# Entanglement Explained with Epistomological Probability Theory

## Main Question or Discussion Point

I'm interested in published papers, if any, addressing the issue of whether Bell type experiments can be explained simply with classical, epistomological probability theory. In particular, can the expected "quantum" result (i.e. the probability that photons A and B will both pass through their polarizers positioned at theta1 and theta2 is equal to 1/2 * cos^2(theta1-theta2)) simply be derived from probability theory and Malus' law without the need to assume non-local communication?

Note I'm not asking if any hidden variable theory can explain the results; merely if there's been published treatment of the hypothesis that entanglement experiments can be explained with classical probability theory.

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Mentz114
Gold Member
Years ago I came across this guy, Thomas Smid who claims to have it. I disassociate myself from his ideas, but you did ask. You can find him with a Google search.

Another one is in the arXiv, the number is quant-ph/0112019. Same caveat.

Hans de Vries
Gold Member
I'm interested in published papers, if any, addressing the issue of whether Bell type experiments can be explained simply with classical, epistomological probability theory. In particular, can the expected "quantum" result (i.e. the probability that photons A and B will both pass through their polarizers positioned at theta1 and theta2 is equal to 1/2 * cos^2(theta1-theta2)) simply be derived from probability theory and Malus' law without the need to assume non-local communication?

Well, almost all published papers about experiments do just this. They try to explain
the results with Malus law and polarizer angles....

This generally fails, Malus law introduces more randomness as observed in the
experiments. It is then said that Bell's-hidden-variable-model fails, where
the hidden-variable is the polarization angle.

The polarization angle is said to be a "hidden-variable" because the experiment
is set up so that the polarization angle of individual photons is unknown. (it is said
to be in a superposition)

Malus law functions as a random generator and the randomness depends on the
polarization angle. At one angle the result is 100% determined while the result is
100% random at angles rotated over 45 degrees.

If a second experiment is set up so that the polarization angle IS known then it's
not a hidden variable anymore. However, Malus law has to fail just as well. The
correlations should not become less....

( The second experiment could have fixed polarization, with the unit containing the
polarizers/detectors slowly rotating during the experiment to average out the angles)

Now, what does this all really prove? In my opinion this is the following:

1) If the results of both experiments is the same then this supports the statement:
A photon in superposition of two polarization states is the same a a photon
NOT in a super position state where the polarization angle is determined by the

2) In any case, it proves that Malus law generally fails in these experiments.
That is, it is NOT the polarization angle ALONE which determines the outcome
of the experiment.

The polarization angle is taken to be determined by the E and B fields thus
they can not be the hidden variables. I would say that the only hidden-variable
candidates remaining from (mainstream) physics are the potentials A and V
which have extra degrees of freedom. They are not uniquely determined by
the E and B fields.

Regards, Hans

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Note I'm not asking if any hidden variable theory can explain the results; merely if there's been published treatment of the hypothesis that entanglement experiments can be explained with classical probability theory.
But of course you are!
That is the entire point of EPR-Bell argument; that there is no classical probability explanation that can describe the results observed in entanglement experiments.

The moment you produce a probability theory using local & realistic rules that does not ditch discrepancies into “lossy observations” but accounts for all events to produce the Malus statistics then you have a viable “hidden variable theory”. You, you do not even need to prove that it is a correct - if there is one there could be another. And the negative proof of EPR-Bell tests are totally dependent on there being no possible such description.
Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.

And the Thomas Smid example is far from a complete description.

I would say that the only hidden-variable candidates remaining from (mainstream) physics are the potentials A and V which have extra degrees of freedom. They are not uniquely determined by the E and B fields.
What exactly are the A & V potentials ?

So what you're saying is that if a classical probability derivation could explain the results, Bell's theorem couldn't be true, and that such a theory in and of itself would prove that there is a hidden variable theory "out there," even if we don't know what it is yet.

I too was wondering what "A & V" meant.

So what you're saying is that if a classical probability derivation could explain the results, Bell's theorem couldn't be true, and that such a theory in and of itself would prove that there is a hidden variable theory "out there," even if we don't know what it is yet.
No that is not quite what I said.
I believe Bells theorem is true, just the conclusions people make from it are wrong.
Meaning the needed classical probability derivation must violate the Bell inequity and match the Malus Line.
May not be proof that a HV is correct; just that the proof a HV is impossible is incorrect.
And since anything goes in piecing such a thing together like this; coming “close” doesn’t count, it needs to produce the Malus Line without "losses".

