Is Bell's Theorem Inconsistent with Quantum Mechanics?

[bhobba]

I'll disagree again because standard probability theory is not a specific probability model for a phenomena. I agree that the manipulations of QM can be formulated as a theory of probability together with a model for applying that theory to physics.

Fair enough - it's the applied vs pure thing which is a whole thread in itself.

What is the reason and what do mean by "Bell"? Do you mean the mathematical theorem of Bell's inequality or the physical interpretation entanglement experiments in the light of that inequality?

Why does QM as a theory give that particular result? There are many papers on the internet that goes through the boring detail. By Bell I mean in this context, the theoretical result that is at variance with realism. The out is FTL. Your paper may be another out - I do not know - but it clearly states the same result - you can't have a local realistic theory.

What the paper tries to show is that if you construct an accurate probability model for entanglement experiments, you get satisfactory numbers. The accurate model includes a representation of the possibilities that some measurements are not made on a given pair of entangled things. I agree that the interpretation of such a model is that there can be non-local effects. What I find interesting is that if a person tries to model precisely what happens in entanglement experiments with standard probability theory, he gets a model where the statistics collected in the experiment need not satisfy Bell's inequality. It shows that pretending measurements not made have outcomes produces a different mathematical model that using a non-measurement as a type of outcome.

There are many way to skin a cat. I do not know if your paper is correct, but its not one of those things that worries me so I am not motivated to go into it. The main thing is you still can't have a local realistic theory.

Thanks
Bill

 

[Fra]

I'll disagree on a technicality. "Standard probability theory" is not a specific probability model for a phenomena. The correct statement is that QM statisical properties disagree with certain conventional probability models. That doesn't demonstrate that we need a new type of probability theory to model entanglement experiments. We may merely need a new probability model (e.g. https://arxiv.org/abs/1406.4886 "CHSH Inequality: Quantum probabilities as classical conditional probabilities")

To trace all these things down to the foundations of statistical methods and foundations of Probability theory is IMO a good path of progress. I argue that this likely makes contact with both unification and QG, so this is not just about "pure interpretations", it will add explanatory and predictive value once understood.

But even within this thinking there are quite some different ways of thinking. From my perspective of genereal inference, regular probability theory is (there are other ways) constructed as a system for manipulating and representing "degrees of belief" (ie. bayesian view). The reason for my preference for bayesian view is that it provides a deeper insight in the "interaction picture". Where you put myself into the position if the interacting system.

Here most axiomatic methods, represents degree of belief, probability by a real number.

You can indeed do this in several ways, one "extension" is to extend it to a complex number, but then one needs to undersand what a "complex" degree of belief is in a consistent way, you can also consider it to be a vector in higher dimensions, as long as you have a sensible idea that this multidimensional "degree of belief" means in terms if the general inference. I have seen several of these attemps along this route but none that i thing adds much value. They all miss one critical details which is the information capacity that constrains representations in a physical realisation of this. (because after all, we arent doing this for the sake of pure math, we are theoretical physicists with a hidden agenda;)

Another way (the one i am working on) is instead suggesting that degree of belief must be represented not in the mathematical real of the continuum but by a unique microstructure of the observer, which is the "host" and the "processing unit" of the inferences. But this has the same problem that you need to have a sensible idea how to make sense out of this and map it to "reality" in a way that are likely to match experiment. In my view the "complex" situation of QM, is emergent as a result of that it is simply more efficient for nature in some situations. So there is no need for different logic, the transition from "classical" to "quantum" is understood the evolutionary way, not my reductionism from QM. I have not published anything but i expect that there is a very nice way to pull this off, and it will put "probability theory" in a context of evolutionary inference systems - at and stage of evolution there is always something that can be cast, one way or the other into some static theory, but the interesting part, and the key part to understand, is the TRANSITION from one logical systel to another, and WHY this happens in nature in particular as you scale the complexity of the observer in theory space. This path does not exist in current theories of renormalization, so it will also have to provide a bigger context for renormalization, where you do not just to lossy reduction, but also explain the physical progress of selforganisation implicit in the scaling that gains information.

But i think there is a lot of research to be done on this. i consider it an open question.

/Fredrik

 

[Dale]

some mentors have advised that we include all in one post, even using editing if we have to.

I have also done multiple short posts and been gently advised the same

To all participants: please stay on topic. This is a specific discussion about the specific argument presented in the OPs paper. Please keep all comments directly relevant.

