Is There a Flaw in Bell's Theorem?

[rikjoh]

John S. Bell's Theorem, from his famous 1964 paper, "proves" that local variables are not sufficient to explain observations predicted by Quantum Mechanics. This is now widely accepted, primarily because the mathematics used is so simple and direct, but his argument is flawed from the very first assumption. I would like to suggest why the first assumption is flawed, and why the rest of his mathematical formulation is therefore meaningless.

We know from QM that if we measure the spin of a photon along the x axis, and categorize it as either x+ or x-, we cannot with precision do a similar measurement along the y and z axes. This is a fact well supported by experiments and observations (or so I'm told, and believe).

The EPR paradox shows that while we cannot do these multiple measurements on a single photon, we can determine two of the values using entangled pairs of particles for which the values must be opposite in order to preserve angular momentum.

So, by measuring x-axis spin on particle A, and y-axis spin on particle B, we get precise measurements for both axes for both particles. We know this can be done, and we know that it needs explanation to allow QM to still be correct, and we know QM is correct, so what is the explanation? Is it a collapse of a wave function? Is it an instantaneous transmission of information across space?

Bell’s paper tries to prove that, whatever the explanation is, it involves the observation on particle A having some mysterious instantaneous effect on particle B. He claims to prove, mathematically, that any possible theory involving only local variables can never explain the results observed by Quantum Mechanics.

To do this he starts with a seemingly obvious assumption. There is some function A on a given axis spin measurement a, and any imaginable set of variables λ, such that A(a, λ) = ±1. That is, the result of the observation, with all variables considered, will be either +1 or -1.

What Bell fails to do is take into account the probabilities that QM requires, and that local variable explanations MUST not violate. The fact is, there is a simple way around Bell’s first assumption, and that is that the order of measurement makes a difference. QM predictions are accurate, the probabilities hold out, but there is something deeper going on.

I would suggest that if we set up an "entangled" system and measure x spin, then y spin, and finally z spin, we will get a different answer depending on the order and manner of the observations made. If this is the case, Bell's initial assumption is wrong, and his equations fall apart. His formulation assumes all values along the z axis are accounted for when a particular result of x and y are found, and that pairs of x and y measurements must be distinct for a particular particle being measured. But in fact this is not so, QM requires that it not be so, and there is no reason to believe it is so. Why? Because of the theory of relativity.
What QM really says is, you cannot measure definitely along x, y and z axes in a single measurement. You need multiple measurements to get multiple definite values, and the type and order of the measurements makes a difference. We know from relativity that absolute simultaneity of events at a distance is not meaningful, and so not possible. And so saying that one set of measurements includes all instances of any other set of measurements is not true. Perhaps this is a clue as to WHY relativity is true.

Going back to the math, the following statements related to sets of observations are all assumed to be true by Bell, but are ALL inaccurate:

(x+, y+) = (x+, y+, z+) + (x+, y+, z-)

(x+, y-) = (x+, y-, z+) + (x+, y-, z-)

(x+) = (x+, y+) + (x+, y-)

A(a, λ) = ±1 (as in Bell's paper)

They are inaccurate because some of (x+, y-) may be the same as the (x+, y+), depending on how the measurements were performed. A(a, λ) is undefined and meaningless. p(λ) is also meaningless. Bell's paper, as you can see, is wrong from assumption 1. The actual observations of (x+, y-) could just as well have been (x+, y+), depending on how the observations were performed.

By adding order of measurement, we invalidate Bell's Theorem, maintain the reality of local variables perfectly, while also agreeing with all predictions of QM. The EPR Paradox holds up, which is to say, QM is correct but incomplete. Bell's Theorem, when it comes right down to it, is all a silly misunderstanding.

One final thought. The real shame is that Einstein did not live long enough to put down this silly "inequality" forty years ago.

 

[Rade]

I have a question--is your hypothesis about "adding order of measurement" to invalidate Bell's theorem (e.g., that reality is non-local), the same as the saying that you have devised a local model of the quantum world in which contrafactual definiteness (or CFD) has been shown to be an invalid assumption ? To my knowledge no one has devised such a local no-CFD picture of reality that is compatible with quantum theory (at least that is what I read in 'Quantum Reality" (1985) by Nick Herbert).

 

[Hurkyl]

The EPR paradox shows that while we cannot do these multiple measurements on a single photon, we can determine two of the values using entangled pairs of particles for which the values must be opposite in order to preserve angular momentum.

The correct word is assumes, not shows.