Hans de Vries
Gold Member
What exactly are the A & V potentials ?
I too was wondering what "A & V" meant.
These are simply the electric potential V and magnetic vector potential A.

The E and B fields determine the force on electric charge but the V and A fields
do modify the QM phase of the electrons because of the interaction with its charge
density. The A and V potentials modify interference patterns even if the E and B
fields are zero.

The B and E fields modify the phase of the moving electron due to the interaction
with its magnetic moment. The derivatives of B and E determine the force on the
electron due to its magnetic moment. (Stern-Gerlach experiment)

Regards, Hans

Randall, I'm just confused by your statement:

Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.
In short, is Bell's theorem compatible with a local, realistic, statistical explanation of entanglement, if one could be found?

JesseM
In short, is Bell's theorem compatible with a local, realistic, statistical explanation of entanglement, if one could be found?
No, Bell's theorem proves absolutely that the results predicted by QM in experiments with entanglement cannot be compatible with any local realist theories. You might take a look at this thread for a discussion of the logic of the proof.

No, Bell's theorem proves absolutely that the results predicted by QM in experiments with entanglement cannot be compatible with any local realist theories. You might take a look at this thread for a discussion of the logic of the proof.
Yes. This is true.
Since local realist theories are ruled out, there are two alternatives remaining:

1.Nonlocal realist theories. Namely where the wave function is a real entity. In this case the detection/measurement itself is a nonlocal(relativity violating) time evolution of a real physical entity.

2. Local nonrealist theories namely the Copenhagen interpretation(CI), where the wave function is not a real entity(thus nonrealist), and where reality(associated whith the quant to be measured) even does not exist until you measure it. Or in other words where we can only talk on potential reality but not actual reality prior measurement.

The choice is matter of taste. I for my part would rather sacrifice relativity (by preferring its Lorentzian interpretation where the apparent/observed validity of Lorentz Transformations for space and time is only an obervational consequence of Lorentz invariant physical laws, thus not a real symmetry of spacetime itself but only an apparent symmetry ) and I would prefer to assume that "we still don't know how the wave function dynamically evolves during measurement", rather then accepting the second one. This is not because I reject to swallow the new hard concept of "potential reality" and its distinction from "actual reality" but because:

1. CI does not answer the question "under which actual real conditions this "potential part" of the reality becomes an actual reality" in other words because it uses the term measurement without presenting us its definition,namely without answering the question which "macroscopical/classical" setup (namely which form of the actual reality) leads to an event that we may call "measurement".

2.No real measurement has an infinitely precise outcome for the value of an observable. Thus even immediately after measurement there is an uncertainity of the apparently observed variable. Thus there is no actual reality in strict sense even after the measurement but only an extreme narrowing of the already existing uncertainty. So in fact in CI the term "measurement" does not mean picking one of the potential realities but it is just a apparantly sudden/stochastic change of the uncertainty function (wave function). Thus describing the measuremnet in terms of potential/actual reality does not make any sense at all even in CI .

Thus I would not have a problem with the idea "God plays dice" . However if a theory contains a claim that there is a fundamentally stochastic(random) process that is fundamentally irreducible to a deterministic process, it should provide us with a quantitative relationship, that describes under which conditions this stochastic events happen or likely to happen. Since CI does not provide this, it is incomplete imo.

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The reason I ask is because probability theory such as Bayes Theorem frequently involves situations where KNOWLEDGE about the outcome of an event affects the probability of another event - even though the two events are not causally connected. So I thought, perhaps, that that concept could explain entanglement in purely epistomological terms without the need to resort to hidden variables or anything else deeper than the statistics themselves.

I also found this paper online which makes such a claim:

http://www.physics.umd.edu/rgroups/ep/yskim/boston/kracklau.pdf [Broken]

But it doesn't appear to be published and I find his purported explanation of Aspect experiments using classical probability rather confusing, and I suspect not logically sound.

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DrChinese
Gold Member
The reason I ask is because probability theory such as Bayes Theorem frequently involves situations where KNOWLEDGE about the outcome of an event affects the probability of another event - even though the two events are not causally connected. So I thought, perhaps, that that concept could explain entanglement in purely epistomological terms without the need to resort to hidden variables or anything else deeper than the statistics themselves.

