-CD size up to size defining smallest subCD size.”
And why is a given point of WCW a 3-surface?!
Something that makes me wonder is that you explain about the creatures of the magic world
of TGD as you see in front of you:-). Your intuition is very admirable.
Last night, I dreamed about infinite dimensional geometry :-) but unfortunately I don’t
remember any details!
10. At 11:19 PM, [email protected] said...
I have also problems with details;-)! Especially so when their number is infinite! Rather
frustrating! What I have learned that infinity is an extremely relative notion. Finite
measurement resolution suddenly makes WCW discrete or even reduces it to a finite set of 3surfaces. This is like magic.
When I refer to a fixed point of the WCW (a 3-surface), I am talking about WCW spinors
and not spinor fields! This difference is very important! Also in the 4-D case, spinors are spinor
fields restricted to a given point of space-time. This all is easy to understand if one consistently
uses the analogies with finite-D case.
The geometrization of Quantum Theory allows us to use only metric structure and its
"square-root" which is a spinor structure. This is why geometrization program is so incredibly
powerful in infinite-D context where the mere existence of geometry requires infinite-D
symmetries. WCW spinor fields must represent physical states. As I explained, WCW spinors
are WCW spinor fields at a given point of WCW which is indeed 3-surface.
WCW spinor fields represent zero energy states. What does this mean? What these 3surfaces are. One can proceed by making gradually more accurate statements
(A) First approximation . Consider only a single CD. 3-surfaces are defined by the ends of the
space-time surface at the boundaries of CD in the first approximation. They have,
therefore, several disjoint components corresponding to space-like three surfaces at Future
and Past ends of CD. So that one has time non-locality which is something new.
(B) Second approximation. One must include radiative corrections to the zero energy state.
They correspond to quantum fluctuations. Something pops out from the vacuum and
disappears. Zero energy state in smaller scale associated with sub-CD. This is like adding
loop corrections to Feynman diagrams down to CP2 scale. They correspond to addition of
sub-CDs and creation of zero energy states associated with it using corresponding included
algebra N.
40
Good guess: interaction vertices in generalized Feynman diagrams are surrounded by subCDs.
(C) This view should be of course be made much more precise. One should develop
correspondence between the twistorial ideas, braid diagrammatic approach to Feynman
diagrams, and inclusions of HFFs. This would be the next approximation.
See this attempt in twistorial context: http://matpitka.blogspot.com/2012/01/proposal-fortwistorial-description-of.html
Precise quantitative formulas - Feynman rules. This is what should be constructed by gradually
sharpening this vision. 2 decades ago, I regarded this a mission impossible. But now I feel much
more optimistic although I am not certainly quite too non-analytic thinker to achieve it. A leftbrained thinker expressing ideas as formulas would be badly needed. Right-brain and visual
thinking is not enough;-)!
Jjust a brief comment. I noticed that WCW spinors fields as outcome of square root of Kähler
geometry correspond in Zero Energy Ontology directly to the complex square-root of
thermodynamics.
Complex square-root of density matrix is the matrix version of complex square-root of real
number. Hermitian square-root of density matrix is analogous to the square-root of real positive
number and S-matrix to a phase factor allowed.
The commutativity of S-matrix and allowed Hermitian square-roots of density matrices
correspond to the commutativity of the modulus and phase of complex number.
The requirement that Hermitian matrices commute also would allow to extend the algebra to the
analog of commutative Kac Moody type algebra involving also the powers of S. This condition
would mean a choice of maximal set of commuting observables.
If one defines the product of the algebra generators as commutator this assumption is not
necessary. Another option which does not require commutativity would be the Jordan product
AB+BA (indeed Hermitian for A and B hermitian).
http://matpitka.blogspot.com/2012/02/one-more-good-reason-for-p-adic.html#comments
topic: "One more good reason for p-adic cognition"
1. At 3:02 PM, hamed said...
Dear Matti,
I want to know evolution of concepts from Classical physics to the GeometroDynamics of John
Wheeler (Superspace [WSP] ) and then to TGD (World of Classical Worlds [WCW] ). So I studied
correspondences between particle dynamic and GeometroDynamics in the book of gravitation by
Wheeler:
(1) Dynamic entity of Particle dynamics is particle and of GeometroDynamics is space ( 3dimensional space).
(2) Descriptors of momentary configuration of first is x,t(event) and of second is 3-Geometry.
41
(3) Classical history of first is x=x(t) and second is 4-Geometry.
(4) At first, every point on the world line gives a momentary configuration of particle. But at
second, every space like slice through 4-Geometry gives a momentary configuration of
space.
Where does WCW similar with superspace on subjects that listed above and where does is
different? Does ADM formalism any position in WCW like superspace?
Maybe if Wheeler had been equipped his superspace with Kähler geometry (and he had your
extraordinary ability of arguments;-)), he could like TGD assigns to each 3-surface a space-time. So
space-time should not mean in superspace without Kähler structure and the space-time is not
fundamental in this view.
As Wheeler wrote: “There is no space-time. There is no time. There is no before. There is no
after. The question of what happens 'next' is without meaning.”
For more clarification, I saw at The Labyrinth of Time by Lockwood: “Every such cosmological
model can be foliated in an infinity of different ways. Each foliation will consist of a sequence of 3geometries. (Wheeler refers to this freedom in the choice of a foliation as many-fingered time.)”
I mean Wheeler speak about some non-determinism of time? Then the time of superspace is
more like Subjective-Time(nondeterministic) of TGD rather than the Geometric-Time(deterministic)
of it?
2. At 8:25 PM, [email protected] said...
Dear Hamed,
It is fun to discuss and answer good questions. Here a brief comparison of WSP and WCW.
(A) In WSP, 3-geometry is the basic entity. In WCW, sub-manifold 3-geometry.
(B) There is no time or space-time in WSP context as Wheeler emphasizes. The theory should
assign in a natural manner to a given 3-geometry a 4-geometry to achieve this.
In WCW context, the definition of WCW Käehler function assigns to a given 3-surface a 4D space-time surface as preferred extremal of Käehler action. This makes Classical physics as
exact part of Quantum Theory and even that of WCW geometry. This new view about Bohr
orbits as something very real instead of being a fiction produced by stationary phase
approximation is the new philosophical viewpoint.
The notion of 3-surface generalizes and eventually one ends up with Zero Energy Ontology
(ZEO) and strong form of general coordinate invariance implying effective 2-dimensionality.
Partonic 2-surfaces and their 4-D tangent space data and CDs within CDs basically due to the
breaking of standard form of determinism.
On might argue that in strictly mathematical sense space-time becomes also in TGD
redundant locally (only locally due to the failure of strict determinism implying the need for
CDs within CDs). Space-time is, however, necessary for the interpretation of quantum
measurements which always assign to quantum events classical space-time correlates such as
42
frequencies. People talking about emergence often forget all about quantum measurement
theory. In any case, imbedding space and time are there and very relevant for the interpretation
of the theory!!
(C) WSP the classical history of 3-surface is a questionable concept since topology change is not
natural in this context. This view about 4-surface is very "Newtonian" and allows only X3xRtype space-time topologies.
In WCW with ZEO, one gives up completely the Newtonian view. Positive and Negative
energy parts of zero energy states as 3-surfaces at the 2 boundaries of CD can have totally
different topologies. Particle creation in a topological sense becomes possible and there is
space-time topology analogous to that of Feynman diagram.
Wheeler's many fingers would in this context become external lines of particle reaction. At
vertices incoming lines are join like lines of Feynman diagram so that space-time surface is not
anymore even 4-manifold. However, 3-surfaces are. Note that in string string world sheets are
2-manifolds but their time=constant sections are not always 1-manifolds.
(D) During the first year of TGD development, I tried ADM formalism but realized that canonical
quantization fails. The connection between time derivatives of imbedding space coordinates
and canonical momentum densities associated with action even in case of YM action is manyto-one and extremely non-linear so that one cannot do nothing in practice.
Standard quantization recipes would also yield horribly nonlinear poorly defined functional
differential equation (p→id/dx recipe generalized) so that a direct generalization from the tiny
hydrogen atom to the entire infinite Universe fails. Perhaps theoreticians were too ambitious at
this time;-)
For a long time, my heuristic guideline was that the non-locality of Kähler action for preferred
extremal as functional of 3-surface is the manner to get rid of local divergences. Reduction to ChernSimons terms brings, however, 3-D locality back but almost-topological character allows us to avoid
divergences now.
I have played now-and-then with the question whether Käehler geometry could be defined in terms
of preferred extremals of curvature scalar. What could these extremals be? How could one bring
complex and Käehler structures to the space of 3-geometries>
In the case of loop spaces, Kähler geometry is unique and there are excellent reasons to expect that
in higher dimensions even the target space containing 3-surfaces is more-or-less unique just from the
existence of the WCW geometry. What is the situation in WSP> Could it be that space-time dimension
is fixed?
In http://tgdtheory.com/public_html/articles/egtgd.pdf , I consider the analog for Wheeler's approach
in TGD based on Einstein-Maxwell action.
(1) Almost topological QFT property would mean that metric appears extremely implicitly in the
theory. It requires that the solutions of field equations involves are such that the action in
reduces to 3-D Chern-Simons term. The conformal invariance of Einstein-Maxwell equation
indeed implies that action reduces to boundary terms.
43
(2) Weak form of electric magnetic duality seems to make the 3-D contributions to action ChernSimons terms.
(3) One must also allow space-time regions of Euclidian signature and CP2 as solution of field
equation. Cosmological constant determining CP2-size scale (CP2 corresponds to nonvanishing cosmological constant) is needed in Euclidian regions. Average cosmological
constant could be quite small and reflect the fraction of Euclidian space-time volume.
(4) This would force a new view about black-hole interiors as Euclidian regions of space-time. CP2
was actually originally discovered as gravitational instanton.
(5) This is very near to TGD. Euclidian regions would carry electroweak and color quantum
numbers and Minkowskian regions classical quantum numbers. Could imbeddability to
M4xCP2 follow as a consistency condition?
Wheeler is quite right in what he says about absence of time in WSP.
coordinate invariance implies also in the 4-D view about General Relativity.
This is what general
In the WCW approach based on Zero Energy Ontology, the position of space-time surface /CD in
imbedding space brings in Geometric-Time and one can speak about the positions of partonic 3surfaces.
Basically, I however think that "before" and "after" as we usually understand them apply to
Subjective-Time and not to Geometric(relativistic)-Time. One must identify Subjective-Time as
something different from Geometric-Time and this leads to quantum theories of Consciousness (and
things get even messier;-).
In quantum gravity based on Schrodinger equation in WSP, time could appear only as the analog of
time parameter in Hamiltonian unitary evolution. The basic equations of ADM, however, lead to
coordinate conditions saying that physical states are analogous to states with zero energy. Easy to guess
since Noether charges associated with diffeomorphisms of space-time vanish identically.
Again, one encounters the basic motivation of TGD. That is how to simultaneously realize Poincare
symmetries and geometrize gravitation. All the difficulties of GRT force to make the same question -what about sub-manifold gravity?
Perhaps the strongest objection that I have invented hitherto against sub-manifold gravity relates to
the superposition of fields. It is circumvented if it is replaced with superposition of effects of induced
fields (simultaneous topological condensation to several space-time sheets).
In path integral formalism, one makes a hypothesis that Schrodinger amplitude as a functional of 3geometry is sum over all space-time surfaces having 3-surface as boundary. Space-time would emerge
as the analog of point particle orbit. Classical space-times would correspond to extrema of Einstein's
action. There are technical problems due to the non-existence of path integral and one must make path
integral functional integral by making Euclidianization. A connection with the time of Special
Relativity is lost and achieved only in perturbative treatment of General Relativity in path integral
formalism around Minkowski space-time.
Spin 1/2 particles is a second problem of Wheeler's GeometroDynamics. In fact, spinor structure
does not even exist in generic space-time. (By the way, CP2 is one example of this.)
44
3. At 2:16 PM, hamed said...
Thank you very much for responding, Matti. Just a little question: why does any map from a
given 3-manifold X3 to M4xCP2 defines a surface?
4. At 12:02 AM, [email protected] said...
The image of continuous map of X3 o H is the image of a 3-D geometric object and therefore a 3D surface.
Concrete example: hk = fk(x1,x2,x3) for k=1,...,8 (H-coordinates) when xi run over their value
range you get point set of H parameterized by 3 coordinates so that it is clearly 3-dimensional.
When H and X3 have p-adic coordinates, the situation is same. The image of X3 is parameterized
by 3 coordinates and in this sense 3-D.
Another basic manner to represent surfaces is as intersections of surfaces. The conditions
Hm(hk)=0, m=1,...5 for independent functions would give intersection of five(5) 7-D surfaces which
is generically a 3-D surface if non-trivial. In algebraic geometry, this is the manner to represent
surfaces.
In this representation, the expressions for induced metric and gauge potentials are not so easy to
deduce as using direct imbedding. One must in principle solve the imbedding space coordinates in
term of three of these functions locally.
[note: . The 30-year development/evolution of Topological GeometroDYnamics (TGD) physics
from Dr. Pitkänen's doctoral thesis at the University of Helsinki, Finland (~1982) to today is
archived at http://www.stealthskater.com/Pitkanen.htm#Evolution . The entire theory and
its many applications is at http://www.tgdtheory.com and selected files are also archived at
http://www.stealthskater.com/Pitkanen.htm in both Word(.doc) and Acrobat(.pdf) formats.]
5. At 11:48 AM, ◘Fractality◘ said...
Matti:
For your consideration:
--------------------------"A team of physicists detected an energy beam coming through the top of the
Bosnian Pyramid of the Sun. The radius of the beam is 4.5 meters with a frequency of
28 kHz. The beam is continuous and its strength grows as it moves up and away from
the pyramid. This phenomenon contradicts the known laws of physics and technology.
This is the first proof of non-Herzian technology on the Planet. It seems that the pyramid
builders created a perpetual motion machine a long time ago and this “energy machine”
is still working.
In the underground labyrinth, in 2010 we discovered 3 chambers and a small blue
lake. Energy screening shows that the ionization level is 43 times higher than the
average concentration outside which makes the underground chambers into “healing
rooms”.
45
Further electromagnetic detection in 2011 confirmed that levels of negative radiation
through the Hartman, Curry, and Schneider grids are equal to zero in the tunnels. There
was no technical radiation (from power lines and/or other technology) found in the
tunnels and no cosmic radioactivity. Ceramic sculptures are positioned over the
underground water flows and the negative energy is transformed into positive. All of
these experiments point to the underground labyrinth as one of the most secure
underground constructions in the World and this makes it an ideal place for the body’s
rejuvenation and regeneration."
--------------------------When I came across what I posted above, I immediately thought of your "TGD and Fringe
Physics". Could that beam be a negative energy phase conjugate wave?
6. At 8:55 PM, [email protected] said...
To fractality:
Impossible to say anything without a detailed documentary.
In laser physics, phase conjugate waves are everyday thing.
The interpretation as negative energy etc. is new but also consistent with Feynman graph picture
allowing us to talk about anti-particles as something propagating in a reverse time direction with
negative energy.
The sole thing differentiating it from what standard physics predicts is the reversed arrow of
Geometric-Time. An experimentally established fact also but something which one should not speak
aloud since the theoretical understanding is so poor;-).
One could imagine all kinds of science-fiction things based on phase conjugate waves. Maybe
some sci-fi writer has done anything along these lines.
7. At 5:54 AM, Ulla said...
I found a man that thinks along the same paths as you. He unifies algebraic and geometric PDEs.
AGOSTINO
PRÁSTARO
http://www.dmmm.uniroma1.it/~agostino.prastaro/HOMEPAGEPRAS.htm
http://www.dmmm.uniroma1.it/~agostino.prastaro/PUBLICATIONS.HTM
These results have opened a new sector in Algebraic Topology that we can formally
define the Algebraic Topology of PDEs. The characterization of global solutions -made by means of integral bordism groups -- has allowed us to obtain applications in
some important PDE's of the Riemannian Geometry and Mathematical Physics as Ricciflow equation, Navier-Stokes equation, and quantum Yang-Mills equations.
Quantum super Yang-Mills equations are discussed in the framework of quantum
supermanifolds, obtaining a new approach to unify the 4 fundamental forces
(gravitational, electromagnetic, weak-nuclear, strong-nuclear) in an unique geometric
structure at the quantum level. The geometric theory of PDE's -- built in the category of
quantum supermanifolds -- gives us a dynamic theory to describe quantum phenomena
also at very high energy levels where quantum-gravity becomes dominant. Quantum
46
black-holes are interpreted as solutions of quantum super Yang-Mills equations with
quantum- (super)gravity in action.
8. At 10:15 AM, Ulla said...
It seems they have worked with working memory in Helsinki :)
Palva et al. "Neuronal synchrony reveals working memory networks and predicts individual
memory capacity".
Proceedings of the National Academy of Sciences, 2010; DOI:
10.1073/pnas.0913113107
http://www.sciencedaily.com/releases/2010/04/100413105704.htm
Orwin's idea about a feedforward-feedback energetic mechanism creating synchrony seems
plausible?
Visual working memory (VWM) is used to maintain sensory information for
cognitive operations ... based on sustained neuronal activity in a complex cortical
network of frontal, parietal, occipital, and temporal areas. The neuronal mechanisms that
coordinate this distributed processing to sustain coherent mental images and the
mechanisms that set the behavioral capacity limit have remained unknown. We mapped
the anatomical and dynamic structures of network synchrony ... Interareal phase
synchrony was sustained and stable during the VWM retention period among
frontoparietal and visual areas in α- (10–13 Hz), β- (18–24 Hz), and γ- (30–40 Hz)
frequency bands.
Furthermore, synchrony was strengthened with increasing memory load among the
frontoparietal regions known to underlie executive and attentional functions during
memory maintenance. On the other hand, the subjects’ individual behavioral VWM
capacity was predicted by synchrony in a network in which the intraparietal sulcus was
the most central hub. These data suggest that interareal phase synchrony in the α-, β-,
and γ-frequency bands among frontoparietal and visual regions could be a systems level
mechanism for coordinating and regulating the maintenance of neuronal object
representations in VWM.
Cognition = working memory (partly?)?
Individual capacity is highly correlated with intelligence measures and reduced in
neuropsychiatric diseases. Simultaneous recordings from monkey parietal and frontal
cortex revealed that visual capacity limitations occurred immediately upon stimulus
encoding and in a bottom-up manner. Capacity limitations were found to reflect a dual
model of working memory. The left and right halves of visual space had independent
capacities and thus are discrete resources. within each hemifield, neural information
about successfully remembered objects was reduced by adding further objects, indicating
that resources are shared. http://www.pnas.org/content/108/27/11252.abstract
network topology and physical distance of synchronization ...
greater cognitive effort caused emergence of a more globally efficient, less clustered,
and less modular network configuration, with more long-distance synchronization
between brain regions. This pattern of task-related workspace configuration was more
47
salient in the β-band (16–32 Hz) and γ-band (32–63 Hz) networks, compared with both
lower (α-band; 8–16 Hz) and higher (high γ-band; 63–125 Hz) frequency intervals.
Workspace configuration of β-band networks was also greater in faster performing
participants ...
demonstrate how cognitive effort breaks modularity to make human brain functional
networks transiently adopt a more efficient but less economical configuration.
http://www.jneurosci.org/content/31/22/8259.full
Arousal? attention? wakenness? Is this part of negentropy maximation? At least not entropy
maximation (homeostasy?)? Then comes naturally the question of emotion and p-adic relations.
Seen also in Piaget? Negative emotions as panic and fear are stronger, creates a higher 'arousal' (an
ad hoc word) together with memories (consciousness)? p-adics create the size of the global network?
Its difference to hbar size of the 'Big Book' remained unclear to me before. But there are also
differences left-right. So these are the Big Book or hbar then? You did get the Jill Bolte Taylor
book?
9. At 10:20 AM, Ulla said...
Does p-adics and hbar work together in creating synchrony?
10. At 4:04 AM, [email protected] said...
Hierarchy of Planck constants and p-adics are correlates. But I am not sure how. Naive guesses
fail. These hierarchies are separate.
I am now working with the implications of Quantum Arithmetics. It is more-and-more clear that
QA is the royal road to Physics as a generalized number theory. A beautiful unification of real and
various p-adic physics emerges when number theoretic universality is realized in terms of the notion
of adele generalized to Quantum Adele: QA again;-). Simple recipe: anywhere where you meat real
number replace it with Quantum Adele!
The notion of adele is central in the Langlands program in which the goal is to understand
Absolute Galois Group -- a mythic objects defined as Galois group for the algebraic numbers as
extension of rationals. AGG is a dragon which has destroyed many brave and brilliant mathematical
knights;-).
The needed generalization is a replacement of adeles with quantum adeles. This brings in an
excellent candidate for an isomorph of AGG commutator group as Galois for the quantum adeles
interpreted as extension of adeles. For ordinary adeles, one has only the Galois for maximal Abelian
extension of rational realized in terms of ordinary adeles.
This leads to a very beautiful re-interpretation of the basic conjectures of Quantum-TGD and a
lot of new awe-inspiring insights. It will take me a week-or-two to polish it. I think I have done it!).
http://matpitka.blogspot.com/2012/02/indeed-is-it-really-higgs.html
topic: "Indeed! Is it really the Higgs?"
48
1. At 5:52 PM, hamed said...
Dear Matti,
I listed theoretical supports of H=M4xCP2. Are there any other supports?
First: H= M4xS leads to exact Poincare invariance and symmetries of standard model leads to
S=CP2 uniquely.
Other supporter: the construction of the geometry of the World of Classical Worlds, Hyperfinite
factors of type II approach, the number theoretic approach (space-time surfaces as hyperquaternionic or co-hyperquaternionic sub-manifolds of the hyper-octonionic imbedding spaces ,
duality of H-M8)
They are a lot ;-)
For theoretical supports of many sheeted space time:
The primary ideas of TGD were “TGD as a Poincare invariant theory of gravitation” and “TGD
as a generalization of the hadronic string model”. Fusion of the 2 approaches by gauge conservation
and RGI hypothesis lead to many sheeted space-time.
Other theoretical supporters of many sheeted space time are:
Hyperfinite factors of type II approach (jones inclusions), infinite primes, and p-adic length scale
hypotheses.
Are there any other supports?
I need the most important experimental supporters of many sheeted space-time?
You speak about CD and sub-CDs and sub-sub-CDs … instead of many sheeted space time in
the recent years. Why? What is other new directly in many-sheeted space-time concept after 30
years?
2. At 8:15 PM, [email protected] said...
Dear Hamed,
You have managed to build quite a nice overall view. It is easy to get detailed view when one
understands the big picture. This is true in my own case at least.
The new view about symmetries is certainly very strong theoretical support and as such leads to
highly non-trivial predictions such as leptohadron physics based on colored excitations of leptons.
I would count the success of p-adic length scale hypothesis (p-adic mass calculations for
instance) as experimental support for TGD at the quantitative level. That the hypothesis becomes
very plausible in quantum arithmetics and Zero Energy Ontology could be seen as a theoretical
support for it. p-Adic length scale hypothesis leads to strong predictions such as scaled-up variants
of hadron physics.
You asked for experimental support for many-sheeted space-time.
49
● What inspired the idea of many-sheeted space-time was the realization that I can really see it
by just looking around. The boundaries of Macroscopic objects as boundaries of spacetime sheets (or possibly as macroscopic partonic 2-surfaces at which signature of induce
metric changes) would be really visible. Also the reduction of matter as shape to spacetime topology would mean enormous ontological simplification.
● The basic objection relates to classical fields: their expressibility in terms of four(4) CP2
coordinates means enormous simplification. But one can argue that it is not consistent with
the linear superposition of fields holding true approximately. Only the effects of fields
need to superpose in many-sheeted space-time where multiple topological condensation is
possible. I have explained a few times what this means so I will not bother to repeat
myself.
● Dark matter has hierarchy of phases with large Planck constant at dark space-time sheets is one
prediction which should be tested. Biology could be interpreted as domain where these
phases dominate and I have proposed that Peter Gariaev's strange findings could be
interpreted as the first photographs about dark matter. Photons go to dark space-time sheet,
are reflected, transform back to ordinary photons, and go to came.
I have been indeed talking about CDs, sub-CDs etc. during the last years. About geometric
correlates of physical system at imbedding space level. I used to talk about space-time sheets before
ZEO. They correspond to the geometric correlates of physical system at space-time level. I think
that the 2 manners to speak are more or less equivalent. ZEO has dominated my thoughts for last 6
years-or-so and this explains why I have been talking about CDs so much.
You asked about what is new in the view about many-sheeted space-time when compared to that
of 3 decades ago.
● ZEO is certainly something new. In the 1990s, I would have identified particles with
boundaries of space-time sheets. Now I prefer to talk about wormhole throats at which
induced metric changes signature and which are identified as orbits of partonic 2-surfaces.
● Generalized Feynman graphs are also a new concept. They provide geometrization of ordinary
Feynman graphs with lines replaced with orbits of wormhole throats and in ZEO lead to a
beautiful vision about how circumvent both UV and IR divergences of QFTs. Also the
connection with twistors and momentum twistors emerges naturally since what propagates
at wormhole throats is always massless and on mass shell and only the sign of energy can
be also negative.
I cannot resist the temptation to mention what might turn out to be one additional theoretical
support for the number theoretic vision. I know that it is too early to talk about this yet but ...
Quantum arithmetics is a notion which allows one to understand canonical identification
mapping p-adics to reals at deeper level. The formulation is still developing.
I am just now working with the formulation of quantum adeles central in the formulation of
Langlands program. Quantum adeles would be a generalization of adele concept fusing together
reals and all p-adic number fields to form single structure. This would be enormous advantage in
50
book-keeping and allow us to formulate generalized Feynman diagrams in number theoretically
universal manner very elegantly.
Quantum adeles also throw light to the conjectures like M8-H duality and space-time as
quaternionic surface since one is forced to think these conjectures simultaneously for reals and all
quantum p-adics.
The quantum version of adeles would be essentially Cartesian product of reals and of all
quantum p-adic fields (indeed fields as it seems). Simple arguments suggest that it is not only ring
as adeles but field analogous to function fields. This would have enormous theoretical impact since
one could replace reals everywhere in the formulation of the theory with quantum adeles. Quantum
adeles could even allow differential and integral calculus of their own! This would be something!;-).
Quantum p-adics are analogous to algebraic extension of p-adics and the absolutely crazy
speculative question is whether quantum adeles could be isomorphic as a structure to algebraic
numbers and their Galois group to Absolute Galois group acting as automorphisms of algebraic
numbers regarded as extension of rationals.
Be as it may, canonical identification appears in a fundamental role in the definition of quantum
adeles so that it would gain a status similar to that of norm function in the definition of reals and padics. One can also resolve many theoretical little nuisances which one should not forget but tends
to forget in terms of quantum p-adics and quantum adeles.
3. At 12:08 AM, hamed said...
So thanks Matti and thanks for encouragement :-). My overall view was very apparent and
outside of TGD and the sea of TGD is very deep. I should learn diving in the sea! and I am so happy
for it.
Quantum Adeles!, it seems very important. I have best wishes for you about understanding it.
I tried to ask my questions in a very simple manner:
When I want to imagine about many sheeted space-time and H=M4xCP2 together, first I imagine
a box with a thickness by CP2 (the box is correspond to H= M4xCP) and a space time sheet is inside
it as a 4-surface (really there is infinite-d configuration space in the box). After that, if I want to add
other space-time sheets in my imagination world! I should place a lot of boxes (from large to small)
on each other one-after-one associated with each of space-time sheets (each space time sheet is
inside one box independently).
But in this view I cannot imagine CDs inside CDs. Something go wrong? And wormhole
contacts correspond to thickness of a box between upper box and downer box?
Another question inside the last question. There are all possible 3-surfaces in the box. But for
each of 3-surfaces there is a 4-surface uniquely (preferred extremal of Kähler action). Then there is
infinite 4 surfaces correspond to infinite 3-surfaces one to one. Each 4-surfaces means a Classical
world and we have in the box a World of Classical Worlds. This is your means of Classical worlds?
Then we have infinite number of space-time sheets inside each of boxes?
51
If you answer the first question wormhole contact in this way that wormhole contact is between 2
space-time sheets, then I can ask which of infinite number of space-time sheets have this wormhole
contact?
4. At 2:30 AM, [email protected] said...
Dear Hamed,
Your box illustration is correct. Also the interpretation of many-sheeted world in terms of spacetime sheets.
Wormhole contacts are regions with Euclidian signature of induced metric. CP2-type vacuum
extremal representing a region having geometry of CP2 is simplified situation. They have light-like
random curve as M4 projection and represent generalization of point-like particle. Their
deformations are more realistic models for the lines of generalized Feynman diagrams.
The number of space-time sheets need not be infinite. With "Classical worlds" I mean different
space-time. Quantum state is quantum superposition of different space-time surfaces just like
electron in atom is superposition of electron at different points. Point→3-suface: orbit of point→
space-time surface. For instance, CKM mixing for quarks is interpreted as quantum superposition of
spherical, torus, sphere with two handles topologies.
These deformed pieces of CP2 can condense Minkowskian space-time sheet: free fermion: in
this case, wormhole throat is Kähler magnetically-charged. For bosons, the wormhole is between 2
space-time sheets and both are Kähler magnetically-charged.
Both fermions and bosons can touch (and very probably touch) other space-time sheets in same
region. This gives rise to interaction describable as interaction with the sum of Classical fields at
these sheets. Only effects of fields sum. Not fields, which does not make sense in TGD.
You asked about CDs. CDs are phenomenon at the level of imbedding space. They do not
follow from the original form of the theory.
(A) ZEO requires places where one can put positive and negative energy parts of the state. CD is
ideal in this respect since its light-like boundaries have huge conformal symmetries due to
the light-likeness of light-like boundary. These symplectic symmetries are fundamental in
the construction of the theory. WCW geometry requires infinite symmetries. This is the
key idea.
(B) Geometrization of quantum measurement theory at WCW level requires CDs. The WCW
geometry must code the choice of preferred measurement axes for spin, color quantum
number. Also rest system must be fixed. The line connecting tips of CD defines unique
time axis and rest system. One must assign also a preferred spatial direction and the
quantization of theory assigns to given CD choices of plane M2 of M4. This assumption is
required also by number theoretic vision: there must exist unique plane which corresponds
to preferred complex plane of (hyper-)octions: M2. There is no breaking of Poincare since
one integrates over choices of M2. In QCD, M2 as collision plane of hadrons makes M2
rather concrete.
WCW decomposes to a union of sub-WCWs associated with CDs in the hierarchy. 4surfaces inside CD having their ends at their boundaries. The 2 ends correspond to the initial
52
and final states in realistic particle physics experiments. In an idealized situation, these states
would be at temporal ± infinity.
(C) This decomposition of WCW is crucial. You can ask whether the space-time sheets inside
given CD end at the boundaries of CD. Feynman diagrammatics suggests that this depends
on situation. For the counterparts of vacuum bubbles in QFT, it would end (and this is my
pedagogical approximation;-). For the vertex regions and loops of Feynnman diagrams, it
does not. Each vertex surrounded by small sub-CD. Is this the correct interpretation? I am
not of course dead sure!
(D) In Consciousness theory, CDs are correlates of conscious entities, selves. Kind of spotlights
of Consciousness, one might say.
http://matpitka.blogspot.com/2012/02/quantum-adeles-as-golden-road-to-number.html#comments
topic: Quantum Adeles as a Golden Road to Number Theoretical Universality?
1. At 11:06 AM, ThePeSla said...
Matti,
I mentioned you on my blog:
"A personal or social consequence in that I have had some direction on the frontiers
with fellow bloggers is that in the case of Matti Pitkänen who's lifework I imagine is as
hard to read like mine and understand, where he relates consciousness as dark matter
phenomena, there is a similarity of these ideas possible in that the idea while to me vague
or vaguely communicated or some lack on my part consequently has some weight after
all on the frontier of our age of new physics."
Now, your current topic here does show some general sense of advanced ideas in the depths of
things. But it was quite a wormhole for me to make the connection as something rather more
concrete. Such effects, such a way to see numbers, and --well, for me -- something a little further
than a quantum foundation as such.
What do you think? I hope this informal post Universal Mind can help. I hope we come to
understand consciousness a little more than we are now aware of but cannot express in words or
formuli.
But while on the science blogs any mention of effects like this for your topic was immediately
dismissed as not scientific. We know better :-)
The Pe Sla
2. At 9:42 PM, [email protected] said...
The mathematics behind the current topic is really hard for anyone. Adeles appear in
mathematics in the framework of Langlands program and reading even the introductory text by
Frenkel is really hard work. No-one would bother to read them unless he were an authority in the
field. Usually these things are of course learned in face-to-face communications. But this is not
possible for those thrown outside the system.
53
I have not even tried to really understand intuitively ideas of the geometric Langlands. I just
understand a little bit about Galois group and Adeles. The only reason why I make attempts to build
something like Quantum Adeles with my minor skills and without the help of helpful discussions
with colleagues (because they are not possible) is that it is something which Quantum-TGD quite
obviously needs.
I have got accustomed to the stupidity of the average colleague and it bothers me just enough to
guarantee the optimal adrenaline level;-). The average colleague has to earn his living and it
requires some ethical compromises to get a formal status of expert.
The Academic world is great theatre. Most of those appearing on the stage as professionals are
nothing but good actors. And as actors they are able to make the most impressive gestures;-). When
you hear some authority to ridicule cold fusion or claim all theoreticians not believing in M-theory
as idiots, you have met an actor.
3. At 4:32 AM, hamed said...
Dear Matti,
Yesterday, I struggle with Quantum Arithmetics, Absolute Galois Group, and Quantum adeles.
At the end I was confused a lot and didn't understand them. (But it was interesting. Perhaps it is
enough for me a concise overall view about them, at this level. And I should not hurry :-)
-TGD leads to existence of U-matrix in two main ways (?):
1. In a non-straight way: Non-determinism of Kahler action in real WCW.
2. In a straight way: Generalization of WCW to a fusion of p-adic and real WCW.
Then What is U-Matrix in the view of Quantum adeles, briefly?
-How inertial-gravitational dichotomy is a direct correlate for the geometric-subjective
dichotomy for Time?
4. At 1:24 AM, [email protected] said...
Dear Hamed,
Thank you for questions. I will do my best to answer.
1. Quantum Arithmetics and related things are the newest layer in the development and I would
not take too seriously anything about it before a few years have passed and I (or maybe
you;-)) have found and corrected all the mistakes or killed the idea;-). Quantum Adeles are
basically just a Cartesian product of quantum variants of p-adic number fields so that
everything reduces to quantum p-adics.
Do these quantum p-adic fields really make sense mathematically as analogs of local
number fields? Are they internally consistent structures ( really number fields with all desired
properties and does differential and integral calculus make sense for them)?
Canonical identification would be the key element. It would define norm instead of p-adic
norm and it would induced well-ordering making definite integral possible. Could canonical
identification map solutions of quantum p-adic field equations to those of real field equations?
This would be fantastic! Physical vision requires and strongly suggests the existence of
54
quantum p-adics and I have not found any killer argument yet.
argumentation forth and back.
Requires a lot of
2. U-matrix follows from ZEO. M-matrices by definition entangle the positive and negative
energy parts of zero energy states. U-matrix is a collection of mutually orthogonal Mmatrices assignable to an orthogonalize WCW spinor field basis. Each M-matrix appearing
as a row of U-matrix define one particular mode of WCW spinor field.
One could say that U-matrix and M-matrices characterize the modes of free spinor fields
in WCW. All interactions reduce to WCW geometry and are coded by these free spinor
fields.
Note that spinor field here is something different from what one might think on basis of
finite-dimensional intuition. It is superposition of pairs of positive and negative energy states
made out of fermions at opposite boundaries of the CD as functional of 3-surface defined by
the ends of space-time surface.
3. I would not pose the questions about how TGD leads to U-matrix in the manner you did.
Rather:
(a) It is ZEO which is motivated by the non-determinism of Kähler action rather than Umatrix.
(b) Number theoretical universality of U-matrix is motivated by the generalization of WCW
by fusion of real and p-adic WCWs.
Here an attempt to answer you remaining questions.
1. Quantum Adelic U-matrix would be quantum adelic-valued spinor field in quantum adelic
WCW.
If the notion of quantum adele makes sense, it provides a convenient manner to talk
formally about entire collection of space-time sheets as a single object defined as quantum
adele. The psychedelic quantum dream would be something like follows.
(a) The basic rule would be simple: replaces real everywhere by quantum adeles.
(b) Adelic WCW spinor fields would correspond to a tensor product of WCW spinor fields
associated with various quantum p-adic sectors and would be quantum p-adic valued
(also real sector would be included). One would have tensor product of Hilbert spaces
belong to different (quantum) number fields. These quantum adelic quantum states
would not have physical meaning as such. One would have entanglement between
different number fields for instance.
(c) To get real probability amplitudes, one would map quantum adelic amplitudes to complexvalued amplitudes by canonical identification.
After that, one could calculate
probabilities using ordinary calculus.
2. "Is inertial-gravitational dichotomy is a direct correlate for geometric-subjective dichotomy of
Time?" I might have made this question somewhere some time. Certainly I would leave the
question unanswered now;-).
55
Inertial-gravitational dichotomy would correspond to the dichotomy with the
Geometric-Times assignable with the imbedding space and space-time surface. One could
see the Geometric-Ttime assigned to a space-time sheet as something "Subjective" since it is
associated with a particular physical system. The Geometric-Time coordinate assignable to
imbedding space could be seen as something "Objective" not assignable to any particular
physical subsystem. Maybe I am playing with the meanings of "Subjective" and
"Objective" now;-). Be critical!
In any case, inertial-gravitational dichotomy is essentially the content of the Equivalence
Principle. And whether the EP is realized in TGD or not has been one of the most longstanding open
problems. At this moment, I believe that EP is realized in a generalized form and its Einsteinian
form emerges only in long-length scales. Just as in string models.
Coset representations for conformal algebras of symplective algebra of delta M4+xCP2 (--inertial)
and Kac-Moody algebras associated with light-like 3-surfaces (---gravitational) imply that inertial
and gravitational quantum numbers are identical. Gravitational = inertial applies not only to fourmomentum and mass but also to all quantum numbers.
http://matpitka.blogspot.com/2012/02/anatomy-of-state-function-reduction.html#comments
topic: The anatomy of state function reduction
1. At 4:52 AM, hamed said...
Dear Matti,
The posting and the last posting is very interesting for me and I am struggling with them now.
Thank you very much for responding my questions, but a question about that:
Why U-matrix should be exist theoretically? I couldn’t find the answer from “The master
formula for the U-matrix” or other chapters. I saw properties of U-matrix rather than the answer of
this question in the chapters by my childish mind.
2. At 6:06 AM, [email protected] said...
Dear Hamed,
There is nothing childish in your mind! I am really grateful for critical questions. They help me
enormously in disentangling the details and identifying the many erratic statements I have made. I
sincerely hope that you or no-one else would not take me as a guru. The optimal strategy would be
that you try to debunk me! Debunking by content is an excellent manner to learn also a lot of things
not directly related to TGD.
In the earlier posting, I have proposed what I would call minimal identification of U-matrix.
A. There are two state basis correspond different arrows of Geometric(relativistic)-Time. For
the first one, the positive energy parts of states have well-defined single particle quantum numbers.
For the second one, the negative energy states. Suppose that the states is such that positive energy
part has well-defined single particle quantum numbers and is therefore the analog of initial state.
B. The simplest identification of U process is in terms a representations of state basis in terms of
state basis with opposite arrow of Geometric-Time.
56
First happens state preparation meaning reduction to a state for which negative energy
part has well-defined single particle quantum numbers. This process is followed by a state
function reduction to the positive energy part and the net outcome is what can be regarded as
a transition between positive energy states. This picture allows the change of the arrow of
Geometric-Time.
The nice feature is that all that happens are transitions in which positive and negative energy
parts of the state become prepared=state function reduced. I do not of course know whether this
picture about U-process is enough for all imaginable transitions.
U-matrix would exist automatically theoretically. The M-matrices served as its building brick
would be defined in terms of time-like entanglement coefficients between positive and negative
energy states for the modes of WCW spinor fields. The only condition is that the single particle
states for either upper or lower boundary of CD have well-defined quantum numbers and linearity
allows to realize this.
This is somewhat analogous to the coding of S-matrix by the solution of Schrodinger equation
which in potential field which approaches at t→-infinity to plane wave solution. The idealization is
that the situation is stationary.
I have continued my own struggle with the quantum p-adics. This stuff is still in total turmoil so
that you should not waste time with it. I have however the feeling that I managed to make a
considerable progress in the understanding of what quantum p-adics could mean.
There is the safe option. But it effectively reduces to ordinary p-adic number fields and to a
modification of canonical identification mapping the coefficients of powers of prime to quantum
integers.
And there is the interesting and highly risky option. The version of this option that I have
proposed turned out to be non-associative with respect to +q and also additive inverse failed to be
unique. This forced the realization that unless one wants just the safe option, one must do something
radical.
1. The attribute "quantum" must be realized somehow. Obviously this means wave function.
Wave function in the discrete space for quantum representatives of given integer - at the orbit
of the analog of Galois group associated with integer n reducing to the product of Galois
groups associated with the primes dividing it.
2.
Remarkably, this forces to realize the equations x+q y=z and x*q y =z as analogs of zero
energy states or quantum transitions represented by 3-vertices! There would be direct
mapping of arithmetic operations to quantum transitions! Algebraic formulas would become
the basic objects represented as zero energy states. That mathematical statements A=B
correspond naturally to zero energy states is not a new proposal.
3. The conditions of associativity and distributivity fix (I guess) uniquely now what the wave
function for z is if the wave functions for x and y are known. This would unify algebra and
co-algebra and mean that Number Theory is transformed to Quantum Physics! Every
algebraic equation A=B could be transformed to zero energy state!
57
Could physical zero energy states represent equations, mathematical statements? Could the
physical world be Platonia?
Only in this manner can one hope that one indeed obtains field structure (or should one say
"quantum field" structure;-)!
http://matpitka.blogspot.com/2012/02/progress-in-understanding-of-quantum-p.html#comments
topic: Progress in understanding of Quantum p-adics
1. At 6:57 PM, hamed said...
Dear Matti,
some questions:
-What is difference between x^3-l and other light like 3-surfaces in the H?
-In many sheeted space time, when we concentrate on two of them, condensing space time is in
the H=M4xCP2 and other space time is in the other H'=M'4xCP'2, then both of space time
sheet with the wormhole between them are in the space H*H'? (Cartesian product or tensor
product of imbedding spaces H and H'?)
-Is the wormhole represented by D3xCP2? Then D3 has Euclidian signature of induced metric?
-If a piece of Generalized Feynman diagram represented by a cylinder, then what is the space of
side? And what is the space of plane perpendicular to axis of cylinder?
2. At 5:41 AM, [email protected] said...
Dear Hamed,
Thank you for good answers. Here are my answers to your questions.
A. There are general light-like surfaces in general and wormhole throats which are light-like
surfaces at which the signature of the induced metric changes. This means that both 4-metric
and 3-metric are degenerate (determinant of the metric vanishes). If I remember correctly, I
use X3l as a symbol for the latter.
B. Imbedding space is just one and unique if one forgets p-adic generalizations and the use of
covering of imbedding spaces as effective tool in the description of hierarchy of Planck
constants. These generalizations might easily lead to confusion.
● All space-time sheets are therefore region of 4-D space-time in M4xCP2. There is complete
analogy with strings and branes.
● Think first in terms of 2-D surfaces in 3-space E3 since this is very concrete and familiar.
Take 2 planar pieces of surface which are parallel and connect by wormhole contacts.
After this generalize: 3-D space to 8-D space-time and 2-D surface to 4-D space-time
surface.
58
● The illustrations at my homepage should help to get an idea what the topological
condensation and wormhole throats mean. There is no Cartesian product or tensor
product involved. See http://tgdtheory.com/figu.html
If you understand the low-D situation, you easily understand the higher-D situation.
