Download to the whole? - Vasil Penchev

Time & Fractal
Vasil Penchev, Assoc. Prof.,
Institute for philosophical research of
the Bulgarian Academy of Sciences
[email protected]
Forthcoming publication (where this
report is posted):
vasil7penchev.wordpress.com
Five theses:
1. According quantum information, a
physical meaning has not only Y2,
but the y-function itself.
2. Two ways to describe a physical
object exist: from the object to the
whole (i.e. as moving object in space
time, from the whole to the object (i.e.
as a concrete asymmetry of a fractal
structure representing the whole).
And the rest three theses:
3. Y-function represents such a concrete asymmetry of a fractal structure in space-time.
4. Physical quantity representing a linear and
Hermitian operator in Hilbert space (i.e.
Y1Y2 transformation) means some movement of an object in space-time expressed by
means of a change of its definitive asymmetry
with regards to the whole.
5. Being of the physical quantity is information.
The meaning of the report
One of the most difficult problems
of the philosophy of physics:
ontological compatibilty of
relativity and quantum mechanics
The first one is a local theory, the
second is a global one.
For example, compatibility of:
• Relativity:
World line
Time
From a part to
the whole
Constancy
Actuality
• Quantum mechanics:
Y-function
? Fractal structure?
From the whole to a
part
Probability
Virtuality
Building Up of:
World line:
point by point
- any point is a
moment of time
from a part (here
and now) to the
whole as development in time
Y-function:
level by level
- any level is a level
of fractal structure
from the whole (here
and now), the 1st level, to the part as
‘th’ level
Meaning of:
• Function of time
Time – t
E = m.c2
ds = icdt + dr
• Fractal structure
Frequency n = t-1
E = ħ.n
dE = idE+cdp
dA = ds.dE = 0, i.e ‘time “” fractal’
2.
(1)
dA = ds.dE = 0, i.e. ‘time “”fractal’
What may it mean for
a part not to be ‘’ to the whole?


