Download Paper

Elaborations
Quantum Mechanics (QM) is a theory of epistemology because
of the probability articulation of its objects of discourse.
Quanton is a generic term for atomic and subatomic particles. Particle is a name
for a complex set of relations focused on pseudo objects such as electron or proton
or gluon, etc. When we speak of a quanton, we do not mean an object in the
classical sense of a thing with an existential boundary, but instead an identifiable
subset of relations with a behavior that is filed under a name such as an electron, a
proton, etc. QM predicts the probabilities of events as they relate to quanton
phenomena. This means that QM is first a theory of probability, a hybrid theory of
probability, but a probability theory nevertheless. What are known in QM are
probabilities, not physical reality as in classical theory.
The role of probability is to enable a conversation about knowing, explaining and
deciding. It is the basis of epistemology, as we know it. The way we know a
thing is by our inference to some degree that the thing is reproducible. Thing here
refers to physical reality. Physical reality is observable, but ideas are pre-things.
Thus, we are always knowing knowing, and in a similar way, explaining
explaining. Deciding is the formation of objects with existential boundaries. It is
the radical construction of objects.
Why should a practitioner of Cybernetics be interested in
quantum epistemology?
QM does not work with objects with existential boundaries, and it suggests that
reality is not composed of objects but of relations that are linked to all relations
always evolving and known within themselves not by an observer, but by logical
realists, i.e., practitioners of cybernetics. Cybernetics encourages an investigation
into being without boundaries and is the proper theater for QM inquiry. Classical
logical positivism and/or realism, the pillars of analytical philosophy are
inadequate systems for quantum epistemology because they work with objects of
existential boundaries. Cybernetics works with relations without boundaries, and
objects of existential boundaries, so that it can develop an epistemology that not
only satisfies quantum mechanics, but classical physical theory as well.
Strategy
We go to a place where the essence of QM is found. This is the famous EPR
Paradox or Einstein-Podolosky-Rosen challenge to the completeness of QM. We
give a synopsis from the abstract of the original EPR paper:
In a complete theory there is an element corresponding
to each element of reality. A sufficient condition for the
reality of a physical quantity is the possibility of
predicting it with certainty. In quantum mechanics in
the case of two physical quantities described by noncommuting operators, the knowledge of one precludes
the knowledge of the other . . . or(2) these two quantities
cannot have simultaneous reality . . . if (2) is also false.
One is thus led to the conclusion that the description of
reality given by the wave function is not complete.
What was bothering Einstein was not QM, but that there was not an intuitive
causal collection of reasons why quantum phenomena existed. He did not deny
the existence; he just felt that something was missing because QM had no
explanation. It just was. That is, quantum phenomena jumped from the laboratory
to mathematical formulation, i.e., probabilistic articulation, without any
conceptual model in between. Classical analytical philosophy called for a
conceptual mode. That is how objects of physical reality were understood. But in
QM this was missing. Therefore, he posited that QM was somehow incomplete
and with his collaborators presented the EPR paradox.
Implication: if EPR was false, then
QM was a complete theory without
a conceptual mode. This is not just
revolutionary physics. It is
revolutionary epistemology.
The EPR Paradox
Heisenberg had established the Uncertainty Principle, namely, that the values of
two observables of a quanton, such as momentum, position, energy, the projection
of spin on an axis, duration, cannot be determined simultaneously. In QM, an
observable is a variable of a quanton that can take on multiple values. Quantons
also have intrinsic characteristics that never change such as mass or charge. EPR
concerns itself with observable. It is a thought experiment. It says consider two
stations, say A and B. Make sure they are spatially separated in a meaningful way.
EPR has two stipulations: (1) completeness of a physical theory.
Every element of the physical reality must have a counter part in the
physical theory.
And (2) a definition of reality:
If, without in any way disturbing a system, we can predict with
certainty (i.e., probability equal to unity) the value of a physical
quantity, then there exists an element of physical reality
corresponding to this physical quantity.
A and B have interacted in the past and now have moved apart, thus, A + B is
known. By measuring the position of A and the position of B, we can have the
quantity, Φ = qa - qb. Likewise, measuring the momentum of A and B, we derive
the quantity ϖ =pa + pb. Then playing some mathematical games on the quantity
[Φ, ϖ], and invoking EPR’s two stipulations, we conclude that the position and
momentum on B can be known with certainty without disturbing B, meaning A
does not disturb B in any way. This violates the Uncertainty Principle and is thus
impossible. So it must be that QM is incomplete. [To say that QM is incomplete
or that the description of reality given by the wave function is incomplete is to say
the same thing.] When we speak of a wave function, think of it as a probability
indicator containing all the predicting information about the quanton we would
need.