C. Wormhole contact is a 4-D object since it is a small regions of space-time surface.
● A simple model of wormhole contact is as a small deformation of a piece of what I call
CP2-type vacuum extremal.
● Take CP2 coordinates as local space-time coordinates so that the roles of M4 and CP2
reversed and assume that M4 coordinates are of form mk = fk(s), s some function of CP2
coordinates and fk some functions. This gives 1-D M4 projection.
● If you assume also that the condition m_kl dfk/dsdfl/ds=0 holds true,
the contribution of M4 to induced metric vanishes so that surface is just piece of CP2 in
induced metric.
● M4 projection is light-like random curve since fk can be chosen otherwise arbitrarily as
well as the function s. This is vacuum extremal of Kaehler action. The educated guess is
that small deformations of these correspond to wormhole contacts defining analogs of
lines of generalized Feynman diagram. The M4 projections of lines would be light-like
curves in this approximation.
● The line of generalized Feynman diagrams correspond to wormhole contact and in
reasonable approximation piece for the deformation of CP2-type vacuum extremal. Piece
is in question. If you regard the line as a cylinder in space-time, then the analog for the
boundary of cylinder is light-like wormhole throat at which induced 4-metric changes its
signature. Black-hole horizon would be a reasonable but not a complete analogy (at a
Schwartshild black-hole, the horizon is light-like but the determinant of 4-metric
determinant is non-vanishing whereas it vanishing for wormhole throat in TGD).
3. At 11:14 PM, [email protected] said...
"Thank you very much Matti. It gave me a fresh perspective, the question about space-time
sheets returned to when I asked this by model of a lot of boxes in my mind, then in really there is
one box and all the space time sheets are in it. But in my mind there is some misunderstanding
yet. If all the space time sheets are in the one H=M4xCP2,then distance between them should be
smaller than CP2 radios. But in TGD, CP2 radius is smallest length scale."
Dear Hamed,
For some reason my blog did not show your question so that I glued it here(above). The answer
is completely trivial but there is some misunderstanding. I hope the following helps.
A. Space-time sheets have typically finite size. They are inside CDxCP2 where the causal
diamond CD is the intersection of Future and Past directed light-cones. [ I often all
CDxCP_" just CD. This kind of laziness is criminal. I am sorry for my sloppiness;-)].
59
The space-time surface and also space-time sheets inside CD ( not usually filling it) have
some finite-sized M4-projection. These projections can intersect (sheets are "on top of each
other") but not necessarily. If they are on top of each other, the distance between them is
indeed of the order of CP2 size. Very very small (about 104 Planck lengths). You are
completely right in this case. The second possibility is that the first space-time sheet of
finite size is here and second in Andromeda. Their distance is essentially the distance using
M4 metric and very very large.
As an illustration, think of 2 very thin glass plates (thinner than CP2) in Euclidian 3space. Imagine that the z-direction is analogous to the directions along CP2 in 8-D space. If
the second plate is here and second in Andromeda, the distance between them is very large.
If both plates are here at Earth at the same position and parallel to x-y plane, their distance
can be arbitrary small as orthonormal distance along z-axis between them. Also, wormhole
contacts can form between them.
B. The fact that sheets "on top of each other" are so incredibly near each other makes very
probable the formation of wormhole contacts between them and as a special case wormhole
contacts gives rise to particles like gauge bosons. If you have fermion modelable as piece of
CP2-type vacuum extremal topologically-condensed to another space-time sheet, it can
touch also second space-time sheet and very probably does so and it feels its presence as
external field. I talked about this in some earlier blog postings. This is very important and a
rather new realization concerning the physical interpretation of the theory.
C. One cannot say that CP2 radius is the smallest possible length since there is no discretization.
Think in terms of the analogy with Kauza-Klein theories. CP2-length scale only defines the
natural geometrically-defined length unit which could quite well be smallest possible
fundamental length scale but not distance!! If one goes to energies at which CP2 radius is
the natural length scale defined by Uncertainty Principle, CP2 begins to be visible directly in
physics. This is of course impossible in accelerates that human kind can build during next
millenium;-) so that CP2 makes itself visible only indirectly. CP2 makes itself indirectly
visible via color interactions. But QCD is expected to be a good first approximation since
CP2 is so small.
What about Planck length which is about 10-4 times smaller than CP2 size? Does it define
fundamental length scale in the TGD Universe? I do not actually know. It might emerge from
dynamics of Quantum-TGD as genuine fundamental scale or be just a parameter popping up only at
the long length scale limit of the theory so that the whole Planck length scale heuristics would be bad
mysticism;-). I however have a nice formula for G in terms of CP2 radius and exponent of Kähler
action for CP2-type vacuum extremal.
What is clear that Planck length L_Pl propto sqrt(hbar G) and if one takes the hierarchy of
Planck constants seriously, then for Astrophysical values of Planck constant given by hbargr=
GMm/v0 Planck length L_Pl is of the order of black-hole radius 2GM as you see just by substituting!
http://matpitka.blogspot.com/2012/02/error-in-opera-experiment.html#comments
topic: "Error in OPERA experiment?"
1. At 1:47 PM, hamed said...
Dear Matti,
60
If it is possible for you, please answer two questions about ZEO:
1. One can assign to a ball on my hand a CD. This CD has 2 parts of positive and negative energies
on its boundaries. Why do I feel only positive inertial energy of the ball when I throw it?
2. “Gravitational energy is the difference of inertial energies of positive and negative energy matter”.
Then Gravitational energy of the ball on my hand is difference of inertial energies of which
matters? More clarifications please.
2. At 10:40 PM, [email protected] said...
Dear Hamed,
Thank you for excellent (and difficult!) questions. I try to answer as well as I can and also make
clear what I do not understand well.
What you feel while throwing a ball is the reaction force. Momentum transfer rather than
energy! But this was not the gist of your question which I identified as "Why we seem to perceive
only the positive energy part of the state?"
A. Clarification: "Positive" is just a convention. I can assign it to either boundary of CDs and they
keep the convention.
B. Why the question is non-trivial? The simplest identification for the U process discussed in
earlier posting suggests that sensory experiences correspond alternately to state function
reductions to positive and negative energy parts of the state. Time flip-flop! We do not,
however, experience this alternation. It would mean a sensory nightmare. Like seeing 2
movies alternately. We do not perceive alternatively the upper and lower boundaries of CD
assignable to environment. Why?
C. What do I perceive sensorily? CD but in what scale? If the perceived world corresponds to a
very large CD compared to my personal CD, then the sensory input is always about the
positive energy part of this very big CD.
This is the brief answer. I consider some issues related to the U process in more detail since I want
to make absolutely clear that I do not understand them satisfactorily;-).
Basic question: Does the U process occur (a) for the *entire zero energy states* or (b) for
*positive/negative energy parts* of zero energy states?
During the years, I have considered both options without clearly distinguishing them. Anything
related to the notion of Time is very difficult to all of us. We do not have the brain for Time.
The minimal proposal: U-process takes place for positive (negative) energy part of the state and is
induced by a state function reduction to the negative energy (positive) part of the state. A kind of Time
flip-flop.
State function reduction and U process are dual to each other as also state function reduction and
state preparation. This interpretation is minimalistic and possible only because of necessary breaking of
time reversal invariance for zero energy states.
61
Objection: Our sensory perception can be identified as quantum measurement assignable to a state
function reductions for upper and lower boundaries of our personal CD. Problem: our sensory
perception does not jump between Future and Past boundaries of our personal CD (containing
sub-CDS in turn containing…)! Why?
Answer: If our sensory perception is about CD which is much bigger than personal CD, the problem
disappears. We perceive from day-to-day the, say, positive energy part of a state assignable to
this very big CD. The World looks rather stable.
Question: Could our sensory perception actually do this jumping so that sensory inputs are
alternatively about upper and lower boundaries of personal CD? Could sleep-awake cycle
correspond to this flip flop?
Answer: The Geometric time span for quantum would correspond to the Geometric time scale for
our personal CD. In wake-up state, we are performing state function reduction at the upper
boundary of our personal CD and sensory mental images as sub-CDs are concentrated there.
When we are asleep, same happens at lower boundary of CD and sensory mental images are
there (e.g., dreams,…).
Question: What is the time scale assignable to my personal CD: the typical wake-up cycle: 24 hours?
Why we do not remember practically anything about sensory perceptions during sleep period?
Why do we forget actively dream experiences? Does the return to childhood at old age relate
with this time flip-flop in the scale of life span. Do we re-incarnate in biological-death at
opposite end of CD with scale of life span?
Question: How the arrow of Geometric-Time at space-time level emerges from the arrow of
Geometric-Time for zero energy states? Why do we experience that we move along spacetime sheets to Geometric-Future or equivalently: space-time sheets move with respect to us to
Geometric-Past?
Answer: The proposal (one of the many, see ...) -- which can be easily ridiculed -- is that the state
function reductions performed by sub-selves assignable to sub-CDs at the boundary of personal
CD and representing mental images induce small time translations of space-time sheet tending
to shift it as a whole to Past. This induces the arrow of Geometric-Time. Space-time sheet is
like film which the curious audience in the movie theatre shifts to a preferred direction.
The subselves representing sensory mental images are tiny conscious entities and they are very
curious! News are in the Geometric-Future assignable to the space-time sheet and they want to know
what is there and they use their volitional resources to induce a small shift to the Geometric-Past.
Why selves would be "curious". Could this be understood by postulating a generalization of
Negentropy Maximization Principle (NMP) stating that the information gain in quantum jump is
maximal? Selves would be hungry information eaters. As a matter of fact, our hunting for metabolic
energy would not be about getting energy but negentropy associated with the entanglement!
You asked:
> “Gravitational energy is the difference of inertial energies of positive and negative energy matter”
Then Gravitational energy of the ball on my hand is difference of inertial energies of which matters?
More clarifications please."
62
This is just one possible identification. Not the only one and I have mixed feelings about it.
In any case, the identification of gravitational and inertial four-momenta based on generalization of
coset representations for super-confromal algebra is the fundamental definition and generalizes the
Equivalence Principle. It does not require this identification but seems to be consistent with the
identification.
The basic motivation for the proposal comes from the study of the extremals of Käehler action which
define space-time correlates for quantum physics.
A. Kähler action has gigantic vacuum degeneracy. Any space-time surface with CP2 projection
which is Lagrangian manifold (2-D CP2 projection and vanishing induced Kähler form) is
vacuum extremal. The symplectic transformations of CP2 and diffeomorphisms of M4 are
symmetries of vacuum extremals. These space-time surfaces as such are not preferred
extremals but very probably their small non-vacuum deformations are.
B. First interpretation: the Einstein tensor associated with the vacuum extremals is proportional to
the average energy momentum tensor assignable to the small quantum fluctuations of the
vacuum extremals. Einstein's equations would result as a kind of statistical description in long
length scales (as in string models). G would be also a prediction.
C. Second interpretation (the one you are asking about): In the scale of CD defining measurement
resolution, sub-CDs have vanishing inertial energy. But what about gravitational energy?
Could it be positive for these sub-CDs?
One would obtain a non-vanishing gravitational energy as difference of positive and negative
energies for zero energy states: E_+-E_-= 2E_+. This would be true for space-time correlates:
vacuum extremals would have vanishing inertial energy defined in terms of Noether currents but
non-vanishing gravitational energy defined in terms of the Einstein tensor.
This would give also the equivalent of Einstein's equations for positive energy part of the state
via E_+-E_-= 2E_+. These 2 interpretations could be consistent. More I cannot say.
3. At 3:43 AM, hamed said...
Wow! Thank you, Matti. It was too beautiful especially about U process. It’s near to cry ;-). I must
control my emotion!
4. At 11:39 PM, Ulla said...
The measurement tool decides the output and the tool we use in our perception only feel the
collapse or state function reduction (compare to a pulse) because this is the result of the phase shift
made from both CD-cones. Are we then in the zero point (the light-like point)? I guess not because
we are made of discrete matter.
The problem is in the measurement, made of tools which can only measure certain things. Today
we have no tool to measure the other side of the cone? We can only measure the result which is
discrete? This for both ordinary and Living matter. But Living matter can computate more and
better because it has an additional CD-cone of adelian charachter joining the zero point (at least at
certain spots=the window-effect?). Remember the double 8D discussed some posts ago.
63
5. At 5:11 AM, [email protected] said...
One could say that our biological bodies could be thought of as collection of partonic 2-surfaces
at the boundaries of CD and smaller ones at sub-CDs, their sub-CDs etc... Fractal structure. One
can also speak of 3-surfaces and space-time surface by holography.
Localization to the tip of CD is wrong.
http://matpitka.blogspot.com/2012/02/progress-in-number-theoretic-vision.html#comments
topic: " Progress in number theoretic vision about TGD"
1. At 7:36 PM, hamed said...
Deep connections between cognition, infinite primes, hierarchy of Planck constants, braids and
… Oh! , that’s really amazing. I don’t know if my small capacity of mind will allow to understand
them or not in the future. This takes a long time process :) I have the best wishes for you.
2. At 11:33 PM, [email protected] said...
Dear Hamed,
No hurry. I took 34 years for me!;-).
We have not talked much about the" dark side" of TGD;-). I have been working since 1990-orso with the TGD-inspired theory of Consciousness and Quantum-Biology. The number theoretic
vision about TGD is partially due to developments in this branch of TGD.
The attitude of colleagues to Biology and Consciousness looks very strange to me. A 10-line
"argument" claiming that Biology involves no new physics and everything above the weak boson
length scale is understood is thought to be good enough justification for forgetting these branches of
Science altogether. M-theorists (who does still remember them;-)?) went even further and
understood everything above Planck scale and much more ;-).
The basic attitude of physicists is rather imperialistic. Lubos once described this attitude
excellently from the point of the believer on it. Physicists are builders of empire. They are invaders
which mercilessly subdue new words under their power.
Biology and Consciousness are troublesome regions of the Big Empire but officially they are
under the control.
3. At 10:46 AM, hamed said...
Although I am now struggling with Riemannian geometry and relation with Einstein equations,
every week some feedback (as overview) to what I will learn in the future is useful for me.
I have some obscure view about the role of Poincare in TGD. I wrote my misunderstanding of it
here:
In GRT, there is Poincare invariance only locally. But in TGD, one can have a global Poincare
invariance at the level of entire WCW and local one at the level of Classical space-time.
64
TGD speaks about 2 super-conformal symmetries that lead to union of symmetric spaces G/H.
Each of symmetric spaces G/H has exact Poincare invariance. Therefore at each of these spaces
there is conservation energy and momentum and this leads to exact Poincare invariance at the level
of entire H=M4xCP2.
In the Space of 3-surfaces in TGD, each of 3-surfaces is a symmetric space and is in
correspondence to each of symmetric spaces.
Classical space-time in TGD as X4(X3) is like space-time of GRT and curvature is not constant
for it and one can have only Poincare invariance locally. Only Classical-TGD cannot solve problem
of Poincare invariance and Quantum-TGD is needed? What is my misunderstanding in these
sentences?
I feel my writing of English had improved in these weeks only because of these questions ;-)
Before these weeks it had been took time entire a morning to write a comment to you! Practice in
writing in this manner was very useful for me.
4. At 10:36 PM, [email protected] said...
Dear Hamed,
Thank you for asking about Poincare invariance. This is a difficult subject although it looked
trivial to me for 34 years ago;-). I will consider it first at space-time and imbedding space level.
A. Symmetries of space-time are identified usually as isometries. Distances between points are
preserved and also angles between vectors. Everything related to size is preserved.
B. In General Relativity, isometries act as isometries of space-time and move space-time points.
The problem… For curved space-times, Poincare symmetries are lost. For Scwartschild
metric for instance, one has only rotations and time translations as symmetries.
Translations are lost and this means that one cannot define the notion of 3-momentum as
conserved Noether charge.
C. In TGD, isometries act as isometries of the 8-D imbedding space (as opposite to space-time in
GRT) and move the entire 3-surface or space-time. This is the big difference and solves
the problems related to the loss of Poincare invariance. Space-time surfaces can be curved
and can have even Euclidian signature of induced metric. The induction of metric is of
course also a central notion.
Talking about space-times instead of space-time makes sense in quantum gravity where quantum
states can be regarded as quantum superpositions of space-time surfaces so that the action of
Poincare on quantum state is well-defined.
This idea looks good. But in Zero Energy Ontology, one encounters what looks like a problem
(maybe more than a minor technical detail).
In ZEO, one effectively replaces imbedding space M4xCP2 with CDxCP2. The causual diamond
(CD) is the intersection of Future- and Past-directed light-cones. Isn't this in conflict with Poincare
invariance in global sense? For instance, translations for points of CD lead out of it near its
boundaries? Is this lethal?
65
1. Sloppy reaction: One might say that this problem is purely academic since only infinitesimal
translations are needed to defined four-momenta. One has local Poincare invariance and
this is enough.
Certainly it is enough. One obtains local Noether charges and this invariance can be
only broken by boundary conditions at the boundaries of CD. For instance, translation of
space-time surface need not be any more a preferred extremal of Käehler action.
2. Less sloppy reaction: Poincare symmetries are actually replaced with their local variants
analogous to Kac Moody symmetries. The translation depends on the point of space-time
surface and one can combine constant translation with space-time dependent translation
which is such that it compensates the constant translation about boundaries of the CD.
Generalization of Kac-Moody type symmetries made possible by conformal invariance
would be the way out of the problem at deeper level.
I could be also worry about non-conservation of gravitational momentum as opposed to
conservation of inertial momentum in relation to Equivalence Principle. But let us leave it to some
other time;-)
You make excellent questions with easily comprehensible English;-). Writing is a very powerful
tool of thinking. Seeing one's own thoughts caught on paper as helpless victims of thinker's skeptic
criticism is very effective feedback;-). Some people write mathematical formulas. This is one form
of feedback. For me, writing of less formal text is the feedback. It is amazing how fantastic ideas
pop up when one just writes out what one does not understand!;-)
A. About G/H, I more-or-less agree. Different G/Hs correspond to different values of zero
modes not appearing in the metric of WCW as differentials but only as external parameters.
The information about zero modes is partially coded by the values of the induced Kähler
form at the partonic 2-surfaces. One can say that Käehler E and B at partonic 2-surfaces are
purely classical variables which do not quantum fluctuate. What does this mean is an
interesting question in itself which I have not pondered.
B. The statement that 3-surfaces are symmetric spaces is wrong. Symmetric spaces are
extremely restricted variety of spaces. They are basically coset spaces of type G/H for Lie
groups. The only compact 3-D symmetric spaces would be SU(2) (3-D sphere S3), SO(3)
(S3 with antipodal points identified). Very few others if any. WCW would contain very
few points!
You asked also about 3-surfaces.
1. Without any further constraints, 3-surfaces would be just intersections of space-time surfaces
with boundary of CDxCP2. Any 3-surface will do. One must assign to 3-surface a 4surface to realize 4-D GCI. This is preferred extremal of Kaehler action whose value
defines Kaehler function of WCW defining Kaehler metric of WCW. Once one knows the
3-surfaces at the ends of CD, space-time surface as analog of Bohr orbit is fixed (forgetting
now delicacies due to the failure of strict determinism). This is holography implied by GCI
alone rather than postulated separately. This was my view for a long time.
B. There are further constraints, however, and they come from strong form of GCI and ZEO. I
have discovered these during the last decade. The strong form of GCI says that both space66
like 3-surfaces at the ends of space-time surface and light-like 3-surfaces code for the same
physics. The only manner to realize this double coding is that the intersections of these two
kinds of 3-surfaces do the coding. This implies effective 2-dimensionality stating that the
partonic 2-surfaces and their tangent space data (briefly 2-data) code for physics. This also
means strong form of holography. All follows from GCI which shows how incredibly
powerful Einstein's postulates become in sub-manifold gravity.
C. Partonic 2-surfaces are defined as the intersections of the space-like 3 surfaces at ends of
space-time surface with the light-like 3-D wormhole throats. Partonic 2-surfaces alone are
not enough. If they were, TGD would reduce to the string model. In addition, tangent
space data is needed. There is also a hierarchy of scales since strict determinism for
Kaehler action fails and preferred extremal must be specified by giving CD plus sub-CDs
plus sub-sub-CDs.... and specifying 2-.data form them.
D. The building of preferred extremals would be rather practical business;-). Forming first a
roughest frameset by giving 2-data at boundaries of CD. Then the same for sub-CD:s and
then for sub-sub-CDs and stopping when measurement resolution is satisfactory. After
this, one should construct numerically or otherwise space-time surfaces for all this CDs.
Classical space-time surface is preferrred extremal of Kahler action. The field equations
defining it can be defined by varying Kähler action and "preferred" selects on the solutions of field
equations when data about boundaries of CDs are given. The field equations are derived in "Basic
Extremals of Kaehler action" at http://tgdtheory.com/public_html/tgdclass/tgdclass.html#class .
Here also the known basic solutions of field equations deduced using symmetry arguments are
discussed. A good future exercise would be the derivation of the field equations in general form
from Kaehler action by varying it with respect to induced metric and Kähler form.
You asked also about space-time surfaces.
1. About X4(X3), you are right in the sense that Poincare invariances as isometries of X4(X3) are
not symmetries. However, they act however as symmetries moving the partonic 2-surfaces
at the ends of space-time surface and give rise to new space-time surface. This is the key
difference between TGD and GRT.
2. You are right when saying that Classical-TGD alone does not solve the problems related to
symmetries. The very assumption that Poincare transformations affect entire space-time
surface rather than only moving points along space-time surface and leaving it invariant as
whole is inconsistent with Classical gravity assuming fixed space-time.
One must speak about quantum superpositions of space-times or strictly speaking of
partonic 2-surfaces and tangent space data from the beginning. For instance, quantum
numbers like quark color and also momentum quantum numbers would not be possible
without these quantum superpositions! In this sense, the TGD Universe is the quantum
Multiverse.
http://matpitka.blogspot.com/2012/03/icarus-measures-light-velocity-for.html#comments
topic: "ICARUS measures light velocity for neutrino"
67
1. At 6:51 AM, hamed said...
Dear Matti,
I learned the basic notions of Riemannian geometry like geodesics, Riemann tensor, and … But
I am skeptical about the basic notions of the manifold. For example, one can assigns to each point of
a manifold a tangent and a cotangent vector space. But I don’t think in TGD a 3-surface composes
of points. Does in TGD Classical space-time points would be replaced by regions of the space-time
as like the viewpoint of C. J. Isham? Then it should be reconsideration in basic notions of manifold.
-Another question:
I have “The philosophy of Quantum mechanics” in the academic term. My teacher said: “In
Bohm quantum theory, one can decomposes psi(wave function) as Psi=R * exp(i*s/h) and the
principle: v=grad(s)/m where v is the classical velocity of the electron.
Therefore in Bohm theory, one can assigns to a particle both a wave function psi and particle
positions(as classical). (some weak similarity with TGD!) Bohm theory is very richer than Bohr
model for describing the orbitals of hydrogen’s atom."
Is there any relation between the Classical position of a particle in Bohm theory and Classical
space-time x4(x3)?
In TGD, Psi replaced with M-matrix and exp(i*s/h) is Generalized to S-matrix. Then what does
it means v=grad(s)/m in this generalization?
2. At 12:48 AM, [email protected] said...
Dear Hamed,
Regarding your first question, I am not quite sure what you mean. 3-surface is locally a
manifold and decomposes to points. In other words, it is chartable and therefore can be represented
by 3-D maps with each page of the map 3-D Euclidian space E3 and there are chart maps identifying
the images of same point at different pages. The chart book about the surface of our planet is an
example about what I mean. There are diffeomorphisms between different pages of the book.
One can assign to it tangent and co-tangent spaces and their tensor products and powers. This is
necessary in order to define forms and vector fields. For instance, induced metric can be interpreted
in terms of induced tangent bundle.
There are of course some delicacies. Local manifold property can fail for surfaces and it does so
for the "lines" of generalized Feynman diagrams at vertices in the same manner as it fails for
ordinary Feynman diagrams at vertices due to the fact that the topology of "Y" is not topology of "I".
There is also the notion of finite measurement resolution which could be also understand as
discretization obtained by replacing space-time regions with points. Consider as a concrete example
all space-time points for which coordinates have same first N decimal digits. This defines certain
space-time region replaced with single point.
About Isham's viewpoint, I do not know enough to say anything.
68
Referring to you second question, I try first to summarize what I have understood about Bohm
theory.
A. I think that the original motivation was to keep theory deterministic and classical by introducing
the hydrodynamical interpretation. The first ad hoc postulate is Guiding equation is that some
points representing Classical particles are "active" and entire solution of Schroedinger
equations serves as guide wave defining particle orbit as a flow line of a hydrodynamical flow
so that one would have a kind of hydrodynamical interpretation. This implies non-locality of
the theory since the Schrodinger amplitude induced "quantum force" acting on the Classical
particle.
Particle motion is determined by the identification of velocity as given by above formula:
Newton's equation is replaced with a first-order differential equation for a flow. This is quite a
big difference from second-order differential equations in Newtonian framework. I think that
one
obtains
Newton's
equations
at
semi-Classical
limit.
See
http://en.wikipedia.org/wiki/Bohm_interpretation#Guiding_equation
B. I do not understand how one could obtain state function reduction from this picture as a
prediction. The reason is that the theory is deterministic and Quantum equilibrium hypothesis
(second ad hoc postulate) stating Born rule is introduced. But according to Wikipedia, it has
not been shown that it follows as asymptotic property of solutions of Schrodinger equation.
C. At the level of formulas Bohm theory makes sense in wave mechanics. In QFT, it ceases to do so
since the highly non-linear formulas cease to make sense in infinite-D context. For fermions
described by Grassmannian variables classically this idea fails.
D. The weakness of the Bohm theory is that if you want to apply it, you must do the practical
calculations using ordinary wave mechanics and then introduce Bohm theory. Just a complex
re-interpretation with 2 questionable hypothesis is in question state function remains a mystery.
You wondered about similarities between Bohm and TGD. I shall first list the differences between
Bohm's theory and TGD.
1. In TGD, one assumes state function reduction governed by Born rule plus Negentropy
Maximization Principle. No analog of quantum equilibrium hypothesis is introduced.
2. Dynamics of space-time surfaces is dictated by Kahler action plus preferred extremal property
rather than by guiding equation.
3. No selection of "active" space-time surfaces is made and the field equations defining space-time
surface are defined by Kahler action rather than wave functional.
There are also similarities.
(i) TGD is also very Classical. At WCW level, one has only Classical spinor fields. At space-time
level Classical physics, which fails to be strictly deterministic except locally - is exact part of
quantum theory and even WCW geometry: space-time surfaces are analogous to Bohr orbits.
This translates to holography in 3-D and even 2-D sense as effective 2-dimensionality (partonic
69
2-surfaces plus 4-D tangent space data). Path integral over 4-surfaces is replaced with
functional integral over 3-surfaces (or 2-surfaces with these data).
(ii) Quantum-Classical correspondence (more-or-less equivalent with holography) requires that the
quantum numbers of quantum state must be coded into the geometry of the preferred
extremals. This is a highly non-trivial condition and I have discussed a detailed proposal for
how this is achieved. The Guiding equation is therefore replaced with much weaker condition.
I cannot imagine any interpretation for v=grad(S)/m since S is not a function in WCW but matrix
between positive and negative energy parts of zero energy states.
3. At 12:31 AM, Ulla said...
You talk of the 3-surface as light-like or Euclidean, sometimes use the massless extremals
analogy.
A wormhole has these characters. How is a wormhole done? Can this be understood as space
without gravity and time too?
Then here would be FTL conditions as a giant plasmoid/particle?
4. At 9:42 AM, [email protected] said...
Massless extremals are 4-D surfaces: correlates for radiation. I would compare them to laser
beams.
Wormhole contacts are formed unavoidably if you have 2 space-time sheets whose projections
are in same region of Minkowski spaces. These surfaces are with distance about 104 Planck lengths
and unavoidably touch here-and-there and form wormhole contacts.
http://matpitka.blogspot.com/2012/05/universe-from-nothing.html#comments
topic: "A Universe from Nothing"
1. At 11:43 PM, ◘Fractality◘ said...
Matti:
If DNA is a topological quantum computer, all actions precede through it?
2. At 11:58 PM, [email protected] said...
Quantum computing-like activities are always possible when 2 molecules or even larger objects
are connected by flux tubes. This information processing is universal. However, DNA-lipid layer
system would be suitable just for this purpose. Minimal function would be realization of memory as
braiding patters updated by flows for molecules.
3. At 2:56 AM, hamed said...
Dear Matti,
Thanks for the posting that would be controversial for me.
70
The sentences like “Physical worlds define the Platonic of the mathematician” are lead to some
beauty direction to thinking. Because in this view, if I study geometry or algebra in a very
abstracted manner then I can think that I am studying the physical world in really!!! But we know
that Mathematics is very wide and it contains very abstracted theorems in branches of it and is
progressing year-by-year. Then for understanding the physical world in a precise manner, one
should learn all of the mathematics!?
For example, for me it should be very interesting if some mathematical spaces like Lp spaces
exist physically! ( http://en.wikipedia.org/wiki/Lp_space ) They are spaces that one deals with pnorm instead of 2-norm.
Or in number theory, I think this view can lead to some very deep understanding of Physics if
one think that what is physical meaning of all of 10 Musean hypernumbers: seditions, w , p , q , m ,
… . also nu number as unifying concept to allow to transition between all the hypernumber types.
And sigma as the creator of axis. And also Anti-numbers. Relation between the 10 levels of
hypernumbers are very interesting for me: http://en.wikipedia.org/wiki/Musean_hypernumber .
4. At 4:02 AM, [email protected] said...
Dear Hamed,
Interesting question. This idea about Platonia as physical world looks controversial. At first, it
seems to be in conflict with the vision that the laws of Physics are unique; that Standard Model
symmetries are somehow very special; etc.
The point is, however, that standard model symmetries would be symmetries of Mathematics
itself! Octonions have SU(3) as automorphism group for instance and CP2 is coset space
SU(3)/SU(2) having interpretation as space of quaternionic planes of octonionic space at given point.
The second point is that Physics should be like a Turing machine. It should be able to emulate
all possible physics which are internally consistent. Finite measurement resolution (if representable
quite generally as effective gauge symmetry) would allow us to emulate extremely general gauge
symmetric theories.
One can also worry about higher dimensional spaces if 8-D space is the imbedding space
dimensions. However, the World of Classical Worlds (WCW) is infinite-D and allows as submanifolds finite-D spaces of arbitrary dimension. Also unions of N disjoint n-sub-manifolds are
effective N*n-dimensional locally. Standard wave-mechanical description of N-particle system
indeed uses N*3-D configuration space.
If the number theoretical Brahman=Atman based on the generalization of real number
introducing infinite number of real units as ratios of infinite integers is accepted, space-time point
becomes infinitely rich-structured and WCW might allow realization as M4xCP2 which more general
definition of space-time point.
There is also the proposal about fractal hierarchy in which arithmetics with + and * are replaced
with direct sum and tensor product for Hilbert spaces. Replacing points of Hilbert spaces with
Hilbert spaces, one obtains hierarchy very similar to infinite primes and now interpretation in terms
of endless second quantization also might make sense.
71
Infinite-dimensionality poses very very strong constraints on mathematical structures. Kahler
metric in loop spaces is unique. Infinite-dimensionality would bring in the laws of Physics! One
might hope that this conditions poses strong enough conditions on the allowed mathematics. For
instance, all finite-D structures would be such that they can be induced from infinite-D structures.
Mathematicians talk about classifying spaces. Probably this is the same basic idea.
It is certainly frustrating to realize how little individual can learn from Mathematics during a
lifetime. I believe that the correct guideline is that the mathematics that one learns or perhaps even
creates must naturally emerge from applications to real world problems (in my case, Physics). When
I was younger, I used to make visits to math library and walk between bookshelves with the idea that
I might find some miraculous cure to my mathematical problems with TGD. I left the library in a
rather depressed mood!;-).
Lp spaces for p=2 are most natural from the point of view of Physics. Bilinearity means linearity
and quantum superposition would be lost for p different from 2. In infinite-D context, p=2 is natural.
5. At 8:39 AM, hamed said...
Thanks. I want to summarize your argument on proofing that “theory is the same as physical
world” and “uniqueness of mathematical structures” in the following (if I misunderstood it, please
guide me):
1. Mathematical structures classify into 2 subcategories:
Some of them like infinite dimensionality are essential for physical world and it is not
possible to have a world without these structures. These mathematical structures are
very rich.
2. These mathematical structures poses very strong constraints on other mathematical structures.
So that because of these mathematical structures are unique, therefore the other
mathematical structures are unique too.
3. Existence of other mathematical structures is very entanglement with these mathematical
structures.
4.
Therefore Essentiality of these mathematical structures for physical world leads to
Essentiality of other mathematical structures under the constraints imposed to them.
6. At 9:08 PM, [email protected] said...
To Hamed:
More or less like this: Note however that finite-D induced structures are very rich. One can
imbed probably any finite-D geometry to infinite-D symmetric space as surface! Only infinite-D
structures are highly unique. Infinite-D mathematical existence is an extremely tricky notion as
perturbative quantum field theorists have demonstrated with huge amount of sweat and tears.
Fundamental structures are infinite-D and highly unique. Kahler metric is a fundamental concept
and its existence relies on maximal symmetries realized a superconformal symmetries characteristic
for 3-D light-like objects, classical number fields, real and p-adic number fields.
72
They induce the remaining structures. In particular, finite-D structures in the sense of
"emulation". Mathematics does not construct n-dimensional spaces for us but only emulates it using
formulas.
This is of course only a dream of the physicist. Today, physicists do not spend enough time
daydreaming;-).
7. At 5:38 PM, ◘Fractality◘ said...
Matti:
Does Zero Energy Ontology (ZEO) imply that the Universe won't extinguish itself (i.e., heat
death) at some point?
Living beings, civilizations, gods are all dissipative systems. Islands of negentropy in a sea of
chaos.
The more complex a phenomenon, the more energy it must consume to maintain its identity and
thus it creates more disorder?
Does ZEO modify any of that?
8. " At 8:36 PM, [email protected] said...
Dear Fractality:
Thank you for a good question.
Universe suffering a heat death is an outcome of theoretical thinking taken to extreme without
taking into account the possibility that the basic assumptions behind the Second Law might not hold
true at the limit of vanishing temperature. To me, it is amusing that so many physicists take "heat
death" so seriously.
The essential assumption is that quantum coherence in the scales considered does not play any
role. At ultra-low temperatures, however, quantum coherence becomes important even in standard
physics. Consider only superfluidity and superconductivity.
You mentioned metabolic energy. This is a good point. The amount of metabolic energy needed
depends on external temperature. Metabolic energy quantum in Living matter is about the same
order of magnitude as physiological temperature. At very low temperatures, the needed metabolic
energy quantum would be very small.
TGD predicts hierarchy of universal metabolic energy quanta identifiable as increments of zero
point kinetic energies in the transfer between space-time sheet corresponding to different values of
p-adic prime p=about 2k. There is evidence for this kind of quanta in visible, UV, and IR as
unidentified spectral lines usually believed to be molecular spectral lines. ATP-ADP would have
same mechanism as a core element.
The new physics elements are also present and bring something new into the picture.
● ZEO predicts infinite hierarchy of CDs (serving as correlates of selves!). The larger the
CD associated with mental images, the longer the time scale of memory recall and
73
planned action for that subself. Electron corresponds to 0.1 seconds assignable to
sensory mental images.
● Hierarchy of Planck constants allowing macroscopic quantum phases. Even at higher
temperatures, Macroscopic quantum phases become possible.
● Number theoretic entropy allowing generation of the islands of negentropy. This modifies
the view about the Second Law dramatically.
In standard physics, there are only islands of small entropy. In the TGD Universe (according to
pessimist), Living matter can pollute environment actively to become more negentropic as we indeed
seem to do;-)!
9. At 8:30 AM, [email protected] said...
To Hamed:
I already thought having answered you but noticed that I was wrong. I attach my answers
between the lines.
[Hamed] In M4*CP2, sometimes you speak about Dynamics of 3-surfaces and sometimes you speak
about dynamics of space-time. I think when you speak about dynamics of 3-surfaces, you dealt
with Geometric-Time and when you speak about dynamics of space-time you speak about
Subjective-Time. Isn’t it? NMP define dynamic of space-time but the minimization of Kahler
action (something like minimal surface in string theory) defines dynamics of the 3-surface.
Isn’t it? But you wrote “Kahler action would define the fundamental dynamics for space-time
surfaces”. It is contradiction with my understanding?
[MP] Sorry. This is just loose language on my side. The strictly correct manner to speak is to
assign dynamics to 3-surfaces. Space-time surfaces are "orbits" of 3-surfaces. I also often talk
about space-time sheets when I should actually speak about 3-surfaces.
[Hamed] If NMP define dynamic of space-time, is it essential to talk about dynamics of space-time
surface in the level of Classical TGD? Because it leads to confusion of the listener.
[MP] NMP does not define dynamics of space-time!;-). It defines dynamics of Consciousness and
tells that the information gain in quantum jumps is maximized. NMP is mathematically
analogous to the Second Law (and implies it for ensembles) in that it tells only overall
direction of dynamics but does not fix time evolution completely as action principles. Kahler
action is the variational principle at space-time level: preferred extremals.
[Hamed] Basic ideas of TGD are very controversial in the view of current physics. So I should be
very attentive when I explain them. Therefore I should explain TGD step-by-step to others.
And when I speak about a basic idea, if it is possible I should try to don’t speak anything about
other basic ideas.
When I explain space-time is a sub manifold in M4*CP2, is it possible to continue about
geometrization of forces without explaining space-time sheets at first? (I think it is not
possible!).
74
Space-time sheets seem very fiction in the view of physicist. For avoiding this, I think that
I should to explain essentiality of many space-time sheets.
[MP] Space-time sheets are just sub-manifolds which are representable as graphs for maps from M4
to CP2 (QFT-like limit of TGD!). There are also other kinds of sub-manifolds. String-like
objects with 2-D M4 projection and CP2 type extremals with 1-D light-like projection! These
are not called space-time sheets.
You can take large number of space-time sheets representing asymptotic regions to
various subsystems. They are small deformations of a canonical imbedded M4 extremely near
to each other. They touch each other here-and-there. This is just the many-sheeted spacetime. The replacement of superposition of Classical fields with superposition of their effects
forces many-sheeted space-time in TGD. Particle touches several sheets and experiences
corresponding forces. Nothing ad hoc!! Sorry for repeating this idea: it is so beautiful!;-)
Multi-sheeted covering of imbedding space associated with the hierarchy of Planck
constants is something different from many-sheeted space-time. I have tried to make this
explicit as often as possible. Here one has effective covering of the imbedding space inducing
multi-sheeted structure for space-time surface. There is a good argument that also this notion
reduces to the basic dynamics of Kahler action. Normal derivatives of imbedding space
coordinates as many-valued functions of canonical momentum densities leads to effective
covering. This is a basic implication of extreme non-linearity of Kahler action which in turn
forced the geometrization of quantum physics in terms of WCW geometry.
These notions are not anything new and ad hoc but follow naturally from the basic
assumptions. Even the (effective( hierarchy of Planck constants, if I am correct. The only
really new and therefore controversial element is sub-manifold geometry as a manner to
realize Einstein's original program.
[Hamed] I think that I can speak about geometrization of forces and space-time sheets without
speaking about “TGD as a Poincare invariant theory of gravitation”. I can explain it after
them. Isn’t it? Or it is essential to explain at first beside them?
[MP] You cannot!;-). The fundamental idea of TGD approach is to solve the energy problem of
General Relativity realized in terms of sub-manifold gravity. This also leads to the
geometrization of Standard Model quantum numbers. ZEO allows us to have consistency with
the fact that apparently energy is not conserved in cosmology. Conservation laws become a
length scale dependent notion. Which is not actually anything new for the pragmatic physicsts
who have talked about renormalization of coupling constants since the times of Dirac.
[Hamed] In really I am thinking that what is best strategy to explain TGD step-by-step without
confusion of the listener. That’s hard ;)
[MP] Good luck! You will need it;-)!
10. At 3:19 AM, Santeri Satama said...
"Second point is that that one ends up with heavy difficulties in physics itself. Quantum
measurement theory is the black sheep of physics and it is not tactful to talk about quantum
measurement theory in the coffee table of physicists. The problem is simply that that the nondeterminism of state function reduction (necessary for the interpretation of experiments in
75
Copenhagen interpretation) is in conflict with the determinism of Schrödinger equation. The basic
problem does not disappear for other interpretations. How it is possible that the world is both
deterministic and deterministic at the same time? There seems to be 2 causalities. Could they relate
to 2 different notions of time? Could the times for the Schrödiner equation and state function
reduction be different?"
To my limited understanding and to give credit where credit is due, Bohm had deep
comprehension of this problem and this basic problem indeed disappears in Bohm's interpretation of
rewriting
Schrödingers
equation
as
quantum
potential:
http://en.wikipedia.org/wiki/Quantum_potential .
This implies other causality which depends only from shape and not from strength and size and
which Bohm calls "active information" which you define as negentropic entanglement.
11. At 5:13 AM, [email protected] said...
To Santeri:
Here I must disagree. We really observe state function reductions and stationary states.
Reductions are inconsistent with the determinism of Schrodinger equation in standard ontology and
we must find interpretation for the situation. Bohm's theory tries to keep quantum world
deterministic. Occam's razor does not favor Bohm's theory (BT).
● BT is hidden variable theory.
● Both classical orbits and evolutions of wave functions are assumed.
● BT brings in hypothetical hydrodynamic flow from which some points are selected.
● BT makes also the ad hoc assumption of quantum non-equilibrium stating that Born rule does
not hold true in quantum non-equilbrium. Then what is probability density? This remains
unclear to me! Here presumably the unidentified hidden variable enter into the game. It is
argued that this assumption allows one to obtain wave function collapse from a theory
which is deterministic. I cannot swallow this.
Bohm's theory as also serious mathematical problems:
● It is argued that the Classical orbits are given by the guiding equation so that they depend on
wave function. I do not see how this description could give rise to Classical Mechanics
where orbits do not depend on wave function.
● The addition of particles does not affect guiding wave. A very strange feature which I find
very difficult to accept.
● A further problem is that the theory makes mathematically sense only in wave-mechanics
context. In QFT (in particular for fermions), the equations defining hydrodynamical flow
do not make sense. Already for bosonic QFT, the analogs of Schrodinger equation makes
sense only formally due to the extreme nonlinearity.
● There are also serious problems with Relativity.
76
Bohm's notion of active information has a counterpart in TGD as negentropic entanglement. But
to me, Bohm's wave mechanics looks like a very ugly attempt to do Quantum Theory without giving
up the ontology of Classical Mechanics.
12. At 2:02 PM, Santeri Satama said...
Matti, I believe everyone agrees that Bohm's interpretation is incomplete and your theory
(building on also Bohm's work and philosophical ideas whether consciously or unconsciously) is
more advanced. But calling BT 'deterministic' does not do it justice.
"When several particles are treated by the causal interpretation then, in addition to the
conventional conventional classical potential that acts between them, there is a quantum potential
which now depends on all the particles. Most important, this potential does not fall of with the
distance between particles so that even distant particles can be strongly connected." (SOC p. 99)
So in BT particles do affect (universal) guiding wave, but holistically and non-locally or in other
words (if I understand correctly) on the level of infinite-dimensional Hilbert space.
Main motive for preserving ontology of Classical Mechanics for Bohm was continuum and
dialogue between theories and interpretations (especially Einstein and Bohr) in order to avoid
fragmentation and communication breakdowns which hinder scientific creativity. In that same spirit
I have the following question:
Bohm's notion of quantum potential and active information seems related not only your
negentropic entanglement (and negentropy maximation) but also deeply connected to quantum
mathematics of Hilbert spaces. This may be extremely naive miscomprehension or deep question
(you decide). But isn't the whole notion and structure of quantum math as Hilbert spaces inside
points of Hilbert spaces dependent from or a manifestation of negentropic entanglement?