I also found this paper online which makes such a claim:

http://www.physics.umd.edu/rgroups/ep/yskim/boston/kracklau.pdf [Broken]

But it doesn't appear to be published and I find his purported explanation of Aspect experiments using classical probability rather confusing, and I suspect not logically sound.
Like a lot of purported classical explanations, it fails to take on the Bell argument directly. He does not address the main arguments of EPR, namely that there are "elements of reality" independent of the act of observation. He basically just tries to say that Malus' Law is classical, and that matches the predictions of QM. But he does not address the main counter-argument of Bell, that there must exist simultaneous values for A, B and C in a realist scenario.

I suspect that would be the approach of ANY purported explanation in classical terms, basically to ignore Bell by waving your hands.

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[Whoops, sorry that post was incomplete]

So I guess the bottom line is that one can indeed abandon "realism" in the sense that the photons truly don't have any properties other than what are observed. Is that really "ignoring Bell" or is it simply abandoning realism in exchange for locality? Sure, there is no causal influence between the two distant particles, but there are also no inherent properties to those particles at all independent of whether they "pass" or "don't pass" through the polarizer.

Randall, I'm just confused by your statement:
“Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.”

In short, is Bell's theorem compatible with a local, realistic, statistical explanation of entanglement, if one could be found?
I’m a little unsure what the confusion might be?
1) What do you think it means.
2) Do you recognize the difference between “Bell” and “EPR-Bell”

That may also help clear up what you mean when you say :
So I guess the bottom line is that one can indeed abandon "realism" in the sense that the photons truly don't have any properties other than what are observed.
Do you expect that any theory in order to be viable must allow for abandoning "realism"? If that is “the bottom line” it would exclude theories currently out there that retain realism but expect a “Non-local reality”.
I don’t think the evidence reviewed here justifies such a bottom line conclusion.

1) What do you think it means.
Is this psychotherapy? :)

I assume EPR-Bell means the EPR paradox that QM is incomplete or local realism is wrong, plus Bell's theorem which says that no local and realistic hidden variable theory can produce the results of QM. So when you say "ERP-Bell" is incomplete do you simply mean EPR-Bell is wrong?

Do you expect that any theory in order to be viable must allow for abandoning "realism"
I said *can*, not *must*.

I said *can*, not *must*. the bottom line is that one can indeed abandon "realism"
It wasn’t clear that you understood you cannot necessarily abandon realism when someone is using a non-local approach that already accounts for the problem.

Is this psychotherapy? :)

I assume EPR-Bell means the EPR paradox that QM is incomplete or local realism is wrong, plus Bell's theorem which says that no local and realistic hidden variable theory can produce the results of QM. So when you say "ERP-Bell" is incomplete do you simply mean EPR-Bell is wrong?
No it’s trying to make sure we are talking about the same thing.
I’m sure we are not, as I take it you do not know the difference in this context.

Bell's theorem “Bell” does not say “no local and realistic hidden variable theory can produce the results of QM”
“Bell” is a mathematical theorem by a Local Realist (J Bell) designed to help define HVs hoping to satisfy the Einstein claim of Local Realism. If by itself “Bell” proved the QM case there would have been no need for Aspect and others to run experiments or interpret real results against the theorem. (Although J Bell agreed more and better experiments were warranted, he acknowledged he considered it unlikely a HV would be found.)

“EPR-Bell” is the application of 1)real observations 2)the theorem and 3)rational Logic; to reach conclusions about the truth of reality. And the widely accepted consciences is the “EPR-Bell” confirms that reality must be “Non-Local” and/or “Unrealistic” with no preference for any individual theory within those types. And it does so by providing a negative proof that: “no local and realistic hidden variable theory can produce the results of QM”.

SO my statement that you were confused by:
“Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.”
Simple means that if you personally without conducting an experiment sat down with Alice giving her a long list of individually numbered photons including details for each photon as many variables (known or hidden in real life) you wish to define. And provide a theorem using whatever “classical epistemological probability theory”, as mentioned in your OP, you want to divide the photon list into two photon groups H & V for a particular measured angle.
But unlike a real experiment Alice can apply your theorem again to the same written set of photon descriptions to as many different measurement angles as you like with every angle having a H & V list created with each photon individually identified. No need to wait for Bob to report measurements made at a distance.
If Alice and Bob are using the same translation against the same set on Data they will both produce the same results.
It is a simple paper exercise to track which photons on each list have the same unique ID to build a correlation pattern.

The challenge is to have the paper theory produce correlations between the various angles that match cos^2 Mauls expectations thus violating the “Bell” inequity line. Any successful effort would falsify the “EPR-Bell” interpretation of “Bell” that “no local and realistic hidden variable theory” can do so.
I.E. it just takes one.