There are some other issues involved with EPR. One is the notion of locality.
This means that station A cannot signal station B without violating Special
Relativity. That is, A cannot communicate with B faster than the speed of light.
Thus, spontaneity is not possible under EPR. The other is local realism. Namely,
that reality is independent of observation. The third issue is Separability. This is
connected to realism. There was a view that the wave function of the two
quantons, A and B, remained intact and only appeared to collapse when a
measurement was made. The idea here was that two particles never really
separated but were part of one wave function. EPR counters this by positing that
the two particles separated into two different wave functions and that this
separation becomes local reality.
Summing EPR, we see that EPR pose that quantons are separated and that QM is
incomplete. It also reaffirms that probability enables epistemology, since reality is
a function of prediction.
We pause here to remind ourselves that if EPR is shown false, then quantons are
not separated and we are in a reality of everything is everything, clearly, the
playground of cybernetics.
Further Commentary on EPR
The conclusion of EPR that QM is incomplete can be stated another way that there
are variables accounting for quantum phenomena that QM has not captured. This
has led to a series of Local Hidden Variable propositions. We will see below that
they are shown to be inconsistent with QM.
For what follows, when we speak of quantum phenomena, we will be referring to
the correlation of spin projections measured along the same axes for paired
quantons. In other words, a quanton has spin orientation, up or down, we will be
speaking of whether the spin orientations of two paired quantons are both up or
down or opposite.
Bell’s Theorem, Hidden Variables and EPR
There are several Bells’ Theorems, but let us join them under one heading. We
give Bell’s own rendition of what EPR posits:
The paradox of Einstein, Podolosky and Rosen was advanced as an
argument that quantum mechanics could not be a complete theory but
should be supplemented by additional variables. These additional
variables were to restore causality and locality. In this note that idea
will be formulated mathematically and shown to be incompatible with
the statistical predictions of quantum mechanics. It is the
requirement of locality, or more precisely that the result of a
measurement on one system be unaffected by operations on a distant
system with which it has interacted in the past, that creates the
essential difficulty.
Bell’s Strategy
Bell creates a mathematical formulation of EPR specifying locality and hidden
variable conditions. His focus is on quanton correlation. He develops in closed
form the “probability marker” associated with this quanton correlation. [ Note
well, that this probability marker is a function of hidden variables λ. The
probability distribution is ρ(λ). The probability marker is in terms of expectation.]
He argues as follows: if EPR is correct that QM is incomplete, the probability
marker of EPR should equal the probability marker of QM without the hidden
variables. In other words, the incompleteness of QM is not that the probabilities
predicted by QM are wrong, but that QM needs more variables to account for QM
results. QM results are not in contention. Think of EPR probability as EPR(λ)
and QM probability as simply ΡQM. The point is that if EPR is correct then
EPR(λ) =ΡQM.
Bell shows that they do not equal. Thus, EPR no longer holds.
Interpretation
No probability model of QM has hidden variables or is consistent with local
realism and Einsteinian Separability. Thus, QM is complete without causality.
The World of Physics: Mermin’s Experiment affirming Bell
Any theorem in physics requires experimentation for affirmation. There have been
a number experiments developed to test Bell’s theorem. In general, they have
solidly supported Bell. There have been some obscure experiments that supported
EPR, but they have been treated with great skepticism in the community. What we
would like to do now is present an experiment by David Mermin that is very clear
and palatable. Mermin imitates Bell strategy by first postulating/deducing what
an EPR(λ) would be in his experiment. In this experiment, Bell’s Theorem is cast
as follows:
If EPR holds, then EPR(λ) ≥ 5/9. EPR(λ) ≥ 5/9 means that the
probability of same color is ≥ 5/9. If EPR is correct then ΡQM ≥5/9.
He then calculates ΡQM and empirically demonstrates that they are not equal, in
particular it is less than EPR(λ).
Specifically, the experiment concerns the correlations of a pair of quantons from a
single source. They are sent to Stern-Gerlach detectors equidistantly placed. The
detectors are looking for the spin orientation of the quantons. The detectors are set
so that when either a spin up or a spin down is detected, a red or green color is
recorded. The detectors are set up to give the same color with opposite
orientations. This means that if the detector A records a spin up and the color red,
and detector B records a spin down, B will register a color red also. The detectors
are set to register spin orientations at 0, 120 and 240 degrees. Those are the three
positions. There are also two colors, red and green. The detectors rotate randomly.