Or in less abstract language, isn't the ultimate foundation of all abstract mathematical structures
love?
13. At 8:45 PM, [email protected] said...
To Santeri:
TGD does not build on Bohm's work (neither consciously nor sub-consciously). TGD's starting
points and philosophy are very different.
1. Bohm tries to keep physics deterministic. This is the basic idea of the whole approach and
was more natural at the time when the theory was proposed. I admit that I simply do not
understand how state function reduction is thought to result from the theory. The notion
of quantum non-equilibrium and hidden variables are thought to make this possible. But
these notions are hopelessly misty.
In TGD, deterministic Classical physics in the sense of generalized Bohr orbits becomes
exact part of Quantum theory. This gives rise to the strong form of holography too. This
does not mean, however, that Classical time evolutions would become real as in Bohm's
77
theory. One has quantum superpositions of classical Bohr orbits instead of single classical
orbit. Only quantum ontology but with Quantum-Classical correspondence.
In Bohm's theory, the feedback from Classical to Quantum is lacking and this leads to
nonsensical predictions. Jack Sarfatti tried to get over this problem but did not get
anywhere.
2. Bohm indeed tried to resolve Einstein-Bohr debate by trying to keep both Classical physics
and Quantum physics. But his attempt was a failure and led to a garden of branching
paths so familiar to any working theoretician. A situation analogous to the landscape in
string models.
In TGD, general coordinate invariance which together with symmetries of Special
Relativity are key symmetries of the theory. In Bohm's theory, one starts from Newtonian
framework (wave mechanics). The difficulties are predictable.
3. Bohm hoped to understand state function reduction as a derived notion and tried to solve EB debate using single time and keeping the deterministic world view. Bohm would have
proposed something different if theories of Consciousness would have been fashion in his
time;-).
In TGD, quantum jump, free will, and non-determinism are taken as facts with no
attempt to reduce. 2 times and 2 causalities. This is the solution of Einstein-Bohr debate.
Amusingly, all this reflects evolution of the Time concept. Newtonian time, time of
Special Relativity, time of General Relativity, and finally the realization that there are 2 times
and 2 causalities. Plus huge number of other more-or-less weird proposals such as no time at
all!
4. The notion of active information is an attractive concept if one does not drown it to the
mathematics of wave mechanics. In a similar manner, Orch OR was drowned to ad hoc
formulas. Theoreticians should avoid formulas as long as possible(;--). But we have the
illusion that formulas make it more scientific.
In TGD, NMP + negentropic entanglement realize the analog of active information. There
is also analogy with Orch OR. I have talked about conscious information, attention,
experience of understanding, rule as quantum superposition of its instances, realization of
sensory qualia, also love, etc. Many interpretations.
About love. I must say that as an inhabitant of extremely cruel world of Science (see some of the
latest postings of Lubos or visit the comment section of Tommaso's blog to understand what I
mean!;-), I find it very difficult to say the word "love". It seems to belong to some another spiritual
plane;-).
I would not reduce love lego piece;-). Sounds too engineerish;-) One cannot give a formula for
love. Mathematics cannot catch it. The core of Krishnamurti's teachings (and all mystic teachings)
is just this.
Quantum Math as such does not need negentropic entanglement. But this notion seems to be
possible to realize in terms of QM.
78
14. At 4:22 AM, Santeri Satama said...
Matti, in regard to the relation of negentropic entanglement and QM, to quote your own words:
> "Negentropic entanglement might serve as a correlate for emotions like love and experience of
understanding. The reduction of ordinary entanglement entropy to random final state implies the
Second Law at the level of ensemble. For the generation of negentropic entanglement, the
outcome of the reduction is not random. The prediction is that the Second Law is not a universal
truth holding true in all scales. Since number theoretic entropies are natural in the intersection of
real and p-adic worlds, this suggests that Life resides in this intersection. The existence
effectively bound states with no binding energy might have important implications for the
understanding the stability of basic bio-polymers and the key aspects of metabolism. A natural
assumption is that self experiences expansion of consciousness as it entangles in this manner.
Quite generally, an infinite self hierarchy with the entire Universe at the top is predicted."
> "This leads to a vision about the role of bound state entanglement and negentropic
entanglement in the generation of sensory qualia. Negentropic entanglement leads to a vision
about cognition. Negentropically-entangled state consisting of a superposition of pairs can be
interpreted as a conscious abstraction or rule: negentropically entangled The Schrödinger cat
knows that it is better to keep the bottle closed. A connection with fuzzy qubits and quantum
groups with negentropic entanglement is highly suggestive. The implications are highly nontrivial also for quantum computatio, which allows 3 different variants in TGD context. The
negentropic variant would correspond to conscious quantum computation like process."
> "Maybe it would be useful to talk about consciousness only when one has negentropic
entanglement. Positive information, knowledge. Otherwise awareness.
I think that emotions are a very high level consciousness unlike often thought. They provide
summaries about the hole and it would be natural to assign them to negentropic fusions of a large
number of mental images giving rise to stereo consciousness."
No doubt the creative conscious experience of fusion of various mathematical ideas and forms
into QM involved also deep intellectual and emotional pleasure. So to say that "QM as such does
not need NE" or active information sounds like removing your self and universal self-consciousness
of creative gnothi seauton from the process.
With Brahman-Atman identity as basis, it should be quite obvious that QM is the number
theoretical realization of the very old and well-known metaphor of Indra's net and the path you took
to your realization to overcome the limitations of the set theory involved the conscious and
emotional aspects of negentropic entanglement you describe in the quotes above. QM as nth degree
of order that allows also a more detailed description of NE does not mean that NE (the very process
of becoming conscious of QM) could and should be reduced to QM alone. Rather, there is
negentropic entanglement between the pair of QM and NE itself. That is, if we are supposed to take
you and your work seriously (enough) ;).
15. At 5:59 AM, [email protected] said...
To Santeri:
79
I want just to emphasize that there are several levels of existence and most problems result from
erratically identifying these levels.
The level giving rise to conscious experience does not reduce to mathematics. The evolution of
state of consciousness does not correspond to a solution of field equations. This is the whole point
and I want to make this absolutely clear since it provides the solution to so many paradoxes.
In hidden variable theories, one can argue that there are physical variables and those related to
consciousness and non-determinism of volition is apparent since the dynamics of physical variables
is that of shadow and only looks non-determistic. This was the dream of Jack Sarfatti.
Probably also the vision of Bohm was that non-deterministic state function reduction could be
understood as dynamics of a shadow. The selection rules of state function reduction makes the
fulfillment of this dream highly implausible.
16. At 7:38 AM, Santeri Satama said...
Dynamics of "Shadow" in the Jungian sense?
The word "existence" comes from the Latin word existere meaning "to appear", "to arise", "to
become", or "to be". But literally, it means "to stand out" (ex- being the Latin prefix for "out" added
to the Latin verb stare, meaning "to stand").
So etymologically, the word refers to process of actualizing (state function reduction) instead of
potential or dynamis to actualize-exist. In Bohm's language explicate and implicate orders. Western
metaphysics has been plagued by the idea 'substance'/'hypokeimenon' whether defined as particles,
quantum fields or vacuums and considered these substance-stuffs "True-Existence" because they are
considered something non-mutable time-invariable. Substance that can be defined, controlled, and
manipulated.
Then there is the mystery of Platonia-substance, substantive form of possible forms and its
dialectical relation with "no-thingness/-vacuum" of ZEO. And despite your denial philosophical
connections to BT, I'm still under the impression that as in BT, the philosophical starting point of
your theory is also what Whitehead calls organic realism instead the substance metaphysics of
materialism.
It's very easy to get drawn into the overly analytic and fragmenting metaphysics of English
language and scholastic philosophy and analytically define more-and-more levels of existence and
substance. And to get entengled into the fighting mode of the science vs. philosophy, theory vs.
theory etc. debates that emanate and radiate e.g. from the Krauss controvercy.
But we can both also speak Finnish and share and comprehend the unity of nonanalytical/synthetic and etymologically more sound phenomenological existence in expressions like
havainnoidutaan, ilmennytään, todellistutaan, ollaan. Tunnetaan, nähdään ja kuullaan.
17. At 8:54 AM, [email protected] said...
Dynamics of shadow in a geometric sense. Shadow behaves apparently non-determistically
since the variables in orthogonal direction serve as hidden variables. Consider mechanics in ndimensional space and restrict the consideration on k<n-dimensional sub-space: shadow. The
80
dynamics of n-k hidden degrees-of-freedom affects also the k-dimensional dynamics. But since they
are hidden variables, you see this as non-determinism.
Existence in the sense you refer to it would be subjective existence. Existence as mathematical
object is a different kind of existence and would be the existence according to materialist.
I call my philosophy tripartistics as opposed to materialistic view of standard physics and
dualistic view of Bohm (non-hidden and hidden variables or classical particles + guiding waves).
The completely new element is subjective existence (quantum jumps). About Whitehead I cannot
say.
I would speak about the vacuum state (not "nothingness") which to academic philosopher means
something different. In positive energy ontology, the vacuum state is the ground state in which
energy momentum and other quantum numbers vanish. It would be fermionic Fock vacuum. In
ZEO, all states satisfy this condition. One could define non-vacuum states as those for which
positive energy part (and thus also negative energy part) has non-vanishing quantum numbers.
Physics needs philosophy. But physicists must build it themselves. Going to the philosophy
library does not help. The statues of academic philosophy did not know anything about modern
physics. The Finnish language indeed expresses more naturally what also mystics talk about. The
intellectual, linguistic manner to see the World is painting pictures using words and picture is never
the reality. One should take it as art rather than warfare.
"Nothingness" is also a problem in set theory. One constructs natural numbers by starting from
empty set. But it is obvious that an empty set has no operational meaning. One ends up with the
well-known problems with infinite sets. Russell antinomy for instance. Could it be that a more
natural definition of natural numbers could be as products of primes just like elementary particles are
building blocks of physical states? In this approach, the notion of infinity would be number
theoretical (divisibility concept) and based on infinite primes.
18. At 10:57 AM, Santeri Satama said...
From
a
philosophers
answer
to
Krauss
(http://rationallyspeaking.blogspot.com/2012/04/lawrence-krauss-another-physicist-with.html ):
In his “The Trouble with Physics”, Lee Smolin laments the loss of a generation for
theoretical physics, the first one since the late 19th century to pass without a major
theoretical breakthrough that has been empirically verified. Smolin blames this sorry
state of affairs on a variety of factors including the sociology of a discipline where
funding and hiring priorities are set by a small number of intellectually inbred
practitioners. Ironically, one of Smolin’s culprit is the dearth of interest in and
appreciation of philosophy among contemporary physicists. This quote is from Smolin’s
book:
“I fully agree with you about the significance and educational value of
methodology as well as history and philosophy of science. So many people today
(and even professional scientists) seem to me like someone who has seen
thousands of trees but has never seen a forest. A knowledge of the historical and
philosophical background gives that kind of independence from prejudices of his
generation from which most scientists are suffering. This independence created
81
by philosophical insight is, in my opinion, the mark of distinction between a mere
artisan or specialist and a real seeker after truth.” (Albert Einstein)
The sets of basic assumptions on which theories are build is often called metaphysics which is a
part of philosophy just like logic etc. But more importantly, philosophy is about philosophical
attitude, not about names and set of books in library. Philosophical attitude towards scientific theory
building (at least in BT and PT) is to consider it a form of playful and creative art and they share the
criticism of anti-philosophical attitude of many materialists who make the set of materialistic
metaphysics into authoritarian dogma to be followed religiously and to be defended by political
bullying and warfare.
When theory building runs into trouble (e.g., search for the axiomatic mathematical foundation
of QFT, a dialogue with philosophers and/or visit to library to pick a copy of Gödel's proof could
and would help to prevent further banging of head against the wall. ZEO or not, TGD process is not
happening in intellectual and social vacuum where narratives of theoretical physics reinvent
philosophy or metaphysics from nothing. Notions of intellectual property and patent rights and
tribalism of academic fields are very poor philosophy of the Ego in the world where novel ideas
appear synchronistically. And again, there are archetypal ideas such as Brahman-Atman identity and
Indra's Net being constantly reinvented and reformulated in various languages now including QM.
Those are ancient philosophical ideas that TGD is based upon. But in what sense "physicists must
build it themselves"?
19. At 8:24 PM, [email protected] said...
To Santeri:
Philosophical attitude includes the historical view: it is no point in reinventing the wheel.
Philosophical assumptions are important but only when theory is relatively well-formulated. One
cannot start by saying "okay, I will construct dualistic physics". The most important aspect of
philosophical attitude is genuine passion to answer the difficult age-old questions related to time,
free will, what "mind stuff" could be. There are also more concrete questions: what is energy, mass,
what is the origin of quantum numbers, what the mysterious state function reduction means. Most of
these questions are taboos nowadays. Standard Model→ GUT→ SUSY→ String models→ Mtheory and the conclusion that those still asking are idiots as one particular besser wisser whom you
certainly know would formulate it! ;-)
The trouble with Physics is that most people doing physics have become mere pragmatic appliers
of methods. When taken to the extreme, this leads to the attitude that the basic goal of particle
physics is to determine experimentally to what point of SUSY parameter space physics corresponds.
This is insanity but a natural outcome of the attitude "science as a mere methodology".
Maybe physicists must rediscover the ancient ideas themselves from their starting points. Here
an open mind is enough.
20. At 1:57 AM, Santeri Satama said...
The
Krauss
debate
brought
up
also
(http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect ):
Aharonov-Bohm
David Albert: "Professor Kraus’ argument for the ‘reality’ of virtual particles, and for the
instability of the quantum-mechanical vacuum, and for the larger and more imposing
82
effect
proposition that ‘nothing is something’ hinges on the claim that “the uncertainty in the
measured energy of a system is inversely proportional to the length of time over which you
observe it”. And it happens that we have known for more than half a century now -- from
a beautiful and seminal and widely cited and justly famous paper by Yakir Aharonov and
David Bohm -- that this claim is false."
http://philocosmology.wordpress.com/2012/04/07/an-explanation-from-nothing/
What's the TGD interpretation of Aharonov-Bohm effect and its metaphysical implications? E.g.
what kind of causality is in question?
21. At 5:51 AM, [email protected] said...
Krauss' argument that "nothing is something" is to me a game with badly-chosen words. I would
not call the quantum physical vacuum state "nothing". In ZEO, any zero energy state can be
obtained from vacuum so that it has infinite potential of producing different structures.
The Aharonov-Bohm Effect is purely a topological effect which does not depend on theory.
Particle going around a closed loop in vanishing magnetic field can experience a non-trivial effect
resulting from so-called non-integrable a phase factor. Any theory involving gauge fields predicts
this effect. I would not call it causality. The effect represents topological physics and topological
QFTs made this branch of physics industry.
22. At 12:32 PM, Santeri Satama said...
Due to my mathematical handicap, I'm forced to question meanings of these words. That if a
"particle" is supposed to be a special case of "field", how can vector potential affect or inform
particle in case of vanishing field?
The jargon of theoretical physics (shorts for deep and difficult mathematical concepts) often
brings to mind the times when priests preached in Latin to congregations that understood nothing of
Latin. A game of badly-chosen words about which philosophers of language and politics and
hermeneutics and science have various and often critical views.
23. At 8:27 PM, [email protected] said...
To Santeri:
The language is a real problem. Iwill try to explain why it is a problem knowing that also here I
encounter the language problem.
The field-particle correspondence is a also difficult conceptually for physicists and involves a lot
of mi-understandings. Basically one has 2 different abstraction levels and their correspondence.
A particle as a point of 3-space and dynamical evolution as particle orbit defines classical
Newtonian ontology. This is simple. Quantum states of particle as wave functions in 3-D space E3
for positions of particle is quantum ontology in Newtonian framework.
This brings in first quantization as abstraction (statements about statements in logic). One can
have only Quantum-Classical correspondence as a many-to-one map. The space of wave functions
is infinite-D: configuration space is 3-D. Particular quantal particle states (say momentum
83
eigenstates) have direct classical counterparts. The choice of this correspondence is of course not
unique.
Indeed, one could call completely localized wave functions particles (well-defined position at
one particular moment). One could also call momentum eigenstates which are completely
delocalized wave functions particles. Wave particle duality relates these 2 alternative QuantumClassical correspondences.
The second quantization brings in further abstraction level and a layer of confusion unless one is
fully aware of mathematics involved (basically hierarchy of abstractions).
Consider photons. The space of wave functions for photons in 3-D space E3 is replaced with the
space of wave functions in infinite-D space of classical gauge field potentials in E3 which is already
infinite-D. Fock state (a state with single photon which is analog of harmonic oscillator wave
function in the infinite-D space of gauge potentials) would be the counterpart of photon as classical
free particle.
If there are non-contractible loops (non-trivial first homotopy) or if the scalar is many-valued,
Bohm-Aharov is possible. For instance, depending on angle around z-axis such that it is changes by
non-integer multiple as one goes over full circle, one has Bohm Aharonov. In TGD, this kind of 3surfaces can be considered.
Concerning your question about vector potential …
By gauge invariance, the gauge field is representable as the "curl" of vector potential. This
symmetry means that only 2 polarizations orthogonal to photon's momentum remain in spectrum.
Photon is massless. Vector potential can be non-vanishing even if field vanishes. It is enough that it
is a gradient of scalar.
If space has no non-contractible loops and if scalar is single valued function, no Bohm Aharonov
effect results.
In his mixture of ontologies corresponding to 2 different abstraction levels (particle state as
position of E3 and particle state as wave function in E3), Bohm would perhaps say that vector
potential informs or affects particle. One cannot say this in the standard quantum ontology. It does
not make sense.
After all this explaining, I must confess that the role of vector potential in particle description is a
QFT-based notion and is now strongly challenged in the twistor approach in which the notion is
given up;-)!
Also in TGD, one describes particle states as wave functionals in the space of 3-surfaces (by
holography effectively partonic 2-surfaces at boundaries of CD) and there is a strong connection to
twistor approach.
Things become conceptually clear once one accepts infinite-D mathematics of "World of
Classical Worlds". In TGD, they are 3-surfaces. In original string model (rather than the horrible
conceptual fuss of M-theory), they are 1-surface strings.
24. At 7:59 PM, hamed said...
84
Dear Matti,
so Thanks,
Re. your answers:
“The strictly correct manner to speak is to assign dynamics to 3-surfaces” and
“NMP *does not define* dynamics of space-time!;-). It defines dynamics of consciousness
and tells that the information gain in quantum jumps is maximized” …
I regarded dynamics and evolution the same meaning. TGD has 2 kinds of evolutions. One is
Informational evolution that is related to consciousness and another is Geometric-Time evolution.
Before this, I thought that the first one is evolution of space-time and the other one is evolution
of 3-surface. But now I learned from the answers that each of them is evolution of the 3-surface. Is
this correct? At the first one, at each quantum jump the 3-surface is replaced with another 3-surface.
A transition from p-adic 3-surface to real 3-surface occur rather than p-adic space time to real space
time? Although it is not difference practically!
As for “NMP is mathematically analogous to the Second Law (and implies it for ensembles) in
that it tells only overall direction of dynamics but does not fix time evolution completely as action
principles”,
I deduced that at the sequence of quantum jumps from a 3-surface to another one, the direction of
evolution is not unique by NMP and there are 3-surfaces at the end that provide the condition of
NMP (there is something like degeneracy). Then what cause makes only one 3-surface of them
occur? Is there only pure chance?! But there is obvious when a person will for doing something, if
all external factors are appropriate, he can do it and exactly the same work without of any chance
that governs on his behavior. Illusion of “I” doesn’t help you for the answer;)
25. At 9:58 PM, [email protected] said...
Dear Hamed,
As any 4-D classical action principle, one can see Kahler action as defining a dynamics for some
3-D configuration. Usually they are field configurations. In TGD they are geometric objects.
Preferred extremal property selects preferred orbits as analogs of Bohr orbits in the TGD Universe.
This is what distinguishes TGD from field theories based on path integrals (all orbits are allowed and
"classical" ones correspond to stationary phase and thus extremals of action).
One can assign to a collection of 3-surfaces at the second end of a CD a space-time surface as
preferred extremal. This is holography. The holography has motivated my somewhat fuzzy use of
space-time sheets and 3-surfaces. If holography would be globally true, then 3-surface at end of CD
would dictate space-time sheet uniquely. This not the case by the failure of strict determinism due to
vacuum degeneracy of Kahler action. (A good exercise would be to look through the Kaehler action
and what vacuum extremals are!). I apologize!
[Hamed] At “NMP is mathematically analogous to the Second Law (and implies it for ensembles) in
that it tells only overall direction of dynamics but does not fix time evolution completely
as action principles”
I deduced that at the sequence of quantum jumps from a 3-surface to another one, the
direction of evolution is not unique by NMP and there are 3-surfaces at the end that provide
85
the condition of NMP (there is something like degeneracy). Then what cause makes only
one 3-surface of them occur? Is there only pure chance?! But there is obvious when a
person will for doing something, if all external factors are appropriate, he can do it and
exactly the same work without of any chance that governs on his behavior. Illusion of “I”
doesn’t help you for the answer;)
[MP]
(a) An important point: quantum states are quantum superpositions of 3-surfaces!!!! To each
of these 3-surfaces in superposition, one can assign space-time sheet satisfying field
equations modulo non-uniqueness due to failure of strict determinism. In this sense (and
only in this sense), Classical physics is exact part of Quantum theory!! Bohm believed
differently. He would have said that it is possible to speak both about quantum
superpositions of 3-surfaces/associated space-time surfaces and single space-time surface.
You have got the impression that I share this belief of Bohm. But I definitely do not!!
One can speak about single space-time sheet only in stationary phase approximation for
vacuum functional which is exponent of Kahler function (Kahler action from Euclidian
regions) and imaginary analog of Morse function (Kahler action from Minkowskian
regions). In this sense TGD and quantum field theories are analogous. Path integral is
however replaced by functional integral with phase factor (hybrid of path integral and
functional integral) and one can hope that it is therefore mathematically well-defined.
(b) What NMP says is about what happens in state function reduction cascade for given
subsystem-complement pair. It is formulated solely in terms of entanglement entropy for
quantum jumps. It defines dynamics for Subjective existence. Kahler action defines
dynamics for Geometric existence.
(c) Quantum-Classical correspondence suggests that there could be however some correlate for
NMP and its outcome Second Law at the space-time level. NMP and Second Law could
correspond to the non-inversibility of the dynamics of Kahler action and for the arrow of
time for zero energy states meaning that they are state function reduced at either end of CD.
The breakdown of strict determinism at some points or sub-manifolds of space-time sheet
is analogous to what happens in hydrodynamics in a flow which becomes supersonic. The
hydrodynamical equations bifurcate and the Second Law is used to select the bifurcating
branch uniquely. Something like this might occur now.
26. At 1:37 AM, hamed said...
I think there are some bases to understanding of your answer about non-determinism correctly
and I must wait :(!
I listed some questions and when think about them, I deduce that each of them relates in some
manner to understanding of M4xCP2! It is very basic building of TGD that is not avoidable :).
I found an article on “STATUS OF SUPERSTRING AND M-THEORY” in
http://arxiv.org/abs/0812.1372v2 and start to read it. It is needed for me to learn bases of string
theories at introductory level. I'd like to read it in the viewpoint of TGD;)
Regarding your answer to Santeri, you wrote that first quantization as abstraction is like
statements about statements in logic. Why? And also second quantization : “basically hierarchy of
abstractions”!!! Then what is the third quantization?!
86
27. At 5:44 AM, [email protected] said...
Dear Hamed,
TGD can be also seen as a generalization of the superstring model so that getting some
background in superstrings certainly helps. Also an article about the old-fashioned hadronic string
model would help.
By the way, the string model started from purely geometric formulation with string sheets
identified as minimal surfaces. Then the Polyakov formulation emerged and one introduced metric
on string world sheets as an independent dynamical variable which for extremals was equal to
induced metric. This allowed to develop calculational formalism but led to astray. Eventually one
made also the geometry of 10-D space dynamical and one had double gravity instead of reduction of
gravity to the geometrodynamics of string world sheets. Pragmatism is not always good in
theoretical physics!
First quantization means replacing configuration space of particle (Euclidian 3-space) with wave
functions in this space. From space to function space. In case of Boolean algebra, this means
transition to the Boolean algebra of Boolean statements about Boolean statements. Reflective level
of Boolean consciousness.
Second quantization means that space of wave functions is replaced with space of functions in
the space of wave functions. Another abstraction.
The hierarchy of infinite primes and many-sheeted space-time lead to the proposal that this
hierarchy of quantizations continues. Hadrons, atoms, etc. and even galaxies are in well-defined
mathematical sense elementary particles at some level of this hierarchy.
http://matpitka.blogspot.com/2012/05/emotional-about-dark-matter.html#comments
topic: "Emotional About Dark Matter"
1. At 7:06 PM, [email protected] said...
The basic question of fQXI contest is to the point. I hope that this reflects more general
awareness that something is badly wrong with the basic assumptions of the theoretical particle
physics.
I once participated in the contest. The nature of Time was the topic. I learned that the same old
names decide about what is good and what is not so that participating would be waste of time.
The problem is that to become a professor, one must be a student of a professor. And one can
become a student only if one accepts the views of the professor. This allows us to understand why
GUT tradition has survived for 4 decades.
2. At 1:56 PM, hamed said...
Yes, as I understand often those professors that are critical about the particle physics aren't
particle physicists!
87
But about your professor when you wrote your thesis. Why didn't you choose a good professor
for the thesis?! Or maybe you thought that he was a good! I can be only hope that it will not occur
for me ;)
3. At 7:53 PM, [email protected] said...
I did not have any supervisor for my thesis. I got the basic idea towards end of 1977. I went to
talk to the leader of the "Institute of Theoretical Physics" (word-to-word translation) and was kicked
out from my job within few weeks.
It took about 4 years to write the thesis. I did it in a kind of "unemployment job" at the Helsinki
University of Technology. I am grateful for the open mindedness of decision makers involved.
Nowadays this kind of hidden research would be hardly possible.
I came with the written thesis published in Journal of Theoretical Physics and with the statement
of John A. Wheeler saying that the work was brilliant. At that time I did not realize that Wheeler's
statement would have been worth gold and I could have used it to get financial support.
Wheeler's statement was probably the reason that forced them to request 2 theoretical physicists
from out-broad to tell their opinion. The first one said the work was brilliant. The second one said
that it was completely worthless. The work was accepted and they had to find a supervisor. The
professor who had kicked me out was the choice and he got additional item to this curriculum vitae.
Later he did his best to prevent me to get any funding for my research and indeed managed
excellently.
About 10 years later I applied for a docenture after I had written the first book summarizing
TGD. 2 young Finnish professors who had got just their positions (second of them with the support
of theoretical physicist community since at the first trial it was another mathematician who was
chosen to the job!) made a statement about my work. According to them, the whole work failed to
satisfy any imaginable criterion for what it is to be a scientific work. Perhaps one need not to be too
cynical to ask whether so-called "Dear Brother Network" so central in Finnish society had been
functioning.
Amusingly, at that time the statement of Wheeler about my work as well as documents relating
to the docenture episode also disappeared mysteriously from my office. Probably those responsible
for the miracle were afraid that I could make them public. I left Helsinki University since the place
made me vomit.
[StealthSkater note: More on the evolution of Wheeler's GD into Pitkanen's TGD is archived
at => doc pdf URL . An insight into the revelation of TGD is Matti's selfdescribed "Great Personal Experiences" at => doc pdf URL .]
http://matpitka.blogspot.com/2012/05/it-is-interesting-to-try-to-develop.html#comments
topic: "Negentropic Entanglement, Metabolism, and Acupuncture"
1. At 2:04 AM, hamed said...
Dear Matti,
88
It is some magic and interesting that only replacing “/” instead of * after SU(3)at gauge group of
standard model “SU(3)*SU(2)*U(1)” leads to a lot of beautiful results! CP2 has very well-defined
structures but the other has not!
“Only 4 of the 8 imbedding space coordinates are dynamical by general coordinate invariance.”
Why? And how many-sheetedness can circumvent objections against this reduction in local
degrees-of-freedom?
At “The replacement of superposition of Classical fields with superposition of their effects forces
many-sheeted space-time in TGD. Particle touches several sheets and experiences corresponding
forces. Nothing ad hoc!! Sorry for repeating this idea; it is so beautiful!;-)”
What does “Effects” means? (More precisely please) I don’t understand what difference is
between superposition of Classical fields and superposition of their effects?
2. At 2:58 AM, [email protected] said...
Dear Hamed,
An amusing co-incidence. As a matter of fact, electroweak U(2) and corresponding sugroup of
SU(3) are closely related because both relate to CP2 geometry. Holonomy group of spinor
connection (spanned by parallel translations around closed loops at given point) and isometry group
acting on CP2 points and preserving distances).
SU(3) acting as isometries defines the color group. And the action of its subgroup U(2) sugroup
on spinor indices defines what might be identified as strong isospin in the model of strong
interactions based on hadrons as basic entities. This is a relatively new result about which I told
month-or-two ago. As a matter fact, the connection between color group and strong isospin is very
unclear in QCD.
One can always take for of H- coordinates as space-time coordinates. They are not dynamical
variables since varying just these coordinates means that one moves along space-time surface and by
general coordinate invariance this does not change the physical situation locally.
Superposition of effects means classically superposition of forces associated with different
space-time sheets carrying fields: F= F1+F2+... Recall that particle has topological sum contacts to
all of them. Quantum-mechanically the particle experiences the sum of effects of gauge potentials.
Superposition of fields would mean that one has just single space-time sheet and various fields at
it superposition: E= E1+E2+... Since field variables are not primary variables, this kind of
superposition is not in general possible. One can superpose only small deformations of space-time
sheet orthogonal to the sheet characterized by 4 coordinate changes. Deformation changing EM
field changes also weak and color gauge field and gravitational field. In ordinary QFTs, the changes
of various primary fields are independent.
This kind of superposition is extremely limited when one poses also the preferred extremal
property: for "massless extremals" superposition occurs only for Fourier components parallel to the
massless extremal.
The enormous reduction in the number of field variables (just 4 instead of hundreds in typical
gauge theories)- would be a catastrophe without many-sheetedness. With many-sheetedness, it
89
becomes a blessing. One must however learn to think in terms of many-sheetedness also about
Macroscopic QED.
The second implication is that Classical weak and color fields are present also in long length
scales. This was a real worry for a long time. Eventually I accepted the fact that TGD predict
hierarchy of QCD and electroweak physics. Maybe they will see copy of hadron physics at LHC
soon. For leptohadron physics, there is a lot of evidence. Also Biology could involve in an essential
manner copies of QCD and weak physics. Anomalous phenomena like cold fusion could involve
scaled variant of weak physics.
3. At 8:36 AM, ThePeSla said...
Matti,
I find it interesting that a Platinum needle can induce an egg to begin development
(parthenogenesis) as of fertilized.
Also interesting is of the 256 chiral forms of the carbons in cholesterol on, one of them is
recognized by the body. How is that for a binary reduction?
There is too much emphasis on the idea that we need to reduce things to some sort of material
process alone. This is a mistake of fundamental principles as in that Scientific American theme this
year (Ulla posted in a comment). Apparently, although we have talked in such areas a long time,
they are reading our blogs :-)
Superposition -- especially where it evokes ideas of dark or mirror matter is a non necessary, not
rigid phenomenon in a higher physics -- so is the use of group theory and dimensions (thus
symmetry).
What of 5 coordinate changes so many state they are not clear about? Are the many sheets not
possibly limited to say 5 Euclidean? How is it in mammal eggs when we reach the number 32 cells
they are individuals and not 32 clones possible beyond that?
There is greater beauty out there still and better reasons. Not all that seems some zero place is
rigid in its scales or energy nor is simply a point. Your idea of particles should deal with these new
forms of say not that some are neutral but are intrinsically matter and antimatter. As I said, it is a
case of logic beyond the ideas or limits of Quantum Theory. Your title suggests that in such deeper
than zero point space negative values can accelerate the bundled otherness of a vacuum. Let us not
just call these mathematical artifacts where we can simply defeat a theory by some arbitrary
interpretation of a sign. (Or we are too rigid and limit the math as did our humble correspondent the
other day.)
4. At 8:25 PM, [email protected] said...
To The Pesla:
I was really surprised that it is as if they had been reading our blogs. I think, however, that string
theory "Big Crunch" and the failure of standard SUSY are more than enough to serve as motivations
for wondering what might have gone wrong in theoretical particle physics.
90
I hope that a change of attitudes could begin. If Lubosian views based on extreme authority
continue to prevail, theoretical particle physics will become the scientific counterpart of Soviet
Union.
I have probably said something about Majorana spinors but let us say it again. The basic
distinction between TGD and superstring models is that Majorana spinors are not possible in TGD
framework. Both B and L are conserved and superpositions of fermions and anti-fermions do not
occur.
Of course, in Zero Energy Ontology superpositions of pairs of positive and negative energy
states such that positive energy state has varying fermion number are possible. This has nothing to
do with Majorana property. Superposition of states with varying number Cooper pairs to form a
coherent state is example about this in superconductivity. In ordinary positive energy ontology, it
would break super-selection rule stating that states have well-defined fermion number. Maybe this
could be seen as an argument by Nature in favor of ZEO;-).
In condensed matter, they appear only as a mathematical artifact and not at fundamental level. It
is a pity that condensed matter physicists have joined to irresponsible hyping creating
misunderstandings at the layman level.
5. At 9:57 AM, Orwin said...
Delbrück's note on "stabilizing" forces in molecular biology, the seed of Schrödinger's
negentropy
concept:
http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/dna/notes/1940a.5.html
Delbrück scattering ( by virtual matter/anti-matter)- confirmed:
http://www.mpg.de/5799885/gold_lenses_gamma_optics?filter_order=L
death of Theoretical Physics!
They say this is the
Topologically-massive photons from anyonic physical observables: http://arxiv.org/abs/hepth/9809134
6. At 9:00 PM, [email protected] said...
To Orwin:
The Delbrueck link talks about diffraction of Z rays and even gamma rays. Theoretically this
should be impossible. The high energy for the ordinary value of hbar makes diffractive effects
extremely small. The proposal of the experimentalists is that the strong electric fields present in
atomic nuclei somehow change the situation.
What comes in mind is hierarchy of Planck constants. Years ago I considered half-jokingly the
possibility that hierarchy of Planck constants could imply quantum effects in much longer scales
than usually. Diffraction would be a typical quantum effect involving interference. Perhaps even
the spots seen sometimes in an ordinary camera lens could be analogous to diffractive spots
generated by diffraction of large hbar visible photons through a hole (they should usually appear in
the scale of visible wavelength about few microns). Take this as a joke.
Scaling of hbar for a fixed photon energy scales up the wavelength of photon. Could large
enough scaling of Planck constant make gamma rays to behave like photons with wavelength of,
91
say, visible photon and imply diffractive effects? Gamma ray could have wavy aspects assigned to
say visible photons!
I also proposed that strong classical EM fields provide the environment inducing increase of
Planck constant at some space-time sheets. The proposal was that Mother Nature is theoretician
friendly. When perturbation approach in powers of 1/hbar fails, Mama Nature scales up hbar to
make the life of her theorizing children easier-). Strong fields would be the manner to generate large
Planck constant phases and dark matter.
Note that cell membrane would be ideal place in this respect. The electric field strength is
extremely strong. I have a vague memory image that it represents upper bound for field strengths
achieved by human means.
Still about Delbrueck, I gave a second look to the popular article about gamma ray refraction. It
is somewhat confusing. On the one hand it talks on refraction which is geometric optics
phenomenon due to different phase velocities of light two media. The direction of light beam
changes. Refraction is a phenomenon of geometric optics alone and must be distinguished from
diffraction.
The article of Max Planck Gesellschaft talks about Delbrueck diffraction of gamma rays on
electron positron pairs created in the field of nucleus as a mechanism causing the change of light
velocity
and
thus
refractive
index.
Delbrueck
diffraction
(http://en.wikipedia.org/wiki/Max_Delbrück ) is scattering of gamma rays in Coulomb field of
nucleus due to the vacuum polarization (electron positron pairs) created by the Coulomb field. If I
understand correctly, this diffraction is much larger than predicted by Delbrueck.
A long time ago I introduced electropions as bound states of color excitations of electron and
positron to explain strange creation of e'e- pairs in heavy ion scattering near Coulomb wall. The
expectation had been creation of pairs from vacuum. But electropions were generated if TGD is
right.
The proposal was that a coherent state of electro-pions is generated in the collision in the nonorthogonal magnetic and electric fields of colliding nuclei. Colered leptons and electropions must
correspond to nonstandard value of Planck constant since otherwise the decay widths of weak
bosons would be too large.
Could one imagine the analog of Delbrueck scattering as scattering/diffraction of gamma rays
from electro-pions in the coherent state of electro-pions? Size scale corresponds to the energy scale
of gamma rays if they have energy of order of MeV. Large hbar could make the scattering
amplitude large. Could one imagine that the Classical electric fields of gamma ray beam and
nucleus superpose to give strong E.B generating the coherent state of electro-pions?
Could the electric and magnetic fields of nucleus superpose at same space-time sheet in nonorthogonal manner? The Silicon nucleus possesses a magnetic moment so that it generates dipolar
magnetic field which is not orthogonal to radial Coulomb field. But why they would reside at same
space-time sheet when they can reside at different space-time sheets?
I found another popular article about the work of Munich researchers:
http://www.themunichtimes.com/news/Munich-researchers-make-groundbreaking-discoveryabout-gamma-rays-1378 . It gives the size of the effect : deviation of n from 1 is of order 10-9!
92
http://matpitka.blogspot.com/2012/06/dark-magnetism.html#comments
topic: "Dark Magnetism"
1. At 8:08 AM, ThePeSla said...
[Pitkanen] "I have been waiting with fear in my heart for the moment when someone
boldly and independently represents the idea about dark matter as phases with large
Planck constant at magnetic flux tubes as a basic structure of Universe (or something
picking up suitable pieces of this vision). Tom Banks (the teacher of Lubos Motl)
has independently represented 2 key ideas of TGD (hyperfinite factors and causal
diamonds) as 'his own'. It is amazing how miserable web skills a prominent
theoretician can have;-). Leonard Susskind as a veteran physicist has understandably
rather poor web skills and has proposed p-adic physics as 'his own discovery' to the
problems of the Multiverse. I of course have been postulating p-adic physics, causal
diamonds, hyperfinite factors, magnetic flux tubes etc. as key components of
Topological GeometroDynamics for decades. … …"
Matti,
Even if someone claims your vision belatedly or even independently, I must add they have no
philosophic skills either because (in my last post) I have the counter to that part of a more general
theory as part of a bigger picture. Does this imply that Lubos would now call his teacher a crackpot
for the "discovery" of some of your ideas? :-)
Magnetism dark or otherwise in the spirit of it I am sure has firm foundation where it applies
(and in the standard eyes is the only game left or something like it) to explain transfer of momenta
from black holes. I am sure our problem where we do not understand each other is one of language
and not the content of ideas.
Now with such computer skills it is all too easy to put some idea out for general discussion such
as I suspect Gardner of alerting Conway to my idea on the matrix and he brought it up on the bulletin
boards so published not as mature article in Scientific American in my opinion. But I have only
begun to catch up with him in the use of the computers over methods by hand in writing and solving
puzzles (not that I don't consider him our greatest current mathematician of our day).
Oh, my problem seems to be having to wait for decades for something to come along as it will
eventually and that could make a difference or might have with people I know for biological reasons.
Still, life is short. Too short to worry about credit for wealth or fame.
2. At 9:14 PM, hamed said...
Dear Matti,
Don’t worry! As ThePeSla said, TGD has firm philosophical bases. Also TGD is not only some
ideas that glue together. Unifying these ideas in a very rich structure without very deep
understanding is not possible. It is not possible in this framework of common physics any big work.
It needed at least 34 years hardworking of a different physicist [you!]:) . I am very optimistic for
TGD. Hardships will be over as soon as you may think.
93
Thanks for the answer about warped imbedding. I struggled with it and now it is simple:).
Although the M4+ projection of the surface is random light-like curve, but in contrary to common
physics, we don’t live in M4 but we live in higher space-time sheet. Then it should be very
difference in interpretation of this in comparison to that?
Kahler form in CP2 is J=-i*g_mnbar*dxi^m*dxibar^n (Excuse me if it is not correct, I am
freshman in Latex notation ;) )
What is physical interpretation of the Kahler form? And why does the Kahler form in CP2
satisfies free Maxwell equations?
3. At 10:13 PM, [email protected] said...
Dear Hamed,
We live in … Or perhaps I should say we are part of a 4-dimensional space-time surface (to be
precise, one should of their quantum superposition;-)). This space-time surface has not only
Minkowskian regions (familiar to us) that I call space-time sheets but also Euclidian regions -deformations of CP2-type vacuum extremals. The latter is the news:-! These Euclidian regions
define generalized Feynman diagrams. Lines are deformations of CP2-type vacuum extremals
defining light-like random curves in M4 as their projections. The notion of the Feynman diagram
is therefore geometrized and topologized.
For CP2-type vacuum extremals and their deformations, the roles of M4 and CP2 degrees-offreedom are changed. For space-time sheets (4-D M4 projection), it is natural to speak about CP2
sigma model like theory in M4. For CP2-type vacuum extremals, one has field theory in CP2 and
dynamical variables are M4 coordinates. There are also string-like objects X2xY2 subset M4xCP2
and their deformations. This corresponds to a string model like sector of TGD. I call these objects
"cosmic strings" and they are crucial in TGD cosmology. Their M4 projection thickness during
cosmic evolution and their energy are responsible for the dark energy and the magnetic pressure for
accelerated expansion of the Cosmos.
Consider first the Kahler form in CP2. The situation changes for the induced Kahler form
somewhat. CP2 Kahler form Jkl is derivable from Kahler gauge potentials Ak via the usual formula.
Therefore one has the analog of U(1) gauge invariance. This means that the analogs of Nabla.B=0
and Faraday law are satisfied. The Kahler current D_lJ^kl vanishes also identically because Kahler
form is covariantly constant. Therefore vacuum Maxwell equations are satisfied. J_kl is self dual
meaning that one has a situation analogous to that of having constant electric and magnetic fields
with same magnitude. Maxwell energy momentum tensor vanishes identically. Also for CP2
vacuum extremals which are inherently just CP2s.
For induced Kahler form, the representation in terms of Kahler gauge potential still holds true so
that in this sense one has U(1) gauge invariance. This implies nabla.B=0 and Faraday's law. The
remaining equations j^alpha=0 (vacuum Maxwell equations) need not be satisfied.
You asked about interpretation of CP2 Kahler form and I already told something. Here comes
something more.
For so-called massless extremals, Kahler current j^alpha is indeed light-like rather than
vanishing so that a deviation from Maxwell's theory emerges. If one takes effective 3dimensionality seriously as a property of action, then for preferred extremals j^alpha must be either
94
light-like or proportional to instanton current so that action reduces to "boundary" terms since
j^alpha A_alpha=0 holds true and to Chern-Simons terms if weak form of EM duality holds true.
You asked about the physical interpretation of Kahler gauge potential. It corresponds to U(1)
piece of electroweak gauge group. Classical photon field is sum of Kahler gauge potential with
certain coefficient and of a neutral component of spinor connection (SU(2)_weak). The different
couplings of Kahler gauge potential to quarks and leptons (n=1 and n=3) explain different charges of
quarks and leptons.
Kahler gauge potential and Kahler action has also different thermodynamic interpretation that
would realize Quantum-Classical correspondence by representation of thermodynamics as spacetime geometry (TGD is the square-root of thermodynamics in Zero Energy Ontology!). This would
also generalize black hole thermodynamics. I realize this from the topological thermodynamics of
Kiehn.
See previous posting http://matpitka.blogspot.fi/2012/05/does-thermodynamics-haverepresentation.html .The posting contains also link to Kiehn's homepage. Kiehn's articles might
provide a good way to learn about differential forms.