 

[Stavros Kiri]

I think you are discussing the premises of the theorem right? not the theorem itself? So the issue is what is a reasonable mathematical representation of "local realism"? Let's characterize the basic logic first before bothering with details.

(A,B outcomes; a,b settings on the device, $\lambda$ is the hidden variable)

As I see it, the premise that the proof depends is essentially the local deterministic realism condition that there are functions f and go such that
$A=f(a,\lambda)$
$B=g(b,\lambda)$

Then we get, given $a,b,\lambda$
$\left<AB\right>=\int_\lambda f(a,\lambda) g(b,\lambda) P(AB|a,b,\lambda) dP(\lambda|a,b)$
and
$P(AB|a,b,\lambda)=1$

So $\left<AB\right>=\int_\lambda f(a,\lambda) g(b,\lambda) dP(\lambda|a,b)$

It is usually also assume that $\lambda$ is totally independent from a and b, something that can certainly be questioned. Not because i believe in superdeterminism, its just that I can't see how it does not follow from any principle of rational inference. [ On the contrary it find it a suspicious and a bit incoherent position to believe in determinism in the sense in question and at the same time think that $\lambda$ would be totally statistically independent from a and b? ]

(But if $\left<AB\right>=\int_\lambda f(a,\lambda) g(b,\lambda) dP(\lambda)$ the theorem follows mathematically)

So without obstructing the logic here with angles and photons, where in this inferential structure is your change? Anything that is changing the premises must change f,g or $P(\lambda|ab)$? Explicit examples are nice, but the can also clog there view of the inferences.

/Fredrik

For the shake of generality I agree. But he already said:

Bell had argued that if nature allowed only local effects, the results of polarization measurements would only depend on polarizer position and a possible hidden parameter. He then concluded that the expectation values of different measurements must be in a certain context, namely, that they followed Bell's inequality. If, as often measured, nature violates Bell's inequality, then, according to Bell, it can not be based on local effects.

Bell has argued imprecisely. His theorem is valid only if the dependency of the polarization measurement results on polarizer position and hidden parameter is the only one possible. If other models are possible, which correctly predict the measured expectation values with entangled photon pairs, his theorem loses its generality. Bell has thus failed to prove the universality. A counter-example suffices to refute his theorem. I presented such a counterexample.

The way I perceive it, instead of looking for those "other models" the OP suffices in trying to find counter-examples. That's legitimate.

 

[Boing3000]

The way I perceive it, instead of looking for those "other models" the OP suffices in trying to find counter-examples. That's legitimate.

There is no counter example to a theorem. I understand that some questions exist about its mapping to physics, but I don't see how the OP example apply. From my understanding the OP "counter example" is a model with two hidden variables ... which reduce to one anyway

 

[Stavros Kiri]

There is no counter example to a theorem.

Unless it's a false one, or based on false premises (original assumptions of the corresponding theory). I think that's what he's up to, trying to refute.
[But so far, myself, I haven't formed a clear opinion as to whether he succeeds or not.]
Who can give a clear view as to what is the verdict so far? (that's in fact a question to all)

 

[Jilang]

For me, as I see it, the model breaks down at assumption 5. This assumption is written into agree with experimental results. But it explicitly states that B is a function of gamma. Given that gamma is dependent on the orientation of P1 this implies that B depends on said orientation. This is a non local influence. I can’t see how you can get round it.

 

[bhobba]

Who can give a clear view as to what is the verdict so far? (that's in fact a question to all)

Its erroneous - like proofs of one = zero - there is a divide by zero in there somewhere. Dr Chinese has put his finger on the precise error - personally I lost patience with picking out the divide by zero proofs eons ago - you have seen a few and after that its boring. Same here.

Bell is airtight. Any paper refuting it should not have passed referees - rather the referee should have spotted the error and returned it to the author.

One thing I have learned here is the referee process is not all it should be. We have seen many papers that should have been rejected. But its not a modern issue. I am reading the book Einsteins mistakes right now, and the number of errors especially in his early papers were staggering - so bad in the collected works they had to have page after page explaining the errors. There was not even the excuse - well its Einstein - who are we to criticize him - most were from his early days before he was famous. Why - beats me - maybe referees don't take it seriously enough - but really who knows.