Bell’s paper tries to prove that, whatever the explanation is, it involves the observation on particle A having some mysterious instantaneous effect on particle B.

I can't speak for Bell's paper, but I can speak of the modern formulation I've seen. It says absolutely nothing about a "mysterious, instantaneous effect", it's simply grinding through the algebra. Whether or not you want to interpret the result as a spooky action at a distance is a separate issue entirely.

The fact is, there is a simple way around Bell’s first assumption, and that is that the order of measurement makes a difference.

This violates the local part of local variables. The two measurement events can have a spacelike separation, which means the phrase "order of measurement" doesn't even make sense.

 

[DrChinese]

1. So, by measuring x-axis spin on particle A, and y-axis spin on particle B, we get precise measurements for both axes for both particles. We know this can be done, and we know that it needs explanation to allow QM to still be correct, and we know QM is correct, so what is the explanation? Is it a collapse of a wave function? Is it an instantaneous transmission of information across space?

...

2. Going back to the math, the following statements related to sets of observations are all assumed to be true by Bell, but are ALL inaccurate:

(x+, y+) = (x+, y+, z+) + (x+, y+, z-)

(x+, y-) = (x+, y-, z+) + (x+, y-, z-)

There are plenty of things wrong with your analysis. So I started with two:

1. You cannot learn the simultaneous x and y values of the particles. This would violate the Heisenberg Uncertainty Principle (HUP). No experiment has ever done that.

2. Bell demonstrated why these are NOT true, not why they were true. You have it backwards. You should consider further study of Bell's Theorem, which can be found on my personal site as: Bell's Theorem and Negative Probabilities. The formulas you presented ASSUME local reality (hidden variables). It is the conclusion of Bell that local reality is INCOMPATIBLE with QM. This view is supported by many experiments, some of which Bell lived to see. Unfortunately, Einstein never knew of Bell's Theorem or he undoubtably would have thrown in the towel on the matter.

 

[DrChinese]

The EPR paradox shows that while we cannot do these multiple measurements on a single photon, we can determine two of the values using entangled pairs of particles for which the values must be opposite in order to preserve angular momentum.

This is not a conclusion of EPR. Perhaps this is where you got off track.

EPR states that either 1) the quantum mechanical description of reality given by the wave function is incomplete (because there are "hidden variables"); or 2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Einstein himself took this to mean that since there MUST be "simultaneous reality to non-commuting operators" (any other position was unreasonable, he maintained), then QM was NOT complete and therefore hidden variables existed. Bell's Theorem, coupled with subsequent experiments, showed that 2) is true and therefore 1) may be false.

 

[Sherlock]

John S. Bell's Theorem, from his famous 1964 paper, "proves" that local variables are not sufficient to explain observations predicted by Quantum Mechanics.

...

... so what is the explanation? Is it a collapse of a wave function? Is it an instantaneous transmission of information across space?

...

Bell’s paper tries to prove that, whatever the explanation is, it involves the observation on particle A having some mysterious instantaneous effect on particle B. He claims to prove, mathematically, that any possible theory involving only local variables can never explain the results observed by Quantum Mechanics.

Knowledge of local hidden variables would make random individual
results predictable. Bell says this in the paper you reference.

But, local hidden variables can't account for predictable results
in combined (or nonlocal, or global) contexts involving two or
more spatially separated, correlated events.

Variable global results -- eg., (A,B) as opposed to just A or
just B -- are determined by global variables. In the typical
optical Bell test, the global variable isn't hidden -- it's the
Theta of the crossed linear polarizers.

Bell's analysis shows that the variability of whatever is incident
on the polarizers (which would, if known, make random individual
results predictable) can't be determining the predictable
global results in a Lorentz invariant world.

It seems to follow then that the variable Theta is analyzing
an unvarying property shared by, or relationship between, the
opposite-moving paired emissions.

Essentially the same thing is being analyzed by the polarizers at
both ends of the setup. This is why you get results that vary as
Theta varies.

Though the hidden emission parameter is assumed to be varying
randomly from pair to pair, for any given pair it is assumed to be
the same at both ends of the setup. That is, in the global context,
the hidden parameter isn't a variable -- and Bell showed that if you
treat the hidden parameter as a variable, then you get results for
some Thetas that don't agree with qm.

Bell's theorem is correct. It's the interpretation of his analysis
that can get a bit garbled in translation. It's not that local
hidden variables don't exist, it's that their variablity isn't
relevant in global, entanglement contexts.