Symplectic transformations of CP2 are not symmetries of Kahler action except for vacuum
extremals since classical gravitational field defined by induced metric is not invariant under them
(the interpretation of vacuum degeneracy is in terms of spin glass degeneracy). Symplectic group
acts as isometries of the World of Classical Worlds, however. This symmetry is very profound and I
wish I would understand it better.
http://matpitka.blogspot.com/2012/09/what-about-relationship-of.html#comments
topic: the relationship of gravitational Planck constant to ordinary Planck constant
1. At 12:18 PM, hamed said...
Dear Matti,
I saw the definition of holonomy group at Wikipedia. I understand it as follow: Holonomy
group of the connection ∇ based at a point x in M is the subgroup of general linear group of the
tangent vector space at the point and consisting of all parallel transport maps coming from loops
based at x. If I understand correct, it is not different for the holonomy group if we replace the
tangent vector space by a tangent spinor space.
You noted that holonomy group of CP2 is U(2) that is electroweak gauge group. I don’t
understand relation between holonomy group and gauge group. In really in the definition of
holonomy group, I don’t see anything relate to gauge potential. Please help me to understand it.
2. At 11:45 PM, Matti Pitkanen said...
Dear Hamed,
Your interpretation of holonomy group is quite correct.
The theory of vector bundles is extremely general and one any linear space is in principle.
Linear bundle is special kind of manifold obtained by replacing the Cartesian product MxV, V linear
space with its local version decomposing pieces of MxV glued together by identification maps which
95
are gauge transformations for a physicist. That is union of finite number of repions MxV and
identified in the patching regions by an element g(x) of structure group G acting in the linear space
V.
Parallel translation of vectors of V and connection performing it can be defined in extremely
general and purely geometrically in this space. But physicists preferred to use the concrete
definition in terms of gauge potentials definition the connection coefficients defining as gauge
potentials A_mu defined as 1-forms having values in the Lie algebra of the structure group.
Riemann connection looks somewhat different but in vielbein basis it also reduces to 1-form.
The tangent bundle of sphere is good concrete example about non-trivial vector bundle and I
suggest that you try to understand it as application of general definitions.
The structure group of spinor connection is covering group of that for vielbein connection. For
instance, for E3 the structure group is SO(3) for tangent and its double covering SU(2) for spinor
bundle. These groups are therefore not the same in general. In case of CP2, the structure group is
SO(4)=SU2_LxSU(2)_R and therefore its own covering group.
In the case of CP2, however, the topology of CP2 implies that ordinary spinor connection does
not exist. The problem is that for a closed curve the gauge transforms representing changes of the
coordinate patch do not sum up to unit transformation but a phase multiplication. The problem can
be overcome by coupling spinors to an odd multiple of Kahler gauge potential. The structure group
gets an additional U(1) factor.
Holonomy group is subgroup structure group and in case of CP2 spinor connection contains
SU(2)_L algebra, neutral part of SU(2)_R and U(1) due to the addition of coupling to Kahler gauge
potential. One can imagine that it is obtained by studying holonomies over infinitesimal
quadrilateral paths in various 2-planes. The holonomy element is by definition exp(iA_mudx^mu) at
this limit and by expanding one obtains 1+iPhi, Phi= F_munudx^udx^nu, the magnetic flux over the
infinitesimal quadrilateral. By dividing with the area of quadrilateral, one obtains an element of Lie
algebra of holonomy group and by taking the commutators of these normalized magnetic fluxes one
obtains the Lie algebra of holonomy group.
The identification of the holonomy group of spinor connection as gauge group is a separate
postulate suggested to realize the geometrization of the electroweak interactions. The motivation is
that the coupling structure is same as for electroweak gauge potential. There is also the fact that
electroweak symmetry breaking is coded by CP2 geometry at Classical level. What is of special
importancen is that the U(1) facor of Spin_c is absolutely necessary physically. If one assumes that
S is symmetric space, then the presence of this factor forces CP2.
3. At 12:57 PM, hamed said...
I started to study the chapter "CONNECTIONS ON FIBRE BUNDLES" in the book of
Nakahara Geometry Topology and Physics. It contains holonomy group and physical examples too.
I try to finish it in the days.
Now I have a question in Quantum-TGD: In Standard QM, the state of a system is represented
by a vector in infinite dimensional complex Hilbert space. In Quantum-TGD, state of a system is
represented by a vector in infinite dimensional Clifford algebra or HFF2. In really, every 3-surface
is represented by a vector in the HFF2. The space of states is at light-like boundaries of the causal
diamond (CD).
96
The state function (or M matrix) is collapsed to zero modes (Classical degrees-of-freedom) in
each quantum jump. Why do you name “zero mode” for Classical degrees-of-freedom? Union of
infinite-dimensional symmetric spaces labeled by zero modes. Therefore in each quantum jump,
state function is localized to some symmetric space. I don’t understand any relation between
Classical degrees of freedom and zero modes.
In standard QM when we measure a quantity like the position of a particle after the
measurement, the state function collapse to the eigenstate |^2. What is this principle of QM in
translating to Quantum-TGD? <X| is a classical degree-of-freedom?
4. At 11:28 PM, Matti Pitkanen said...
Dear Hamed,
Thank you for excellent and very stimulating questions. I thought that I should post it first as a
background and answer your questions after that.
(a) Also in TGD, state space is basically Hilbert space. But Hilbert space as such is extremely
general notion. Only when one gives it additional structure and concrete realization one
obtains the space of quantum states.
b) In TGD, this structure comes when one identifies states of Hilbert space as WCW spinor
fields. The analogy with ordinary spinor field helps to understand what they are.
I try to explain by comparison with QFT.
1. What happens in ordinary QFT in fixed space-time?
Ordinary spinor is attached to an space-time point and there are 2^D/2 dimensional space
of spin degrees-of-freedom. Spinor field attaches spinor to every point of space-time in a
continuous/smooth manner. Spinor fields satisfying Dirac equation define in Euclidian metric
a Hilbert space with a unitary inner product. In Minkowskian case, this does not work and
one must introduce second quantization and Fock space to get unitary inner product. This
brings in what is essentially basic realization of HFF2 as allowed operators acting in this Fock
space. It is operator algebra rather than state space which is HFF2. But they are of course
closely related.
2. What happens TGD where one has quantum superpositions of space-times?
(a) First guess: space-time point is replaced with 3-surface: point to 3-surface representing
particle. WCW spinors are fermionic Fock states at this surface. WCW spinor fields are
Fock state as a functional of 3-surface. Inner product Fock space inner product plus
functional integral over 3-surfaces. One could speak of quantum multiverse. Not single
space-time but quantum superposition of them. This quantum multiverse character is
something new as compared to QFT.
(b) Second guess forced by ZEO, by geometrization of Feynman diagrams, etc.
*3-surfaces are actually not connected 3-surfaces. They are collections of components at
both ends of CD and connected to single connected structure by 4-surface. This is like
97
incoming and outcoming particles in connected Feynman diagrams. Lines as regions of
Euclidian signature or the 3-D boundaries between Minkowskian and Euclidian signature.
*Spinors(!!) are defined now by the fermionic Fock space of second quantized induced
spinor fields at these 3-surfaced and by holography at 4-surface. This fermionic Fock
space is assigned to all multicomponent 3-surfaces defined in this manner and WCW
spinor fields are defined as in the first guess. This brings integration over WCW to the
inner product.
(c) Third, even more improved guess motivated by the solution ansatz for preferred extremals
and for modified Dirac equation giving connection with string models.
*The general solution ansatz restricts all spinor components but right-handed neutrino to
string world sheets and partonic 2-surfaces: effective 2-dimensionality. String world
sheets and partonic 2-surfaces intersect at the common ends of light-like and space-like
braids at ends of CD and at along wormhole throat orbits so that effectively discretization
occurs. This fermionic Fock space replaces the Fock space of ordinary second
quantization.
To sum up, the core idea is expressed in item 1. The rest is just gradual detailing and refining.
I already sent the summary about basic conceptual picture. Here are some comments to what you
are asking.
A. You say: "In Standard QM, the state of a system is represented by a vector in infinite
dimensional complex Hilbert space. In Quantum-TGD, state of a system is represented by a
vector in infinite dimensional Clifford algebra or HFF2."
My comment: To be precise, HFF2 belongs to the algebra of operators acting in fermionic
Hilbert space. As linear space this algebra can made itself Hilbert space. The technical details
related to the topology go over my head. One can say that vector in HFF creates Hilbert state from
vermionic vacuum, Dirac sea. One can normal order this operator so that all creation operators act
first so that this vector seems also unique. In this sense the Hilbert space states and operators
creating them are in one-one correspondence.
B. You say: "In really, every 3-surface is represented by a vector in the HFF2".
This is not quite true. It is the Clifford algebra of fermionic Fock space which has HFF2
property but also a lot of other physical structure. 3-surface cannot be seen as a vector in HFF2. For
instance, WCW is strongly non-linear object (union of symmetric spaces) and its points cannot be
added as those of HFF2. 3-surface is generalization of point appearing as an argument of spinor
field. This is the good intuitive starting point. I tried to clarify this issue in the first response.
C. You say: "The state function (or M matrix) is collapsed to zero modes (Classical degrees-offreedom) in each quantum jump. Why do you name “zero mode” for classical degrees-offreedom? Union of infinite-dimensional symmetric spaces labeled by zero modes. Therefore
in each quantum jump, state function is localized to some symmetric space. I don’t
understand any relation between Classical degrees-of-freedom and zero modes?"
98
My comment: Here there is a slight misunderstanding. I would not say that state function is
collapsed to zero modes. WCW is (as I conjecture!) a union of symmetric spaces labelled by zero
modes. I try to explain.
*Zero modes are fixed when the induced Kahler form is fixed in 4-D tangent spaces of partonic
2-surfaces (and maybe also of 4-D tangent space of string world sheets). This pattern of
values of induced Kahler form defines "purely Classical degrees-of-freedom", zero modes.
They do not contribute to WCW line element.
*Quantum fluctuating degrees-of-freedom correspond degrees-of-freedom of WCW contributing
to WCW Kahler metric. The natural conjecture is that they are parametrized by the
symplectic group of delta CDxCP2 leaving induced Kahler form invariant (and therefore zero
modes) and acting as isometries of WCW.
*This symplectic group (or presumably some coset space of it) becomes the space of Quantum
degrees-of-freedom. This space would be an infinite-D symmetric space. And each pattern
of the induced Kahler form identified in proposed manner would correspond to one almost
copy of this kind of symplectic space (Kahler metric could contain a conformal factor
depending on zero modes).
*Zero mode part of the state can entangle with quantum fluctuating part. Measurement
apparatus would indeed create a correlation between quantum fluctuating parts of the state
and zero modes. For instance, the electron's different spin directions would correspond to
slightly different patters of induced Kahler form at tangent spaces of these 2-surfaces. In
state function reduction, a localization in zero modes occurs and leads to a selection of one
particular outcome for quantum state. Or the other way around! It is difficult so ay which
causes which.
*Localization occurs *only* in zero modes!! In Quantum fluctuating degrees-of-freedom, one
has still delocalization. This is almost synonymous for being quantum fluctuating! These
degrees-of-freedom are analogous to vibrational degrees of string.
*WCW is not HFF of type II as I noticed since it is not linear space nor algebra. But the group
algebra associated with infinite discrete subgroups of the symplectic group defining Quantum
fluctuating degrees-of-freedom probably are! What is so nice that these group algebras are
discrete analogs for wave functions in WCW: orbital degrees-of-freedom of WCW spinor
field.
* WCW spinors define a canonical HFF II1 so that both WCW-spinorial (fermionic) and WCW
"orbital" degrees-of-freedom are HFFs. The Interpretation is as analog of supersymmetry at
WCW level.
I try to explain …
(a) In nonzero modes, WCW is symplectic group of delta M^4_+xCP2 (call it Sympl) which
reduces to the analog of Kac-Moody group associated with S2xCP2 where S2 is radius
constant sphere of light-cone boundary and z is replaced with radial coordinate.
Finite measurement resolution -- which seems to be coded already in the structure of
preferred extremals and of solutions of modified Dirac -- suggests strongly that this
99
symplectic group is replaced by its discrete subgroup or coset space. What this group is
depends on measurement resolution defined by the cutoffs.
(b) Why these discrete subgroups of Sympl would lead naturally to HFFs of type II?
*There is a very general result stating that group algebra of enumerable discrete group which
has infinite conjugacy classes and is amenable so that its regular representation in group
algebra decomposes to all unitary irreducibles is HFF of type II.
See
http://en.wikipedia.org/wiki/Hyperfinite_type_II_factor .
*These group algebras associated these discrete groups would thus be HFFs of type II1 and
their inclusions would define finite measurement resolution: included algebra would create
rays of state space not distinguishable experimentally. The inclusion would be characterized
by the inclusion of the lattice defined by the generators of included algebra by linearity. One
would have inclusion of this lattice to a lattice associated with a larger discrete group.
Inclusions of lattices are however known to give rise to quasicrystals (Penrose tilings are
basic example) which define basic non-commutative structures. This is indeed what one
expects since the dimension of the coset space defined by inclusion is algebraic number
rather than integer.
An interesting question remains: What about zero modes? They are certainly discretized too.
One might hope that one-to-one correlation between zero modes (Classical variables) and Quantum
fluctuating degrees-of-freedom suggested by quantum measurement theory allows to effectively
eliminate them.
5. At 6:05 AM, hamed said...
Dear Matti,
Thanks a lot, sorry for delaying. I could not access to internet in my free times. Some questions
in bellow sentences:
“Zero modes are fixed when the induced Kahler form is fixed in 4-D tangent spaces of partonic
2-surfaces (and maybe also of 4-D tangent space of string world sheets). This pattern of values of
induced Kahler form defines "purely Classical degrees-of-freedom", zero modes.”
At “induced Kahler form is fixed in 4-D tangent spaces of partonic 2-surfaces” is something
dimly for me. As I learned in the past, induced Kahler form is component projection of Kahler form
of CP2 on the space-time surface. This was in Classical-TGD. But in Quantum-TGD, is it induced
on every space-time surface in quantum superposition of them?
If it is correct, I follow another question. When you say it can be fixed in 4-D tangent spaces of
partonic 2-surfaces, I understand from this sentence: The induced Kahler form on the space-time
surfaces is in really in the 4-D tangent spaces of some space and not on the space-time surfaces
themselves. And if it is fixed to partonic 2-surfaces, this pattern of values of induced Kahler form
defines zero modes? I think my last sentences are very incorrect:).
6. At 8:15 AM, Matti Pitkanen said...
Dear Hamed,
100
Thank you for questions. I really enjoy these discussions since they allow me to retrieve the
basic ideas in more detail. I hope you can get the gist of arguments.
Your question: "As I learned in the past, induced Kahler form is component projection of Kahler
form of CP2 on the space-time surface. This was in Classical-TGD. But in Quantum-TGD, is it
induced on every space-time surface in quantum superposition of them?"
My answer: You are right. In Quantum-TGD and Classical-TGD, the situation is exactly same.
Classical physics defined by preferred extemals is an exact part of Quantum physics in TGD since
WCW metric assigns to 3-surface space-time surface as a kind of Bohr orbit.
As I explained, 3-surface corresponds to ends of space-time surface at boundaries of CD or orbits
of partonic 2-surfaces (wormhole throat orbits at which signature of the induced metric changes).
Strong form of holography requires that it is actually the intersections of space-like ends and
wormhole throat orbits defining partonic 2-surfaces plus the 4-D tangent space of them which codes
for physics.
Your question: "In quantum superposition, one has zero modes for each surface is superposition
and a natural postulate would be that quantum fluctuating part of state correlates with zero mode
part. What this exactly means is not quite clear."
My answer: The point is that zero modes represent Classical variables. "Position of the pointer
of measurement apparatus" is the poetic metaphor for this. When state function reduction selecting
one particular state in superposition of states occurs, it must fix the pointer to corresponding
position. This requires correlation. That is entanglement and thus sum SUM c_m(N) |m> |N> where
|m> corresponds to zero mode state and |N> to quantum fluctuating state. Zero modes are here
symplectic invariants and complete localization is suggestive.
I have been retrieving what I have said about zero modes and realized that my loose claim that
all zero modes are symplectic invariants is wrong.
The fluxes of induced CP2 Kahler form and delta M^4_+ Kahler form over regions of partonic
surfaces (Kahler magnetic fluxes) are certainly zero modes and also symplectic invariants (therefore
Classical variables).
There are also, however, zero modes which do not seem to correspond to Classical variables
since they are not symplectic invariants.
(a) The point is that the symplectic group of delta M^4_+xCP2 is generated by Hamiltonians.
They are products of 3 factors: S2 Hamiltonian (rM constant sphere of light-cone boundary
parametrize by theta, phi) assumed to have well-defined SO(3) quantum numbers; CP2
Hamiltonian with well-defined color quantum numbers; and power r_M^n. r_M is in the
same role as powers of z in the definition of Kac-Moody algebra and one can indeed identify
the algebra as a generalization of KM algebra with the finite-D Lie-algebra replaced with
symplectic algebra of S2x CP2. Only the generators with n different from 0 contribute to the
WCW metric. So that zero modes are in question. But are they Classical variables?
101
(b) What is then the role of n=0 sector: the symplectic algebra of S2xCP2. One can assign to this
sub-algebra of Sympl hierarchy symplectic measures obtained by wedge powers of WCW
symplectic form and restricted to finite-D symplectic manifolds and one would have inner
product. Does the finite dimension of the symplectic sub-manifold define part of
measurement resolution. Wave function in this manifold instead of complete localization.
In this sector, one does not have metric measure but has a hierarchy of symplectic
measures defined by exterior powers of symplectic form restricted to finite-D symplectic
sub-manifolds. This is enough for inner product.
(c) Do these zero modes deserve interpretation as Classical degrees-of-freedom? The following
argument suggests that this is not the case.
*In Kac-Moody analogy, they would correspond to n=0 KM generators defining ordinary
finite-D Lie algebra and ground states of Kac-Moody representations transform according to
them. Perhaps zero modes are not in question but ground states of the representations of full
symplectic group analogous to KM. For instance, in WCW spinor sector, ground states of
fermionic KM representations are defined byM4xCP2 harmonics for imbedding space
spinors. This is assumed in p-adic mass calculations.
*Besides zero modes there are also other parameters such as the conformal moduli of
partonic 2-surfaces defining global variables depending only on conformal equivalence class
of partonic 2-surface.
To conclude, the structure is really infinitely rich. The magic is that by finite measurement
resolution the entire WCW could reduce to an enumerable discrete space and the theory of HFFs of
type II1 provides general results allowing us to gain a lot of understanding about the general
architecture!
http://matpitka.blogspot.com/2012/10/two-attempts-for-understand-pk.html#comments
topic: Two attempts to understand PK (psychokinesis)
1. At 9:22 PM, ◘Fractality◘ said...
Matti:
If you could clarify please.
You have said: "Intentional generation of motor action would involve a negative energy signal
(say in EEG frequency range) from the 'personal' magnetic body to the brain of Geometric-Past
where it would initiate neural activity leading to motor action."
How is this negative energy signal generated?
2. At 11:33 PM, Matti Pitkanen said...
Negative energy signal is negative energy signal only because for it the Arrow-of-Time is nonstandard.
102
In Zero Energy Ontology, zero energy states (pairs of positive and negative energy states at
opposite boundaries of CD) have necessarily arrow of imbedding space time. Either the state at the
lower or upper boundary of CD is prepared. At opposite boundary it is not and represents
superposition of states with varying particle numbers and ill-defined single particle quantum
numbers. Subsequence state function reductions mean that the prepared boundary is upper, lower,
upper, etc. Unitary U-matrix relates the states with opposite arrows-of-time.
By quantum correspondence, this corresponds to arrow of time at space-time sheets. Classical
dynamics breaks time reversal invariance (what happens in the case of shock waves is determined by
second law and provides an analogy).
Depending on the arrow in question, one can speak of positive and negative energy signals. For
instance, phase conjugate laser waves obey the Second Law but in reversed direction of GeometricTime and would correspond to negative energy signals.
http://matpitka.blogspot.com/2012/10/could-hyperbolic-3-manifolds-and.html#comments
topic: Could hyperbolic 3-manifolds and hyperbolic lattices be relevant in Zero Energy
Ontology?
1. At 9:09 AM, Stephen said...
I've been playing around with code implementation of the Extended Kalman Filter recently. Is it
possible something like this could solve the measurement/observer problem? Looks like someone
has thought of it? Feedback Quantum Control.
https://docs.google.com/viewer?a=v&q=cache:RkL9hRjmmg4J:soar.wichita.edu/dspace/bitstrea
m/handle/10057/632/grasp0614.pdf%3Fsequence%3D1+&hl=en&gl=us&pid=bl&srcid=ADGE
ESihU37klU2-SF7OT7qIpX0KppRdrheL7DPnylCtBVdCsl81_rSZ83dA4dV71yfFEGrWWH9Csz5z0W9dhv7bmVzFmVlZ4CyXMpvdke9vMHOGAdOcTd5f15pFHLXkbZk5eqq2r2&sig=AHIEtb
Tq1cmgAwiR3MtTmSjeZoNXNrTZdA
"In Quantum Mechanics when the system has been measured, the system will collapse to one of
the eigenstates. This result is chosen randomly according to probability. The purpose of this
research is to find the state feedback control law such that a quantum measurement can be
engineered to collapse onto the eigenstate of our choice. The system should be globally stabilizing
for any spin. The unscented Kalman filter will be used to estimate the state of the system."
Also, I thought of TGD when I read this:
http://phys.org/news/2012-10-real-physicists-method-universe-simulation.html
2. At 8:31 PM, Matti Pitkanen said...
If I understood correctly, the idea is that non-linearization of Schroedinger equation and random
feedback could allow one to mimic deterministic evolution by Schroedinger equation and combine it
with state function reduction. One can safely say that this is doomed to fail as any other attempt to
simulate state function reduction Classically.
103
Kalman filter seems to involve randomness based on classical probability. I do not really get the
idea about how to use it to mimic state function reduction. The deep fact however that in quantum
theory probability amplitudes replace probabilities. This means that this is just partial mimicry at
best.
The state function reduction involves deep problems (basically related to our wrong view about
the relationship between Experienced-Time and the Geometric view about time). Many people
recognize that something is wrong (t'Hooft is the latest name doing this) but somehow they fail
totally to realize what the source of difficulties is and try all kinds of tricks like reduction of
Quantum theory to Classical deterministic theory. Equally, many manage in cheating themselves to
see no problem at all.
3. At 8:20 PM, hamed said...
Dear Matti,
I want to learn about modified gamma matrices and modified Dirac equation. I summarize what
I understood and ask my questions.
(In the bellow, G is modified gamma matrices and g is generalization of 4 gamma matrices to 8D
)
G^alphaD_alpha psi = 0
G^alpha = T_l^alpha.g^l
Psi is the octonion valued 2-spinors. Therefore it contains 16 real components!!!
T_l^alpha is canonical energy momentum tensor.
I see the last formula at the topic “Super-symmetry forces modified Dirac equation”
I can guess the two octonion in the 2-spinor are referred to positive and negative energy states or
particle and antiparticle states respectively. This can be seen as analogy of zero energy ontology but
in the case of spinors"?
In the modified dirac equation, there isn’t any projection to space-time surface. Why?
In TGD, there is modified dirac equation and a field equation deduced from kahler action. These
are 2 basic equations of TGD that I learned until now. As I know, there are no primary Classical
gauge fields in TGD. Therefore there is no room for ordinary electroweak equation or
chromodynamics equation of the Standard Model when is translated to TGD framework? It is little
hard for me to throw away these beautiful equations :) Because every term of the equations has
physical meaning.
4. At 9:48 PM, Matti Pitkanen said...
Dear Hamed,
You say: "I want to learn about modified gamma matrices and modified Dirac equation."
Here is a brief summary about modified gamma matrices and their octonionic counterparts.
104
First about modified gamma matrices without any reference to whether they are "ordinary" or
octonionic.
(A) Modified gamma matrices are linear combinations of 8-D flat space gamma matrices (M8).
The coefficients are analogous to vierbein coefficients e_k^a. Recall that one has
gamma_k= d_k^agamma_a where gamma_a are flat space gamma matrices.
(B) Modified gamma matrices are defined as
Gamma^alpha= Pi^alpha_k* gamma_k = Pi^alpha_k*e^a_k *gamma_a
where gamma_a 8-D flat space gamma matrix (they can be ordinary or octonionic!).
Pi^alpha_k is the canonical momentum current associated with any general coordinate
invariant action principle for the space-time surface. In TGD it is Kahler action. A string
theorist would suggest volume giving minimal surface equations which are actually obtained
also in TGD for the general ansatz.
C) The expression for Pi^alpha_k is given by Pi^alpha_k= partial L/partial (partial_alpha h^k).
For M4 coordinates, these coefficients reduces to components of energy momentum
current T^alphabeta hkl h^l_beta coming from the variation of induced metric alone. In CP2
degrees-of-freedom, these is additional contribution due to variation with respect to the
induced Kahler form.
!!!! I might have made in some context a hasty and definitely wrong statement that
reduction to energy momentum currents takes place generally. If you remember the exact
place where I have said this, tell me so that I can make a correction!
(D) Modified gamma matrices defined via their anticommutator what I call effective metric.
If the action density L is four-volume, one obtains minimal 4-surfaces and modified
gamma matrices reduce to induced gamma matrices: Gamma_alpha= partial_alpha h^k
gamma_k and effective metric is just the induced metric. For Kahler action, this is not the
case and effective metric G^alphabeta need not even have inverse as a 4x4-matrix.
There are differences with respect to ordinary 4-D gamma matrices.
(1) All 8 gamma matrices contribute to 4-D gamma matrices. This is a big difference with
respect to ordinary gamma matrices.
(2) Modified gamma matrices are not covariantly constant. Only the covariant divergence
vanishes: D_alpha Gamma^alpha=0. This is implied by Classical field equations for the
action principle so that spinor dynamics and space-time dynamics get correlated. This
condition in turn implies super-symmetries in the sense that there is infinite number of
conserved fermion currents contractions ubar_n Gamma^alpha Psi where Psi is second
quantized induced spinro field and u_n any classical solution of modified Dirac equation.
What I have said above actually generalizes to the n-dimensional extremals of any general
coordinate invariant variational principle in n+k-dimensional curved space.
105
Consider next the octonionic representation of gammas.
(A) For ordinary gamma matrices in D=8 tangent space, rotation group SO(1,7) is in the role of
gauge group. One can indeed select the local basis of flat space gamma matrices in arbitrary
manner.
(B) In dimension D=8 one can define also octonionic gamma "matrices" defined as tensor
products of selected 2-D Pauli sigma matrices and octonion units. These objects are not
actually matrices since octonion units are not associative. For quaternionic 4-surfaces, they
give rise to associative induced gamma matrices.
Octonionic gamma matrices correspond to a reduction tangent space vielbein rotation
group from SO(1,7) to G2 which is the automorphism group of octonions. SO(1,7) has
dimension 28 and G2 dimension 14. G2 acts on the imaginary octonion units only and
therefore is subgroup of 21-dimensional SO(7) for a special choice of time axis representing
real octonion unit. In Zero Energy Ontology, octonion real unit corresponds to the time-line
would connecting the tips of causal diamond (CD).
(C) Question: Is it induced or modified gamma matrices or modified gamma matrices span
quaternionic 4-plane of octonions? It seems that induced. For induced gammas, this 4plane is tangential to space-time surface. For modified, it would not be in general. For
modified gamma matrices, this 4-plane could also degenerate to lower-dimensional plane.
I have not been able to decide whether octonionic representation is necessary or not. The notion
of quaternionicity can be defined also for ordinary gamma matrices. Maybe the octonionic
representation is just a curiosity.
Complexified octonionic spinors have indeed 2*8=16 components. One must introduce quark
and lepton octonion spinors separately so that one 16+16 "real" components. Ordionary spinors in
D=8 have 8 +8 =16 complex components =32 real components corresponding to two 8-D chiralities
(quarks and leptons, recall that color corresponds to CP2 partial waves -- not "spin").
You say: "In the modified Dirac equation, there isn’t any projection to space time surface.
Why?"
There is!! Modified gamma matrices Gamma^alpha are labeled by space-time coordinates
x^alpha (to be distinguished from imbedding space coordinates h^k).
You say: "In TGD, there is modified Dirac equation and a field equation deduced from Kahler
action. These are 2 basic equations of TGD that I learned until now. As I know there are no primary
Classical gauge fields in TGD, therefore there is no room for ordinary electroweak equation or
chromodynamics equation of the Standard Model when is translated to TGD framework? It is a little
hard for me to throw away these beautiful equations :). Because every term of the equations has
physical meaning."
This is true. But only to very limited extent.
106
(A) Classical electroweak and color gauge field arise purely geometrically. Classical EW gauge
potentials are just projections of spinor connection to space-time surface. Color gauge
potentials projections of CP2 Killing vector fields to space-time surface.
This predicts extremely strong correlations between various Classical fields but manysheeted space-time allows to circumvent the claim that superposition is lost for these fields
so that basic assumption of perturbation theory ceases to hold true.
Particle having topological sum contacts on several space-time sheets experiences the
sum of gauge and gravitaional forces caused by them. Effects superpose, not the fields.
(B) At the Quantum level, QFT description is only a long length scale approximation just as it is
in string models. Certainly beautiful but only an approximating treating 3-D particle
surfaces as points. Field quanta correspond geometrically to deformations of CP2-type
vacuum extremals defining regions of space-time surface with Euclidian signature of metric
identifiable as 4-D lines of generalized Feynman diagrams. This is something totally new.
In standard QFT, space-time is just Minkowski M4 and Feynman diagram has no geometric
counterpart at space-time level.
Much of the recent work in TGD has been concentrate to attempt to gain understanding about
generalized Feynman diagrams and Zero Energy Ontology implying twistor description combined
with huge symmetries of TGD, are very powerful guidelines.
Electroweak gauge symmetries in and color symmetries emerge as dynamically for the solutions
of the modified Dirac equation (http://tgdtheory.com/public_html/tgdgeom/tgdgeom.html#dirasvira
). It is absolutely essential that the solutions are localized to 2-D surfaces of space-time surface
(string world sheets and perhaps also to partonic 2-surfaces. This is due to single condition: EM
charge defined in spinorial sense is conserved for the extremals. This gives rise to a very profound
connection with string theories but with knot theory and braid theory as additional structure coming
from 4-dimensionality of space-time.
Thanks for mentioning the formula for modified gamma matrices. As I said, they are expressible
in terms of canonical momentum currents and besides term involving energy momentum tensor there
is a term coming from the variation with respect to induced Kahler form. For some reason I had
neglected it.
The chapter "The recent vision about preferred extremals and solutions of the modified Dirac
equation" indeed contains some wrong formulas assuming that the CP2 contribution is absent
(subsubsection "Definition of quaternionicity based on gamma matrices) . I am correcting them.
5. At 9:18 PM, hamed said...
Dear Matti,
Thanks a lot. When I was thinking on your answers, I needed to reconsider the concept of
Vierbein. As I understood, the Vierbein is the same as the frame vector field that is consist of n
orthogonal vector field. If it is correct, the choice of the frame is arbitrary related to our purpose. In
the article “The geometry of CP2 and its relationship to the Standard Model”, you choose a special
kind of the Vierbein of CP2 space. What is your purpose on the choice?
You wrote there: s_kl= R^2*sigma(e_k^A*e_k^A)
107
Is e_k^A, the component of e^A on the spherical coordinates of CP2?
6. At 9:36 PM, Matti Pitkanen said...
Yes. Vierbein is a choice of 4 vector fields orthogonal in induced metric and giving the
components of the induced metric in the flat space inner product. Local rotations respect these
conditions and Riemann connection and its various variants (spinor connection for instance) can be
seen as gauge potentials associated with this gauge symmetry.
The choice of Vierbein in the case of CP2 (not mine originally!) is dictated by symmetry
considerations.
Cognition seems to breaks gauge invariance. There are natural and easy choices and most
choices are not easy. In fact, I have been forced to seriously consider the possibility that cognition in
p-adic sense breaks the gauge symmetries and also other symmetries (also general coordinate
invariance) to their discrete variants.
7. At 1:19 AM, hamed said...
Dear Matti,
I gained a very introduction to modified dirac equation. But now, I think that I need to learn
another important base of TGD about superconformal algebra and super Virasoro and super KacMoody algebras. Please guide me how can start to learn them step-by-step. Thanks.
8. At 2:13 AM, matti Pitkanen said...
Dear Hamed,
You are making progress!
Conformal field theories and super-conformal algebras are mathematically rather heavy notions.
At least they still remain so for me and create horror in me! My childish understanding of them is
basically physical and TGD-centered. I however think that physical understanding is the best way to
proceed.
1. The original motivation for them came from the attempt to describe 2-D critical systems
thermodynamically. The great discovery was that scaling invariance generalizes to 2-D
conformal invariance which dictates 2-point functions completely and 3-point functions also
albeit not uniquely. Fusion rules allow us to construct higher n-point functions. One can
say that symmetries are so huge that dynamics reduces almost to dynamics.
In string theory, one can reduce the situation to conformal field theory at Euclidianized
string world sheet: also the formalism using hypercomplex numbers works.
2. 2-D conformal field theory is the basic notion. Alexander Zamoldchikov et al wrote a classic
about these and this is must I think. See the reference to Nucl. Phys. B at
http://en.wikipedia.org/wiki/Alexander_Zamolodchikov . I suggest that you try to find this
108
reference. The Wikipedia article at http://en.wikipedia.org/wiki/Conformal_field_theory
gives links to related topics.
2-D conformal field theory has 2-D conformal transformations (analytic transformations
of complex variable) as symmetries. Super-conformal symmetry is very much analogous to
local gauge symmetry but is different. Often this symmetry is broken by the generation of
central extension in conformal/super-conformal algebra or associated Kac-Moody type
algebras.
3. Super Virasor algebras
(a) (N=1) Super Virasoro algebra is the Lie algebra of conformal transformations with central
extension.
See this => http://en.wikipedia.org/wiki/Super_Virasoro_algebra
This algebra involves Majorana fermions and is not relevant to TGD since in TGD, B
and L are separately conserved and one has at least N=2 super conformal symmetry.
(b) N=2 Super Virasoro algebra extends this algebra by bringing in conserved charge (say
fermion number). Fermions are not anymore Majorana fermions. I would say that in
TGD, one has large N super-conformal algebra associated with string world sheets. If I
understand correctly, N would be in TGD be the number of fermionic oscillator operator
families accompanying spinor modes localized to string world sheets. The oscillator
operators within given family would be labeled by conformal weight n=0,1,2...
See
this
to
get
some
http://en.wikipedia.org/wiki/N_=_2_superconformal_algebra
perspective
=>
4. (Super) Kac-Moody algebras accompany very naturally (Super) conformal algebras.
Unfortunately http://en.wikipedia.org/wiki/Kac-Moody_algebra
helpful.
does not seem very
One might say that Kac-Moody algebra is much like algebra of infinitesimal gauge
transformations but with non-trivial central extension. Super-Virasoro generators can be
expressed as quadratic expressions of Kac-Moody generators. The article of Zamolodchikov
et al might help here. Some physicist-friendly introduction would be of enormous help (at
least for me the reading of mathematical articles is virtually impossible). Maybe arXiv org
could help here.
The application of conformal field theory to TGD involves some special features.
(A) The basic objects are light-like 3-surfaces (parton orbits) which are metrically 2-D (one
coordinate is light-like and does not contribute to induced metric). This implies that
conformal invariance generalizes. This gives generalization of Kac-Moody algebras and
one can loosely say that the super-conformal invariance more or less reduces physics at 3-D
light-like surface to that at partonic 2-surfaces at its ends.
(B) The light-like boundary of M4 projection of CD and of M4 light-cone is metrically 2-D and
one obtains now generalized symplectic structure for delta M^4_+/- xCP2. Hamiltonians
109
can be though of as functions in delta M^4_+/-x CP22 and delta M^4_+/- can be written as
S2xR_+ where S2 is radial coordinate r_M= constant sphere and R_+ is the half line along
with r_M varies. The Hamiltonians can be written as products r_M^nxHamiltonian in
S2xR_+. r_M is in the role of complex coordinate for ordinary Kac-Moody algebra and
Kac-Moody algebra is replaced with infinite-D symplectic algebra generated bt the
Hamiltonians of S2xCP2 allowing decomposition to products of S2 partial waves with welldefine spin and CP2 partial waves with well-define color quantum numbers. This is a huge
extension of ordinary Kac-Moody algebra.
(C) What I have done with these super-conformal symmetries (besides applying super-conformal
partition functions to p-adic thermodynamic) is basically attempts to demonstrate their
plausibility. I have not worked with super-space formalism but have constructed directly
the fermionic generators of various super conformal algebras. The recent work with the
modified Dirac equation takes this work to rather firm basis and gives also connection with
gauge symmetries interpreted as Kac-Moody symmetries and there quite not identical with
genuine gauge symmetries.
These two super-conformal symmetries relate to the structure of WCW spinor fields.
Spin degrees-of-freedom of WCW spinor field (fermionic Fock space) corresponds to KacMoody in EW, color, stringy degrees-of-freedom. "Orbital" degree- of-freedom in WCW
correspond to super-symplectic degrees-of-freedom.
http://matpitka.blogspot.com/2012/11/quantum-dynamics-for-moduli-associated.html#comments
topic: Quantum dynamics for the moduli associated with CDs and the arrow of GeometricTime
1. At 9:41 PM, hamed said...
Dear Matti,
In the chapter "Time and Consciousness", I have some questions:
“1. In standard picture, the attention would gradually shift towards Geometric-Future and
space-time in 4-D sense would remain fixed. Now however, the fact that quantum state is
quantum superposition of space-time surfaces allows to assume that the attention of the
conscious observer is directed to a fixed volume of 8-D imbedding space.”
I don’t understand the sentence "the attention of the conscious observer is directed to a fixed
volume of 8-D imbedding space.”
Let me make clear what I understand. I mean conscious observer a mind-like space-time sheet
with sequence of finite time duration space-time surfaces as subselves glued to a larger space-time
sheet as larger self (is it correct). So what does it means attention of sequence of finite time duration
space time surfaces?!
In another paragraph you noted “Both the landscape and observer space-time sheet remain in the
same position in imbedding space. But both are modified by this shift in each quantum jump.”
I understand from it: two space-time sheets change their relative position as shift in each
quantum jump but they are located at the same position yet!!! How it is possible? Maybe I think
about them very Classical ;-)
110
2. At 10:44 PM, Matti Pitkanen said...
An excellent question. Before I say anything about time, I must tell that there are 3 chapters
related to the problem and they reflect the evolution of ideas during 15 years-or-so. I have had
several quite different views about this relation.
"Time and Consciousness" at
http://tgdtheory.com/public_html/hologram/hologram.html#timesc is the oldest chapter.
"Time,
Spacetime,
and
Consciousness"
http://tgdtheory.com/public_html/hologram/hologram.html#time came next.
at
"About
the
Nature
of
Time"
at
http://tgdtheory.com/public_html/tgdconsc/tgdconsc.html#timenature is the latest one and
summarizes several approaches in chronological order. The last sections of this chapter represent
the mechanism that I believe is nearest to the truth. I have also done my best to update the older
chapters by telling something about the newest views.
[Hamed]: “1. In standard picture, the attention would gradually shift towards geometric future and
spacetime in 4-D sense would remain fixed. Now however, the fact that quantum state is quantum
superposition of space-time surfaces allows to assume that the attention of the conscious observer
is directed to a fixed volume of 8-D imbedding space.”
I don’t understand the sentence: "the attention of the conscious observer is directed to a fixed
volume of 8-D imbedding space.”
[Matti]: This statement refers to the Classical model in which CD which is taken to be "spotlight of
consciousness". I assumed that it is just fixed for the reason that I did not have idea about how to
introduce the dynamics of CD! Nor even idea of introducing this dynamics! The arrow of
imbedding space-time corresponds to quantum arrow of zero energy state: upper/lower boundary is
prepared and opposite boundary not. This is somewhat unsatisfactory. One would like to have
something more concrete.
The arrow at the level of space-time surface correspond to the arrow implied by dissipative
dynamics due to multifurcations relating closely to the emergence of effective values of Planck
constant coming as multiples of ordinary Planck constant. Multifurcations are there because of huge
vacuum degeneracy of Kahler action.
This leads to "bath towel argument". Each zero energy state resulting in the sequence of state
function reductions at opposite boundaries of CD gives rise to a "quantum average space-time
surface" inside fixed CD. These space-time surface can be thought of as forming the analog of
folded bath towel ranging from lower boundary to upper and then back to lower and so on. There is
inherent arrow of Geometric-Time due to the Second Law so that the self associated with this spacetime sheet does not observe the change of the imbedding space arrow of time but experiences single
arrow-of-time. This argument is of course open to criticism.
In this posting I propose the dynamics for CDs by making purely Classical view about self
quantal. CD is replaced by quantum superposition of CDs which all have fixed second tip.
(a) Self corresponds to quantum superposition superposition of CDs of various sizes and Lorentz
boots with a fixed lower/upper tip. Next state function reduction implies localizes of
upper/low tip and delocalization of lower/upper tip. This brings in more concrete
111
imbedding space arrow of time. The reason is that the space labeling CDs consist of
hyperboloids for which the temporal distance between tips is integer multiple of CP2 time
scale. This space is analogous to half line and quantum transitions induce diffusion leading
gradually to the direction of the Future. This is variant of basic argument saying that inside
light-cone there is more room in the Future than in the Past.
Note however that both ends of CD drift downwards in M4. If ends correspond to
different selves, then they both have fixed arrows of imbedding space time which are
opposite. If one assumes that imbedding space is M4± x CP2, then the drifting at the lower
boundary eventually stops since it is not possible to get below the Big Bang and one has just
one arrow of time and timeless self near the moment of Big Bang!
(b) Also now arrow-of-time at space-time level results from the "fold bath showel" argument and
the new element is argument for imbedding space time as resulting from gradual growth of CD.
Spotlight of consciousness suffers cosmic expansion!
[Hamed]: Let me make clear what I understand. I mean conscious observer a mind like space-time sheet
with sequence of finite time duration space-time surfaces as subselves glued to a larger space-time
sheet as larger self (is it correct).
[Matti] Self has both space-time correlates and imbedding space correlates. What you say above is my
original articulation for the idea that hierarchy of space-time sheets glued to each other
corresponds to hierarchy of selves. These space-time surfaces would be within CDs each defining
spotlights of consciousness.
[Hamed] So what does it means attention of sequence of finite time duration space-time surfaces?!
[Matti] This is a question which goes to the point and leads to the basic question which I made also in
the posting.
"Does the space-time surface within CD continue outside the CD in which case CD would
represent attention directed to a region of CD or does it end in which case CD would represent small
sub-Universe possible in ZEO? Or are both options realized?"
I have not been able to provide a clearcut answer to this question.
[Hamed] In another paragraph you noted “Both the landscape and observer space-time sheet remain in
the same position in imbedding space but both are modified by this shift in each quantum jump.”
I understand from it: two space-time sheets change their relative position as shift in each
quantum jump but they are located at the same position yet!!! How it is possible? Maybe I think
about them very Classical ;-))
[Matti] Also this statement assumes non-dynamical and non-quantal CDs. The above argument explains
how the arrow-of-time at space-time level emerges and I do not repeat it.
The important point is that I do not assume that shift of position for space-time sheet in fixed
direction is responsible for the flow of time and its arrow. This mechanism would of course be a
very natural guess. I have also played with it and also with its variant in which CD shifts towards
fixed time direction. This however leads to artificial scenarios and one does not obtain arrow of
imbedding space time naturally. I only can build a consistent view by reducing the arrow-of-time to
112
the gradual increase of average CD size in the sequence of quantum jumps. The mechanism is
essentially same as for diffusion in light-cone. Particle necessary drifts to the direction of the Future.
http://matpitka.blogspot.com/2012/11/to-deeper-waters.html#comments
topic: To deeper waters
1. At 11:06 PM, Hamed said...
Dear Matti,
In the TGD-inspired theory of Consciousness, there are some basic concepts and let’s I define
them from my simple intuition about them. After this I make comparison with TGD to make my
questions clear.