JesseM
“Bell” is a mathematical theorem by a Local Realist (J Bell) designed to help define HVs hoping to satisfy the Einstein claim of Local Realism. If by itself “Bell” proved the QM case there would have been no need for Aspect and others to run experiments or interpret real results against the theorem.
I don't get your argument here. Bell did prove that the theoretical predictions of QM were incompatible with local realism; the point of the experiments was just to test whether the predictions of QM were in fact correct with regards to entanglement. But if you think there's any possibility that QM's predictions could be exactly correct in all circumstances and local realism could be true, then you're wrong, this has been ruled out definitively.
RandallB said:
SO my statement that you were confused by:
“Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.”
Simple means that if you personally without conducting an experiment sat down with Alice giving her a long list of individually numbered photons including details for each photon as many variables (known or hidden in real life) you wish to define. And provide a theorem using whatever “classical epistemological probability theory”, as mentioned in your OP, you want to divide the photon list into two photon groups H & V for a particular measured angle.
But unlike a real experiment Alice can apply your theorem again to the same written set of photon descriptions to as many different measurement angles as you like with every angle having a H & V list created with each photon individually identified. No need to wait for Bob to report measurements made at a distance.
If Alice and Bob are using the same translation against the same set on Data they will both produce the same results.
It is a simple paper exercise to track which photons on each list have the same unique ID to build a correlation pattern.
Suppose we replace the written list of information with a computer program which stores the properties of each numbered particle, and then the computer has some algorithm to decide what result Alice will get on each numbered particle (based on these stored properties) depending on which of three measurements she chooses to make (perhaps she has a choice of typing "A", "B" and "C" for each simulated particle). Suppose further that we send a copy of the program to Alice and another copy to Bob. Certainly we can design the programs so that it is guaranteed that whenever Alice and Bob choose to make the same measurement on identically-numbered particles, they will get the same result back. But if Alice and Bob make their choices independently of each other, and there is a spacelike separation between the events of each making their choice, then in a local realist universe it is absolutely impossible to design the programs in such a way that they always get the same results when they make the same measurement, and that the Bell inequalities, which concern the results Alice and Bob get when they choose to make different measurements on identically-numbered particles, will be consistently violated. Bell's theorem proves this impossibility. The proof is completely rigorous, and therefore we can be sure that no one will ever come up with an example of a program that would allow us to violate these inequalities in a local realist universe, in the same way that the proof of [URL [Broken] last theorem[/url] allows us to be sure that no one will ever come up with three nonzero integers a, b, and c which satisfy a^n + b^n = c^n, where n is some integer > 2. Would you disagree that the proof is rigorous in this sense?

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The proof is completely rigorous, and therefore we can be sure that no one will ever come up with an example of a program that would allow us to violate these inequalities in a local realist universe,
Indeed, I tried doing exactly this. Oddly, the program violated the inequalities sometimes, but I think only by random chance, and not by as much as the QM results do. There are local realist models one can program to get very close to the QM results, such as pre-programming results for every conceivable polarization angle, but it's never perfect.

What would be a good example of a local, non-realist interpretation of QM or entanglement? Is MWI local and non-realist?

I don't get your argument here. Bell did prove that the theoretical predictions of QM were incompatible with local realism; …. local realism has been ruled out definitively.
(the proof of Fermat's last theorem) Would you disagree that the proof ( of ERP-Bell ) is rigorous in this sense?
You know very well I’m a Local Realist, so of course the EPR-Bell proof is nowhere near as logically rigorous as the proof for Fermat's last theorem, how could you expect my opinion to be any different.
Einstein today would say the same thing.
If you really thing the scientific community as a whole agrees with your position you need to explain why reputable science continues to design and test, including requesting and receiving funding for “closing Loopholes in EPR-Bell” experiemnts? Or do you consider the Kwiat Group at Illinois a crackpot group wasting time and money?

EPR-Bell is not “completely rigorous” just because you say it is. What principles of logic, and conclusive and complete understanding of the tools used to make EPR measurements, define the ERP-Bell conclusions as “completely rigorous”?

And how could “Bell” by itself be a rigorous proof against LR (that would have meant Aspect EPR-Bell testing was unnecessary) when the author John Bell though the theorem could help find LR HVs.
There is no more justification for such a “rigorous proof” claim here as there is for MWI or BM over oQM.