• a part
an element
• the whole
the set

  a: a  {a} = a
  a: a  {a} = 
 a: : b(0,1), b=:0,1  ‘’, ‘’
1
About 
• Constancy: 
• Probability: 
So constancy converts
into a special case of So probability is
the relation of
a
relation
probability, i.e
between ‘part’
the relation of
‘part’ and ‘whole”
and ‘whole’
Any element:
• represents the
whole as identity
of the levels of
fractal similarity
• This is the basis
of a vector space
(for example Hilbert space)
• represents it itself as difference (deflection)
between the
levels
This is an
element of a
vector space
So any motion as a relation between
two elements may be represented by:
• change of the basis of the vector
space (i.e. covariant change)
• change of the element of the vector
space (i.e. contravariant change)
Relativity: no experience might differ
anyway change of the basis from change of the element
From “special” to “general” relativity:
Any motion “by itself” represents
a change of a vector space.
The simplest special case is then
when the vector space is “flat”: the
vector space coincides with its
conjugate space (for example Riesz
theorem)
More about that simplest special case:
Any part is independent of the
whole, to which ‘belongs’. We may
also say that the whole is always
the same. That’s way the relation
between ‘whole’ and ‘part’ is equal
to some property of the part
The simplest special case about
subjective and objective probability
• Subjective
probability:
waiting for the
future
• Objective
probability:
experiencing the
past
They are  if and only if : 1) any future
event is independent of any past event;
2) present is but a point
Present is curvature of time!
• subjective probability
• waiting
• objective probability
• experiencing
The “length” of present is the measure
of time curvature! This time length is
period of de Broglie’s wave, so it is
inversely of mass: the macro-world is
already “timely flat”!
Now about: whether any future event
is independent of any past one?
• The future event
repeats merely
the preceding
• The future event
is absolutely
independent of
any past one
The future event may be causally
conditioned by any past one!
Get started a new comprehension of
causality!
• Fractal
repetition
• Absolute independence of future from
past (Markov chain)
Causality represented by implication
Model:
Cause ‘0’ ‘0’ ‘1’ ‘1’
Effect
‘0’ ‘1’ ‘0’ ‘1’
Causality ‘1’ ‘1’ ‘0’ ‘1’
AB  (AB)  (A)
• a fractal part:
effect repeats
‘fractally’ cause
• a Markov part:
effect is absolutely
independent of
cause
Probabilistic causality means:
Cause causes effect with
some probability ‘p’: AB
If cause is available, then
effect is available with
probability p. If p = 1:
classical causality; if p=0:A, B
are absolutely independent
Which would the difference
between correlation and
probabilistic causality be?
• Correlation pre- • Probabilistic
suposes that there causality excludes
is a real ‘true’
such
a
real
‘true”
cause, which is a
hidden (compare cause
with ‘hidden
parameter’)
• A correlates with B• A causes B
‘probabilistically’
It means for us
to reject:
BB
Then ‘probabilistic causality’
means the following:
• The universal set
being common for
both A, B doesn’t
exist. We may think
that they belong
to two different
univer-sal sets
• We may also think
that the universal
set changes: t1t2
(AUt1 )  (BUt2 )
So some elements
of A may disappear,
but new elements
may appear in B
Returning to classic causality…
• The whole is the
same
• Time is Newton one
• Energy is conserved
• Correlation requires
for a hidden cause to
exist
• All
are
equal
Returning back to probabilistic
causality…
• The whole is not the
same
• Time is not Newton
one
• Energy is not conserved
• There are correlations, but there aren’t
hidden parameters
This is the
Realm of
quantum
mechanics
and information
Probabilistic causality
generalizes per se… relativity
Now: no difference whether
any part or
the whole
changes
Probabilistic
causality means
relativity of
whole and part
Generalized relativity presupposes that motion
of whole and motion of part are equivalent
We know much
about the
It means change of a fracmotion of
tal structure into
part. What another. That is not a
about the
change
in
time.
motion of
Heidegger
has
spoken
of
whole?
history of being
We would be able to comprehend
‘history of being’ as ‘change of whole’
• On the one hand, • On the other hand,
better to think for
we may think
‘history of being’ to
‘history of being’
be as Braudel’s
as Plato’s eons
changing each other long run [la longue
in millenniums
durée]
From our, human point of view…
And now: an unexpected comparison
… with the math definition of info:
I=f(t) ln f(t) .dt
I=f(t) ln f(t) .dt
f(t)– a slow change, long run
f(t) – an usual run of time
ln – slows down f(t) to f(t)
I=f(t) ln f(t) .dt – a measure
of slow change, of long run
Sat sapienti (a hint in future)
• The function of • The function of ln
ln transforms
transforms an
multiplicative
axis of Hilbert
(fast) groups
space into an
into additive
inertial reference
(slow) groups, so frame, so a point
a field into a
of it into a world
(double) group
line
Two points of view:
1. From the whole the motion is
motion of whole. So
any physical
quantity is a linear (Hermitian)
transformation of the
whole – in
quantum
mechanics
2. From the part:
the motion is
motion of part. So
any physical
quantity is a
linear transformation
of part’s world line –
in relativity
The concept of (quantum) information units
both of them
A= y(x) F [y*(x)] .dx
Any physical quantity in QM
F: y(x)  F [y*(x)] is a transformation of the whole –
the measuring instrument
I= World line (t).ln y(t).dt
More about: I= W (t).ln y(t).dt
Granted F: ln
y(t) = Force{W (-t)}
Full analogy:
Operator
in QM, F
 y(x) F [y*(x)] .dx
Physical quantity
A
Classical force
acting ‘now’, F
 W (t). F{W(-t)}.dt
Information
of
I
motion I
A general principle in two forms:
• Expressed by the
motion of whole:
Quantum
mechanics
Operator
Physical quantity
• Expressed by the
motion of part:
Relativity
Reality as
virtuality
Reality as
actuality
Force
Motion information
A basic idea of the report:
A basic idea of the report:
No Already Boundary –
since 1989’s falling the wall!
Two ways to describe a physical
object exist:
• TA way is: from the • AAnother way is:
from the whole to
object to the whole
the
object
–
as
a
– as a moving object
concrete
asymmetry
in space-time
of a fractal
structure
representing the
whole
Y-function represents such a
concrete asymmetry of a fractal
structure in space-time
Physical quantity means some
motion of an object in space-time
expressed by means of a change of its
definitive asymmetry with regards to
the whole
Being of the physical quantity is
information