In my view, when I experience my around, what is experiencer is not merely my body but in
really it is a conscious entity beyond my body. This is called “I”.
In TGD there is the notion that you called it “self”. As I understand, the notion of “self” is the
same as “I” for Living matters. But you generalize the notion and say in generally self is a
subsystem able to remain un-entangled under the sequential quantum jumps. Henceforth the
definition isn’t only for Living matters but for non-Living matters too.
Concerning the term “entanglement” in the definition of self, in TGD it is not a primary term
catching the current physics without variation. But there are some differences.
For example, there are 2 entanglement in TGD -- “Bound state entanglement’ and “Negentropic
entanglement”? In the first, the entropy of 2 systems will be increased. And in the other,
negentropy is increased (or entropy is reduced).
Entanglement between 2 electrons in standard QM is an example for bound state entanglement
and some cognitive processes like love are negentropic entanglement.
By these types of entanglements, please explain to me more clearly in the definition of "self".
2. At 8:07 PM, Matti Pitkanen said...
Dear Hamed,
Your first question relates to "I" and self and its generalization. I hope that I am boring when I
list the basic notions and ideas.
(A) Quantum jump as a moment of consciousness (moment of recreation) is basic notion. The
natural guess was that self results as a fusion of quantum jumps just as matter arises as
fusion of elementary particles.
It seems possible, however, to identify self and quantum jump so that quantum jumps =
selves form a hierarchy with quantum jumps within quantum jumps. Hierarchy of selves as
a fractal hierarchy of moments of consciousness. Self has subselves as mental images
giving rise to the experience about flow of time. Self in this sense corresponds to a
primitive awareness (no self model yet).
113
Self can be also empty of mental images/ subselves/sub-CDs/topologically-condensed
space-time sheets. Deep meditative states might represent this kind of situation.
Concentration to single mental image by eliminating thought by preventing metabolic
energy feed to these subselves. Self as a gardener eliminating all undesired plants.
(B) Self must have imbedding space and space-time correlates. CD and space-time sheets are
these. Again one has hierarchies. I have talked in previous postings about a connection
with the arrow of Geometric-Ttime resulting basically from state function reductions at
opposite boundaries of CDs. In quantum theory, one must allow wave functions in the
moduli space of CDs and these correspond discretizations of partial waves in M4± x CP2.
Every reduction involves localization of either tip of all CDs in quantum superposition and
delocalization of second tip. Interpretation is in terms of wave particle duality.
(C) Cognitive aspects of consciousness might be present at the elementary particle level as p-adic
space-time sheets. Cognitive representations are obtained as intersections of real and padic space-time sheets consisting points in an algebraic extensions of rationals. The higher
the evolutionary level, the larger the algebraic extension. "Common point" makes sense
also at the WCW level. Some partonic 2-surfaces make sense both as real and p-adic
surfaces belong to the intersection of real and p-adic worlds (say surfaces determined by
polynomials with rational coefficients). The postulate is that Life resides in this this
intersection of cognition and sensory worlds.
(D) I/ego serves as a model for self and is constructed by brain. The brain is a builder of
standardized mental images responsible for conscious intelligence. Primary sensory
percepts at the level of sensory organs. The ability to zoom is essential for Conscious
intelligence. The hierarchy of effective Planck constants makes this possible. The larger
the value of hbar, the longer the time span of memory and planned actions. Scaled
representations for pieces of history emerge. Lifetime can be abstracted to a story of few
minutes. Or time span of nanosecond can be scaled to minutes in a computer model of
meso-physics constructed by brain.
(E) In the TGD Universe, the biological body provides the basic sensory input responsible for the
sense of self. The layers of onion-like magnetic body receive it via EEG and its (also
fractal) variants. The relative motion of biological and magnetic body (involving also
deformations of magnetic body) would be essential for the sensations about own body.
Out-of-Body Experiences in situations (in which sensory input is absent) reveals its
existence. Also experiences like train illusion in which the magnetic body moves with
respect to the biological body.
Your second question was about entanglement and its role the definition of self and also about
bound state entanglement and negentropic entanglement.
Bound state entanglement is stable for energetic reasons. De-entanglement would in general
require decay of the bound state not favored energetically. Negentropic entanglement is stable by
NMP. Repeated state function reduction at the same end of CD is possible. Nothing happens since
negentropy is at maximum. This together with absence of subselves/mental images could relate to
the experience of "timelessness" typically reported by mystics.
114
(1) Anatomy of quantum jump: cascade of quantum jumps proceeds from largest CD in cascade
downwards and leads to splitting of subsystems to unentangled subsystems and stops when
bound state entanglement or negentropic entanglement is reached. By NMP, the followup
quantum jumps at same end of CD do not change the situation. Eventually state function
reduction occurs at the second end of CD and the second tip of CD is localized. Could
sleep-awake cycle correspond to this alternation and therefore be completely universal?
(2) Negentropic entanglement does not represent information about either entangled system but
about their relationship. Interpretation is as a quantum representation for a rule.
abstraction A--B as superposition of instances ai--bi. The Schroedinger cat is good
example. Note that the choice of basis ai and bi is not unique. For instance if entanglement
matrix is unit matrix, all unitarily related basis are possible. This explains why the
information associated with this kind of states ("enlightment") is not communicable.
Experience of understanding without knowing what one understands! When the
entanglement ceases, memory is formed and since some basis has been chosen in state
function reduction, communication of the memory is possible. Communication involves
also quantum measurement!
(3) NMP provides the basis of emotions. Negentropic entanglement is accompanied by
positively-colored emotions (love, joy, experience of understanding).
Entropic
entanglement by negatively colored ones. Negentropic entanglement in principle requires
no binding energy. The high-energy phosphate bond of the ATP molecule is fundamental
in metabolism. It carries metabolic energy. Could this bond have negentropic
entanglement so that NMP would make the bond stable rather than binding energy? This
would make ATP the basic carrier of information and fight for survival would be fight for
negentropic entanglement.
(4) Living matter is building quantum rules by building negentropic entanglement. Systems with
large number of energetically degenerate states are ideal for this purpose. If their number
is power of prime p, the number theoretic entanglement negentropy is maximized for this
prime. 4-D spin glass degeneracy of the TGD universe due to vacuum degeneracy of
Kaehler action makes possible large degeneracy. Systems with very large degeneracy of
Macroscopically equivalent ground states have large ensemble entropy of the macroscopic
ground state and are ideal if they are able to negentropically entangle. The Second Law
has also its positive aspects! (BTW, do not confuse the ensemble entropy with
entanglement negentropy!)
3. At 12:46 AM, Ulla said...
Entropic entanglement? That means loosening of entanglements?
Homeostasis is a problem. It is a basic regulating concept in Biology. It has to be energetic,
going towards entropy, and in that way following the Second Law.
Still, there are a nonzero basic level -- maybe due to the nerve signals (Josephson junctions?) -that are always working. If not in any other ways, they are sponanously firing to keep up the basic
disturbance level (the back of the 'Big Book'). Can this then also be said to keep up the basic
entanglements and the basic 'smaller' Self? The enlightment and growing of Self would be to have
more entanglements, encompassing other selves? Note the problem of ego/self. Maybe even some
kind of fusing?
115
You talked about a jail of free will? Matter usually doesn't count in this context? What makes
ordinary matter so rigid and different from Living matter? They are the same atoms. You have
talked of Living matter as an anyonic state, as instance, more basic than fermionic/bosonic matter.
Then it would be more like the interaction itself or in your words the "consciousness"? The
entanglements are much reacting/forming like bosonic matter?
To go towards entropy means more harmony and stability. To go towards negentropy means
more disturbance, fight? This is seen very well in the brainwaves. Disturbances gives peaks. And
when the message is understood, the peaks are gone.
4. At 3:07 AM, Matti Pitkanen said...
To Ulla:
Entanglement is entropic if one uses standard Shannon entropy to define entanglement entropy.
This applies for generic entanglement probabilities. The interpretation is that this entropy describes
the lack of information about state of either entangled system. We do not know for sure whether the
Schrodinger cat is dead or alive.
If entanglement probabilities are rational numbers or numbers in algebraic extension of rationals,
the notion of number theoretic entanglement entropy makes sense. The logarithm of probability
appearing in the formula is replaced with logarithm of p-adic norm of probability which makes sense
with the above restriction on probabilities. Still, the entropy has standard defining properties. One
might somewhat poetically say that this definition makes sense in the intersection of real and p-adic
worlds where the Life resides.
The news is that number theoretic entanglement entropy can be negative unlike ordinary one and
thus becomes negentropy for suitably chosen primes. It is very large if the probabilities are of form
m/pN where p is the p-adic prime used to define the p-adic number. If the number of states
appearing in superposition of pairs of states is pN, this is achieved.
The interpretation is that number theoretic entanglement negentropy characterizes (not the
ignorance about single particle state in entangled system) but information carried by superposition of
state pairs axb in state AxB. Superposition would represent a rule whose instances are pairs axb: a
and b imply each other. When the larger then number of instances in superposition of state pairs, the
more information the rule carries. Living matter would build this kind of rules about reality and this
would help it to survive.
http://matpitka.blogspot.com/2012/11/about-basic-assumptions-behind-p-adic.html#comments
topic: About the basic assumptions behind p-Adic mass calculations
1. At 1:55 AM, Hamed said...
Dear Matti,
I want to learn Quantum-TGD step-by-step. I think it is more useful for me to learn it as like
TGD evolved from first years of your thesis to now. This process helps me to understand the
motivations behind it and how the concepts generalized step-by-step as TGD evolved. I know it will
be a long process but I'll try to be patient ;).
116
Therefore I am concentrating on the space of 3-metrics of Wheeler precisely. I will ask the
questions about it in following days.
2. At 3:13 AM, Ulla said...
Yes, I also think that is the way to go. This is why all those old texts also should be save,
although there are mistakes and wrong guesses. Mark McWilliams (aka K.R.A.M.) does a good
service in saving them too.
3. At 8:48 PM, Hamed said...
Dear Matti,
If it is possible, please write a program step-by-step for studying Quantum-TGD in the first of
your thesis. As Ulla pointed, it would be very good if it contains mistakes and wrong guesses. I
hope you remember them after more than 30 years ;-). Thanks a lot.
If you want, it would be useful for other readers if you devote a new posting about it.
4. At 8:15 PM, Matti Pitkanen said...
Dear Hamed,
Sounds like an excellent idea. I could try to write this after I get my recent project done. An
extremely nervestaking programming task at this age. Takes still few days probably.
I have been worked hardly to learn Unix command level language (Bash) from the Web. This
just to rationalize the hopelessly complex latexing procedure of tex files (MacLatex does not work
properly so that I need both command Level Unix and Python as auxiliary tools). T his would make
possible batch operations: all chapters of all books latexed simultaneously.
5. At 10:32 AM, Ulla said...
On the Vixra blog, you say "In TGD framework, this is even more the case since at microscopic
level bosons consist of fermion-antifermion pairs meaning that all bosons emerge."
Can bosons then be seen as a BEC? In Biology, the carbon (can be a boson) and light interaction
is a basic signal and the interaction is in the gap as a superposition?
Light interaction and the quantum jump as a "particle" for a cognate can then be the same thing?
Also in the other interactions is light emitted as radiation as Popp has explained. The DNA as a
quantum computer has also difficulties with the epigenetic (light-interactive sheet around genes?
Light overrules carbon regulation sometimes. This also links light and time as matter and antimatter
are linked.
Space-time sheets with negative time orientation carry negative energies.
Is it any difference in energies between light as a particle or light as a wave? When light (and
information entangled with light) forms a BEC and is teleportated, it is dissipationless as is much the
superconduction in nerves? The dissipationless state makes time impossible (instant) or then the
117
negative time is very compressed, almost presens? (Or very diluted like the diluted energy in 'lower
than Planck scale' labeled with primes?)
6. At 8:48 PM, Matti Pitkanen said...
To Ulla about bosonic emergence and BEC:
Bose-Einstein condensate is quantum field theoretic notion. I have a proposal for the
microscopic counterpart of BEC in TGD developed during my long Higgs Odysseia which I have
summarized as a chapter at http://tgdtheory.com/public_html/paddark/paddark.html#higgs .
If TGD has QFT limit (I suggest a concrete construction of this limit at the end of Higgs
chapter), BEC makes sense also in TGD as an approximate concept at least. Of course, microscopic
description could bring in daylight some new aspects about this process.
A basic objection to BEC in TGD is that for members of fermion-antifermion pair exclusion
principle holds true. Can one really put two such pairs at same position (at single point at QFT
limit)?
Maybe many-sheeted space-time allows us to solve the problem. There is room in CP2 degreesof-freedom. One can put the bosons as pairs of space-time sheet on top of each other as parallel
space-time sheets so that only their M4 projections overlap.
The space-time interpretation for a generation of large value of Planck constant is as a
multifurcation generating N-branched space-time. Could this also have something to do with BEC
like process?
http://matpitka.blogspot.com/2012/12/how-coupling-constant-evolution-could.html#comments
topic: How coupling constant evolution could make itself visible as properties of preferred
extremals?
1. At 9:44 AM, Stephen said...
Absolutely brilliant. I think I grasped most of this post. I'm still trying to develop intuition about
preferred extremals, though. How should we think about these things and what are they exactly? Does
this notion exist outside of TGD?
2. At 7:18 PM, Matti Pitkanen said...
Dear Stephen,
Yes, it is;-)!
The basic difference between TGD and the Standard path integral approach to QFT/string models
derives from the extreme non-linearity of Kaehler action implying that path integral (which as such is
mathematically ill-defined) is totally spoiled by the infinities due the local vertices appearing in
arbitrarily high orders.
The solution of the problem took me about 10 years and relies on a generalization of Einstein's
geometrization program. Physics as Kahler geometry of "World of Classical Worlds") (WCW) allowing
us to also realize general coordinate invariance (GCI) in strong form. This is something extremely
118
natural but something which superstring theorists refuse to consider under any circumstances and prefer
to continue their lonely and desperate wandering around the landscape.
● Instead of path integrating over all 4-surfaces, one functionally integrates over all 3-surfaces to
which Kahler metric assigns a unique 4-surface (the preferred extremals). 3-surfaces consist of
at least 2 parts located at the light-like boundaries of a causal diamond (CD). The good news is
that functional integral is a genuine integral (not a mere formal algebraic trick).
● The expectation is that local 4-D action becomes non-local functional of 3-surface meaning
allowing to expect absence of local divergences. As a matter-of-fact, one obtains 3-D ChernSimons terms so that effective 3-D character (holography) results. 3-D Chern-Simons action is
local but not plagued by local divergences.
What preferred extremals the are? The answer to this question has been the tough
challenge and here a dramatic progress has taken place during this year.
● Their construction is a generalization of that for minimal surfaces (string world sheets). A
generalization of conformal structure to 4-D case is needed in both Minkowskian and Euclidian
signature for induced metric. As a matter-of-fact, the preferred extremals are also 4-D minimal
surfaces as well as solutions of Einstein-Maxwell equations with the cosmological constant. It
all boils down to simple algebraic conditions due to the generalized holomorphic structure. G
and Lambda are predictions and can have spectrum.
● In fact, this holography is even stronger since one can require that light-like 3-D orbits of
wormhole throats are equivalent in sense of GCI with space-like 3-surfaces at the ends of
space-time surface about light-like boundaries of causal diamond. The 2-D intersection of
these 3-surfaces with 4-D tangent space data dictates the physics. Strong form of holography =
= Strong form of GCI.
The second breakthrough took place in the understanding of solutions of the modified Dirac
equation. All induced spinor fields except right-handed neutrino are localized at 2-D string worldsheets
so that stringy mathematics finally finds the physical application it deserves.
One of the big deviations from Standard Model SUSY is that SUSY in the TGD sense is not the
standard N=1 SUSY predicting Majorana fermions and non-conservation of B and L and being now in
grave difficulties admitted even by the Russian discoverer of SUSY. But again, colleagues seem to have
decided that it is either Standard SUSY or no SUSY at all;-).
The third breakthrough (perhaps!) is Quantum-Classical correspondence realized in terms of
statistical geometry of preferred extremals. This promises to make the calculation of correlation
functions involving WCW functional integral very concrete. Just Classical correlation functions for
single preferred extremal could be all that is needed!
http://matpitka.blogspot.com/2012/12/is-there-connection-between-preferred.html#comments
topic: Is there a connection between preferred extremals and AdS4/CFT correspondence?
1. At 1:24 AM, Ulla said...
http://backreaction.blogspot.com/2012/12/adscft-predicts-quark-gluon-plasma-is.html
119
AdS/CFT predicts the quark gluon plasma is unstable.
The gauge-gravity duality is a spin-off from string theory and has attracted considerable attention
for its potential to describe the quark gluon plasma produced in heavy ion collisions. The last news
we heard about this was that the AdS/CFT prediction for the energy loss of quarks or gluons passing
through the plasma does not agree with the data. The AdS/CFT community has so far been
disappointingly silent on this issue, which has now been known for more than a year.
http://backreaction.blogspot.com/2011/10/adscft-confronts-data.html
2. At 7:31 PM, Matti Pitkanen said...
To Ulla:
I think I wrote about the discrepancy of the AdS/CFT model for quark gluon plasma as a
commentary to a very nice posting by Sabine Hossenfelder.
In higher energy QCD, one would expect quark gluon plasma. This prediction is definitely
inconsistent with the observations about correlated charged particle pairs moving in same or
opposite directions and strongly bringing in mind a decay of string-like object. The problem is that
string-like objects make sense only in low energy QCD, not at very high energies in proton-proton
collisions!
The TGD explanation in its original form was based on the identification of string-like objects
as color magnetic flux tubes containing quarks in liquid-like phase - color class. Only recently did
I realize that these flux tubes could be nothing but the hadrons of M89 hadron physics so that RHIC
would have observed the basic prediction of TGD for - was it 7 years ago! If I am not wrong
(usually the physicist who speculates is wrong;-)), particle physics cannot avoid a scandal. People
are desperately searching Standard SUSY and other signals for new physics. And new physics is in
front of their eyes!!
I want clarify the distinctions between the meaning of this word in string theory context and its
possible meaning in TGD framework.
AdS5 x S5 correspondence is used in M-theory inspired approach to model quark-gluon plasma
and one obtains color glass picture (i.e., liquid-like state of partons instead of plasma and explaining
the observed correlations). This approach has some problems about which Bee wrote earlier and I
also did.
M-theory inspired AdS5 x S5 correspondence is very different from the strong form of
holography of TGD. In TGD framework, constant Ricci scalar property would suggest that strong
form of holography can be seen as a generalization of AdS4 correspondence. This posting
demonstrated that AdS4 defines a piece of vacuum extremal so that this conjecture might make
sense.
There are important differences which should not be forgotten.
(a) In TGD, (superstring) 10-D AdS5 x S5 is replaced with the real 4-D space-time realized as 4surface in M4 x CP2. There is no need to replace the original physical system with blackholes in 10-D. Strong form of holography is the basic principle which can be seen as a
generalization of AdS4/CFT correspondence.
120
(b) String worldsheets in 4-D space-time carrying fermion fields (right-handed neutrino is the
exception) are real physical objects would replace the strings in fictive 10-D target space.
(c) In AdS5xS5, one has 4-D Minkowski space-time as a conformal boundary of AdS5. Now M4
is replaced by light-like 3-surface at which the signature of the induced metric changes and
which represents line of generalized Feynman diagram. By the strong form of holography
(of general coordinate invariance), one can say that it is replaced with space-like 3-surfaces
at the end of causal diamonds (CDs).
d) In AdS5, conformal symmetries of M4 defined conformal symmetries of CFT. In TGD,
conformal symmetries of light-like 3-surfaces forming infinite-D group are the conformal
symmetries. This is huge extension of conformal symmetries of 4-D QFT in M4 and very
closely related to stringy conformal symmetries.
e) Last but not least, the origin of standard AdS/CFT correspondence in its Standard form is a
mystery. But in TGD framework, the mystery disappears. The strong form of general
coordinate invariance implies its counterpart as strong form of holography.
3. At 7:38 AM, Hamed said...
Dear Matti,
some questions …
A comparison between TGD and GR:
In GR, space time is distinguished from matters or physical fields. The gravitational field is
not a physical field but a geometric field that is the origin of space-time. In the framework, can one
say “space-time tells matter how to move; matter tells space-time how to curve”.
In TGD, space time is distinguished from the Kahler field because the origin of space time is
from induced metric on the sub-manifold of the imbedding space that is the same as gravitation. But
the origin of the Kahler field is from induced kahler form on the sub-manifold. Therefore can one
say “space-time tells the dynamics of Kahler field and the Kahler field tells space-time how to
curve”?
This Kahler field is only superposition of the effects of physical fields on the submanifold not
themselves(?). In similarly gravitational field or induced metric on the submanifold is superposition
of effects of gravitational fields of matters? But I don’t see any room for placing these
superpositions in the Kahler field or gravitational field because these fields are just induced from
imbedding space.
I use the word submanifold instead of space-time because the Kahler field is not something over
space-time as like physical fields in GR are over space-time. In other words, space-time is not most
fundamental than the Kahler field. Induced metric makes space time over the submanifold and
separately induced Kahler form makes the Kahler field over the submanifold. Is there any wrong
here?
Because Kahler action doesn’t contain gravitational field, one should write another Lagrangian
density for gravity in addition to it? Just as in Einstein formalism, there was a term for gravity
“scalar curvature” and other terms related to the Lagrangian of physical fields.
121
Can one call the Einstein tensor just the energy momentum tensor of gravitation field? Is it
deduced from the Lagrangian of gravity “curvature Scalar” as the same as energy momentum tensor
of Kahler field is deduced from Lagrangain of Kahler field? Therefore intuitionally Einstein
equation tells that sum of energy momentum tensors of gravity and other physical fields should be
zero!
What is wrong in my arguments? Or one can say this is just a little view of Zero Energy
Ontology!? If you see, the Einstein tensor depends on Riemannian tensor as very similar to energy
momentum of Kahler field depends on the Kahler field (induced Kahler form).
4. At 2:26 AM, Matti Pitkanen said...
Dear Hamed,
Thank you for some excellent questions. I add comments to your text.
[Hamed] In GR, space-time is distinguished from matter or physical fields. The gravitational
field is not a physical field but a geometric field that is the origin of space-time. In the
framework, can one say “space-time tells matter how to move; matter tells space-time how
to curve”.
[Matti] One can distinguish between matter and geometric fields. However, the dream of
Einstein was the geometrization of physics so that both gravitational and other fields
would reduce to geometry. In the attempts to quantize GRT, the vision of Einstein was
given up and one treated the gravitational field as one particular massless field. Also in
superstring models, one gave up the geometrization of Classical fields and assigned them to
massless modes of a string.
[Hamed] In TGD, space time is distinguished from the Kahler field because the origin of space
time is from induced metric on the sub-manifold of the imbedding space that is the same as
gravitation. But the origin of the Kahler field is from induced Kahler form on the submanifold. Therefore can one say “space-time tells the dynamics of the Kahler field and the
Kahler field tells space-time how to curve”?
[Matti] You are right in the sense that Kahler action defines the dynamics via its preferred
extremals.
However, you are wrong in that also in TGD Einstein's original statement is true in the
sense that preferred extremals are solutions of Einstein's equations with a cosmological
term. The only difference from Einstein's theory in gravitational sector is that metric is
induced metric. This means extremely strong restriction to allowed 4-geometries. For
instance, overcritical and critical cosmologies have a finite duration.
There are several induced structures. Both the metric of imbedding space and Kahler
form of CP2 are induced to space-time surface. One can induce also the components of
spinor connection of CP2 just by projecting them to space-time surface and obtain Classical
electroweak gauge potentials. The projections of CP2 Killing vector fields define
candidates for Classical gluons. Gamma matrices and spinor structure can be induced.
This means that classical dynamics reduces to that for the shape of space-time surface
Classically and to that for induced spinor fields at elementary particle level.
122
[Hamed] This Kahler field is only superposition of the effects of physical fields on the
submanifold not themselves(?). In similarly gravitational field or induced metric on the
submanifold is superposition of effects of gravitational fields of matters? But I don’t see
any room for placing these superpositions in the Kahler field or gravitational field because
these fields are just induced from imbedding space.
[Matti] There is some confusion here. Induced Kahler form is purely Classical and geometric
notion. It is the analog of the Classical Maxwell field but not equal to the Classical E-M
field but to its U(1) part. Preferred extremal property means that there are very few Bohr
orbit like patterns of Classical gauge fields - psychologist might speak of "archetypes".
This would lead to contradiction with what we know without the many-sheetedness of the
space-time.
Test particle (small 3-surface) topologically condenses (form topological sum contacts)
to all sheet having non-trivial projection to the region of M4 in which it resides and particle
experiences the sum of the Classical fields associated with them. This visual argument is
"must". Superposition for fields is replaced with that for their effects. I have said this
many times but this is indeed an overall important difference from field theories. This is
what allows enormous reduction of dynamical field like variables. Just 4 imbedding space
coordinate when 4 of them are eliminated using general coordinate invariance.
[Hamed] I use the word submanifold instead of space-time because the Kahler field is not
something over space-time as like physical fields in GR are over space-time. In other
words, space-time is not most fundamental than Kahler field. Induced metric makes space
time over the submanifold and separately induced Kahler form makes the Kahler field over
the submanifold. Is there any wrong here?
[Matti] There is;-). The induced Kahler form is like any Classical field defined in space-time. It
is however not a primary field variable. Imbedding space coordinates take this role. What
is fundamental is the identification of space-time as a 4-surface. This reduces the
dynamics to that of 4-D drum membrane. Every Classical field is induced by that
dynamics as a byproduct.
[Hamed] Because Kahler action doesn’t contain gravitational field, one should write another
Lagrangian density for gravity in addition to it? Just as in Einstein formalism there was a
term for gravity “scalar curvature”’ and other terms related to the Lgrangian of physical
fields.
[Matti] Kahler action contains induced metric and thus Classical gravitational field! Kahler
action density is
J^{munu}J_{munu} sqrt(g4)
J^{munu}= g^{mualpha}J^{nubeta} J_{alphabeta} is obtained by index raising from
J_munu which indeed does not contain gravitational field. The metric determinant
sqrt(g4) also contains gravitational field. Only in the approximation that induced
metric is flat M4 metric the dependence on Classical gravitational field disappears.
There is no need to add curvature scalar. Preferred extremals satisfy Einstein-Maxwell
equations with the cosmological term and also minimal surface equations. This is solely
123
due to the generalized conformal structure which I call Hamilton-Jacobi structure in
Minkowskian regions.
This of course does not mean that Kahler action would reduce to Einstein-Maxwelll
action with the cosmological term!! The only condition needed to get E-M equations is the
requirement that energy momentum tensor for Kahler field has a vanishing covariant
divergence. This condtion is needed for preferred extremal property. The same condition
can be used to derive Einstein's equations without mentioning action at all.
[Hamed] Can one call the Einstein tensor just the energy momentum tensor of gravitation field?
It is deduced from the Lagrangian of gravity “curvature Scalar” as the same as energy
momentum tensor of Kahler field is deduced from Lagrangian of Kahler field? Therefore
intuitionally the Einstein equation tells that sum of energy momentum tensors of gravity
and other physical fields should be zero!
What is wrong in my arguments? Or one can say this is just a little view of Zero
Energy Ontology!? If you see, Einstein tensor depends on Riemannian tensor as very
similar to energy momentum of Kahler field depends on the Kahler field (induced Kahler
form).
[Matti] What goes wrong is that in TGD, one has just Kahler action and field equations imply
Einstein-Maxwell equations with Lambda for preferred extremals (so I strongly believe!).
They are not obtained from a variation of Einstein-Maxwell actions.
Indeed, in Einstein's approach one would have Maxwell action plus curvature scalar
plus volume term.
This would give by Noether's theorem for the action of
diffeomorphisms (gauge transformations by general coordinate invariance) T- kG-lambda g
=0 so that all conserved quantities associated with diffeomorphisms vanish as they should.
(In particular, they vanish for local Poincare transformations whose identification is far
from unique.)
This is the Noetherian catastrophe of GRT and leads to endless attempts to identify
conserved quantities in some ad hoc manner. This is avoided in TGD framework. We can
accuse Hilbert for leading us to wrong path by discovering that Einstein's equations are
obtained by adding to the action the curvature scalar;-)!
There are very strong objections against Einstein-Maxwell action. For instance,
curvature scalar does not have a definite sign. This leads to problems even if one makes
Wick rotation and integrates over metrics with Euclidian signature in path integral.
There are however speculations that supersymmetric variant without matter term might
give rise to a divergence-free perturbation theory. The idea that gravitation could be in
some sense a square of gauge theory is behind this thinking. In TGD, one goes further. By
bosonic emergence bosons as quantal objects are "squares" of fermions residing at string
worldsheets. Gravitons are actually 4th powers of fermions;-).
5. At 9:56 PM, Hamed said...
Dear Matti,
Thanks a lot.
124
[Matti] “Test particle (small 3-surface) topologically condenses (form topological sum contacts)
to all sheet having non-trivial projection to the region of M^4 in which it resides and
particle experiences the sum of the Classical fields associated with them. This visual
argument is "must". Superposition for fields is replaced with that for their effects.
I don’t understand yet how these effects is contributed to the Kahler action? Kahler action is just
from Lagrangian density of Kahler field that is a function of induced metric and induced Kahler
form. How these effects appear in the Lagrangian density?
For example, if we have some distribution of matters on the space-time, in GR one can calculate
energy momentum tensor from the distribution of matters and Einstein equation gives us metric of
space-time. How do you the same thing in TGD?
6. At 1:44 AM, Matti Pitkanen said...
Dear Hamed,
This is a good question since I see this point as enormously important.
(a) In practice, all field theories are linearized in the lowest order approximation. If one wants to
calculate interactions, one forms the sum of various fields generated by the particles and
calculates the effects of the resulting field on various sources: F= q(E +vxB)=
q*\sum_i(E_i+v\tme B_i) for electrodynamics! This procedure works nicely for discrete
set of sources. But for continuous sources one meets problems with self-interactions.
(b) In TGD framework, there is no linear superposition of Classical fields at any level. Not for
induced metric, various gauge potentials, nor induced Kahler form since they are nonlinear
in the primary field variables and their gradients. Primary fields are imbedding space
coordinates from which 4 can be eliminated by taking them space-time coordinates. Linear
superposition is also impossible for primary field variables.
(c) How does one get the physical counterpart of linear superposition? The crucial observation is
that we observe only the superposition for effects of fields and not for the fields
themselves. This fact has been forgotten by theoreticians a long time ago although basic
textbooks (such as my old Alonso-Finn) emphasizes it. The linear superposition of fields is
quite too strong a hypothesis.
(d) What one obtains in the recent case then? The linear superposition for fields is replaced with
the set theoretic union of space-time sheets carrying the fields. This is the king idea: +
goes to U!
One has space-time sheets. Think of 2-D space-time sheet in E3 with extremely small
distance of the order of CP2 radius between them. By their vicinity they tend to touch each
other by forming wormhole contacts and therefore interact. These wormhole contacts do not
carry magnetic charge and are therefore unstable so that they do not represent elementary
particles.
These wormhole contacts mean interaction between a particle-like space-time sheet and
bigger space-time sheets carrying effects of external sources. The effect on the particle is in
the first approximation just the sum of effects (say, gauge forces and gravitational
acceleration).
125
There is of course feedback as in the standard description. Particle also modifies the
space-time sheets a little bit since the generation of wormhole contact changes the preferred
extremals in question a little bit.
(e) Consider now your example. In the case of the gravitation, the effective deviation of metric
experienced by particle would be estimated as follows. Use common (say linear) M4
coordinates for the space-time sheets. One sums up the deviations of the corresponding
induced metrics from flat M4 metric at various space-time sheet. This defines the effective
metric giving rise to the gravitational acceleration experienced by the test particle idealized
to point particle. Particle experiences sum of gravitational accelerations just as in the
Standard description. Similar prescription applies to Classical gauge forces.
(f) The effects do not appear in the form of Lagrangian density. There is no need to add any
interaction terms in Kahler action. The value of Kahler action of course changes by terms
which can be interpreted as interaction terms. Wormhole contacts are created and spacesheets are slightly deformed in the interaction by the condition of being preferred exremal.
You asked earlier "Can one say “space-time tells the dynamics of the Kahler field and the Kahler
field tells space-time how to curve?"
I did not get your point completely. The Kahler field indeed replaces matter understood
Classical fields. So that in this sense you are correct. What is new that both Kahler field as a
"matter field" and metric are dictated by the surface property in terms of imbedding space
coordinates and gradients. This means a reduction to a deeper level completely analogous to that in
string models.
However, do not forget that also induced spinor fields are present. The consistency of their
couplings to the purely geometric degrees-of-freedom requires that one must use in Dirac action
modified gamma matrices which satisfy the condition D_alpha Gamma^alpha=0 which implies field
equations for Kahler action. This also implies supersymmetry. There exists an infinite number of
conserved fermionic charges.
For induced spinor fields for which conservation of electric charge implies restriction to 2-D
string worldsheets (right-handed neutrino is an obvious exception) so that a very close connection
with string theory in 4-D space-time emerges.
http://matpitka.blogspot.com/2012/12/scattering-amplitudes-and-positive.html#comments
topic: Scattering Amplitudes and the Positive Grassmannian
1. At 8:44 AM, Santeri Satama said...
To continue attempts to understand TGD, first a quote from Ekeland's 'Best of All Possible
Worlds' with interesting parallels to Matti's vision. Sorry it's in Finnish as I don't have English copy
available:
………………………………………………………
………………………………………………………
………………………………………………………
Ekeland continues by discussing multioscillators (cf. pendulums) and finding periodic solutions
to Lagrange-Euler equations in convex hypersurfaces of 2 degrees-of-freedom and states resent
126
proofs showing that they can can have only either 2 or infinity of periodic solutions of closed
circuits.
So both approaches end up with book metaphor whereas Matti's approach goes much further and
combines the space-time sheets into global book where they can communicate at the level of p-adic
areas.
In the article discussed in above: "While a global picture is still missing, a huge amount of data
has been generated..."
Here's my current attempt for a global vision. Matti has said that all p-adic areas get in some
sense the value of one. This to me sounds highly untrivial, though I'd like to comprehend better how
exactly. Maybe and hopefully Matti can explain.
Any case, I vision that p-adic unity as the Center or Source of a ball-like "phase space", first
surrounded by p-adic regions or layers and then the "hypersurface" consisting of rational areas
shared by p-adics and reals which binds together the space-time sheets of how Matti visions the book
or books. This hypersurface divides the "phase space" of p-adics and reals (etc.?) into inner and
outer regions, inner areas (at first glance!?) converging in p-adically infinite "singularity" and outer
areas scattering as infinite extensions of reals. This view could also help to explain the interest in
non-provable "imaginary" black hole -singularity objects presumably "out there" as an attempt and
act of gnothi seauton.
So when you generalize from a simple harmonic oscillator to multi-oscillators, you still get only
2 countable results -- either duality or infinity. Which I suppose also presupposes and requires
infinite primes which can among other things describe various layers of the hypersurface I
previously visioned?
Another question about causal diamonds: Aren't they multi-oscillators that Ekeland discusses?
Also I expect that both points of the arrows must touch infinity. What is the relation of real and padic infinities here, if any?
2. At 5:02 AM, Matti Pitkanen said...
To Santeri Satama:
Thank you for a nice summary of Ekeland's vision. Ekeland describes basic notion of
mechanics: energy constant surface of phase space at which particle orbit in phase space resides by
energy conservation. This notion is central in Thermodynamics.
Causal diamonds are not dynamical systems such as multi-oscillators. They are not energy
constant surfaces in phase space. They contain the dynamical systems defined by space-time
surfaces. At the quantum level, zero energy states have wave function in the moduli space of CDs
(CD has position, it can be Lorentz boosted and rotated and translated). CD's size scale is assumed
be quantized for number theoretic reasons and come as integer multiple of CP2 size.
What matters in Zero Energy Ontology is that causal diamonds have 2 light-like boundaries at
which positive and negative energy parts of zero energy states are localized. The "upper" and
"lower" ends of space-time surfaces (restaurants at the ends of the Universe are possible in the TGD
Universe!;-)) at the 2 light-like boundaries of CD. The analogs of initial and final state of a physical
127
event. CDs contain the space-time surfaces in the superposition of preferred extremals (analogs of
Bohr orbits) defining zero energy state.
The interpretation of CD suggested by the TGD-inspired theory of consciousness is as an
imbedding space correlate for self, kind of spotlight of attention.
Light-likeness of the boundaries of CD implies a generalization of conformal symmetry at the
boundaries. It is essential that one has 4-D Minkowski space x CP2. These conformal symmetries
form only half of the conformal symmetries of TGD. Also light-like 3-surfaces defining parton
orbits possess generalized conformal symmetries. The 4-dimensionality of both M4 and space-time
surface are crucial [I would be happy if this would finally induce a "click" in the learned heads of
colleagues ;-) although I know from bitter experience that although I can bring a horse to the
fountain, I cannot force it to drink;-)].
Number theoretic vision inspires a speculative picture about a connection between the hierarchy
of infinite primes and hierarchical structure of space-time sheets of many-sheeted space-time. Why I
take this vision seriously is that the hierarchy of infinite primes is a number theoretical correlate for
a hierarchy of second quantizations whereas the many-sheeted hierarchy is classical space-time
correlate for it.
You mention frequencies. In the hierarchy of infinite primes, frequencies labeling fermionic and
bosonic oscillator operators are replaced by logarithms of primes. I remember that also in chaos
theory, frequencies comings as logarithms of primes appear. I do not however not the deeper
mathematical reason.
3. At 6:34 PM, Santeri Satama said...
Thanks for your response. Fully accepting my limitations in capacity of mathematical
imagination, one can only hope that my simple reflections have some meaningful relation to your
vision. And keep on questioning.
The CD as "spotlight of attention" sounds like a promising approach. Not necessarily limited to
such movements. But the "pendulum" or "oscillator" of attention shifting between introspection and
extrospection seems common experience. Common enough to raise the question if the introspective
areas are characterized by p-adic areas and extrospective by real areas, can that be applied to CDs?
e.g. describing the lower or "introspective" part or "light-like boundary" of CD p-adically and upper
"extrospective" part by reals? Assuming those areas can be mapped on each in dynamic fashion. Or
are the theory dependent and/or mathematical reasons denying such possiblity?
Or if the question above does not get even close, what is the TGD-inspired vision of
introspective and extrospective movements of attention? And in that vision, does mathematical
contemplation and imagination belong to either category?
PS: You mentioned somewhere seeing "spots" a long time after your Great Experience. Though
you are not supporter of multiverse theories at least in the Standard Model form, I have a hunch that
those might represent other universes, perhaps characterized by other transcendentals than those
revealed to us. But dunno. Maybe this hunch can be relevant to your question about WCW, maybe
not. Just thought maybe this would be worth mentioning.
4. At 10:21 PM, Matti Pitkanen said...
128
I would tend to assign introspection and extrospective areas to conscious information about the
space-time sheets of observer on one hand and on space-time sheets of external world.
The recent vision discussed in the posting about blackholes and blackhole evaporation is that the
spacetime sheet defining "me" as something separate from the external world defines the line of
generalized Feynman diagram (rather thick as compared with line of ordinary Feynman diagram!)
and therefore has Eucdlian(!) signature of the induced metric with time and space in the same
position. External world would correspond to Minkowskian signature.
This is just one possible proposal. Real space-time sheets correspond naturally to sensory
experience and p-adic space-time sheets to cognition. You are thus saying that introspectionextrospection difference corresponds to sensory-cognitive dichotomy. I would argue that I have
sensory experience from both external world and internal world so that I would disagree.
Mathematical imagination would naturally correspond to p-adic sector. The non-determinsm of
p-adic differential equations suggests an interpretation in terms of the non-determinism of
imagination.
p-Adic number fields have infinite number of algebraic extensions analogous to complex
numbers and thus having arbitrarily large algebraic dimensions. Could it be that our ability to
imagine higher dimensions corresponds to a geometric realization of these dimensions p-adically?
Evolution would correspond to a gradual increase of the algebraic dimension.
We cannot imagine what it is to be sensorily higher-dimensional (at least I cannot;-)) and this
could relate to the absence of higher algebraic extensions of reals.
You certainly noticed that I tried to cheat here!;-) Complex numbers definea 2-D algebraic
extension of reals so that one might argue that we are able to see 8-D dreams in 4-D space-time!
My defense is the following. The preferred extremals of Kaehler action define a generalization
of 2-D complex structure to 4-D case in both Minkowskian and Eucdliian space-time regions. One
can say that physical space-time is 2-D in "complex" sense just as complex plane is 1-D in complex
sense. As also strong form of holography (saying the quantum states depend on partonic 2-surfaces
and their tangent space data only) states.
Maybe you mean with "spots" the flow that I perceived by closing my eyes in peaceful state of
mind (say after having worked for few hours). The flow is to and from a kind of tunnel leading
somewhere. I have considered the possibility that this flow is along magnetic flux tube connecting
me somewhere.
Neuroscientists could certainly represent a trivializing and pathologizing explanation for this
flow and colleagues would list this experience as an additional strong support for the conjecture that
I am completely "mad" as they have thought from the beginning!;-)
5. At 8:22 AM, Santeri Satama said...
You bring up sensory experience. It's an area where we run into problems of definition. What
and how is sensing and what experiences do we classify as sensual experiences? For example,
Buddhist
philosophy
consider
thinking
just
another
sense.
Wiki
article
129
(http://en.wikipedia.org/wiki/Sense ) gives a list of many "internal" senses in addition to the 5
classical "external" senses and also what it considers non-human senses.
I've also sometimes wondered in connection to attention concentrating on "internal" body sense
(not implying that it ends at skin level but can be also sensual experience of the whole "magnetic
body"), how many dimensions such "internal" sensual experiences contain and is such a question
even meaningful?
Assuming based on phenomena of synaisthesia etc. that various senses are filters of holistic flow
of information rather than purely classical mechanisms of data-receiving and neurological
reproduction and representation, is for example the experience of orthogonality (that we sense most
directly with our sense of balance (and gravity towards Earth's gravity center) necessary for
experience of dimensionality?
I cannot really imagine a ball containing more than 3 orthogonal axes. But I can imagine (and
internally feel!) a ball consisting of infinity of directions emanating from the center and give that
infinity of directions at least symbolic interpretation of n-dimensionality.
6. At 2:51 AM, Matti Pitkanen said...
To Santeri Satama:
Thank you for interesting questions and Happy New Year.
[SS] You bring up sensory experience. It's an area where we run into problems of definition. What
and how is sensing and what experiences do we classify as sensual experiences? For example,
Buddhist philosophy consider thinking just another sense.
Wiki article
(http://en.wikipedia.org/wiki/Sense ) gives a list of many "internal" senses in addition to the 5
classical "external" senses and also what it considers non-human senses.
[MP] Certainly the definition of sensory experience requires some assumptions. It is very difficult to
separate pure sensory qualia from the cognitive representations constructed from them. The
sensory input must be decomposed to objects and this requires a lot of processing. Essentially
standardized mental images are generated using a virtual sensory input to sensory organs which
would be seats of primary sensory qualia (the "phantom limb" is one basic objection which can
be circumvented in the TGD Universe).
Concerning qualia, my basic assumptions are roughly
http://tgdtheory.com/public_html/hologram/hologram.html#qualia .
the
following.
See
(a) Sensory qualia are the building bricks of sensory experience. Since a moment of
consciousness corresponds to quantum jump and quantum states are labeled by quantum
numbers, sensory qualia are characterized by increments of quantum numbers. Different
kind of quantum numbers would correspond to different kinds of basic qualia. For
instance, colors would correspond to increments of color quantum numbers of quarks and
gluons so that the term "QCD color" would not be a mere algebraic joke. This of course
makes sense only if one accepts the almost-prediction of TGD about hierarchy of QCD-like
theories in various scales (in particular in the scales of a Living cell). If the people at the
LHC discover M89 hadron physics, we are rather close to asking whether this radically new
vision really makes sense.