Consider the schematic below:
Stern Gerlach
Laser
Stern Gerlach
Quanton
Quanton
Sample Spaces of Mermin Experiment and Data
Sample Space of Mermin’s Experiment
ASSUMING INDEPENDENCE AT BOTH
DETECTORS: BOTH DETECTORS
TREATED AS INDEPENDENT RANDOM
VARIABLES
1R
2R
3R
1G
2G
3G
TOTAL
1R
11RR
12RR
13RR
11RG
12RG
13RG
2R
21RR
22RR
23RR
21RG
22RG
23RG
.166
3R
31RR
32RR
33RR
31RG
32RG
33RG
.166
1G
11GR
12GR
13GR
11GG
12GG
13GG
.166
2G
21GR
22GR
23GR
21GG
22GG
23GG
.166
3G
31GR
32GR
33GR
31GG
32GG
33GG
.166
.166
.166
.166
.166
.166
1.00
TOTAL
.166
.166
ALL MARGINAL PROBABILITIES ARE EQUAL SINCE
WE HAVE EQUAL PROBABILITY IN ALL CELLS.
Ρr Same Color) = ½ (18/36) < 0.556 (5/9)
EPR(λ) >ΡQM
Sample Space of Mermin’s Experiment
WITH QUANTUM PROBABILITY CONSTRAINTS OF SPIN
CORRELATIONS OF PAIRED QUANTONS
1R
2R
3R
1G
2G
3G
TOTAL
1R
11RR
12RR
13RR
0
12RG
13RG
2R
21RR
22RR
23RR
21RG
0
23RG
TBD
3R
31RR
32RR
33RR
31RG
32RG
0
TBD
12GR
13GR
11GG
12GG
13GG
TBD
1G
0
TBD
2G
21GR
0
23GR
21GG
22GG
23GG
TBD
3G
31GR
32GR
0
31GG
32GG
33GG
TBD
TBD
TBD
TBD
TBD
TBD
TBD
1.00
TOTAL
MARGINAL PROBABILITIES NEED TO BE
DETERMINED BY EXPERIMENT. QUANTUM
MECHANICS PREDICTS THAT PAIRED QUANTONS
MEASURED AT THE SAME ANGLE AT THE
DETECTOR WILL BE PERFECTLY CORRELATED,
THUS, THERE WILL NOT BE ANY MIXED COLORS AT
IDENTICAL POSITIONS.
Data from one run of Mermin’s Experiment
WITH QUANTUM PROBABILITY CONSTRAINTS OF SPIN
CORRELATIONS OF PAIRED QUANTONS
1R
2R
3R
1G
2G
3G
TOTAL
.156
1R
.04
.013
.013
0
.036
.054
2R
.027
.054
.027
.027
0
.04
.174
3R
.009
.004
.049
.049
.022
0
.134
1G
0
.027
.054
.063
.018
.004
.165
2G
.04
0
.054
.022
.063
.022
.201
3G
.031
.063
0
.018
.004
.054
.170
TOTAL
.147
.161
.196
.179
.143
.174
1.00
Ρr(Same Color) = ∑ Χi,j,kk (Cell Probabilities indexed
by i,j from 1 to 3, and kk being either R or G) =
0.504<0.556 [There are some very minor rounding errors
and this is only one run. What happens over the many
runs is that the Pr(Same Color) converges to 0.50, clearly,
less than 5/9. Thus, Mermin has produced empirical
evidence supporting Bell’s theorem.
Further discussion on the epistemic reality posed by EPR, Bell
and you.
There are many ongoing developments in QM that do not hold such strong
opinions as I have interpreted Bell to mean. Yet, the question of causality seems
to be at rest. QM does not need causality to be articulated. The epistemic model
using conceptual causality is clearly challenged by Bell and while the issues are
still being debated, causality in QM would refute Bell. That is impossible to do,
thus causality if it were to gain some stature would be of something heretofore not
seen. In this vein, we move to focus more on formal epistemology construction.
On Causality, Probability and Epistemology.
The idea of a thing is its existence and its existence is known through its
replication, thus, its predictability. This does not preclude the naming of
seemingly unique things such as works of art of special combinations of materials.