Thanks
Bill

 

[Mentz114]

QM in general is a different generalized probability model to ordinary probability theory - in fact the next simplest after ordinary probability theory. It allows continuous transformations between pure states - normal probability theory does not allow that. It does it because probabilities are not positive numbers - but complex numbers which of course the Kolmogerov axioms do not have.

That's interesting. I haven't seen anything about this in any textbooks. Can you give some not too hard references, please ?

That is the reason for Bell. If however you want to interpret it in a more classical manner - you can - but you need FTL ie non-locality.
Thanks
Bill

It is possible to violate CHSH with FTL but not every detail.

 

[bhobba]

That's interesting. I haven't seen anything about this in any textbooks. Can you give some not too hard references, please ?

Sure - but I have posted them many times:
https://www.scottaaronson.com/democritus/lec9.html
https://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[emuc]

Dear emuc

See https://www.physicsforums.com/threads/is-bells-theorem-correct.937619/#post-5927002

You state that
“It is assumed that a photon can be simultaneously in different p-states depending on the value of a parameter λ and a chosen direction relative to the polarization of the photon. That means some of the photons with polarization α are also in p-state β and thus pass a polarizer set to β with certainty. As p-state and polarization are different physical entities ambiguous polarization states are excluded.”
This definition is at odds with realism. The p state cannot be decided until the chosen direction is. I think it is generally accepted that locality can be preserved if realism is not. How does your model differ from that?

The p-state is a property which determines which polarizer output a photon will take. See model assumption M1. The p-state can be calculated if lambda is given for any direction prior to a measurement.

 

[emuc]

No, reducing it to H or V is the challenge. And for the 3 d1/d2 angles I specified, 0/120/240 degrees. It's your formula, and I expect you calculate the specific determinate value you claim exists. You said there are p-states that determine the outcomes with certainty. Let's see those babies, no more hand-waving.

Can you please explain what you mean with H and V? In the coordinate system used in my paper H is 0° and V is 90° defined by the H and V outputs of the source. This is arbitrary but fixed. So we could have a polarizer settings 0°/90°, 120°/210°, 240°/330°. for P1 and P2 respectively. These were used in the calculations.

 

[emuc]

Look up "tautology". Again. You use an assumption to prove the same assumption.

It is no secret that once you know the choice of detection angle for Alice, you can design an algorithm for a QM compliant result for Bob. And that depends that result being an input variable for Bob's result. That is precisely what Bell explicitly said could not be allowed. It's in the first paragraph of Bell:

"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."

Note that your formula is not separable. You use the result of a measurement on photon 1 to calculate the result of photon 2.

Can we agree upon photon 2 and photon 1 being connected by a time stamp of a coincidence measuring device as I've assumed in section 2 of my paper?
That means the experimental results consist of a list
setting P1; result P1 (=1); setting P2; result P2(=1 or 0).
If that is so it is possible to construct algorithms to predict these results.

 

[emuc]

In QM the precise statement is it is silent on if such action exists. In QM we do not know if after it has left the source it even has a physical existence for such to be meaningful.

Thanks
Bill

In order to understand the phenomenon we can not use the formalism of QM. It doesn't tell us anything about temporal sequences. Only sound physical reasoning helps.

 

[Lord Jestocost]

The way I perceive it, instead of looking for those "other models" the OP suffices in trying to find counter-examples. That's legitimate.

Following Richard D. Gill (in “Statistics, Causality and Bell’s Theorem”, Statistical Science 2014, Vol. 29, No. 4, 512–528):

“Both the original Bell inequality, and Bell-CHSH inequality (4), can be used to prove Bell’s theorem: quantum mechanics is incompatible with the principles of realism, locality and freedom. If we want to hold on to all three principles, quantum mechanics must be rejected. Alternatively, if we want to hold on to quantum theory, we have to relinquish at least one of those three principles.”

To my mind, a counter example to Bell’s theorem would thus be a physical model which

a) is based on the principles of physical realism, locality and freedom

b) is able to predict detector responses in question for a number of identically prepared entangled systems (the “DrChinese challenge”), viz. to generate a gap-less N x M list (N rows, M columns) of numbers +/-1 (detector responses predicted by the model) for M given detector settings and N hidden variable’s values

c) is able to reproduce (based on this list) the experimentally observed correlations between detector responses after the measurement on a huge number of identically prepared entangled systems

 

[emuc]

For me, as I see it, the model breaks down at assumption 5. This assumption is written into agree with experimental results. But it explicitly states that B is a function of gamma. Given that gamma is dependent on the orientation of P1 this implies that B depends on said orientation. This is a non local influence. I can’t see how you can get round it.