130
(b) Sensory experience contains also purely geometric information. Vision, touch, and hearing
do so. This information corresponds to 4-D geometry so that also dynamical information
becomes geometric with this definition. I have talked about geometric qualia (angles,
distances,...). What is interesting is that topologist Barbara Shipman found that honeybee
dance has a mathematical description in terms of a flag manifolds associated with QCD
color. Different choices of quantization axes (2 kinds of them corresponding to the Cartan
algebra of SU(2): color isospin and color hypercharge) for color form a flag manifold
SU(3)/U(1)xU(1) and this space is involved with her model.
[SS] I've also sometimes wondered, in connection to attention concentrating on "internal" body sense
(not implying that it ends at skin level but can be also sensual experience of the whole
"magnetic body"), how many dimensions such "internal" sensual experiences contain and is
such a question even meaningful?
[MP] A model for OBEs and various sensory illusions leads to the view that various sensations could
relate to the movement or imagined movement (say the nasty feeling in stomach when one
imagines falling down to nearby cliff or moving train illusion) involve relative motion of
physical body and magnetic body whose conformation provides a representation for it and
maybe also for the environment. Motion of magnetic body alone gives rise to imagined
sensory experience and motion of biological body alone to purely real sensory experience.
OBEs would relate to the relative motion of magnetic body. The perceptions would result
from the change of the hologram defined by the radiation exchanged between magnetic body
and biological body.
[SS] Assuming, based on phenomena of synaesthesia etc. that various senses are filters of holistic
flow of information rather than purely classical mechanisms of data-receiving and neurological
reproduction and representation, is for example the experience of orthogonality (that we sense
most directly with our sense of balance (and gravity towards Earth's gravity center) necessary
for experience of dimensionality?
I cannot really imagine a ball containing more than three orthogonal axis. But I can
imagine (and internally feel!) a ball consisting of infinity of directions emanating from the
center and give that infinity of directions at least symbolic interpretation of n-dimensionality.
[MP] Angle π/2 is special. Hilbert space is one basic example. More I am unable to say.
I have a strong temptation to interpret imagined higher-dimensional structures as p-adic
constructs. As I probably already mentioned, p-adics allow an infinite number of algebraic
extensions and also non-algebraic extensions which are infinite-D. These are higher-D
structures in the same sense as complex numbers are a 2-D structure. That we experience the
world as 3-D and are not able to sensorily imagine higher dimensions could be simply due to
the fact that we ourselves are 3-dimensional in real sense! Our cognitive me's can have an
arbitrarily high dimension. We are what we perceive;-). Buddhists would be correct when
they interpret also cognition as sensory perception if cognitive perception is p-adic sensory
perception.
http://matpitka.blogspot.com/2012/12/could-n4-susy-have-something-to-do-with.html#comments
topic: Could N=2 or N=4 SUSY have something to do with TGD?
1. At 9:50 AM, Hamed said...
131
Dear Matti,
I am logged on yet superposions of the effects in TGD;-).
About my last question, I asked from you: ” If we have some distribution of matters on the
space-time, in GR one can calculate energy momentum tensor from the distribution of matters and
Einstein equation gives us metric of space-time. How do you the same thing in TGD?”
You answered me: “In the case of the gravitation the effective deviation of metric experienced
by particle would be estimated as follows. Use common (say linear) M4 coordinates for the spacetime sheets. One sums up the deviations of the corresponding induced metrics from flat M4 metric at
various space-time sheet. This defines the effective metric giving rise to the gravitational
acceleration experienced by the test particle idealized to point particle. Particle experiences sum of
gravitational accelerations just as in standard description. Similar prescription applies to classical
gauge forces.”
For doing the superpositions of the effects, one must have induced metrics of various space-time
sheets. Hence one must write independently for every space-time sheets a field equation to get
induced metric? (Multiplying energy momentum tensor by second fundamental form and equal the
result to zero)
When you say in GRT there are superpositions of gravitational fields themselves, I don’t
understand it clearly. In GRT we only sum up the energy momentum tensor for dust and
electromagnetism. After it, one can derive Einstein tensor from Einstein equation and from it,
equations of motion are deduced. Where is the “superposition of gravitational fields themselves”?
For deriving induced metric, because it is deduced from second fundamental form (?as I think!),
one must have energy momentum tensor. In GRT, the energy momentum tensor is sum of the stress
energy tensors for the dust (all of the Macroscopic objects are in the form of dust) and
electromagnetism. But in TGD, it is energy momentum tensor of Kahler field. There is a
contribution of energy momentum tensor of electromagnetism in U(1) part of Kahler field.
As I understand, it is not needed to take account contribution of dust because dusts are in form of
space-time sheets and only effects of the space time sheets are contributes as sum of deviations of
metric fields from M4 for every space-time sheets. Hence when an object is on a larger space-time
sheet, its gravity doesn’t contribute to curvature of the larger space time sheet? Because it doesn’t
contribute in energy momentum tensor of Kahler field of it.
Now I think that I don’t regard anything from boundary conditions of every space-time sheets. If
it is important in your answers, please make it clear.
2. At 1:52 AM, Matti Pitkanen said...
Dear Hamed,
Thank you for good questions again. And Happy New Year!
[Hamed] "Multiplying energy momentum tensor by second fundamental form and equal the result
to zero"
[MP] This is indeed true for preferred extremals for which Einstein-Maxwell equations with
cosmological term guarantee the vanishing of second term proportional to contraction of
132
Kahler current in Kahler field. Physically this means that 4-D Lorentz force vanishes
(equilibrium condition) so that Kahler energy momentum tensor has vanishing divergence just
like Einstein tensor and metric. Cosmological constant Lambda and Newton's constant are
predictions.
Every space-time sheet satisfied the field equations independently in regions far from wormhole
contacts. Near wormhole contacts and in their Euclidian interior, situation of course changes.
[Hamed] For deriving induced metric, because it is deduced from second fundamental form (? as I
think!)
[MP] No! You ask about the relationship between induced metric and second fundamental form.
(a) Induced metric is deduced just as a projection: you have metric tensor hkl of the imbedding
space. You have coordinate gradients partial_alpha hk defining tangent vectors for the
space-time sheet. The induced metric is the projection of hkl to space-time surface:
g_{alphabeta}= h_{kl} partial_alpha hk partial_beta hl. Same recipe applies to components
of spinor connection and gauge fields.
(b) Second fundamental form is formed by the covariant derivatives of tangent vectors and is
orthogonal to space-time surface as H-vector. H^k_{alphabeta}= D_beta h^k_alpha. It
contains second derivatives of imbedding space coordinates. Minimal surface equations
g^{alphabeta} H^k_{alphabeta}=0 are geometric counterpart for a massless wave equation
and are also satisfied by preferred extremals. That 3 kinds of different field equations are
true simultaneously is due to the generalization of complex structure to Hamilton-Jacobi
structure in Minkowskian regions and to 4-D complex structure in Euclidian regions. It is
this structure which codes the entire dynamics.
A still open question is whether it implies or/and is implied by the quaternionicity
(associativity) of tangent spaces with integrable distribution of M2:s (hypercomplex plane)
in tangent spaces. For preferred extremals, the local distribution of M2:s code for a
distribution of local planes of light-like momentum and of polarization directions so that
physically the equivalence is highly suggestive.
[Hamed] Where is the superposition of gravitational fields themselves??
[MP] In GRT as in all interacting theories, the superposition of fields is an approximation. In the
case of gravitation, the extreme weakness of interaction makes this approximation excellent
and one can develop a classical perturbation theory and attempt to quantize GRT are based on
this expansion. In low energy QCD, the situation is different.
In TGD, linear superposition is replaced with a set theoretic union of space-time sheets and
the formation of wormhole contacts between test particle space-time sheet and the space-time
sheets in the union gives to a superposition of various effects (gravitational,
electromagnetic,...).
[Hamed] Hence when an object is on a larger space-time sheet, its gravity doesn't contribute to
curvature of the larger space time sheet? Because it doesn't contribute in energy momentum
tensor of Kahler field of it.
133
[MP] This is true only in the first approximation. In GRT applied in Macroscales, the energy
momentum tensor (I will call it just T) is what you say. In the QFT approach to GRT, T is
deduced as energy momentum tensor of the matter part of the action which is ad hoc. Noether
theorem would give vanishing energy momentum currents associated with Noether currents
reflecting the fact that general coordinate invariance is gauge symmetry. One could perhaps
cautiously say that in TGD, Kahler action codes for the matter Classically (note however that
induced spinors are present also and that one does not have Einstein-Maxwell action!).
Condensing space-time sheet deforms the larger space-time sheet and vice versa!!
Wormhole contacts are formed and larger space-time sheet it is deformed near the wormhole
throats. Is a small gravitational deformation created also in faraway regions? Or is gravitational
interaction mediated by MEs connecting the masses condensed at space-time sheet? String
world sheets having their boundaries at the light-like wormhole contacts associated with the 2
subsystems would be a natural candidate for a microscopic description very much analogous to
that provided by AdS5 correspondence. Are both views correct and correspond to descriptions in
different scales?
The two space-time sheets can form also form a bound states. Magnetic charges are needed
to make wormhole contacts stable. These occur in pairs and have interpretation as elementary
particles. Closed magnetic flux tube defines a string like object indeed containing closed string
world sheet carrying spinors (right-handed neutinos form an exception). When bound states are
formed in this manner, simple cylindrical MEs with constant light-like momentum and fixed
polarization representing free propagation are deformed so that a bound state of them results.
The motion assignable to MEs is not linear anymore and momentum exchange takes place so
that only the total momentum which is time-like is conserved. The massless momenta of MEs
sum up to the massive momentum of particle. The Minkowskian preferred extremals (apart for
cosmic string-like objects) are generalizations of MEs. There are also string like objects with 2D M4 and CP2 projections. This leads to a concrete picture about how twistorial description (for
which masslessness is absolutely essential) and possibly the analog of N=2 or N=4 SYM as part
of TGD emerges in TGD framework.
The interaction of particle on background geometry corresponds to the direct action on
space-time sheet and in the vicinity of wormhole contact and in its interior of course there is a
new contribution also to the curvature of the large space-time sheet. A simple idealized model
for the condensation of massive space-time sheet to canonically imbedded M4 (CP2 coordinates
are constant) deforming it to an imbedding of Schwartschild or Reissner-Nordstoem metric as
extremal.
I
have
studied
these
imbeddings
in
http://tgdtheory.com/public_html/tgdclass/tgdclass.html#tgdgrt . The ansatz is same as for the
imbedding
of
AdS4
metric
blog
in
the
recent
blog
posting
at
http://matpitka.blogspot.fi/2012/12/is-there-connection-between-preferred.html .
3. At 4:32 AM, Hamed said...
Dear Matti,
[Matti] "Induced metric is deduced just as a projection”
Yes, induced metric is deduced just as a projection but this is in theory. My question was in
practical sense when we have some distribution of matters in some region and we want to deduce the
value of components of the metric of the larger space-time sheet containing these matters.
134
For example in GRT about Schwarzschild solution, we are concerned with a solution of the
vacuum field equations. Therefore we request T_munu=0 and from G_munu=0 we can deduce the
value of components of metric tensor.
Another my practical question is how one can deduce the value of components of energy
momentum tensor of Kahler field from distribution of matters?
4. At 9:28 PM, Matti Pitkanen said...
To Hamed:
Thanks for good questions. Here is the first one.
[Hamed] My question was in practical sense when we have some distribution of matters in some
region and we want to deduce the value of components of the metric of the larger space-time
sheet containing these matters.
[MP] This question involves hidden assumptions. In GRT, the perturbations would indeed add as
deformations of metric in single space-time. Now the perturbations are associated with
different space-time sheets; sum is replaced with union of space-time sheets; and only their
effects on test particle add.
I summarize what I believe I know.
(a) Preferred extremals (PEs) are known in general form. The challenge is to find a description
for their interaction with a test particle (small space-time sheet) which is expected to be via
touching. I will return to this.
(b) In Minkowskian regions, PEs can be seen as radiation with local light-like wave vector and
transversal local polarization. Massless extremals (MEs) for which massless momentum
vector and polarization are in constant direction are simplest example. From more complex
ones, one can build elementary particles as bound states by putting between them
wormhole contact pairs with magnetic charges. Thus one can say that elementary particles
and thus all systems are accompanied by preferred extremals representing radiation to
which test particle responds. Basically all interactions are via radiation as already in
Classical ED (this also makes the twistor approach possible).
(c) Only the effects of external sources on test particle add. One must describe the situation
using only the preferred extremals associated with the matter - ultimately elementary
particles. This microscopic picture is basically that provided by generalized Feynman
diagrams.
You can imagine of having a tests particle, a small space-time sheet, and space-time
sheets assignable to the various systems generating gravitational fields at their own sheets(or
more generally at space-time sheets assignable to them). The "space-time sheets assignable
to them" would correspond to radiation fields represented by preferred extremals having
same general structure than massless extremals (MEs).
To calculate the
acceleration/associated 4-force, one would add the effects of various space-time sheets
(basically MEs) and get effective metric for which deformations from various space-time
sheets would add.
135
(d) This kind of effective metric very rarely allows imbedding in M4xCP2. The space-time with
this effective metric (General Relativity) becomes an effective theory to describe the
situation. The Universe of GRT is therefore only a fiction (albeit very practical fiction) in
Astrophysics.
Only in some idealized cases such as Sun describable as a static point-like mass and planets
describable as test masses GRT description using Schwarthild or Reissner-Nordstrom metric,
the metric is imbeddable. When one must take into account the response of planets, this
description fails in TGD framework. Although GRT is a convenient fiction, a huge amount of
information and predictivity is lost since the constraints due to imbeddability condition and
preferred extremal property are forgotten. There is no hope about microscopic quantal
description if one starts from this picture directly. And as we know, the quantization of GRT
indeed fails also technically. This is like trying to describe atoms using classical
hydrodynamics.
[Hamed] Another my practical question is how one can deduce the value of components of energy
momentum tensor of Kahler field from distribution of matters?
[MP] This question also involves the hidden assumption that single space-time sheet is enough. This
is not true in TGD framework where one can speak only about superposition of effects and
forces from material objects.
If one introduces the effective metric in which deformations of metric add up, then one is
using General Relativity as an effective and fictional description which could be quite
practical. Einstein-Maxwell system with cosmological term would be a good guess for the
action. Reissner-Nordstroem solution and Scrwartschild solution would be basic building
bricks.
Although induced Kahler field is fundamental at the level of TGD, in GRT approximation
it is the four-momentum assigned to effectively point like sources which matters in
astrophysics and is described phenomenologically without any attempt to do it
microscopically.
The attempt to describe matter microscopically in terms of Kahler field would lead to TGD
and generalized Feynman diagrammatics.
(a) This attempt would lead to the discovery of Euclidian space-time regions. CP2-type
extremals carrying very strong Kahler fields and behaving like instantons.
(b) Also the discovery that elementary particles correspond to closed wormhole flux tubes
represent would emerge sooner or later.
(c) The realization that the interiors of black holes are actually Euclidian space-time
regions assignable to any objects in the scale of object would emerge in the process.
(d) Sooner or later would come the discovery of "cosmic strings" and the realization that
dark energy is identifiable as Kahler magnetic energy of magnetic flux tubes of
cosmological-size scale.
136
A general vision about galaxies as string-like objects and about their organization along cosmic
strings would develop. One would eliminate galactic dark matter and replace it with long-range
gravitational fields created by the dark energy associated with these strings.
A further positive surprise would be explanation for the magnetic fields filling the cosmos but
having no explanation in terms of Standard cosmology. But all this will take one century if
colleagues continue their discoveries with their recent pace...;-)
Just a couple of random remarks about topological sum (touching) of space-time sheets) and the
detailed description for the interaction of test particle and preferred extremals representing radiation.
(1) One could argue that touching is the mechanism of interaction. Touching certainly creates
region of Euclidian signature and thus something which could correspond to a line of
generalized Feynman diagram. Is this something which much be added to the general
Feynman diagrammatics? Note also that string world sheets can touch each other. And
what about string world sheets carrying the fermion fields (all except right handed
neutrino) which are present in TGD?
(2) The touching occurs at single point for two 4-D space-time surfaces in 8-D imbedding space
occurs unavoidably at discrete points. When you have two 2 slightly deformed pieces of
Minkowski space which are "parallel" and within distance about CP2-size scale, one
expects touchings to occur with very high probability. This is like 2 threads in extremely
narrow tube. They will touch with very high probability.
(3) The description for the formation of wormhole contacts must be statistical. Quantal
description by generalized Feynman diagrams could be the only reasonable description.
From this,one would deduce QFT limit and finally get to the practical level. Since
Einstein-Maxwell equations hold true classically, one expects that Einstein-Hilbert action
with a small cosmological term is a reasonable approximation for the effective action at
QFT limit.
5. At 2:17 PM, ThePeSla said...
Matti,
If you have time, I would like your take on the articles of this week on the idea of negative
temperature below (but hotter than at minus infinity) from the TGD perspective. I also continue to
mention you in my blog in relation to recent generalizations of systems theory.
http://www.sciencedaily.com/releases/2013/01/130104143516.htm
If you follow, from a philosophic view at least, how I use groups as you seem to do here and
from a wider than the limited standard viewpoint, how close is it to what is actually such views as
physics?
6. At 8:41 PM, Matti Pitkanen said...
In thermodynamical equilibrium for a closed system, entropy is maximized subject to the
constraint that average energy per particle is fixed. The probabilities for single particle energies E
are proportional to exp(-E/kT). Temperature T must be positive in order that probabilities stay finite
as E becomes infinite. E is the sum of kinetic energy and interaction energy which can be also
negative. Usually the kinetic energy grows without limit.
137
Negative temperatures are possible when the energy spectrum changes from the usual spectrum
extending to plus infinity to a spectrum which extends to (- infinity) or to very high energies. This
requires the presence of strong negative interaction energy between particles (attractive force) and
some kind of cutoff on kinetic energies. Cutoff can be effectively realized by starting from a
situation in which one has very low but positive temperature.
In the experimental situation, an attractive interaction is generated between particles. This
corresponds to negative interaction energy. Thermal equilibrium exists only below some time scale
and researchers compare the situation to a pyramid which stands on its top. The negative interaction
energy stabilizes the situation.
(A) Researchers mention also antigravity. Effective antigravity is possible if negative gravitational
interaction energy overcomes the kinetic energies and there is cutoff for kinetic energies.
For a gas in a box at the surface of Earth, the smallest magnitude for E corresponds to
largest height so that particles tend to be near the top of the box for negative temperatures. This
would be the effective antigravity.
Could this have something to do with the Podkletnov effect? Superconductors at low
temperature are present. Could the temperature of Cooper pairs become negative in the
gravitational field of Earth? And could "antigravity" inside rotating superconductor cause the
Cooper pairs to leak to the air above the superconductor and induce the claimed flow of air
upwards? Just asking;-).
(B) Question: could the ability of superfluid flow to apparently resist gravitational force is due to
negative temperature?
This situation is realized only if one can pose an effective cutoff on kinetic energies. This
requires very low starting temperatures.
(C) Electron holes in condensed matter systems have in natural manner negative energy and one can
imagine that they are in thermal equilibrium with negative temperature.
(D) In Zero Energy Ontology, the ends of CD can be said to correspond to opposite signs of energy
and therefore also of temperature in thermal equilibrium. Phase conjugate laser rays would be
a standard example of negative sign of energy and they obey the Second Law in reverse time
direction. One can assign to them negative temperature naturally.
7. At 11:42 PM, Ulla said...
And the dark energy perspective? Zero temp is analog to cosmological constant?
8. At 8:39 PM, Matti Pitkanen said...
To Ulla:
This dark energy speculation is hype. Also the claim that negative temperatures are something
totally new is not true. It was mentioned already in my book of statistical physics which I studied
1970+ few years.
138
9. At 9:35 AM, Stephen said...
Matti, can you discuss a TGD based explanation for http://phys.org/news/2013-01-non-causalquantum-eraser.html#jCp ? This is cool!
In the new experiment, this second photon is so far separated from the first photon that no
transfer of information whatsoever (the velocity of which can never exceed the speed-of-light)
would be fast enough. Yet the first photon behaves like a wave or like a particle, still depending on
the measurement performed on the second.
While the results of such experiments are fully consistent with quantum physics, a clear
explanation in terms of causality is impossible as according to Einstein's relativity theory, any
transfer of information is limited to the speed-of-light.
10. At 8:39 PM, Matti Pitkanen said...
To Stephen:
The result is consistent with Quantum Theory. Quantum entanglement implies correlations
which are non-causal and there is no need to send signals.
Quantum-Cassical correspondence, however, requires that also this phenomenon has classical
space-time correlate. Standard physics with point-like particles does not allow this.
Generalization of particle to space-time sheet leads to the view that the entanglement of distant
particles has flux tubes/massless extremals/... connecting the 2 systems as space-time correlates so
that they effectively form a single particle.
The replacement of point like particle with 3-surface which can have arbitrarily large size that
any system has elementary particle-like aspects at large space-time sheets resolves many of the
mysteries of Quantum Theory basically due to the lack of Quantum-Classical correspondence. How
simple and elegant and how hopelessly difficult to communicate!
11. At 3:54 AM, Hamed said...
Dear Matti,
First I have a humble request. When you answer the questions, please answer at this level. The
concepts of Quantum-TGD or recently views of field equations in TGD makes me confuse and
makes my process slow. Although for you, different concepts of TGD aren’t separable. But in the
process of teaching TGD, you can for simplification at each step concentrate on some concepts and
assign other concepts to next steps. So let’s go in logical way step-by-step without intermixing steps
together :-).
I think learning TGD (in principle not practical!) is simpler than M-theory or TQFT or any
physical theories with advanced mathematics because intuitions in TGD makes learning TGD simple
so that advanced mathematics in TGD are very intuitional. But this is only possible practically if the
process of teaching be logically step-by-step!
At TGDHistory.pdf:
139
“At this period I did not have yet the alternative view idea TGD as a generalization
of string model. I wanted Einstein's equations and conservation laws! Curvature
scalar was therefore the obvious first guess for the action density.”
At this period, did you know about space-time sheets? If yes, first lets we don’t know about it!!
It makes easier for me to understand it. Although description of gravity without space-time sheets is
not possible, but let to me to start without space-time sheets. And when I understand basic views
correctly, you can show me that without space-time sheets these views lead to contradiction.
Therefore I explain a review of what I know and ask my questions:
There is a global space-time in M4xS2. The metric of the space-time is induced from M4xS2.
Curvature scalar was the first guess for the action density in TGD (although it is a wrong action).
This is like derivation of Einstein equation from the Einstein–Hilbert action in General Relativity.
Only seeming difference is the metric is induced from imbedding space.
This leads to the field equation as G time to H equal zero. Energy momentum tensor of the
action is a constant multiple of Einstein tensor.
What is the physical meaning of this energy momentum tensor of the action? Is it gravitational
energy?
In this framework that is without space-time sheets as like GRT, physical fields make the global
space-time curve? Therefore the correct formula for field equation is G time to H equal to sum of
energy momentum tensors of these physical fields like in GRT?
12. At 5:36 AM, Matti Pitkanen said...
I learned about space-time sheets, massless extremals, and string-like objects and cosmic strings
as call the, during the first years by finding solutions of field equations which are highly symmetries.
For instance, space-time sheets emerge when one tries to imbed constant magnetic field as surface.
Imbedding exists only in finite volume and the question is what happens at resulting boundaries.
Are they real boundaries or causal boundarires at which the signature of metric changes?
General Relativity based on single space-time sheet is utterly unphysical. Typical solution of
Einstein's equations requires rather high-dimensional imbedding space.
Second very essential difference is that the geometry of surface dictates gravitational dynamics
and U(1) gauge dynamics as submanifold dynamics. This is a very essential element and
manysheeted space saves the situation concerning the failure of linear superposition even
approximately.
[Hamed] What is physical meaning of this energy momentum tensor of the action? Is it gravitational
energy?
[MP] It is essentially energy momentum tensor of matter which for preferred extremals coincides
with what you obtain from Einstein-Maxwell. To answer this detail I need to have a model for
particle in the Minkowskian and Eucdian region. By quantum classical correspondence I
*assume* that the sum of lightlike moment associated with Minkowskian preferred extremals
(in first approximation MEs) is the momentum of particle which is identified as wormhole
140
contacts structure between them, All momenta are light-like at the level single space-time
sheet.
[Hamed] In this framework that is without space-time sheets as like GRT, physical fields make the
global space-time curve? Therefore the correct formula for field equation is G time to H equal
to sum of energy momentum tensors of these physical fields like in GRT?
[MP] One cannot obtain Einstein-Maxwell system in any natural manner without long and tedious
path to the recent situation. Hilbert's approach is certainly purely ad hoc since Noether
theorem gives identically vanishing conserved charges infinitesimal general coordinate
transformation.
I am not sure would you mean with G time to H. Curvature scalar as action give
Tr(GH^k)=0. This is equivalent with conservation of isometry currents so that his part of
dream would be achieved.
Most of the text in the chapter http://tgdtheory.com/public_html/tgdclass/tgdclass.html#class
is about single space-time sheet. The challenge would be to understand how wormhole contatcs
and massless preferred extremals are combine to more complex structures. Here only physical
intuition can help at recent stage.
A little comment about Einstein's equations.
● One thing is sure. They do not follow from a variational principle in TGD. In TGD
framework, the only possible conclusion is that attempts to quantize General Relativity by
starting from curvature scalar as action have been a wrong track.
● One natural guess would be that Einstein's equations are predicted only at the long length scale
limit of the theory. This is the view provided also by string theory. This was my belief for
a long time. But it seems that this was wrong.
● That Einstein-Maxwell with cosmological constant equations follow from the condition that
the Maxwellian energy momentum tensor has vanishing divergence (which in turn is
necessary to satisfy the field equations for preferred extremals) was a total surprise (this
condition is also the manner to end up with Einstein's equation without mentioning Hilbert
action). Notice however that G and Lambda are now predictions of the theory rather than
input parameters and one can consider the possiblity that they have a spectrum. Lambda
certainly has: Lambda should decrease with cosmic time roughly as 1/a2 from the estimate
following from p-adic length scale hypothesis.
13. At 9:58 PM, Hamed said...
Dear Matti,
So thanks. I gradually taste the beauty of gravity in this sense of TGD :-).
Question about extremals of Kahler action:
Solutions of field equations are extremals of Kahler action. One can classify them as dimension
of CP2 projection in one way (in respect to phases of matter) and in other way are classified as
vacuum extremals and non-vacuum extremals.
141
Vacuum extremals are in 2 basic types: CP2-type vacuum extremals for which the induced
Kahler field and Kahler action are non-vanishing and the extremals for which the induced Kahler
field vanishes.
Non-vacuum extremals are in 3 basic type string-like objects, ME and Maxwell’s phase. Now
ordinary Macroscopic objects are in which of them?
One can say that these solutions aren’t Classical and we need some preferred ones. These
preferred extremals can be obtained from Quantum-TGD. In other words, Quantum-TGD can say
what are Classical extremals!
14. At 12:11 AM, Matti Pitkanen said...
Dear Hamed,
It was good that you listed the basic type of extremals as I have given them in the chapter I gave
link to. I found that my views have become obsolete about Maxwell phase.
I try so summarize the situation as it as between 1980-1990 when worked with extremals of
Kahler action.
(A) The idea about Maxwell phase relates to MEs and the fact that they allow extremely
restricted linear superposition. That is only for modes moving in the same direction and all
wave-vectors in 4-D sense must be parallel or antiparallel. ME is like a wave tube inside
which excitations with arbitrary transversal dependence move to single direction with lightvelocity without change in the shape of pulse. This like having left- (or right-) movers but
not both. MEs are very much like space-time correlates for field quanta which conforms
with Bohr orbitology.
(B) Guided by simple common sense I however hoped linear superposition in a more general
sense (albeit only approximately). I called this desired phase Maxwell phase. I proposed
the identification of Maxwell phase as small deformations of vacuum extremals with
vanishing Kahler form and assumed that they are separate from MEs and their
generalizations. Something very natural at least when one considers Kahler form. My
sincere hope was that this would give the analog of Maxwell's ED for single space-time
sheet. I was wrong.
At that time (1980-1990) I did not have a slightest idea about the replacement of linear
superposition for fields with linear superposition for their effects realized in terms of set
theoretic union of space-time sheets representing field modes. This is like geometric
counterpart of Fourier decomposition with each mode represented as space-time sheet.
Geometric form of quantization.
Does Maxwell phase exist at all? Are extremals known at that time and their generalization to
the ansatz for preferred extremals relying on Hamilton-Jacobi structure and complex structure in
Minkowskian/Euclidian regions enough?
(1) The existence of Hamilton Jacobi-structure implies that all Minkowskian pieces of preferred
extremals represent a space-time region which could be called space-time correlate for a
massless quantum. Polarization vector and light-like wave-vector are, however, local
rather than constant. By adding wormhole contacts, one can engineer "bound states" of
142
these objects. This transforms simplest linear MEs to "curved" MEs and more general
preferred extremals.
This does not support the view that Maxwell phase could be realized at the level of single
space-time sheet.
(2) Does one then obtain the analog of Maxwell phase at all? Yes. But it is indeed many particle
system in the sense that many space-time sheets are involved and as the term "phase"
would suggest. My choice of the terminology happened to be correct!
If you have large number of preferred extremals in single region of Minkowki space,
however, the summation of their effects on particle having topological sum contacts with
them implies that effectively one has superposition of Fourier components of fields with
different wave vectors. Hence this many-sheeted situation would correspond to Maxwell
phase as I thought it.
Quite generally, the very-many-sheeted situation quite generally corresponds to the
Classical limit of the the theory in accordance with the basic philosophy that Classicality
emerges at the limit of large quantum numbers.
[Hamed] Now ordinary Macroscopic objects are in which of them?
[MP] I dare cautiously believe;-) that I have now a reduction of the dynamics of Kahler action at
basic level to Minkowskian and Eucldiian preferred extremals with first ones representing
spacetime correlates for radiation in very general sense. All elementary particles could
effectively consist of massless quanta in the sense that massive four-momentum of the particle
would be sum of massless but non-parallel momenta.
What about Macroscopic objects? One identification for the space-time representative of
Macroscopic objects is as the analog of line of Feynman diagram, that is space-time region
with Euclidian signature. Basically a deformation of CP2 vacuum extremals which can
increase the E3 projection from that for a point to arbitrarily large would be in question.
Line of Feynman diagram is something very quantal so that this is consistent with the
vision that quantal aspects are present even at macroscopic level. One way to end up with this
vision was a view about blackhole interiors as Euclidian regions. Then I realized that
blackhole property in the sense that there very strong gravitational fields present is not
essential. As a matter of fact, this brings in mind with the present tendency to describe
everything in terms of blackhole via Ads/CFT and wormhole contacts are indeed blackholelike objects.
[Hamed] One can say that these solutions aren’t Classical and we need some preferred ones. These
preferred extremals can be obtained from Quantum-TGD. In other words, Quantum-TGD can
say what are Classical extremals!
[MP] Here I think that we think differently. The motivations for preferred extremals are different.
(a) The starting point is construction Kahler geometry of WCW. It consists of 3-surfaces but one
must realized 4-D general coordinate invariance.
143
The very definition of Kahler function should be such that it assigns a unique space-time
surface to a given 3-surface for general coordinate transformations to act on.
One must also have direct connection with classical physics which must exact part of
quantum physics. This is achieved if Kahler function is identified as Kahler action
associated with a preferred extremal containing a given 3-surface X3. Preferred extremals are
like Bohr-orbits since instead of infinite number of 4-surfaces solving field equations and
going through X3 one accepts only single one (the "preferred one"). General Coordinate
Invariance implies obviously also holography since knowing the 3-surface means that one
knows space-time surface. It is GCI which implies automatically very quantal classical
behavior as Bohr orbitology. This is something totally unexpected and shows how powerful
GCI is in the case of sub-manifold gravity.
(b) The question has of course been what "preferred" means. My first guess was that it could
mean absolute minimum for Kahler action. Number theoretical universality does not
conform with this idea. In p-adic context, the absolute minimum is however not a sensical
notion since p-adic numbers are not well-ordered.
Number theoretical universality suggests that one should be able to completely algebraize
the "preferred".
Hamilton-Jacobi structure/4-D complex structure does this in
Minkowskian/Euclidian regions and leads to deep analogies with string theory. What is so
nice is that all tensor contractions in field equations vanish automatically thanks to this
structure. In string models, holomorphy leads to the same outcome. The hypothesis that
space-time surfaces are quatermionic in some sense does the same and I hope that the
identifications are actually equivalent.
It is amusing that Equivalence Principle (the second great principle of GRT) holds true
for preferred extremals!
http://matpitka.blogspot.com/2013/01/anomalies-anomalies.html
topic: Anomalies, anomalies …
1. At 2:46 AM, Matti Pitkanen said...
… Verlinde's idea has been already tested (neutron diffraction in Earth's gravitational field) and failed
in the test. Besides this, the idea is extremely primitive and confused. I am really astonished that a
person working with refined string mathematics can suffer such a regression. Probably Verlinde is a
victim of his own fame. If he had the patience to wait for a few months before publishing the first
preprint, he could have decided to abstain from publishing it at all.
That this kind of idea can receive financial support at all (not so say anything about millions of
euros) demonstrates the fatal consequences of "famous name worship" in TheoreticalPphysics.
We are living very depressing times in Theoretical Physics. The field is badly in need of young
brave intellectuals but continues to be dominated by old farts and their courts.
The posting of Lubos (http://motls.blogspot.fi/2013/01/quantum-physics-doesnt-depend-on.html )
is a good example of the ultraconservative attitude that Quantum Theory is final theory and every
problem worth of solving have been solved by superstring approach. In particular, Consciousness is a
144
pseudo problem which does not deserve scientific study because existing quantum theory says nothing
about it. We must be happy with superstrings unless we want to be labeled as idiots.
2. At 6:03 AM, Santeri Satama said...
… To give you something else to think, His Holiness (the Dalai Lama) asked during the day two
morning session could Dark Matter have existed before or independent of Big Bang. How would you
answer that question?
3. At 6:31 AM, Matti Pitkanen said...
To answer the question posed by his Holiness, one must first answer what the 'Big Bang' means.
In TGD, one express the situation by saying that the 'Big Bang' is replaced with a silent whisper
amplified to a rather big bang. Means that mass per comoving volume vanishes near the boundary of
light-cone defining what we usually call the 'Big Bang'.
Also hierarchy of cosmologies within cosmologies is predicted (this means Russian doll structure).
Before Big Bang means bigger Big Bang containing the smaller one as topologically condensed spacetime sheet (or actually pair of them glued together along boundaries - flattened ball instead of disk).
Dark matter is present everywhere in 4-D sense.
One must of course be careful with what one means with dark matter. Most of so-called galactic
dark matter could be Kahler magnetic energy associated with magnetic flux tubes originating from
primordial cosmic strings (TGD counterpart for dark energy). This magnetic energy associated with
flux tubes would create gravitational fields giving rise to constant velocity spectrum of stars.
What is beautiful that the velocity spectrum comes automatically correctly and there is no need for
elaborate fits. Basic prediction is free motion of galaxies along long string along which they are
organized.
Dark matter in the TGD sense would be these large Planck constant phases and something very
different from standard dark matter candidates. One big difference is that dark matter has standard
electroweak and strong interactions with itself.
Ordinary and large hbar particles do not appear however in same vertex. My belief is that this is
enough for experimental purposes. Recently it has been indeed observed that contrary to the standard
beliefs dark matter has self interactions as I told in the posting.
Evidence for TGD view is slowly but steadily accumulating. Therefore it would be wonderful if
communication with academic colleagues were possible. The problem of recent-day physics is that
only "big names" and "influential power" matter instead of content.
4. At 8:17 AM, Santeri Satama said...
To clarify, are the Russian Doll Dosmologies characterized by different values of hbar, larger
inclusive cosmologies with larger values than the smaller smaller topologically condensed space-time
sheet pairs? Or is each level of cosmology characterized by some spectrum of hbar? Or is this
question total misunderstanding of your hypothesis?
145
5. At 3:35 AM, Matti Pitkanen said...
There are 3 hierarchies involved. Hierarchy of space-time sheets labeled by selected p-adic primes
charactering their size scales. At imbedding space level the hierarchy of CD with size scale defined by
what I call secondary p-adic length scale. And dark matter hierarchy with levels labeled by positive
integers defining the multiple of effective Planck constant.
All are present and cosmology in given scale would involve all these 3 hierarchy levels. Those
associated with CD and space-time sheets with ordinary hbar being our cosmology (space-time sheets
and its field body). Non-standard values of effective Planck constant would correspond to dark worlds
to us. (Do not ask about further details;-).
6. At 8:33 AM, Santeri Satama said...
> Matti: "Do not ask about further details;-)."
Why, isn't that where the devil lurks? ;)
The presentations with Dalai Lama have been fun and interesting. Someone said that QM is very
simple. Just the Schrödinger equation and that's it. No need to presuppose or demand any world view
behind it (as any such attempt leads to paradoxes). And it also seems that the Galilean view of time as
isochronic pendulum is also already contained in that wave function. Wiki gave a nice Feynmann
quote: "Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything
you know. It came out of the mind of Schrödinger."
Speaking of Wiki, if you ever consider rewriting or reformatting your texts, a single hypertext file
(e.g. Wiki-format) would be in many ways preferable to several pdf's.
7. At 9:34 PM, Matti Pitkanen said...
You are asking too much! I simply cannot give details! This is like asking Columbus to give a
detailed satellite map of the new contintent or whatever he thought it to be!
Filling them would be a collective effort of theorists and experimentalists. Consider only the
understanding of single scalar particle: the Higgs. Still the situation is experimentally and theoretical
half open! Despite enormous theoretical and experimental work done for for decades.
But thank you for the nice questions.
Wave mechanics is very simple if you forget the problems of quantum measurement theory as a
good Copenhagenist is taught to do. Lubos has been an excellent pupil. Maybe because of his
childhood background in authoritative political system has made him so good a student;-) who has
now become Prussian Schulemeister for new generations;-). This belief has led to a stagnation of
Theoretical Physics lasted almost century.
I do not agree with Feynman about the Schrodinger equation. Times have changed when Feynman
mystified the Schrodinger equation.
● Already Feynman knew that Schrodinger equation can be derived from the Dirac equation at
non-relativistic limit. This in turn follows naturally from QFT where spinor structure has
146
geometric interpretation. Maybe the geometric aspect was perhaps not too familiar for
Feynman who also wanted to see gravitaty in terms of interactions of matter and spin two
particles in Minkowski space rather than as curvature of space time.
● When one replaces point like particles with 3-surfaces, about this Feynman knew nothing. With
all respect, the same is regrettably true about most of my colleagues in their ivory towers;-) -one is forced to construct Kahler geometry and spinor structure of "World of Classical Worlds"
(WCW).
● Spinor structure for WCW in turn requires second quantized spinor fields (a purely geometric
structure) at the space-time level. This means geometrization of Fermi statistics and fermions
(not possible in standard QFT). Suddenly the mysteries disappear! What resolves them is the
realization that particles are not mathematical points.
● By infinite-dimensionality of WCW, the basic rules of quantum theory are unique (probabilities
as squares of inner products bilinear in quantum states). They cannot have any other than
standard form because more complex expressions are mathematically ill-defined. This is the
magic of infinite-D geometry where wrong mathematical form automatically leads to the
appearance of infinities. The functional integral over WCW simply cease to exist. Infinite-D
calculus is enormously restrictive discipline as compared to its finite-D counterpart. This is the
reason why it took so long to find first candidates for QFTs free of infinities.
The core of the above arguments was that the basic formalism of QFT is forced by infinitedimensionality of WCW.
This is however only one half of the story. Quantum measurement theory and its mysteries
remain. Copenhagen interpretation would mean givng up the idea that WCW spinor fields represent
something real. Taking into account the beauty and elegance of this notion, this would be simply
idiotic.
In Zero Energy Ontology, WCW spinor fields correspond to zero energy states and are analogs of
physical events in the usual positive energy ontology (something very real and geometric). No mystics
involved.
The identification of quantum jump as moment of Consciousness is what removes the paradoxes
revolving around the notion of state function reduction.
The new ontological element is that single object reality as quantum state of the universe is
replaced with an infinite number of possible and in principle reachable realities (zero energy states).
Evolution as quantum jumps (moments of recreation) replacing zero energy state with a new one
emerges automatically and connections to Biology and Consciousness are obvious.
One can also resolve the paradoxes produced to the wrong identification of Subjective-Time with
Geometric-Time and a radically view about time ("times" to be precise) emerges.
To me this option is much more attractive than sticking to century-old dogma giving up completely
the idea of physical reality (realities in TGD framework) and taking physical theory as a mere
collection of rules.
147
http://matpitka.blogspot.com/2013/01/robert-kiehns-ideas-about-falaco.html
topic: Robert Kiehn's ideas about Falaco solitons and generation of turbulent wake from TGD
perspective
1. At 5:59 AM, Hamed said...
The speed of progress of TGD is more than me about learning of TGD ;-).
> “One identification for the space-time representative of Macroscopic objects is as the analog of
line of Feynman diagram which is space-time region with Euclidian signature.”
We see Macroscopic objects as 2-surfaces that are boundary of 3-surfaces. So the space-time
representative of macroscopic objects is the 2-surfaces that are evolving in larger space-time sheet. I
deduce from your sentence that the evolving for the 2-surfaces have Euclidian signature. This is
inconsistent with what I understand from Special Relativity. I think I misunderstood your sentence.
In path integral formalism, what is physical Intuition behind wick rotation? In QFT it is only a
mathematical tool. What is about TGD?
I myself intermix the Quantum and Classical together. Yet it is unavoidable;-). Sorry for my
request in some comment ago. Obviously you know very better how to say about TGD.
2. At 8:57 PM, Matti Pitkanen said...
Dear Hamed,
here are my comments.
[Hamed] "One identification for the space-time representative of macroscopic objects is as the analog
of line of Feynman diagram, which is space-time region with Euclidian signature."
[MP] This is okay. An alternative identification of generalized Feynman diagram is as the light-like
wormhole throat at which the signature changes since one can assign quantum numbers to this
region.
[Hamed] We see Macroscopic objects as 2-surfaces that are boundary of 3-surfaces. So the space-time
representative of macroscopic objects is the 2-surfaces that are evolving in larger space-time
sheet. I deduce from your sentence that the evolving for the 2-surfaces have Euclidian
signature. This is inconsistent with what I understand from Special Relativity. I think I
misunderstood your sentence.
[MP] Evolving 2-surfaces define 3-D light-like wormhole throat orbits since they have have neither
Minkowskian nor Euclidian signature and thus have degenerate signature of 4-metric. 4-D
tangent space of space-time surface becomes metrically 3-D at the orbit of wormhole throat.
All boundaries between various objects have this character.
TGD of course generalizes dramatically the views of Special Relativity and General
Relativity about space-time. In Special Relativity, one has just M4. In TGD, it is replaced with
imbedding space M4xCP2 so that symmetries are not lost. In General Relativity one allows
only Minkowskian signature. In TGD, one allows both signatures. This is a rather radical
departure.
148
[Hamed] In path integral formalism, what is physical Intuition behind wick rotation? In QFT it is only
a mathematical tool. What is about TGD? I myself intermix the Quantum and Classical
together. Yet it is unavoidable;-). Sorry for my request in some comment ago. Obviously
you know very better how to say about TGD.
[MP] I see Wick rotation as a pure mathematical trick analogous to analytic continuation allowing to
make the 4-dimensional loop momentum integrals well-defined in QFT.