Bell does not "try to prove that, whatever the explanation is, it
involves the observation on particle A having some mysterious
instantaneous effect on particle B." Bell was exploring how the
global observational context might be formulated. The
conclusion is that if you want to formulate it as a function
of a variable hidden parameter, then this formulation will not
reproduce some of the predictions of qm -- and, in order to
reproduce all of the predictions of qm while keeping a variable
hidden parameter as the determining factor, then the two
ends of the setup would have to be influencing each other
in some superluminal way.

Just keep in mind that the individual results aren't correlated wrt
each other -- they're correlated (combined) first wrt a common
time interval, and second wrt some particular Theta.

 

[rikjoh]

Hi guys. I'll ignore the attempts to simply deride or move the discussion off track, and answer the main point that seems genuine.

The confusion here seems to be in distinguishing between simultaneous realities, and simultaneous observations. My suggestion is that perhaps the realities can in fact be simultaneous, but the nature of the universe prevents the observations from being made simultaneously. This is a subtle difference, but would explain a lot. I think Bell's paper lumps together simultaneous realities with simultanious observables, and that this is his fundamental error.

Added to this is the unexplainable way that realities seem to shift suddenly and randomly at this scale. Saying something is precisely real at a given, indivisible instant, is along the lines of what I think Einstein tried to show by publishing the EPR paradox paper. I also think most scientists who try to interpret QM today would lean away from this perspective, toward one where there is some kind of superluminal influence going on that transcends space and time in order to bring the Universe into focus for an observer, even though it is fundamentally out of focus while unobserved.

 

[ZapperZ]

The confusion here seems to be in distinguishing between simultaneous realities, and simultaneous observations. My suggestion is that perhaps the realities can in fact be simultaneous, but the nature of the universe prevents the observations from being made simultaneously. This is a subtle difference, but would explain a lot.

Come again?

Isn't "the nature of the universe" is ALL there is? You are suggesting that there's something else beyond "the nature of the universe". How do you know? Isn't this an untestable assumption, and you're using this to validate everything else you're trying to argue?

This is no longer an argument against EPR-type experiment, nor Bell theorem. This is an argument against QM. If you wish to do so and propose your own individual theory, then may I suggest you first reread the PF guideline that you have agreed to upon joining this forum and consider submitting this to the appropriate section of PF.

I will let this thread stays open till I see which way it is going.

Zz.

 

[rikjoh]

Wow, I didn't know they still burned heretics. Hey, it's your forum. Burn me if you wish.

My argument is not an attack on QM in any way, shape or form, and could hardly be more reasonable. I am not creating a new theory. I am pointing out a very small change in perspective that would, unfortunately, dash some very cherished beliefs held by some very brilliant people. If it makes anyone so uncomfortable that they would censure the topic and burn the heretic, I apologize.

 

[ZapperZ]

Wow, I didn't know they still burned heretics. Hey, it's your forum. Burn me if you wish.

My argument is not an attack on QM in any way, shape or form, and could hardly be more reasonable. I am not creating a new theory. I am pointing out a very small change in perspective that would, unfortunately, dash some very cherished beliefs held by some very brilliant people. If it makes anyone so uncomfortable that they would censure the topic and burn the heretic, I apologize.

Er.. you DID read the guideline upon joining, did you? So how is this surprising?

Note that if *I* were in a possession of any evidence, be it experimental or theoretical, to clearly prove that Bell Theorem is WRONG, I would have sent it to Nature, Science, PRL, etc.. etc. where I would receive unbounded recognition and adulation!

You are not the first to come here (or any other open forum) with such claim. Our policy here is that if you think you are in possession of an idea that counters conventional physics, not based on any previously peer-reviewed papers, and you somehow chose not to pursue the proper route of submitting it to peer-reviewed journals, then you may only submit it to the IR section of PF, not in the MAIN section where only established physics are allowed. You have agreed to this, so don't look surprised.

Note also that no where in your OP were you "asking" or seeking refutation. It was essentially a presentation of your "theory". I let it stand rather than have it deleted because there are several experts on Bell theorem who can quickly respond to the obvious misconception that you have about QM (DrChinese has addressed several). However, you seem to take those to be "attempts to simply deride" rather than address the points being made - and they ARE relevant to the issue. You cannot address Bell theorem without understanding QM!

PF is unlike other forums, if you haven't discovered that already. Just because you have an opinion, doesn't mean it has to come out, especially if it's based on ignorance. If you feel that you have a compelling and valid idea, than take up the IR challenge.

https://www.physicsforums.com/forumdisplay.php?f=146

Zz.