For in such unique things, the components are known in the replicable sens. Thus,
unique things are composed of known things. However, here should be caution:
all things are unique. A pen in your hand is not as any other pen. It is not as
grand as the Mona Lisa, but it is unique nevertheless. So then, all things are
unique. This makes sense since a thing is never by itself. A thing is known by its
predictability. Thus, a thing comes into being by its own construction. Its
construction is from all that is. Viewing things this way, we are able to see that
quanton correlations are quite natural. What may give us difficulty is why we
exist. That question aside, what would a suitable epistemology for QM that also
allowed for traditional logical realism? How would we construct such a system?
How would we know that such a system was viable? Would we need incremental
proof, validating one theorem after another? What would constitute knowing
knowing? Would it be an appeal to comfort or reductionism? Could we actually
form a system without causality? Would we be creating hidden contradictions?
Would multivalued logics be employed? Or would we be looking for sweeping
generalizations incorporating categories of theorems? Before we venture there,
we reflect on how cybernetics views knowing, namely knowing knowing and
explaining explaining.
Knowing knowing and explaining explaining
To know a thing is to measure a thing. To measure a thing means that a property
attributed to the thing is observable. To observe, i.e., to observe a thing is to
observe a property attributed to the thing. To observe a property attributable to the
thing is to attribute a change in the system created to observe the property
attributable to the thing when observing the thing. A change in the system created
to observe the property attributable to the thing is anything so described by the
observer, and if required, by a collection of observers within a theater of what is
commonly described as organised science of any kind. An organisation is any
collection of two or more conscious beings including the observer. Hence,
observation, measurement and change are words used to know a thing. As
observation, measurement and change change, then so does the thing since a thing
is known in the act of knowing. Thus, we speak of knowing knowing. In a related
manner, one can speak of explaining explaining.
We have already posited that to know a thing is to measure a thing. Now, we will
try to explain what we mean by explaining a thing. To explain a thing is not to
know a thing. To know a thing and to explain a thing are different things. To
explain a thing is to show how to know a thing. To show how to know a thing is
to prescribe a set of instructions to arrive at the property attributable to the thing
that has been observed by the giver of the set of instructions.
One knows a wall by all the properties attributed by the observer to what which
she or he designates is a wall and we say, “We know a wall.” We do not say,
“How do we know a wall?” It is the set of instructions that becomes the wall.
When we speak this way, we imply that we have the essence of the wall in our
sentence of knowing what a wall is. We are in conversation with the wall.
How have we explained the wall? The wall is in conversation with us in
conversation about what the wall is. I.e., these properties attributable to our wall
are what converses with the wall so that we can observe the wall in conversation
with us. This conversation is private, thus, we write or otherwise show an
approximation this conversation and we call this approximation, instructions.
To know a thing is to know it systematically. To explain a thing is to
approximate.
The instructions are then translated, i.e., interpreted by the user. The user can be
the observer. Hence, the explanation of a thing applying her/his instructions for
interpreting instructions is at least a second order explanation of a thing. Thus, we
speak of explaining explaining. This process can recursively continue ad
infinitum, but humans being macro objects converge the iteration to a working
limit. It is a characteristic of non-quantum living. Underlying the relation that
enables knowing is the leap of consciousness in knowing: conversations are
private, thus human-to-human communication requires a receptivity to
approximations. This idea may be incorrect. We may all be in the same wave
function, but need Einsteinian Separability for purposes heretofore unknown to us.
It could be a punishment from the gods, consider, Genesis, Chapter Three, 22-24:
22
And the Lord God said, Behold, the man is become as one of us, to know
good and evil; and now lest he put forth his hand, and take also of the tree of life,
and eat and live for ever:
23
Therefore the Lord God sent him forth from the garden of Eden, to till the
ground from whence he was taken.
24
So he drove out the man, and he placed at the east of the garden of Eden,
the Cherubim, and the flame of a sword which turned every way, to keep the way
of the tree of life.
25
And to assure that man would not circumvent the Cherubim, Cybernetics
was invented. (Smile)
Nevertheless, we put forth a cybernetic epistemology that to address QM, EPR and
the issues of causality and local realism therewith. We call it logical realism. It
has the following characteristics:
1.
2.
3.
4.
5.
6.
Probability theory is a language construction whose purpose is
explaining what is known so that what is known is knowable.
Knowable things are based on measurement, observation, change and
conversation. These are observable guided by the cybernetic notions
of knowing knowing and explaining explaining.
Independent is a word that implies that an object has an existential
boundary.
Every method of proof that yields objects is valid.
A proof is anything wherein the cause of the object lies in the
existence of the object.
Universal constants and their implications, such as locality, hold until
they can be discarded.