In twistor
Grassmannian approach, the idea is a kind of residue calculus: the loop integrals can be reduced
so one obtains only integrals over massless on mass-shell virtual momenta which can be
however complex. They are expressed in terms of twistor variables. In the similar manner,
integral of analytic functions over real axis can be expressed in terms of residues at poles in
either upper or lower complex plane.
I remember vaguely that I have considered the possibility of Wick rotation in the proposal
for how the space-time surfaces could be seen as (in some sense) quaternionic sub-manifolds of
octonionic M8. For this option, I considered octonion real analytic functions and put imaginary
part of the function to zero to define a four-surface. In complex plane, the vanishing of a
complex function defines a curve. At this moment I am not too enthusiastic about this kind of
approach although it would provide general solution of field equations by M8-M4\times CP2
correspondence.
We experience the World as Classical and proper Quantum theory must explain this. The
challenge is not to eliminate fuzzy quasi-Classical arguments from the theory but make
Classical physics a precise part of the theory. And Classical physics as exact part of Quantum
physics follows from single principle.
General coordinate invariance realized at the level of WCW. GCI implies immediately
holography, even in strong form. "Bohr orbitology" follows as by product of general coordinate
invariance. All this demonstrates the amazing power of GCI. The great principles of Einstein
transcend much beyond GRT.
http://matpitka.blogspot.com/2013/01/is-there-inert-neutrino-there.html
topic: Is there an inert neutrino there?
1. At 3:24 AM, Matti Pitkanen said...
… … The right-handed neutrino is the mystery of recent-day physics. Neutrino is massive which
seems to require that both right- and left-handed neurino mix. Therefore right-handed neutrino should
exist. It however does not couple to known interactions except gravitation. What interaction would
cause the mixing? This is the problem for all extensions of the Standard Model.
An additional problem is that there are some indications for inert neutrino and purely righthanded
massless neutrino would be excellent candidate here. It should be, however, in thermal equilibrium
with other massless particles during radiation dominated era. Is this possible if it interacts only
gravitationally? Could mixing cause the thermalization?
In the Standard Model, it is hopeless to try to put these pieces together. In TGD, the localization
of all particles except purely right-handed neutrinos to 2-D string world sheets forced by the condition
that electric charge is well-defined (different charge states do not mix) might allow us to achieve this.
149
Right-handed neutrino would also generate SUSY. The guess is that is unbroken. But this is just a
guess motivated by the fact that it is extremely difficult to detect purely right-handed neutrino. One
can also imagine that there is more delicate SUSY breaking mechanism. The p-adic length scale
characterizing different superpartners is different; otherwise they obey same mass formula. The
situation is open.
The dynamics of the right-handed neutrino would be simple. Follow the leader, the ordinary
particle which it accompanies. This correlates the momentum direction of right-handed direction with
that of the leader and means correlation possibly making possible thermal equilibrium. Also the
mixing of ordinary 2-D string worldsheet neutrino and 4-D right-handed neutrino could take place and
thermalize.
http://matpitka.blogspot.com/2013/04/riemann-hypothesis-and-quasi-lattices.html#comments
topic: Riemann Hypothesis and Quasi-Lattices
1. At 9:56 AM, Stephen said...
Saw this on slashdot. http://arxiv.org/abs/1304.2785
From the abstract: "The recent Planck satellite combined with earlier results eliminate a wide
spectrum of more complex inflationary models and favor models with a single scalar field as reported
in the analysis of the collaboration. More important, though, is that all the simplest inflaton models
are disfavored by the data while the surviving models -- namely, those with plateau-like potentials -are problematic.
We discuss how the restriction to plateau-like models leads to 3 independent problems. Iit
exacerbates both the initial conditions problem and the multiverse-unpredictability problem and it
creates a new difficulty which we call the inflationary "unlikeliness problem." Finally, we comment
on problems reconciling inflation with a standard model Higgs as suggested by recent LHC results.
In sum, we find that recent experimental data disfavors all the best-motivated inflationary
scenarios and introduces new, serious difficulties that cut to the core of the inflationary paradigm.
Forthcoming searches for B-modes, non-Gaussianity, and new particles should be decisive. "
2. At 8:27 PM, [email protected] said...
Hi Stephen,
Maybe I have written something about the problems of inflation scenario. At least I wrote about
TGD-inspired approach replacing inflation => http://tgdtheory.com/public_html/articles/inflatgd.pdf .
I have always wondered how anyone in his or her right mind can take so horribly ugly theory as
inflation seriously. The plateu makes me vomit;-). But fashions are fashions and defy rational mind.
The basic fact is that 3-space has vanishing curvature scalar in good approximation. This we must
explain.
(a) In GRT-based approach, this is obtained from exponential expansion.
150
(b) In TGD framework, quantum criticality assignable to a phase transition. In the phase transition
for some space-time sheets, an increase of Planck constant takes place.
Criticality of the phase transition implies a vanishing of curvature scalar as something dimensional
and means critical gravitational mass density for vacuum extremal of Kahler action. The interpretation
is that gravitational mass represents topologically-condensed matter.
This does not imply exponential expansion, only accelerated one. The Robertson-Walker metric is
unique apart from its finite duration serving as a parameter from imbeddability so that the killer
problems of inflationary scenario are avoided.
3. At 11:25 PM, Hamed said...
Dear Matti,
If symplectic transformatons of deltaM4 time to CP2 acts as isometries, the value of Kahler form at
partonic 2-surfaces are zero modes. Symplectic transformations leaving kahler form invariant and
isometries leaving distances between points invariant. How a symplectic transform can acts as
isometric transformation? In really, relation between them is not clear for me.
4. At 2:21 AM, [email protected] said...
Dear Hamed,
The point is that symplectic transformations of delta M4xCP2 act as isometries of "World of
Classical Worlds" (WCW)! Not imbedding space! This is of course a very natural conjecture about
isometries of WCW geometry. The motivation is that these symplectic transformations are
approximate symmetries of Kahler action for surfaces representable as maps from M4 to CP2 broken
only gravitationally: that is due to the deviation of the induced metric from flat Minkowski metric.
For vacuum externals, they are exact symmetries.
A note about "symplectic". Strictly speaking, in delta M4 the "symplectic transformation" should
be replaced with "contact transformation". Delta M4 is effectively 2-D metrically and thus allows
natural symplectic structure J2=-g by its metric 2-D property. Symplectic transformations are those of
S2 made local with respect to radial light-like direction (delta M4= S2xR+). Lorentz transformations
define different composition of this kind and one can speak about moduli space for symplectic
structures.
Hamiltonians for the transformations can be expressed as products of delta M4 Hamiltonians and
CP2 Hamiltonians and can be assumed to possess well-defined colour and spin quantum numbers and
correspond to irreducible representations of SO(3)xSU(3)/Z3. They can be thought of being made
local gauge group by localising with respect to the light-like radial coordinate. This gives rise to the
counterpart of conformal invariance.
http://matpitka.blogspot.com/2013/04/a-vision-about-quantum-jump-as.html#comments
topic: A vision about quantum jump as a universal cognitive process
1. At 8:47 AM, Stephen said...
151
http://www.dailygalaxy.com/my_weblog/2013/04/speed-of-light-not-a-constant-it-varies.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+TheDailyGalaxyNew
sFromPlanetEarthBeyond+%28The+Daily+Galaxy+-Great+Discoveries+Channel%3A+Sci%2C+Space%2C+Tech.%29
I think we already knew this might be the case, right?
Interesting thoughts about quantum jumps. The CD idea is such wonderful. I wish it were more
generally considered among the wider set of thinkers and "doers" out there.
2. At 8:12 PM, [email protected] said...
The variation of light-velocity is interesting possibility.
The approach of your reference is totally different from TGD approach and Quantum version of
what you find in textbooks of Physics. This means vacuum polarization and propagation in which
light is absorbed and re-emitted. I am not enthusiastic about this kind of approach since rather strange
ad hoc assumptions are made.
TGD approach is purely geometric and involves now ad hoc assumptions. Just sub-manifold
gravity. The light-like geodesics at space-time surface are in general not light-like geodesics of
imbedding space H=M4xCP2. In the general case, they are time-like curves as curves of H. The
effective light velocity determined from time to propagate from point A to B decreases since the
length of path increases.
The effect appears certainly in Astrophysical scales. The time taken for light to travel to Moon
and back changes gradually as if the light velocity were changing. What changes is the effective lightvelocity in cosmic scales whereas at the level of the Solar System it is constant since the Solar System
does not participate in cosmic expansion. The prediction is quantitatively correct.
For neutrinos change of c from the maximal, one could have been present. But its magnitude, that
I could not predict, turned out to be too small.
3. At 3:23 AM, Ulla said...
It is popularly said that when time goes backwards, it creates antimatter that annihilates and give
then energy? Is this THE quantum jump? I have long thought that the word consciousness have lost
its meaning due to so much nonsense written about it. This would also give it a time scale, as you say
the difference in reactions between protons and electrons, of scale 10? But in this case the dark
current was PRIOR.
Another scientist also says about carbon/methylation that the impulse/intention ALWAYS come
from the dark side or 'negativity' as he says. The same is seen for DNA. If we use Schrödinger or
Dirac, they too oscillate around dark-light spectrum or virtual-real? What about quarks that pop inand-out of existence? But the bigger proton is more stable, so that's why we get this time-scale of 10?
4. At 9:27 PM, [email protected] said...
This is an interesting question. I am still not completely sure about the answer. I have, however,
gradually began to think that one cannot apply Feynman's picture applying in positive energy ontology
in ZEO.
152
At the level of Feynman diagrams, one could regard antiparticles as particles traveling backwards
in time.
In TGD, both matter and antimatter appear in both positive and negative energy states located at
opposite boundaries of the CD and forming pairs with zero net quantum numbers and analogous to
initial and final states of physical event.
The state function reduction occurring alternately to opposite boundaries of the CD creates
quantum states with opposite arrow of imbedding space time and both matter and antimatter possess
same arrow of time for given kind of state. The overall arrows are opposite, however, in these two
kinds of states. This arrow relates to dissipation and thermodynamic arrow of time. ZEO also forces
us to accept syntropy as entropy in reverse direction of imbedding space Geometric-Time.
Biology is full of syntropic effects. But syntropy does not fit to the framework of existing physics
so that it has been "forgotten".
In ordinary QFT, the Dirac equation allows solutions which have positive and negative energies.
When theory is second quantitzed, both particles and antiparticles have positive energies. In TGD, both
particles and antiparticles have positive (negative) energies at "lower" ("upper") boundary of CD.
In TGD, positive and negative energies correspond to different view about what exists. One could
say that quantum states are replaced by events. Pairs of positive and negative energy states (opposite
net quantum numbers) which corresponds in ordinary ontology to initial and final states of physical
event.
One might say that this is much more "Eastern", assumes much less, and is much more flexible
view about reality as the "Western" view. No absolute never changing reality is postulated and
leading to unpleasant questions like "What is the total energy of the Universe?" These zero energy
states/events which can be created from vacuum in quantum jumps so that any Universe can be recreated from vacuum.
If God exists, she is very happy since in ZEO he can do anything she wants. The "Western" God
is severely limited in his creative actions by conservation laws and the God of classical physics must
accept also determinism so that he can only create the Universe but cannot interfere with it after that.
(My comment about Gods was written half-jokinly. I hope that none of them has hard feelings for
this.)
My impression was that James and already Leibniz((!) had understood about consciousness much
more than the narrow-minded Quantum Consciousness theorists trying to reduce it to the narrow frame
of Wave Mechanics and reductionism.
Spiritual aspect allowing us to see things in bigger perspective is so often lacking. There are of
course quantum spin doctors having popular talks and writing books about quantum consciousness.
But the soul purpose seems to be business. Their teachings are hopelessly shallow play with
buzzwords.
5. At 10:28 PM, [email protected] said...
To Ulla:
153
I cannot get excited about light-velocity derived from the vacuum structure. This approach does
not conform with the vision about geometrization of physics which is my own guiding principle. I
could of course be wrong. But it is too late to change the mind now;-).
For electromagnetism in empty space the parameters epsilon0 and mu0 can be taken to be equal to
1 in suitable units as also c. Therefore their values do not seem to have genuine physical meaning.
Situation changes when one wants to model the effects of the presence of matter to the propagation
of E-M fields. The dimensionless parameters epsilon/epsilon0 and mu/mu0 are genuine physical
parameters characterizing these effects in linear model.
In quantum vacuum, there are indeed polarisation effects which affect also the propagation of light
and are summarized in terms of vacuum polarization tensor for photon. This is standard QED. But
the effect is not interpreted in terms of change of light-velocity.
For these reasons the attempts to derive epsilon0 and mu0 and therefore c from quantum vacuum
does not seem very attractive to me. Geometrization program gives a beautiful interpretation for light
velocity and in sub-manifold geometry one can also talk about its variation in a purely geometric
sense.
And as I mentioned, this approach predicts correctly the observed variation of distance of moon
(about this Riofrio talked a lot and made some nonsense conclusions) as something apparent (and thus
not as a real variation or the change of the local maximal signal velocity in the Solar System).
6. At 12:34 AM, Ulla said...
[MP] "In TGD, both particles and antiparticles have positive (negative) energies at "lower"
("upper") boundary of CD."
How are the energy then changed from positive to its ani-matter fashion (fuzzy words but when
positive is negative and negative is positive)? I know that you say the back of the book is in the
soliton, but also the vacuum is told to be 'measured' by a harmonic soliton. So there is a tiny little
space that is responsible for this 'adiabatic' expansion? Negative as we use to see it but with different
chirality? What is time in this? I thought it has to be the first perturbation,so it must then come from
the chirality and be the second (or emergent?).
7. At 7:16 AM, [email protected] said...
This has nothing to do with solitons. As I already explained, the QFT statement that antiparticles
have negative energies and propagate to the Past is equivalent to saying that antiparticles have positive
energy and travel to the Future. Standard QFT is based on positive energy ontology.
In Zero Energy Ontology, the situation changes. One can distinguish between zero energy states
with different time orientations by the arrow of imbedding space Geometric-Time. Their difference is
that the are prepared at the opposite boundaries of CD. This is something genuinely new and relates to
generalization of S-matrix to a collection of M-matrices defining rows of unitary U-matrix.
154
http://matpitka.blogspot.com/2013/04/self-or-only-model-of-self.html#comments
topic: Self or only a model of self?
1. At 9:17 PM, [email protected] said...
This Blog post could have been formulated in more general level as an objection against the basic
philosophy of TGD.
Postulate: Quantum jumps represents moment of conscious so that consciousness requires always
change.
Objection: How it is then possible to have conscious information about something which does not
change in quantum jump? Invariants represent usually the useful information and
negentropic entanglement is invariant with respect to the dynamics defined by NMP.
A: Interaction-free measurement for negentropically-entanged subsystems gives this information.
These subsstems are not changed but the photon interacting with them experiences the
needed change. It is absorbed by either detector so that conscious experience about the state
of the memory (not just bit/bomb) is obtained without destroying the mental memory.
The interaction-free measurement is originally formulated in terms of photons. It can also,
however, formulated for sound waves using phonon detectors and acoustic waves traversing through 2
different paths.
There are good reasons to believe that sound waves correspond at fundamental level correspond to
oscillations of string-like objects at 4-D space-time surface connecting different particles and carrying
fermion fields (note: right-handed neutrino is an exception). This brings in the fundamental 2-particle
character of sound waves. Sound would be as fundamental phenomenon as photons and other
massless bosons.
The conclusion would be that photon and photon absorption would define fundamental conscious
representations of information represented in terms of negentropically-entangled states unchanged
under state function reduction in good approximation. Photons correspond to seeing usually
unconscious-to-us which we call Imagination. Phonons correspond to hearing and internal speech
which is also essential for Cognition.
One can speculate about direct translation between words of language and visual pre-images. In
fact, during my first "Great Experience" ( doc pdf URL ) I was able to see my thoughts and
discovered that this kind of correspondence seems to exists. I played by uttering words and
immediately getting visual image to my visual field as a response!
http://matpitka.blogspot.com/2013/05/comparison-of-tgd-inspired-theory-of.html#comments
topic: Comparison of TGD-inspired Theory of Consciousness with Other Theories of
Consciousness
1. At 9:33 PM, ◘Fractality◘ said...
Would you consider iterative algorithms conscious/intelligent?
155
2. At 11:15 PM, [email protected] said...
If algorithm is computer algorithm, this would be functionalism and I do not believe in it.
Quantum jump is necessary for Conciousness. In reading of memory representation, memory
representations are not changed. But there are detectors which absorb the photons (or possibly
phonons) having interaction free interaction. These produce the conscious experience such as
geometric mental image or internal speech.
Conscious living systems can of course develop algorithms. But these are not deterministic.
I agree more-or-less with Prieur. It is nonsensical to claim that phenomenal experience and qualia
are illusory "folk psychology" as elimative materialists might put it. It is also nonsensical to deny the
existence of objective realities obeying laws of physics as the idealist would do.
TGD is compromise between the 2 views. Zero energy states are quantum superpositions of
objective realities and quantum jump takes place between these and gives rise to phenomenal
experience and qualia.
Self model emerges also. Quantum states can contain parts which are negentropically-entangled
and in good approximation invariant under quantum jumps. They define a model for the Sself and the
External World. Interaction-free measurement allows us to get conscious information about these
sensory/cognitive/memory representations.
Each sensory perception would be indeed like a process leading to the discovery of the Higgs.
Endless arguments and counter arguments, confusion, and wrong alarms … and finally everything is
clear.
3. At 1:04 AM, ◘Fractality◘ said...
Thanks in advance for replies.
If you do not believe in functionalism, does that mean you do not believe in conscious AI? What
about using recursive algorithms in the process of divination/geomancy?
4. At 1:59 AM, [email protected] said...
I do not believe in functionalism and conscious AI. The problem is that phenomenal
consciousness lacks or must be postulated as epiphenonon in completely ad hoc manner or just denied
as eliminativists do! This is general failure of all materialistic approaches.
Chalmers as dualist believes on variant of functionalism in which consciousness is pure
epiphenomenon without any causal powers: this in order to avoid contradiction with laws of physics.
Effectively one has emergent materialism.
Both approaches fail also because there is absolutely no idea about how to assign this
epiphenomenal qualia to the physical state of the system.
It is ironic that all the theories discussed by Revonsuo in his excellent book belong to monistic or
dualistic theories whose failures are more than obvious. Quantum theories of Consciousness are not
counted. Not too much is lost. Most quantum consciousness theorists do not even realize the deep
philosophical problems involved and think that Wave Mechanics is enough.
156
The sad situation reflects the simple fact that if you want to make a career, you must think as your
professor does! Things are much better at the experimental side as the book or Revonsuo reveals.
I failed to understand your second question. Sorry.
http://matpitka.blogspot.com/2013/07/evidence-for-m-89-pion-at-lhc.html#comments
topic: Evidence for M89 pion at LHC?
1. At 1:14 PM, Hamed said...
Coleman-Mandula theorem states that there is no way to unify gravity with the Standard model.
Supersymmetry defeats the Coleman-Mandula theorem by using lie super algebra.
How TGD does defeats the theorem? Or what is the hole of the theorem in the viewpoint of
TGD?
2. At 6:33 PM, Matti PItkanen said...
Dear Hamed,
A nice question.
What Coleman-Mandula (http://en.wikipedia.org/wiki/ColemanMandula_theorem) says is that there is no non-trivial manner to combine Poincare symmetries and
and internal symmetries. "Nontrivial" is essential here!
A. In the case of SUSY, one generalizes the notion of symmetry by modifying the notion of
algebra to super-algebra. Super-generators anticommute mutually to bosonic generators
and bosonic generators commute to bosonic generators and fermionic and bosonic
generators commute to fermionic ones.
In TGD framework, supergenerators appear just in this manner. Induced spinor field is
second quantized and one forms as bilinears of c-number valued modes and second quantized
induced spinor fields. By modified Dirac equation, these currents are divergenless and
define supercharges carrying fermion o antifermion number (actually lepton or quark
number). There is no need for assuming Majorana spinors and this is impossible in D=8.
What is essential is that one is forced to replaced the counterpart of massless Dirac
equation with modified Diract equation involving modified gamma matrices in order to
obtain the supersymmetry.
A nosy note: Usually one introduces super-space formalism. But I see it as purely
formal trick with no real geometric content. It is a pity that colleagues have wasted decades
with such a formal trick with known results;-).
Genuine geometric content emerges at the level of World of Classical Worlds.
Anticommuting (supersymmetry!) gamma matrices are super-generators of super algebra
defined by isometry algebra of WCW and gamma matrices!
157
B. In the case of TGD, internal symmetries and Poincare symmetries indeed combine in trivial
manner in full accordance with empirical facts: color and electroweak symmetries and
Poincare define Cartesian factors of overall symmetry group. This corresponds to the fact
that imbedding space is Cartesian product of M4xCP2.
Despite the Cartesian product structure correlations between four-momentum, spin and
internal quantum numbers are possible and of course predicted.
What Coleman-Mandula prevents is the fusion of Poincare and internal symmetries using
4-D space-time which is abstract 4-manifold. Space-time as surface in M4xCP2 instead of
abstract 4-manifold is the TGD-based manner to circumvent Coleman Mandula so that
gravitation and standard model can be combined. Classical gravitation becomes induced
gravitation and Classical gauge potentials induced spinor connection.
3. At 7:53 AM, Hamed said...
Thanks,
"Genuine geometric content emerges at the level of World of Classical Worlds:
anticommuting (supersymmetry!) gamma matrices are super-generators of super
algebra defined by isometry algebra of WCW and gamma matrices!"
Interesting and makes supersymmetry more clear for me.
http://matpitka.blogspot.com/2013/07/about-art-of-rediscovery.html#comments
topic: "About the art of rediscovery (of TGD by other physicists)"
1. At 8:10 AM, Hamed said...
Dear Matti,
In modified Dirac eq uation, gauge potential generators is not concluded in the covariant derivative
term. So there is the question that how can regard the interactions? One can add the Cartan algebra
generators of isommetries of imbedding space and it contain strong interactions. Also strong
interaction contains electroweak interaction because U(2) is subgroup of SU(3). This view is very odd
and interesting.
2. At 8:07 PM, Matti Pitkanen said...
To Hamed:
Your view looks correct. I just restate from slightly different emphasis.
Covariant derivative term is(!) present in modified Dirac equation and of same form as for the
counterpart of massless Dirac equation. The gauge potentials are the spinor connection are however
induced that is components of CP2 projected to the space-time surface: A_mu= A_k partual_mu s^k.
This is an important difference. Everything comes out from geometry. No fields are
postulated as primary entities.
158
This gives couplings to Classical electroweak gauge potentials. Color gauge potential couplings
are not obtained at the Classical level since color is not spin like quantum number but analogous to
angular momentum. Color partial waves emerge at the level of WCW but not at the level of spacetime. Here is distinction between TGD color and QCD color.
The conjecture is that color interactions are at the QFT limit of point-like particles necessarily
gauge interactions since there is no other option in QFT context. Since the mathematical structure is
that of generalized Kac-Moody algebra and Kac-Moody algebra is very near to gauge algebra, there
are excellent reasons to believe that this is the case.
More concretely, at WCW level one can assign to given state a color partial wave in cm degreesof-freedom of partonic two-surface. In these degrees, the fermion is represented as a partial wave of
imbedding space spinor. The imbedding space coordinates are interpreted as cm coordinates.
For quark chirality, imbedding space spinor has triality t=1 ( t=-1 for antiquarks) and for leptons
it is triality. This comes from different couplings to induced Kahler gauge potential needed to
achieve acceptable spinor structure. This predicts the existence of colored excitations of leptons and
quarks: most them have masses with CP2 mass scake and are unobservable in recentday physics.
For spinor harmonics of CP2,trialities are correct but the correlation of color and electroweak
numbers is wrong. The correct correlation is possible to obtain since the analogs color Kac Moody
algebra and symplectic algebra of delta M4xxCP2 (analog of Kac Moody algebra associated with
symplectic group of S2xCP2) is needed to build states with vanishing conformal weight from those
with negative (tachyonic conformal weight). These allow us to have the correct color quantum
numbers which do not depend on weak charges.
3. At 8:00 PM, Hamed said...
I make my last question more clear …
At Quantum-TGD, the spinor field in modified Dirac equation is a map from the space of 3surfaces to elements of G/H?
At the Classical level, the spinor field takes the point of space-time at imbedding space as
argument and gives the spinor associated with the point. Components of the spinor are complex
numbers.
At the Quatum level, seond quantized induced spinor field takes point of WCW(3- surface) and
gives WCW spinor. Components of WCW are many fermionic states. The fermionic states are
elements of G/H. the algebra of G/H acts on the 3-surfaces of WCW. Is there any incorrect?
4. At 8:21 PM, Matti Pitkanen said...
To Hamed:
There is indeed correlation between colour and electroweak quantum numbers for solutions of
ordinary massless Dirac equation in CP2 and imbedding space. As I explained, this is wrong but
colour Kac-Moody algebras associated with vibrational degrees of freedom of partonic 2-surfaces
and its center of mass degrees-of-freedom help to build massless states as colour singlets for leptons
and colour triplets for quarks.
159
I have been perhaps too lazy. Some mathematical work might allow to improve understanding
of this connection. This connection between holonomy and isometries is somewhat analogous to the
connection between magnetic and electric fields discovered by Maxwell at his time and coming from
Lorentz invariance.
About spinor field formalism.
(A) Induced spinor fields are analogs of second quantizer free spinor fields and the oscillator
operator algebra is used to build the generators of various super algebras. One can say that
all bosonic quanta are fermion antifermion bound states so that no second quantized gauge
fields appear in the theory. Only the spinors and the purely geometric degrees of freedom
assignable to partonic 2-surfaces and their 4-D tangent space data.
(B) The space of 3-surfaces is union of sub-WCWs which are symmetric spaces labelled by zero
modes (WCW coordinates appearing in line element as parameters only). Sub-WCW is
indeed coset space G/H. G is full symplectic group of delta M4xCP2 and H its subgroup.
This means huge injection of mathematical well-definedness to the theory. Mathematicians
are intensely studying symplectic groups. Again I must however confess my laziness. The
would be a lot of learning from what is known.
5. At 8:00 PM, Hamed said...
Dear Matti,
Thanks. I didn’t see this before. Interesting:
“Negative and positive energy space-time sheets are space-time correlates for bras
and kets and the meeting of negative and positive energy space-time sheets is the
space-time correlate for their scalar product. Negative and positive energy spacetime sheet meet at X3.”
Hence the geometric correlate of the scalar product is X3. What is similarity between them leads
to the geometric correlation?
I can only understand from the scalar product the interpretation as probability amplitude for the
state ket to collapse into the state bra. So does this interpretation have any similarity with X3?!!!
6. At 4:50 AM, Matti Pitkanen said...
I have probably said this in positive energy ontology.
It is good to re-articulate it in Zero Energy Ontology. In ZEO, the quantum superposition of
space-time sheets inside CD is replaced in each qjump with a new one.
They have 3-surfaces at their ends and in quantum jumps the geometric arrow of time changes at
imbedding space level. The dissipation for the dynamics of Kahler action as space-time correlate of
quantum dissipation takes in opposite directions of imbedding space-time.
Given X3 as end point of space-time, evolution becomes initial point of space-time evolution in
reverse time direction. In this sense the positive and negative energy space-time sheets indeed meet
at X3.
160
7. At 3:46 PM, Anonymous said...
Is there any relation between Euclidian areas and zero energy states, between Minkowskian and
positive/negative areas of space-times? What time is it in the Euclidian area? ;)
8. At 8:11 PM, Matti Pitkanen said...
To Anonymous:
Interesting questions.
1. One could define volumes of various sub-manifolds using (a) the square-root of the determinant of
the induced metric or (b) of its absolute value. Both are general coordinate invariant
definitions.
2. Space-like areas in Minkowskian and Euclidian region obtained using definition (a) obey same
formula since minus signs cancel. For Minkowskian 2-surfaces the area is imaginary. String
world sheets are prediction of the theory and it would not be surprising if they would
contribute exponent of imaginary area to the dependence of quantum state on this surface.
3. For definition( a) and induced 4-metric, the determinant is negative in Minkowskian regions and
positive in Eulidian regions. In the definition of exponential of Kahler action, I use this
definition. Exponential from regions with Euclidian signature is exponential of negative real
valued action and means that the integral over infinite-D World of Classical Worlds is
converging integral and makes sense mathematically. Minkowskian regions give imaginary
exponential giving rise to interference effects. The two parts of Kahler action define Kahler
function of WCW on one hand and Morse function on the other hand (its saddle points would
provide information about the topology of WCW).
Time coordinate in Eucdlian regions is just like spatial coordinates with respect to induced
geometry. That is in abstract internal geometry without any information about sub-manifold
property.
With respect to imbedding space-time, the situation is different. For instance, CP2-type vacuum
extremals have same Kahler and symplectic geometry as canonically imbedded CP2 in M4xCP2 (M4
coordinates constant). They however have light-like random curve as M4 projection and describe
massless particle moving randomly with light velocity. Hence the time coordinate has dynamical
meaning at imbedding space level. The light-likeness condition also gives rise to Virasoro
conditions so that one has conformal invariance.
9. At 6:12 PM, Hamed said...
Dear Matti,
At the measurement of position of an electron, the electron is measured at a certain position.
Hence at this moment, one can say it is a point-like particle. But in TGD, there is no point-like
particle at all. Just 3-surfaces. How is it possible?
Suppose the state of an electron is in a linear combination of |z+> and |z-> that are eigen states of
spin in Z direction. I mean these eigen states Classical degrees-of-freedom(zero modes) and the
linear combination of them a quantum degree-of-freedom. Is this correct?
161
I don’t understand the meaning of localization in zero modes. I understand from the
“localization”, something is localized to something other. But last year you noted my
misunderstanding that there isn’t something localized to zero modes. So in the case of zero modes,
which thing is localized to which thing?
Maybe in the last example of spin, if you explain the localization, I can understand better.
10. At 10:09 PM, Matti Pitkanen said...
Dear Hamed,
The situation you describe is encountered in string models and much earlier in atomic and
nuclear physics. The measurement of position generalizes. In the WCW, 3-surfaces associated with
particle has center of mass coordinates (M4хCP2) and "vibrational coordinates" characterizing the
shape of the 3-surface.
Localization in position measurement means localization in center-of-mass degrees-of-freedom
particle like 3-surface labelled by points of M4. This is just same as treating a Macroscopic object
such as a planet as a point. In "vibrational" degrees-of-freedom, localization does not occur. But
one obtains delocalized eigenstate of color charges and other observables.
WCW spinor field becomes localized in M4 degrees-of-freedom in position measurement . More
precisely, it is cm degrees-of-freedom associated partonic 2-surface with upper or lower boundary of
CD in which localization takes place. This is due to the strong form of holography.
There are delicate issues related to the Uncertainty Principle. I have talked about this earlier and
will not go into this here.
You ask also about zero modes.
Non-zero modes - quantum fluctuating degrees-of-freedom - by definiotion correspond to
degrees-of-freedom whose complex coordinates contribute to the line element of the WCW Kahler
metric. Complex character of the coordinates allows description of these degrees-of-freedom in
terms of Kac Moody type algebras constructible using oscillator operators. These degrees-offreedom define a coset space of symplectic transformations of delta M4xCP2 divided by its suitable
subgroup defining measurement resolution.
Zero modes are those degrees-of-freedom which do not contribute to the line element. For
instance, the values of induced Kahler form are zero modes and various magnetic fluxes associated
with Kahler form define zero modes.
http://matpitka.blogspot.com/2013/08/some-fresh-ideas-about.html#comments
topic: "Some fresh ideas about twistorialization of TGD"
1. At 9:11 AM, Stephen said...
Ahh, so M4xCP2 is the product of Minkowski space and the complex projective plane.
retrospect, things seem much more clear …
162
In
2. At 7:52 PM, Matti Pitkanen said...
To Stephen:
Both M4 and CP2 allow twistorialization. Since the existence of twistor structure is a very rare
occurrence and does not occur for general four-manifold, this is is a strong additional support for
sub-manifold gravity.
This was meant to be the original message of the article as I started to write it. It however turned
out that one ends up to a proposal for twistorialization of the "World of the Classical Worlds"
(WCW) providing completely new insights about meaning of the basic incidence relation. Again,
Zero Energy Ontology is in crucial role.
Grassmannian representation of scattering amplitudes whose core-elments would be formally
practically identical with the twistorial representation in N=4 SUSY. This could make TGD a
calculable theory at a fundamental level.
The gigantic form preserving generalization is the replacement of pairs of spinors defining
twistors with fermionic parts of zero energy states. There are 3 interpretations.
(1) Incidence relation would state Quantum-Classical correspondence. Fermionic parts of zero
energy states corresponds to light-like 3-surfaces.
(2) At the level of Consciousness theory, incidence relation has also interpretation. Boolean
cognition described by fermions corresponds to geometry characterized by light-like 3-surfaces
(sensory perception roughly).
(3) A third interpretation of incidence relation is in terms of WCW supersymmetry. Bosonic
sector that is WCW geometry corresponds in one-to-one manner to fermionic sector. WCW spinor
fields which correspond to fermionic parts of zero energy states.
If this picture is true, Grassmannian formalism would be much much more that an elegant
calculational tool.
My original vision about the twistorialization of vibrational degrees of freedom of WCW
assumed too much.
It seemed that the twistorialization has an analogy in terms of Kac-Moody algebras. Incidence
relations correspond to the condition that sum of bosonic Kac-Moody generators and fermionic
generators bilinear in fermion and anti-fermion annihilate physical states. This is analogy for the
expression of momentum as something quadratic form of the spinors defining twistor.
The crucial condition expressing momentum conservation as expression quadratic in twistors
does not generalize, however. The reason is simply that one cannot assign to vibrational degrees-offreedom infinite-D analog of momentum since Kac-Moody type algebras develop central extension
and only cm degrees-of-freedom define conserved quantum numbers.
In any case, twistorialization generalizes to M4 and CP2 since both have self-dual Weyl tensor.
Hawking and others indeed discovered CP2 as gravitational self-dual instanton but did not realize the
connection of its symmetries with the Standard Model.
163
One can also select between various options for the details of generalized Feynman
diagrammatics. The most conservative option is realised. (Maybe the ultraconservative Lubos Motl
is right here;-).
Still a little comment concerning the differences between TGD and N=4 super Yang Mils:
In SYM, the 3-vertex is fundamental in twistorial formulation. For real momenta, the light-like
momenta are parallel and this induces infrared divergences which are the basic problem of gauge
theories. The momenta on internal lines are massless but complex.
In TGD framework, 4-fermion vertex is fundamental and the emission of gauge boson
corresponds to emission of fermion and antifermion at opposite throats of wormhole contact. The
real momenta need not be parallel anymore and there is no IR divergence. Also the internal lightlike momenta can be real as has been assumed. This implies huge reduction in the number of
contributing twistor and fermion diagrams.
Also, N=4 SUSY could have a TGD analogy. Covariantly constant right-handed neutrinos with
two spin directions plus their antiparticles could generate the analog of this symmetry but without
Majorana fermions. The breaking of SUSY could be due to different p-adic primes characterizing
different members of super-multiplets. The mass formulas would be identical. No super counterpart
of Higgs mechanism would be needed.
3. At 4:51 AM, Hamed said...
Dear Matti,
I want to hear your critique against the following sentence about supersymmetry in TGD
viewpoint. A strong support for Standard SUSY is unification of coupling constants at high energies
in well accuracy.
4. At 10:51 AM, Matti Pitkanen said...
Dear Hamed,
An excellent question.
The unification of couplings constants is assumed in Grand Unified Theories (I think around 10-4
Planck masses or so; correct me if I remember wrong).
It is of course interesting SUSY is consistent with this unification of coupling constants and even
predicts this. I do not know how general gauge groups this holds true (you might actually tell
something about this;-).
The GUT approach has severe problems, however (about problems of SUSY approaches we who
live post-LHC era of course know). For instance, the choice of GUT gauge group is very ad hoc and
does not explain why Standard Model gauge group is what it is. Just the question "Is the Standard
Model gauge group mathematically very special?" might lead to breakthrough.
Proton decay is predicted but has not been observed and this leads to fine-tuning. The value of
Higgs mass leads also to fine tuning and the recent situation is seen by specialist as rather desperate
(see the posting in Resonaances). Also the huge desert between TeV and Planck scales looks
extremely implausible to me.
164
In light of these arguments, I see the unification of coupling constants as an unlucky accident
which has delayed the development of theoretical particle physics for decades (actually a rather short
time as compared to 4 centuries from Newton to Einstein and Bohr;-)).
If I should defend supersymmetry (certainly I want to do it since it is mathematically quite too
beautiful to be not realized in some form), I would speak about super-conformal symmetry and give
up the N=1 assumption since it forces Majorana fermions and non-conservation of B and L. In my
uneducated opinion, the basic problem of SUSY approach is the same as that of superstring models.
Quite too strong and also quite unnecessary assumptions quite too early (and made only to make
calculations possible). Lazy philosophers is what theoretical physics desperately needs;-).
5. At 9:54 PM, Hamed said...
Dear Matti,
Thanks,
> "The choice of GUT gauge group is very ad hoc and does not explain why Standard Model
gauge group is what it is"
But if we see the whole picture, do you think it is ad hoc yet?
I note the following from Baez:
GUT can explain "Why do both leptons and quarks come in left- and right-handed
varieties which transform so differently? Why do quarks come in charges which are in
units 1/3 times an electron’s charge? Why are there the same number of quarks and
leptons? Also, the seemingly ad hoc hypercharges in the Standard Model must be
exactly what they are for this description to work."
I hope you don't say all of these are unlucky accident, too;-).
6. At 8:38 AM, Matti Pitkanen said...
Of course, GUTs can reproduce these empirical facts. But they do not predict them. I am
convinced that there are endless number of other spectra which GUTs can reproduce in internally
consistent manner. There is not a slightest idea for why just the Standard Model group is realized.
If this were the case, the theoreticians would not be telling that Physics has achieved a state in which
only anthropic arguments are possible.
The same number of quarks and leptons is also an empirical fact -- not a prediction of GUT but
only a reproduction of empirical fact. GUT however also predict that the proton should decay. No
decays have been detected.
The problem of GUT is that they are not ambitious enough. To get out of the recent dead alley,
theoreticians should finally start to pose more ambitious questions (they could have done it for three
decades ago;-)) .
Why Standard Model gauge group? Is quark color really what we believe it to be? What is
behind family replication? For the mass differences between various families, GUT description in
terms of symmetry breaking is extremely ugly. Is it enough to have just 2 scales (elementary particle
mass scale and Planck scale)? The huge desert between weak scale and Planck scale is simply
physical nonsense.
165
I do not have anything against these people. I am only sad that they are beating their brilliant
heads against the wall.
7. At 7:00 PM, Hamed said...
Thanks, you are right. GUT reproduce the empirical facts not predict them. This can be interest
thinking.
I realized something better and it leads to some better view about TGD. I write them below. If
anything is misunderstood, please tell me.
One can construct a configuration space from the Space of all 3-surfaces at boundary of the CD
or G/H so that the points of the configuration space are 3-sufaces. WCW spinor fields are physical
states. Their arguments are the 3-surfaces.
One can go to the next level. At the level, I guessed all possible physical states of before are the
points of the new configuration space. I tried to form abstraction hierarchy. But after, I understood
it isn't correct in TGD. The correct is that for this level there is another G/H corresponds to space of
3-surfaces at boundary of CD at this scale and WCW spinor fields are new physical states at this
scale. Continue this process and make hierarchical structure of Quantum-TGD:-)
On the other hand, in my mind there is a hierarchy of Jones inclusions. The space M/N would
correspond to the operators creating physical states modulo measurement resolution. It seems for
me that these physical states are different from the before that were spinor fields of WCW? Because
in before, there was not any cutoff process for making spinor fields of WCW at each scale. But in
the latter, it is needed. If it is different, what is the physical states creating by M/N?
8. At 7:13 PM, Matti Pitkanen said...
You are beginning to understand my vision! I am happy to learn that I am not just a madman
who believes in some weird nonsense ideas!
Hierarchies of causal diamonds (CDs) characterized by their scales and hierarchies of space-time
sheets topologically condensed on each other correspond to inclusion hierarchies in WCW. Spinor
field for the inclusion hierarchies correspond to hierarchies at the level of quantum states in ZEO if
the size of the topologically condensed sheets or CDs defines the scale resolution (also in time
direction).
States created by smaller scale WCW spinor fields. That is, physical states consisting of various
particles are interpreted in ZEO quantum fluctuations whose contribution correspond to radiative
corrections/loop corrections.
Here is something which I do not understand well. The electron is a stable particle characterised
by the Mersenne prime M127.
(a) Common sense says that in the case of topological condensation hierarchy labeled by p-adic
primes, one should treat it as a point-like particle in the p-adic length scales longer than
M127 scale.
166
(b) What about the electron in the scales of CD (of observer) longer than 0.1 seconds for M127?
The electron has always delocalized wave function in the space of CDs involving CDs of all sizes.
Delocalization of upper or lower boundary of CD depending on previous quantum jump. If this
wave function has cutoff in CD size, then quantum fluctuation would be in question. If not, then it is
a real electron lasting forever. An experimenter characterized by CD defining her spotlight of
consciousness cannot distinguish between these 2 alternatives. M127 would characterize the minimal
CD for electron. This interpretation seems okay for me. But is it okay?
About the inclusion hierarchy at the level of WCW:
Symplectic group for delta M4xCP2 corresponds to non-zero modes of WCW. The factor
spaces of it by its normal subgroups are also groups and one obtains a hierarchy of normal subgroups
in division by normal subgroups. These normal subgroup hierarchies are good candidates for the
hierarchies defined by Jones inclusions. These hierarchies would appear as arguments of WCW
spinor fields and would define measurement resolution hierarchies.
9. At 11:47 PM, Hamed said...
The minimal CD for electron means the least time interval for creation and annihilation of
electron positron pair as virtual particles?
> "Symplectic group for delta M4xCP2corresponds to non-zero modes of WCW. The factor
spaces of it by its normal subgroups are also groups and one obtains a hierarchy of normal
subgroups in division by normal subgroups."
This means that at G/H, H is a normal subgroup and one can divide H by its normal subgroup
too. If i call it H2, H has the role of G in H/H2. Is it correct?
Suppose that G/H corresponds to an object at the level of WCW. H/H2 corresponds to its
molecules?
10. At 12:07 AM, Matti Pitkanen said...
Your point about minimal interval is good. Annihilation can of course occur much faster than
than 0.1 seconds if the electron and positron are near enough each other. Could one say that 0.1
seconds is the minimal size of CD for observer able to perceive electron? This time scale would tell
more about observers able to detect electrons!
Your interpretation of normal subgroup seems to be correct. One could say that Hn defines
measurement resolution for Hn-1. Going down the latter would improve measurement resolution.
The number of degrees-of-freedom in ideal resolution would be reduced at each step as it should and
the subgroup defining measurement resolution would become smaller.
Is also G/Hn group that is is Hn normal subgroup of also G if it is normal subgroup of Hn-1?
This does not seem to be the case since G is larger than Hn-1 and its action can lead out of Hn. (An
exercise for you;-).
11. At 4:18 PM, Hamed said...
Thanks dear Matti,
167
Suppose there is a CD that is at the scale of an ordinary object. At the level of Quantum-TGD,
the molecules of the object corresponds to 3-surfaces at G/H.
> “3-surfaces are actually not connected 3-surfaces. They are collections of components
at both ends of CD and connected to single connected structure by 4-surface. This is like
incoming and outcoming particles in connected Feynman diagrams”
It is because the molecules colliding with other molecules at the Classical view?
In this picture, those paths of molecules that have velocity of faster than light aren't possible
Classically but they considered at the level of Quantum-TGD. Therefore if we want to calculate
entropy of the system, the number of degrees-of-freedom at Classical is smaller than it at Quantum.
So entropy at Classical is smaller than it is at Quantum level?
If the object is solid, there should be very constraints on the motion of the molecules. How these
constraints can be considered at Quantum-TGD?