B and A are local definitions as lambda and delta are local. A(delta, lambda) is defined by equations 2-5. Using M5 B(delta, lambda) is defined by equations 8-11.
Photon 1 and photon 2 of a pair share the same lambda.

 

[Fra]

B and A are local definitions as lambda and delta are local. A(delta, lambda) is defined by equations 2-5. Using M5 B(delta, lambda) is defined by equations 8-11.
Photon 1 and photon 2 of a pair share the same lambda.

One locality part in the "local realism" premise of the theorem is that the choice of measurement setting made at A should be independent from B. The fact that the theorem makes a prediction for the case where there happens to be a certain relation between a and b and you have perfect anti-correlation, does not mean that this relation must be confused with a dependence.

As far as I can see from what you did, it seems to me that you tried to transform away the a and b, by delta which is is determined by a and gamma, OR by b and gamma, thus you have two different deltas, don't you?
$$\delta_a = w(a,\lambda)$$
$$\delta_b = v(b,\lambda)$$
So what you should have at this point is
$$A=f(\delta_a, \lambda)= f(\delta_a, w(a,\lambda)) = f'(a,\lambda) $$
$$B=g(\delta_b, \lambda)= g(\delta_b, w(b,\lambda)) = g'(b,\lambda) $$
So far, all you did was a change of variables, but you still are stuck in the original form.

Now the premise of the theorem is that a and b are independent. In your case you seem to inappropriate link them together so that the "accidental case where the free choices conincide" becomes forced in your case. This is also why you have dependence between delta_a and delta_b.

This effectively means that you have,
$$A= f'(a,\lambda) $$
$$B= g''(a,\lambda) $$
So IMO what you did is replace the premises that normally consistutes what is "local realism".

I think is somewhat disguised with your mixing in the \delta, though. This is is the reason why i tried to note the general form in the other post to see the big picture before the details. Perhaps i got something wrong in your paper?

/Fredrik

 

[DrChinese]

Can you please explain what you mean with H and V? In the coordinate system used in my paper H is 0° and V is 90° defined by the H and V outputs of the source. This is arbitrary but fixed. So we could have a polarizer settings 0°/90°, 120°/210°, 240°/330°. for P1 and P2 respectively. These were used in the calculations.

The output of your splitter is H or V. It can be aligned anywhere across 360 degrees.

The issue is for you to tell me what the output values would be for the 3 angle setting for each photon, each run. That's 6 H or V answers per run. If you feel more comfortable using 0°/90°, 120°/210°, 240°/330° for P1 and P2 respectively - thus inverting mismatches to matches when comparing - that's fine. The objective here is to have the perfect correlations be obvious. So 0°/90°for P1 and P2 respectively will always be a match.

 

[DrChinese]

1, Can we agree upon photon 2 and photon 1 being connected by a time stamp of a coincidence measuring device as I've assumed in section 2 of my paper?
That means the experimental results consist of a list
setting P1; result P1 (=1); setting P2; result P2(=1 or 0).

2. If that is so it is possible to construct algorithms to predict these results.

1. Sure, the pairs can be matched.
2. That's what I understood. I just want to see that in action.

 

[bhobba]

In order to understand the phenomenon we can not use the formalism of QM. It doesn't tell us anything about temporal sequences. Only sound physical reasoning helps.

Seriously are you saying analysis of QM problems via QM is invalid. These experiments are QM problems. Just think about that for a moment - can't you see how contradictory it is. I have zero idea what you mean by QM doesn't tell you about temporal sequences - exactly what does QM have in its formalism that does not allow it to analyse sequences? Sound physical reasoning - sounds a lot like physics must be about reality. Trouble is in physics I think most would say the formalism is the reality - you can interpret it in all sorts of ways and that's fine, but without experimental verification they are just conjectures - more mental cruxes and aids in understanding the formalism than anything.

Thanks
Bill

 

[Dale]

With that, it is time to close this thread. The paper has been adequately reviewed and the discussion is now veering away from established science.

I remind the OP in particular, that all posts on PF must be consistent with the professional scientific literature. The formalism of QM most assuredly can be used here!