And I don’t think you understood my whole point:
I disagree with Local Realism demands that discard “Bell” as part of rejecting the conclusions of “EPR-Bell” as if QM predictions might not be accurate.
IMO LR must retain the standard defined by “Bell” requiring a valid LR theory must not only violate Bell theorem inequalities, but must match the cos^2 line. Thus leaving EPR-Bell accurate but incomplete, making the idea of “entanglement” unnecessary.
Essentially, That is what the OP described and obviously one has not been produced as yet. But, one valid example would falsify the EPR-Bell conclusions.
That is how my version of Local Realism differs from those in LR that wish to in one way or another discard or ignore “Bell”. Rather the only practical goal for LR IMO is to produce the example described in the OP.

If you think Bell's theorem is not rigorously proven then where do you think the flaw is?

My question was really more whether probability theory alone can lead us to Malus' law without the need to even ask whether there's local or non-local information exchange. For example, you could have the Monty Hall problem where opening one door *seems* to affect what's behind the other doors, but really all it does is alter the probability over the long run. Perhaps the same is true of entanglement, was what I was wondering. But, it would appear the answer is no, as the Bell inequalities cannot seemingly be violated unless there is some kind of exchange between the two entangled particles, whether that exchange happens at the time of measurement, or at the time of correlating the measurements, no one knows.

If you think Bell's theorem is not rigorously proven then where do you think the flaw is?
Again, I did not say "Bell" was flawed and I take it as a given.
It is the conclusions of "EPR-Bell" that are flawed, as I said before there is a difference.

My objective is to identify that flaw and satisfy “Bell” with a LR explanation using only local provided HV information and no post separation information exchange.
IMO what I’ve published so far has been incomplete but on the right path (Discussed in https://www.physicsforums.com/showthread.php?t=180831").

It has been a long search, but I think I’ll have a complete description ready to publish by Summer

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JesseM
If you really thing the scientific community as a whole agrees with your position you need to explain why reputable science continues to design and test, including requesting and receiving funding for “closing Loopholes in EPR-Bell” experiemnts? Or do you consider the Kwiat Group at Illinois a crackpot group wasting time and money?
Did you completely ignore what I was saying here?
Bell did prove that the theoretical predictions of QM were incompatible with local realism; the point of the experiments was just to test whether the predictions of QM were in fact correct with regards to entanglement. But if you think there's any possibility that QM's predictions could be exactly correct in all circumstances and local realism could be true, then you're wrong, this has been ruled out definitively.
The point is that you have to distinguish between the theoretical proof and the experimental evidence. The theoretical proof says, "if QM is precisely correct, the local realism is false". But it's still an experimental question whether QM is precisely correct in entanglement experiments; one could imagine that the real laws of physics are very similar to those of QM, but are subtly different in entanglement experiments, in ways that allow for Bell inequalities to seem to be violated when detection rates are not 100% or when there is not a spacelike separation between the two experimenter's decisions of what to measure, but which would cause real physics to diverge from the predictions of QM if all the conditions of Bell's proof were precisely satisfied (100% detection rates, spacelike separation, etc.), so that in this case the Bell inequalities would be satisfied rather than violated as in QM.

There is nothing crackpottish about trying to test whether the actual universe does match QM's predictions in EPR-type experiments when the conditions of Bell's proof are enforced as best as we possibly can. However, there is something crackpottish about saying that it might be true that QM's predictions are perfectly correct and local realism is true--if this is the argument you want to make, you're definitely going against an established conclusion of mainstream theoretical physics, so you shouldn't be doing it on this forum but instead in the "independent research" forum.
RandallB said:
And I don’t think you understood my whole point:
I disagree with Local Realism demands that discard “Bell” as part of rejecting the conclusions of “EPR-Bell” as if QM predictions might not be accurate.
IMO LR must retain the standard defined by “Bell” requiring a valid LR theory must not only violate Bell theorem inequalities, but must match the cos^2 line. Thus leaving EPR-Bell accurate but incomplete, making the idea of “entanglement” unnecessary.
I gathered that this was your point, but it's simply wrong. Bell's proof showed that it is impossible that local realism (with certain specified conditions, like no superdeterminism) could be compatible with QM's prediction of a cos^2(theta) probability for experimenters getting the same (or opposite) result when the angle between their detectors is theta; the experimenters running tests of EPR experiments like the Kwiat Group you mentioned would not disagree, rather they are checking for experimental violations of the cos^2(theta) rule.