12. At 10:24 PM, Matti Pitkanen said...
I will try to answer from iPad. Iwould assign to CD secondary n p-adic length scale much longer
than the primary one. Size of the order eart (0.1 lightseconds) viz electron compton length in case of
electron.
Generalization of point-like particle with three-surface: this is the basic idea.
The notion of vitual particle is different from the usual allowing tachyonic vitual momenta. Also
vitual fermions have light-like momenta which can however have negative energy. Therefore virtual
bosons defined by wormhole contacts wit fermion and anti-fermion at opposite throats can have
space-like momenta. Virtual fermions have non-physical helicity. This is what guarantees that they
give nonvanishing contribution to diagram. Quantum-TGD is very classical!
The number of contributing twistor diagrams is very small from kinematic constraints.
13. At 5:29 AM, Hamed said...
Thanks,
If you are in travel and it is difficult to answer by iPad, I will wait.
Different pieces are glued together gradually. This is very beautiful:)
Macroscopic particles are fermions! Yes, we know they can't be at the same position like the
notion of familiar fermion. Now I can understand why fermionic oscillators operator associated with
its CD must create them, not any other! But
(1) What does it means spin of a Macroscopic fermion? Rotating around its axis? Therefore it
isn’t intrinsic with the size of half integer also from spin statistic theorem?
(2) But about bosons, Macroscopic bosons seem very different form familiar notion. Why?
Please tell some similarities.
168
(3) For an observer at the scale of CD of the Earth, we are in superposition of generalized
Feynman diagrams. Oh my god;-). All possible configurations exist. But where are they?
And why we don’t see them? As you know, this is basic critique against many world
theories.
P.S.: A mistake in my comment:
The fermionic oscillator operators create fermionic fock states and not 3-surfaces. My argument
doesn't work now!
14. At 6:35 AM, Matti Pitkanen said...
Dear Hamed,
There is probably some misunderstanding. I am not talking about Macroscopic fermions. With
fermions I mean even something more elementary than the observed fermions.
Observed fermions (like gauge bosons) correspond in TGD framework to 2 wormole contacts
connected by magnetic flux tubes. A closed flux tube going along "upper" space-time sheet turning
back at second wormhole contact and reducing along the lower space-time sheet and through first
wormhole contact to the upper is formed. The Kahler magnetic charge of wormhole throats forces
this picture.
The "ur-fermions" associated with induced spinor field are located at the wormhole throats
whereas observed fermions like the electron are expected to contain neutrino and anti-neutrino at the
wormhole throats its second wormhole to neutralize weak isospin. This is just the simplest picture I
am able to imagine.
There are only fermionic oscillator operators associated with second quantized spinor fields and
the bosonic generators of symplectic algebra and Kac-Moody algebra of light-like 3-surfaces
available to create states. The latter are analogs of bosonic creation operators and excite states in
WCW degrees-of-freedom. This is something new as compared to QFT picture.
Concerning scales, there is some confusion.
(a) CP2 scale (104 Planck lengths) is the scale of wormhole throat. For dark large hbar particles, it is
scaled up accordingly.
(b) Compton length is the primary p-adic length scale proportional to sqrt(p) characterizing the
space-time sheet containing elementary particle.
(c) The scale of particle's CD -- secondary p-adic length scale proportional to p -- is the scale
characterizing perhaps the field body of particle. This is new.
One can argue that the secondary p-adic time scales for particles are actually seen. 0.1 second
timescale for the electron defines a fundamental biological rhythm and also the alpha rhythm of
brains. Cooper pairs of electrons might be behind this and are key players in the TGD-inspired
model of the cell membrane as high Tc superconductor.
That we are in superposition involving field bodies in Earth scale and even longer scales can be
also argued to be directly visible. We have EEG at frequencies correspond to a wavelength of the
order of Earth's size. EEG correlates strongly with contents of consciousness so that it should
communicate something to someone. This "som-one" could be our magnetic body. We know from
169
experiments of Libet that our sensory data is a fraction of second old as if it would come from
biological body to someone (why not the magnetic body?).
http://matpitka.blogspot.com/2013/10/no-susy-dark-matter.html#comments
topic: "No SUSY Dark Matter"
1. At 9:07 AM, Hamed said...
In classical TGD, what does it cause that a 3-suface has some determined components of induced
metric and induced Kahler form? Or what are the things that make a 3-surface this induced metric or
Kahler form and not another possibilities? Also in another words, how one can change the induced
metric or induced kahler form of an object? Maybe when we warm the object, it’s induced metric
changes?
2. At 9:01 PM, Matti Pitkanen said...
Dear Hamed,
Induced metric, Kahler form, spinor connection, etc. are known once the surface is known.
These tensors are just projections of the imbedding space tensor quantities (metric, Kahler form,...)
to space-time surface obtained by contracting with the gradients of imbedding space coordinates.
This is the content of geometrization of physics at classical level in TGD framework. It gives
extremely powerful constraints since only 4 field-like variables remain and one has not only
extremals but preferred extremals of Kahler action. What allows us to avoid contradictions is the
notion of many-sheeted space-time allowing to get the counterpart of superposition for fields in
terms of union of space-time sheets. Effects are superposed, not fields.
About your example: When we warm the object, its induced metric certainly changes a little bit
since the space-time surface representing the object is deformed. When you raise your hand, the
space-time surface representing your hand is deformed.
Here we must of course be cautious. At the quantum level, one has only quantum superposition
of space-time surfaces. Quantum state idealized as single space-time surface is indeed an
idealization. One can assign to quantum state single space-time surface only modulo measurement
resolution: as quantum fuzzy geometry and topology.
In string models using Polyakov formulation, one introduces metric to string world sheet as
independent dynamical degrees-of-freedom rather than as induced metric as in TGD and then
eliminates it using conformal invariance and Weyl invariance. What remains are imbedding space
coordinates in some preferred metric for world sheet (gauge choice) plus Faddeev-Popov ghosts. In
TGD, one replaces the notion of path integral approach with that of WCW geometry.
3. At 7:12 PM, Hamed said...
Dear Matti,
Thanks, I have presumptions on GRT and this leads to misunderstanding about TGD. Therefore
I'll try to ask about superposition of effects to understand better about it:
170
Suppose there is a test particle on a space time sheet. Now the test particle moving along the
geodesics in the effective metric. This effective metric is sum over deviations of induced metrics
from flat M4 metric at various space-time sheets.
Let us create a new object on the same space time sheet that the test particle was on it. The
induced metrics of the various space time sheets (also at other regions outside of the object) are
changed by the object. Hence the object influence on the test particle by changing the metrics of
various space-time sheets.
In GRT, one can say the new object only influence on the space-time(that is one). But here it
influence on the various space-time sheets.
But how can calculate that what is the amount of the influences on each of space-time sheets?
For example, the Ssun because of its mass, influence on the space time sheets of Solar System and
the Milky Way galaxy. In other words, can one calculate counterpart of Sun to metrics of spacetime sheets of solar system and of Milky Way galaxy at every point.
4. At 9:28 PM, Anonymous Matti Pitkanen said...
Dear Hamed,
Quite a challenge! Thinking in terms of preferred externals it is clear that the formation of
wormhole contact (touching) between test particle and various space-time sheets assignable to
massive bodies certainly affects the space-time sheets of the massive objects. The challenge is how
to calculate this.
The approach that I take serious is QFT/string-inspired. It assumes at the fundamental level
quantum superpositions of space-time sheets but does not deal explicitly with them. The outcome is
essentially stringy description at the level of imbedding space. Getting rid of details is possible
thanks to the gigantic symmetries involved.
● If one can construct QFT approach allowing to describe also graviton scattering, one can argue
that one one forget all the details and apply the results even in Astrophysical context. Since
particles are space-time sheets at fundamental level, it would seem to me that Feynman
diagrammatic approach is the only approach that can be practical.
● This gives amplitudes and by very general arguments the result must be same as those
resulting from general assumption such as spin 2 character of the graviton. Twistor
Grassmann approach would allow to skip over all details involved and approximate the
situation by stringy variants of twistor diagrams in M4xCP2. It is quite essential that string
world sheets connecting wormhole contacts are involved even in the description of
ordinary physical particles. The wormhole contacts itself are building bricks. Without the
presence of another contact, one would have single Kahler magnetic monopole not allowed
by field equations.
The beauty of this approach is that it automatically takes into account momentum conservation
and the reaction of test particle to the motion of particle. To me this looks the most realistic
approach as far as the response of central mass to test particle is considered at the level of
momentum balance.
171
How to translate this picture to space-time geometry? Suppose that approximating of system
with single space-time sheet makes sense with a finite measurement resolution (he objection that
colour quantum numbers require superposition in CP2 cm degrees-of-freedom can be circumvented).
Does the Classical approach really work? Or should one consider motion as sequence of
Quantum jumps in which the Classical space-time surface assignable with the central mass or test
particle is replaced by a new one and defines "instantaneous eternity" moving in M4?
For "istantaneous eternity" option, the proper time coordinate along orbit would define a
sequence of "instantaneous eternities" (in the approximation that the duration assignable to quantum
jump vanishes). This option seems more attractive to me. With these assumptions, the origins of
space-time sheets with asymptotic Schwarschild metrics would move along the orbits of central
mass and test particle in M4.
One should also say something more concrete about these "instantaneous eternities". What it
really means when "test particle is on a space-time sheet". Particle has wormhole contact
connections to several space-time sheets. This question is also encountered in approach A leading to
stringy amplitudes.
(a) The most fundamental wormhole contacts correspond to the structure of particle itself and
there is Kaehler magnetic monopole flux through them stabilising the contacts. One might
call these two space-time sheets the fundamental ones and they are expected to be glued
along their boundaries to form single 2-sheeted structure - say in the scale of Compton
length (it seems difficult to satisfy boundary conditions if one allows real boundaries).
Then there are also the sheets which particle just touches: these wormhole contacts are
unstable. In this sense, the particle can reside at several space-time sheets simultaneously
and experience the superposition of effects. Particle exists at space-time sheet when it has
Kahler magnetically charged wormhole contact to it. This looks good.
(b) Schwartschild metric allows imbedding as vacuum extremal and non-vacuum extremals
could be small deformations of Schwartschild metric asymptotically. In the zeroth
approximation, only that of test particle. In the next approximation, the M4 positions of
also central mass would change quantum jump by quantum jump. M4 momentum
conservation (not available in GRT) should help to evaluate this motion. The projection of
the orbits to M4 would be an essential part of description lacking from GRT description and
give the Newtonian description in terms of forces.
5. At 6:42 PM, Hamed said...
Dear Matti,
One can say there are two Hamiltonians. One for vibrational degrees-of-freedom of the 3surface in space of simplectic orbits of the 3 surface and another for cm degrees-of-freedom of the 3
surface. Sum of the two Hamiltonians are the total Hamiltonian. Is that a correct picture?
6. At 8:41 PM, Matti Pitkanen said...
Dear Hamed,
The key idea is that scattering amplitudes for graviton exchanges at the level of imbedding space
is the correct approach to gravitation.
172
This gives automatically rise to scattering with reaction from momentum conservation whereas
in the approach of General Relativity (geodesic lines) based on abstract space-time geometry one
loses four-momentum and can speak only about acceleration.
The use of single space-time surface to describe the entire scattering is perhaps too strong and
idealisation. "Instantaneous eternity" would replace single space-time with a sequence of them
parametrized by proper time coordinate. The best approach is perhaps to accept WCW picture from
the beginning since it is indeed used to deduce scattering amplitudes.
You talk about Hamiltonians in the sense of Classical Field Theory. Essentially as generators of
time evolution for 3-surface in WCW or rather phase space associated with it. I am skeptic about the
usefulness and even existence of this kind of description in TGD framework. Just this skepticism
led to the notion of WCW and to geometrization of Quantum Theory.
(A) In the usual Classical QFT, one can introduce formally Hamiltonian formalism once one has
Lagrangian. This requires extension of the configuration space of fields at time=constant
slice (analog of WCW) by introducing canonical momentum densities so that one obtains
phase space as symplectic manifold (that is analogs of q and p in wave mechanics).
Conserved energy for fields gives Hamiltonian acting in phase spac, and one can
formulate time evolution in terms of this Hamiltonian and also perform quantisation by the
usual rules extended to infinite-D context. Of course, the usual problems emerge. Normal
ordering difficulties and infinities in perturbation theory due to squares of delta function.
The approach works only formally since the replacement of Kronecker delta by Dirac delta
does not work.
This problem relates deeply to 3 different algebraizations of quantum theory proposed by
von Neumann. The use of factors of type III correspond to the naive replacement of
Kronecker by Dirac. Hyperfinite factors of type II does not perform this replacement. Finite
measurement resolution is the key notion expressed in terms of inclusions of HFFs and it
effectively keeps Kronecker deltas since finite measurement resolution implies discretization
at space-time and imbedding space level.
(B) In TGD framework, this naive field theory approach fails. One can define canonical
momentum densities but cannot solve time derivatives of imbedding space co-ordinates as
single valued functions. The basic reason is that action principle becomes extremely
degenerate at space-time surface defined by canonical imbedding of the empty Minkowski
space. In lowest order, the action is 4th order in gradients around M4 so that one cannot
defined propagator in terms of kinetic term quadratic in gradients.
Perturbation theory fails completely because one cannot define propagator for small
deformations of M4. One could even define Hamiltonian as conserved energy formally. But
one cannot define the phase space so that it does not help much.
To sum up, Hamiltonian cannot define time evolution of space-time surface in TGD framework.
Hamiltonians appear in TGD (or my vision about TGD) in completely different manner as
representations for Lie-algebra of the infinite-dimensional space of 3-surfaces. More precisely, the
action is on partonic 2-surfaces at boundaries of CDs and field equations for preferred externals
allow to continue its action to partonic 2-surface to that on entire 4-surface. This is delicacy but an
important one.
173
(1) WCW (or rather that part of WCW, which corresponds to quantum fluctuating degrees-offreedom which by definition are those contributing to the line element of the metric of
WCW) can be regarded as infinite-D symplectic group possessing a unique metric invariant
under the group action. Here one can consider also coset spaces (finite measurement
resolution and conformal symmetries). But this is technical detail.
(2) The exponentiation of these Hamiltonians generates one-parameter subgroups of this
symplectic group. These orbits are analogs of particle orbits with Hamiltonian dynamics.
But I believe that one cannot chose any specific Hamiltonian as "THE Hamiltonian" (this
for the reasons that became already clear).
(3) These Hamiltonians define isometries of WCW (but not of imbedding space in general). This
is important since it means that WCW has infinite-D isometry group. Without this, there is
no hope about well-defined Riemann connection in WCW as became clear already in the
case of loop spaces.
(4) These Hamiltonians can be taken to be function basis for delta M4xCP2 and they can be
labeled by color quantum numbers, angular momentum, integer n labelling the dependence
on power of light-like radial coordinate.
Your decomposition to vibrational and cm degrees-of-freedom but Hamiltonian interpreted in
terms of time evolution of TGD does not make sense in TGD framework but does have an analog in
this picture. Those Hamiltonians of CP2 that represent isometries indeed act on CP2 cm degrees-offreedom of 3-surface. In delta M4+, the Hamiltonians representing rotation of delta M4+ (r=constant
sphere S2) are also isometries. M4 translations do not allow representation as WCW Hamiltonians
since they lead out of delta M4+. But this is another problem.
What probably makes it difficult for one to understand TGD are the thinking habits from General
Relativity and from Classical Field Theory.
(A) In GRT, one thinks in terms of abstract 4-geometries (no forces, just geodesic motion). In
TGD framework in terms of 4-D surfaces so that 4-momentum conservation and
description of gravitational scattering in imbedding space M4xS replace pure space-time
description (forces as momentum exchanges make a comeback!).
This is what happens already in string models formulated in M10. Of course, this is an
unphysical option. This fantastic outcome was lost, however, since people wanted to get
space-time out of the theory describing physics of 2-D space-times either by spontaneous
compactification or by introducing "branes". The introduction of stringy landscape
probably is (and hopefully remains) the silliest sidetrack in the history of Theoretical
Physics.
In TGD, the fundamental approach relies on WCW. One gives up the notion about
unique space-time and replaces it with quantum superposition of space-times. One can of
course hope that unique space-time could emerge as a reasonable approximation made
possible by finite measurement resolution.
(B) Standard canonical quantization and path integral formalism fail in TGD even at a formal
level. Actually they fail also in QFT as the problems with infinities demonstrate.
174
The solution is geometrization of Quantum physics by introducing WCW and represents
something completely new having not counterpart in officially existing theoretical physics.
WCW is the counterpart of configuration space. No counterpart of phase space is
introduced since this is not possible. Finite measurement resolution (no replacement of
Kronecker by Dirac) meaning use of hyperfinite factors of type II1 is the mathematical
counterpart for this approach.
http://matpitka.blogspot.com/2013/11/nmp-and-consciousness.html#comments
topic: Negentropy Maximization Principle (NMP) and Consciousness
1. At 8:49 AM, Hamed said...
Dear Matti,
Thanks for the new postings.
> “bosonic emergence means that gauge bosons are identified as bound states of fermion and
antifermion at opposite light-like throats of wormhole contact.”
I can’t imagine that. Opposite light-like throats of wormhole contact means intersection of lightlike throats of wormhole contact with two opposite boundary of Causal Diamond? But this is
partonic 2-surface. Hence the two partonic 2-surface identified as Fermion and anti-fermion? There
is misunderstandings for me.
2. At 9:10 AM, Matti Pitkanen said...
Dear Hamed,
There is a misunderstanding. "Opposite" does not refer to opposite ends of causal diamond but
to wormhole throats at two space-time sheets connected by wormhole contact.
● Imagine two space-time sheets very near to each other and wormhole contact connecting them.
● Fermion is at another throat and anifermion at another one. The stability of wormhole contact is
guaranteed by monopole Kahler flux through it.
● Since flux lines must be closed, there must be a second wormhole contact so that one obtains
closed flux tube traversing from throat to another one along "upper" space-time sheet and
returning along lower one. This is the minimal model of elementary particle and also
automatically includes the graviton.
3. At 7:30 PM, Hamed said...
Dear Matti,
Thanks. But as i understood, the fermions and anti-fermions are only like the ordinary fermions
and not equal to them.
I write an analogy and ask my questions:
Special Relativity says that velocity is relative because we measure only rate of changing of the
position of an object with respect to ourselves as velocity and not absolute velocity.
175
Just like this, can one say that Kahler field is relative because we can measure only difference in
Kahler potential of some space time sheet with respect to our spacetime(by fixing gauge of Kahler
potential equal to zero at our spacetime sheet). Hence, Kahler field is not absolute like velocity.
Another analogy: I saw at the articles that at high electric field, permittivity of matter vary. Hence
by analogy between 1/2*mv2 and 1/2εE2(ε is permittivity of matter), this is like mass vary at high
speed. Hence just like 1/2*mv2 is not correct at high velocities and it is an approximation of mc2 m0c2 for low velocities. It seems 1/2εE2 must be replaced with another relation maybe εE_max2(like
mc2) or some other relation.
L=J^mnuJ_munu is not exception so that it seems it is not correct at high density of Kahler field
and the Lagrangian must be replaced with another relation. What do you think?
4. At 8:55 PM, Matti Pitkanen said...
Dear Hamed,
You are right about Special Relativity. All boils down to the statement that four-momentum is
Lorentz vector. Also p-eA is four-vector in M4 which is the more standard manner to say that
Kahler potential is "relative". The representation of A indeed depends on what M4 coordinates we
use for the space-time sheet.
I would not use the analogy between kinetic term for particle and "kinetic term" for Kahler
action. They are not so directly related. Maxwell and Kaehler action are essentially uniquely
determined from the condition that they do not involve dimensional parameters other than CP2-size
scale. This makes space-time dimension D=4 unique.
Note that in induced geometry, Kahler action is extremely non-linear with respect to imbedding
space coordinates. Much more nonlinear than Einstein action with respect to space-time metric.
The rapid variation of CP2 coordinates leads to the change of the signature of induced metric to
Eucldiian as is easy to understand by studying the expressions for the components of induced metric
(in particular g_tt). These regions correspond to elementary particles so that the extreme nonlinearity has easily understandable effects. Cosmic strings are another implication of non-linearity
meaning "compactification" of two space-time dimensions.
5. At 11:52 PM, Hamed said...
Dear Matti,
You wrote that Kahler potential is relative. ence suppose there is two small 3-surface located in
imbedding space. One has Kahler potential B1 and Kahler form J1 and another has Kahler Potential
B2 and Kahler form J2.
Hence, the relative Kahler potential is B1-B2 and one can conclude that relative Kahler form is
J=J1-J2=d(B1-B2).
Hence Kahler form is relative too and not absolute. is this anything wrong in the argument?
Another question:
176
In Special Relativity, the distance between two point as (C2t2-X2-Y2-Z2) is invariant under
transformations of observer with different velocities.
n TGD, space-time sheets are
hyperquaternionic subspace of hyperoctonion space.
Suppose there is two observer approximating as two 1D light curve located in the hyperoctonion
space. What is invariant between them? Is the minimum distance between two point in
hyperoctonionic space is invariant between the two observer? As i understood hyperoctonionic
space is flat but M4xCP2 that is dual description is not flat.)
6. At 12:50 AM, Matti Pitkanen said...
I said that Kahler gauge potential is "relative" and meant that it behaves as vector field and thus
4-vector just like four-momentum. This is all that is needed. You mean above relative in stronger
sense.
This stronger sense holds true only in the sense that you can add to Kahler potential gradient of
scalar without affective Kahler form. U(1) gauge invariance.
Concerning your second question, hyperquaternionicity is conjecture about preferred externals.
It is difficult to imagine deeper fundamental dynamical principle than associativity. But it could be
wrong!
Suppose one has two light-like curves - say assignable to the two wormhole contacts or two
particles: distances are of course defined in appropriate natural resolution.
If one restricts consideration to the either boundary of the CD, then the distance along fermionic
string connecting the points at different throats would define natural distance. It could be calculated
either in the induced metric or just considering the end points as points of imbedding space and
calculating the distance along geodesics connecting them. This would give shorter distance. Hyperoctonionicty is not involved in any many in this definition of distance.
7. At 7:27 PM, Hamed said...
Dear Matti,
This is as very last texts: “all 3-surfaces on the orbit of 3-surface X3 must be physically
equivalent so that one can effectively replace all 3-surfaces Z3 on the orbit of X3 with a suitably
chosen surface Y3 on the orbit of X3. The Lorentz and Diff4 invariant choice of Y3 is as the
intersection of the 4-surface with the set delta M4xCP2 where M4 denotes the boundary of the light
cone”
As I understand, X3 and all 3-surfaces belong to its orbit like Y3 beginning at either end of CD
and ending to the other end of CD. The orbit of X3 means a symplectic transformation of X3 that
leaves induced kahler form invariant. You noted that the 3-sufaces in the orbit are separated by a
zero distance from each other in the configuration space metric. Why is there zero distance between
them?
8. At 9:06 PM, Matti Pitkanen said...
Dear Hamed,
177
That the orbit of X^3 is dictated by a symplectic transformation is too strong a statement. It
would be completely analogous to a statement that the orbit of particle is obtained by a translation:
this would make sense only for three particle.
Symplectic transformations appear only as symmetries just as translations do in translationally
invariant system (note that all particles are translated in the same manner!).
The action of symplectic transformation is most probably limited to just partonic 2-surfaces and
their tangent space data at the ends of CD and the 4-D space-time surface is dictated by field
equation. Stronger form would allow their action 3-surfaces at the ends of CD and to light-like
orbits of partonic 2-surfaces. That symplectic transformations would act in this manner as
symmetries is non-trivial.
The construction of WCW geometry favors strongly the minimal option. The point is that superconformal invariance requires that induced metric does not appear in the expressions of WCW
Hamiltonians as Kahler fluxes weighted by Hamiltoans restricted to partonic 2-surfaces. If 2-D flux
integrals are replaced with 3-D integrals, one cannot avoid the presence of induced metric.
The third coordinate of X3 would correspond to gauge conformal degree of freedom analogous to
the z coordinate in case of strings and one could choose the value of light-like radial M4 coordinate
rM of light-like CD boundary freely as function of other two coordinates of X3. Analogous statement
would hold true for light-like coordinate at the orbits of partonic 2-surface.
Note that this manner of action does not mean that Kahler action remains invariant and one
obtains conserved charges. If this were the case, WCW metric obtained in terms of second
functional derivatives of Kahler action would be trivial in symplectic degrees of freedom!
Therefore symplectic transformations define isometries of WCW but do not act as symmetries of
Kaehler action.
I have considered the possibility that the slicing of space-time surface to partonic 2-surfaces and
string world sheets could define different choices of representations for partonic 2-surfaces and
tangent space data and these choices would correspond Kahler functions differing by real part of
analytic function of WCW complex coordinates. This does not affect WCW Kahler form as is easy
to see and corresponds U(1) gauge transformation for Kahler gauge potential of WCW.
Cconcerning your question about zero distance between 3-surfaces in the orbit, I would guess that I
have talked about light-like orbit of partonic 2-surface at which 4-metric changes signature. I would
also guess that I have referred to the distance between partonic 2-surfaces at the orbit defined by
induced metric. This is naturally zero just like the distance between spheres of expanding light-front
vanishes. Light-like 3-surface is just like light-like geodesic but for extended object.
This statement made at the level of WCW is unnecessarily strong. All that is needed to consider
are the partonic 2-surfaces and tangent space data at the ends of CD. Saying something about
partonic 2-surface between them seems u-necessary as far as scattering amplitudes are considered
but could bring in flexibility. This is of course the essense of (the strong form of) holography.
General coordinate invariance as almost free choice of differ related representatives for X3 is
probably possible only in some sufficienty small space-time region. In any case, this inspires
questions.
178
● Can one use any partonic 2-surface at its light-like orbit as representative? If so, how can one
formulate construct elementary particle vacuum functionals if the conformal equivalence class
described by moduli varies along the orbit? Restriction to boundaries of CD would solve these
problems.
● Can one slice the space-time surface to partonic 2-surface parametrized by string world sheets as
the structure of preferred externals suggests (decomposition to longitudinal and transverse
degrees of freedom defined by local light-like momentum and orthogonal polarisation)? I tend
to believe that this slicing can be true only in sufficiently small regions of space-time since the
slicing must develop singularities.
● Partonic 2-surfaces assigned with CD boundaries is in certain sense maximal choice. Upper and
lower space-like 3-surfaces have maximal time-like distance. Could one shift boundaries of
CD by upwards and downwards to obtain a family of parallel light-cone boundaries? Could
this slicing have physical meaning? What about its singularities?
9. At 12:00 AM, Hamed said...
Dear Matti,
So thanks, I understand now that I confused between X3 that is space like 3-surface and Xl3 that
is light like 3-surface! Hence I thought your means of orbit is symplectic orbit of light like 3surface(that WCW is space of symplectic orbits of light like 3-surfaces).
But it was
misunderstanding.
In QFT, between two electrons there are photons as propagators creating from one electron and
annihilated at another. But in TGD, photons are emerging from two wormhole throat at two space
time sheet that connect through a wormhole contact.
1- Hence in my imagination of TGD, there are a lot of wormhole contacts going from one electron to
the other electron?
2- It seems for me this makes photons heavier than electrons. Because electron is just one space
time sheet glued to the larger one but photon is two space time sheets.
3- In TGD, the gauge fluxes going from of one wormhole throat to the other. But in QFT, gauge
fluxes is quantized and appears as paths of gauge bosons in Feynman diagram and noting
remain as gauge fluxes. Hence gauge fluxes in TGD are something different that not
quantized. What are them?
10. At 12:55 AM, Matti Pitkanen said...
Dear Hamed,
Here are my answers.
1- The picture about Feynman graphics and its twistorial counterpart is very similar to stanard one
but requires imaginative muscles!
● If particles were just wormhole contacts, then wormhole contacts would split in two when
electron emits photon. The electron would carry fermion number at second throat and
photon fermion and antifermion at its two throats.
179
● The picture is actually more complex.
- Stable wormhole contacts must carry magnetic flux throught them and this reuqires that also
second wormhole contact is present. The flux flows to second wormhole contact throat,
through that contact, and returns along second sheet to the original wormhole contact. You
get closed flux loop as the absence of isolated magnetic charges requires (monopole flux is
possible but due to topology of CP2).
-
Feynman/twistor diagrams are relaced by their stringy variants. The visualization would be
in terms of open strings. Think of open string with finite length as incoming string. Then it
is doubled to two travelling at different directions. I think that Ed Witten actually proposed
this kind of diagram in his variant of string field theory based on generalization of ChernSimons action. Now something this happens at both space-time sheets. Here my ability to
imagine is meeting its limits (but you have a younger brain;-).
2- I do not see why photon should be heavier than electrons. Also electron has second space-time
sheet (at least interacting electron. The second throat need not however carry fermion number.
It could however carry excitations generated by the superconformal algebra.
If mass comes from p-adic thermodynamics, it is possible to understand why photon is very
light (probably not however exactly massless). The second throat must carry neutrino-right
handed neutrino pair to neutralize weak isospin above weak scales. It is also possible that right
handed neutrino is opposite to fermion carrying electron quantum numbers.
I do not understand the details of p-adic massivation completely at this level. One challenge
would be to perform p-adic mass calculations by bringing in detailed model of particle. I am too
old and too lazy and not angry enough to start a project requiring so much adreline;-).
3- I am not quite sure what you mean. In TGD, magnetic fluxes can be assigned to flux tube like
structures with transversal cross section which is closed two-surface and obtained as a
deformation of cosmic string with infinitely thing M4 projection and CP2 projection which is
sphere in the simplest case but can have also higher genus. The fluxes are quantized! This
gauge flux is exactly similar to a gauge flux point Adl in Abelian gauge theory allowing
magnetic monopole. Now of course, the monopole is homological and relates to non-trivial
CP2 homology.
11. At 4:30 AM, Hamed said...
Dear Matii,
1- At the time of interaction, a lot of gauge bosons (maybe infinite number of them) interacts with
the fermion at the same region of space time.
2- in other hand, there are space time sheets that these bosons and the fermion touch to them. Each
of the space time sheets contributes in the momentum of the fermion at point-like limit as p-->
p-eA1-eA2-eA3...) where Ai is the induced spinor connection of CP2 to i-th space time sheet at
the region. This is superposition of effects at this level.
In my imagination, the number one and the second are very separately. How it is relation
between interactions of bosons with the fermion and Ai at space-time sheets?
180
12. At 5:05 AM, Matti Pitkanen said...
Dear Hamed,
1. I did not understand what you mean with this statement. Picture is essentially similar to the
ordinary one and at QFT limit (forgetting heavier string excitations) should be what one expects
from QFT.
2. I think I understand the source of confusion here. Let us think in terms of QFT first.
The Feynman diagrammatics or twistor diagrammatics gives the amplitudes in absence of external
Classical fields.
In practice, one must however describe the presence of complex external systems (which might
contain something like 1023 particles as Classical fields and add to the action corresponding source
term.
This gives rise to additional terms in the perturbative expansion. Description of atom sis
excellent example of using external classical E-M field of the nucleus. Actually the only one really
working!
Same happens now. One has the twistor Grassmann diagrammatics in absence of space-time
sheets carrying the Classical fields of various systems involved. These give rise to additional
interaction vertices. Interactions are additive although the Classical fields are not at the level of
space-time sheets.
13. At 8:06 PM, Matti Pitkanen said...
Hi Stephen,
Canonical quantisation is what leads to Wheeler-deWitt equations. The procedure is formal
application of what one does in Wave Mechanics and as such would be a huge extrapolation.
In GRT, the problems in its application are due to general coordinate invariance (GCI) and one
must somehow fix the space-time coordinates to build Schroedinger equation in the space of 3geometries ("World of Classical Worlds" in TGD consisting of 3-surfaces - equivalently of spacetime surfaces by holography realising general coordinate invariance).
As a consequence of GCI, the action of Hamilton describing time evolution on physical states
vanishes identically. The reason is that Time translation is just one particular general coordinate
transformation. This means that there is no unitary time evolution. One loses Time. This is a big
problem. Barboux has even proposed that Time is illusion.
The r problem is the following. Time translation acts as isometry in Special Relativity and the
existence of Hamilton follows by Noether theorem. Now Time translation is just a general
coordinate transformation and "gauge transformation" so that Hamiltonian vanishes.
One should be able to realize translations as genuine isometries. But they cannot be isometries
of space-time. Here from this point, the path to TGD is very short. Space-time as a surface of M4xS
and translations as isometries of M4!
181
As I started TGD, I tried to apply canonical quantisation to TGD. It failed completely since time
derivatives of imbedding space-coordinates were many-valued functions of canonical momentum
densities and the relationship was hopelessly non-linear. A few years ago, I realized that this manyvaluedness might actually be behind the effective covering spaces associated with the hierarchy of
Planck constants since this many-valuedness indeed can be described in terms of covering space.
Canonically-imbedded M4 represented the worst case. In this case, Kahler action density was
fourth order in the gradients of coordinates so that kinetic term was identically vanishing. For this
reason also the path integral around M^4 failed. The propagator was simply 1/0! I was forced to
find totally new approach.
Around 1985 I discovered the idea of WCW geometry ("configuration space" at that time). It
took about 5 years to finally discover how WCW Kahler geometry could be constructed and that
WCW must have maximal isometries in order that this geometry even exists. Super-conformal
invariance, generalization of Kac-Moody symmetries, etc. are necessary for WCW geometry to
exist. Physics is unique from its mathematical existence.
http://matpitka.blogspot.com/2013/12/one-mind-theory-akashic-records-and.html#comments
topic: One Mind theory, Akashic records, and Negentropic Entanglement
1. At 8:27 PM, Hamed said...
Does spinor wave function an objective reality that associate with CP2 and induced on the spacetime surface? For example, can one say it is some another objective reality that relates to space-time
as square root of metric of space-time?
I am really interested to know that what do you think about g=h+e that h is Lie algebra of
rotation and e is generators of boost. Can one say that Jones inclusion has classical counterpart that
relates to finite dimensional matrices of rotation and boost included to larger finite dimensional
matrices of rotation and boost!?
2. At 10:59 PM, Matti Pitkanen said...
Dear Hamed,
An interesting question. I must put my words cautiously since I did not understand the first
question;-). Instead of trying to answer "yes" or "no", I just state what I believe are the facts. I hope this
list has something to with your question;-).
The function of second quantized induced spinors is to define WCW spinor structure with gamma
matrices constructed as combinations of oscillator operators. Also fermionic quantum states are
constructed using the oscillator operators. One has always quantum superposition of the surfaces
carrying these fermionic states.
The induced spinor fields do not carry color - only electroweak quantum numbers. Imbedding space
spinor harmonics carry color quantum numbers and are assignable to ground states of the conformal
representations. These ground states correspond to elementary particles at point-like limit.
182
Thus it seems that induced spinor fields are like spinor fields assigned with string world sheets.
They are not directly visible at the level of elementary particle physics but are necessary to understand
it.
Same applies to space-time sheets. One has always superposition of them in quantum states. One
can speak about single space-time surface only in finite measurement resolution - as an equivalence
class of space-time sheets.
An interesting conjecture inspired by quantum classical correspondence is that the Classical
correlation functions for local quantities (averaging of products over point pairs with same M4
coordinate differences) are identical with the quantal ones for all space-time surfaces in the
superposition. One could say that "quantum average space-time" corresponds to the equivalence class of
these space-time surfaces. This would be fuzzy geometry at space-time level!
Also Classical Noether charges in Cartan algebra would be identical with their quantum counterparts
for all space-time surface in the superposition if quantum classical correspondence is taken really
seriously. I earlier raised an interesting question. Could it be that classical Noether momentum for
Kahler action could correspond to inertial momentum and equal to the quantal four-momentum
assignable to super-conformal representations and identifiable as gravitational four-momentum?
One could also argue that the fermionic Fock states for all space-time surfaces in superposition have
same fermionic quantum numbers. Manyfermion states are interpreted as Boolean statements and in
Zero Energy Ontology as equivalence of Boolean statements A<-->B associated with positive and
negative energy parts of the state.
Could one require that Classical correlation functions for modes of the induced spinor fields are
same as quantal correlators. And could one identify correlation functions for gauge bosons expressed
using representation in terms of fermonic oscillator operators with correlation functions defined by
classical gauge boson fields?
Concerning your second question, one can assign to the series of Jones inclusions a hierarchy of
quantum phases coming as roots of unity and to these one can assign simply laced Lie-algebras and
corresponding quantum groups with fractional dimension.
I have been always thinking in terms of compact groups associated with these algebras. Where also
complex forms of the algebras (say SO(3,1) ) allowing to talk about boosts make sense is not clear to
me. This area of mathematics makes is magic to me. I know only some magic results but cannot deduce
them.
http://matpitka.blogspot.com/2013/12/about-notion-of-four-momentum-in-tgd.html#comments
topic: About the notion of four-momentum in TGD framework
1. At 9:00 PM, Hamed said...
1. At the level of Classical TGD, metric of space-time is induced from CP2. Does metric of the
WCW is induced from another space? I can guess this space is some algebra in infinite
dimensional Lie algebra. In really infinite dimensional analogous of SU(3)/U(2). This is
correct? Or at least one can assume this?
183
2. Irreducible representations of Poincare group gives classification of particles. The particles are
sources of Classical gauge fields. What does irreducible representations of G/H or G gives?
Can one say they are source of some more abstract field at the level of WCW? Some infinite
dimensional Lie algebra counterpart of electroweak theory!
My intuition is that the irreducible representations of G/H (or maybe G) are chemical
elements! Hence one can bring all the chemistry at the level of mathematics!
3. What do you think about the new hierarchy?:
In TGD, there are 3-level at partonic level, at imbedding space level, and at WCW. One can
say there is another level. That each point of it is a WCW! This is level of Chemistry.
One can go ahead. Aanother level is level of Biology. Every animals or insects are at this
level as very abstract entities.
Concepts of morality is at another level!
imaginations!!!
I think God is at top of them!
Beyond the
2. At 12:52 AM, Matti Pitkanen said...
Dear Hamed,
1. WCW metric is not induced. It is given rather than dynamics. The conjecture is that it is fixed
completely by the existence of Riemann connection and the condition that it is Kahler. This
would mean that physics is unique by this existence condition.
In the case of loop spaces, this is the case. WCW would be a union of infinite-D symmetric
spaces labeled by zero modes appearing as parameters of the metric. The symmetry spaces in the
union are infinite-D analogues of CP2 which is also symmetric space. Note that there is also
decomposition to sub-WCWs assignable to CDs.
2. Particles as modes of WCW spinor field would define irreps of G in G/H and this would give
infinite multiplets analogous to those obtained for super-conformal representations. Masssquared would obey stringy mass formula. The size of these representations would be huge since
symplectic group is infinite-D.
The massless states of these representations would correspond to massless elementary
particles getting mass by p-adic thermodynamics- that is slight mixing with ultra massive
excitations. In ZEO this mixing makes sense.
Euclidian stringy excitations would be associated with wormhole contacts with ends of string
at wormhole throats. Second kind of stringy excitations (Minkowskian strings) are associated
with the ends of string connecting two wormhole throats. Actually Euclidian and Minkowskian
strings combine to form a closed string: lower to upper wormhole throat- to wormhole throat of
second wormhole contact-upper to lower wormhole throat- back to the throat were one started.
They seem, however, define rather independent degrees-of-freedom. This my vision. Take it
with a grain of salt.
The Minkowskian pierces of strings would be associated with hadrons. They could be
associated with molecules too as flux tube contacts and maybe chemical bond could have
184
something to with them. The hierarchy of Planck constants suggests that long flux tubes (stringlike objects) are central in biocatalysis and communications and make possible coherence of
Living matter.
3. I am not quite sure what you mean. In any case, hierarchies are predicted to be there and would
be realised in various manners. As hierarchy of space-time sheets, hierarchy of Planck constants,
hierarchy of CDs, p-adic length scale hierarchy, hierarchy of selfs, hierarchy of infinite primes.
Biology would involve in essential manner large values of Planck constants making possible
negentropic entanglement and its generation as "Akashic records". The entire Universe could
be called 'God'.
3. At 3:04 AM, Hamed said...
Dear Matti,
Thanks, I mean at the last question something that I guess. Maybe it is just misunderstanding. But I
want to know your viewpoint:
The way that you deepening from imbedding space to WCW and hierarchy of it, one can deepening
from WCW to deeper level.
I think this level is level of hemistry. At this level, there are hierarchy of chemistry from small to
Cosmological scale. I have little imagination of the new level. But try to picture it.
First: ach point of a bent space time sheet(at imbedding space) is flat space time(Special Relativity)
tangent to it.
Second: each point of WCW is a imbedding space.
Third: each point of the new level is a WCW!
Each point of the new level is infinite dimensional Lie algebra.
I expect from the level of Chemistry that all possibly chemical elements are predictions inside theory
at this level. Or all possible insects are inside the theory at the level of Biology!
For example, chemical elements are not just union of electrons and protons and neutrons together
with some fields with small to larger Planck constants. But they are more abstract entities.
Rvery chemical element is one entity in the new level. One can act a transformation on it at the new
level and change the chemical element. Generators of diffeomorphism of 3-surfaces are finite
dimensional Lie algebra.
Very small changing the chemical elements are infinite dimensional Lie algebra! But making
enough changing that transform one chemical element to another is by acting infinite time infinite
dimensional Lie algebra!
4. At 7:49 PM, Matti Pitkanen said...
Dear Hamed,
185
You imagine a hierarchy of WCWs. One can imagine several hierarchies of this kind.
The idea about WCW as analog for the space of imbedding spaces is in my opinion not very
promising.
*First because its introduction would bring TGD to the same catastrophic situation as prevails in
superstring models: landscape problem. Predictability would be lost.
*Second reason is that in infinite-D context, the existence of Riemann connection is extremely
powerful constraint and in the case of loops spaces fixes the Kahler geometry essentially uniquely as
that of symmetry space with Kac Moody type symmetries. In TGD, one would have union of symmetric
spaces assignable to symplectic group of boundary of CD and labeled by zero modes.
In the case of general imbedding space, one certainly loses symmetric space property and therefore
WCW geometry. The isometries of imbedding space and symplectic transformations of delta CD are
absolutely essential for the existence of WCW. Equally importantly: the existence of twistor space with
Kahler structure is possible only for M4xCP2. Mathematical existence of infinite-D WCW geometry
would resolve landscape problem which exists in much more general sense than in string models.
I agree with the spirit of your idea about "chemical elements". Many-sheeted hierarchy with
hierarchy of space-time sheets is one realization this hierarchy but chemical elements replaced with a
hierarchy of physical systems in various scales realized as space-time sheets (quantum superposition of
them -to be precise). This hierarchy might give also concrete realization for the hierarchy of infinite
primes having interpretation as a hierarchy of number theoretic second quantisations of supersymmetric
theory. This would have also an interpretation as a hierarchy of abstractions, thoughts about thoughts.
What is nice and makes this more than mere mathematical technology is that the idea about
hierarchy of second quantisation might be testable. We of course approximate proton has fermion. But
it could be fermion in precise sense rather than only in the approximation neglecting decomposition to
quarks.
In this framework, the symplectic transformations act on "chemical elements" which however are
quantum superpositions of space-time surfaces.
The hierarchy of infinite primes gives a lot of food of thought for a mathematical theologist. For
instance, one can construct endless variety of numbers as rationals formed from infinite integers which
as real numbers equivalent with number 1 -roots of unity having arbitrarily complex number theoretical
anatomy. This would mean that each point of real line and of imbedding space would correspond to
infinite dimensional space of these units.
The crazy holographic proposal is that WCW could be realised as this space. Single space-time
point would represent the World of Classical Worlds (WCW). Brahman = Atman. Could one test this
hypothesis? Or at least physically interpret it?
This might be possible! I have proposed that zero energy states correspond to infinite rationals
which define real units (the integers defining numerator and denominator would correspond to positive
and negative energy parts of the zero energy state). This would realise physically the notion of
"Oneness" about which mystics have been talking.
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