Bell inequalities from the incompatibility of experiments:

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Sun Nov 18, 2018 12:51 pm

You perform the experiment independently many times and probability should be seen as statistics.
Classicaly you would say that there is a probability distribution among 8 possibilities: measuring A and B, there is some probabibility distribution of C:
Pr(C=1) = Pr(AB1) / (Pr(AB0) + Pr(AB1))

Anyway, classicaly measuring only A and B, there is still some value of C, just unknown ... but this would lead to the inequality, violated in QM formalism.

Hence, C is not only unknown, but needs to be literally undefined to violate the inequality - what does it mean?
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Re: Bell inequalities from the incompatibility of experiment

Postby FrediFizzx » Sun Nov 18, 2018 12:59 pm

Jarek wrote:You perform the experiment independently many times and probability should be seen as statistics.
Classicaly you would say that there is a probability distribution among 8 possibilities: measuring A and B, there is some probabibility distribution of C:
Pr(C=1) = Pr(AB1) / (Pr(AB0) + Pr(AB1))

Anyway, classicaly measuring only A and B, there is still some value of C, just unknown ... but this would lead to the inequality, violated in QM formalism.

Hence, C is not only unknown, but needs to be literally undefined to violate the inequality - what does it mean?


Well, if you want to keep tricking yourself into thinking there is some kind of violation, nobody can stop you. But I suspect you are actually trying to make a different point. Try making your point without any mention of violation.
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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Sun Nov 18, 2018 1:19 pm

But the problem is that QM formalism, often also experiment, allows to violate this kind of looking obvious inequalities.
To understand it, we need to point incorrectness in their derivations - like that this "coin" C needs to not only have unkown value, but literally have no value ... what does it mean?
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Mon Nov 19, 2018 2:46 am

minkwe wrote:
Jarek wrote:"tossing 3 coins, at least 2 are equal".

Sure, tossing 3 coins once each (ABC), 2 will be the same (A=B or B=C or A=C), but What about tossing two of the three coins each time 3 times (AB, AC, BC)? Will you still expect (A=B or B=C or A=C). If you think so, do the experiment and post your results.

This is the Bell delusion.

The counterargument Bell-believers of statistical proclivities make is that if you toss two of the three coins each time for a large number of times then you will get (A=B or B=C or A=C). :lol:

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Mon Nov 19, 2018 3:58 am

The counterargument Bell-believers of statistical proclivities make is that if you toss two of the three coins each time for a large number of times then you will get (A=B or B=C or A=C)

Imagine you independently "toss 3 coins" a large number of times (prepared in identical way) and calculate proportions for all 2^3 = 8 possibilities: \sum_ABC Pr(ABC) = 1.
Whatever this Pr(ABC) probability distribution is (e.g. there can be dependencies), as derived earlier it satisfies Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.

Now imagine you still toss 3 coins, but only look at two of them (ignore third one) - it still needs to satisfy Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1

However, thanks to Born rules, QM formalism allows to prepare a state giving Pr(A=B) + Pr(A=C) + Pr(B=C) = 3/4.
It wouldn't be possible if we measure all three "coins" at a time - hence, the violation says that it is a crucial that while counting statistics for Pr(A=B), the unmeasured C has literally no fixed value.
There is a crucial difference between ignoring the third value and not measuring it - what is this difference?

Ps. Here is a setting using uniform probability distribution of paths to get Pr(A=B) = Pr(A=C) = Pr(B=C) = 1/5
Image
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Re: Bell inequalities from the incompatibility of experiment

Postby FrediFizzx » Mon Nov 19, 2018 10:06 am

Jarek wrote:But the problem is that QM formalism, often also experiment, allows to violate this kind of looking obvious inequalities.
To understand it, we need to point incorrectness in their derivations - like that this "coin" C needs to not only have unkown value, but literally have no value ... what does it mean?

It doesn't mean anything. What you are really talking about in your paper is that quantum correlations are "stronger" than correlations presented by the Bell inequalities. But there is never "violation" of the Bell inequalities since different inequalities are used. All you have to do to fix your paper is to carefully reword anywhere you mention "violation". Sure..., it is easier to just say "Bell violation" but it simply is not true since it is mathematically impossible.
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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Mon Nov 19, 2018 11:03 am

The word "violation" is widely used in the society, but sure we can replace it e.g. with "disagreement": of looking obvious inequalities, which surprisingly turn out not always satisfied in QM formalism and experiments.

If we want to really understand QM, we need reasonable models also allowing for not satisfying e.g. Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.

And path ensembles already allow for that (through Born rules) - as euclidean path integrals, or nearly equivalent MERW ( https://en.wikipedia.org/wiki/Maximal_E ... andom_Walk ) - as corrected diffusion: in agreement with (Jaynes) maximal entropy principle (required by statistical physics models), by the way repairing lack of localization property in standard diffusion models.
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Re: Bell inequalities from the incompatibility of experiment

Postby minkwe » Mon Nov 19, 2018 1:34 pm

Jarek wrote:Whatever this Pr(ABC) probability distribution is (e.g. there can be dependencies), as derived earlier it satisfies Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.


And what is Pr(ABC) for the Bell experiment? It doesn't exist. It is impossible to measure at 3 angles simultaneously so the inequality does not apply not because of QM or other mystical reason but purely due to common sense. And if Pr(ABC) is meaningless, so is Pr(A=B) + Pr(A=C) + Pr(B=C). It makes no sense to add 3 probabilities like that when Pr(ABC) does not exist? We don't even have to bring QM into it.

There is a crucial difference between ignoring the third value and not measuring it - what is this difference?

Yes! The difference is that once you measure it, it exists as an experimental outcome. If you don't measure it, it does not exist, so Pr(ABC) does not exist. You can only claim the existence of Pr(ABC) if you measure all three simultaneously and the existence of Pr(ABC) is required to derive the inequality.
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Mon Nov 19, 2018 2:09 pm

***
We have pointed this out to Jarek before: viewtopic.php?f=6&t=318&p=7838#p7855

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Mon Nov 19, 2018 2:23 pm

The original Bell inequality or CHSH leave some hope to understand that it is not always satisfied.

However, Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1 is just "tossing three coins, at least two have the same value" - it is obvious, doesn't have any angles: just three binary variables ... leaving no hope not to satisfy it - I really recommend trying to find such example.

For that we need some "combined 3 coins": some 8 state system (000,001,010,011,100,101,110,111), independently prepared and measured many times.
Measuring all three we get Pr(ABC), which leads to Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.

So what can happen when we only measure A and B?
How to build a model and state which identical copies independently measured many times give Pr(A=B) + Pr(A=C) + Pr(B=C) < 1 ?

I can do it with path ensembles above - and would really gladly hear/discuss other approaches allowing for that?
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Tue Nov 20, 2018 1:11 am

***
General remarks: The flaw in Bell's argument is exceedingly simple to understand. The argument considers three or four incompatible experiments that are physically impossible to perform simultaneously, in any possible world, classical or quantum; because they involve three or four mutually exclusive measurement directions. This allows Bell and his followers to use a rather trivial inequality, first discovered by George Boole some 102 years before Bell. The obvious incompatibility of the experiments --- and hence the blatant physical flaw in the argument --- is then obscured by Bell and his followers by invoking the assumption of "statistical independence" of averages such as << A(a)B(b) >> and << A(a')B(b) >> in the large N limit, where a and a' are mutually exclusive measurement directions. For a sufficiently large number N of experimental trials, however, the bounds on the said inequality are not respected. Mystical explanations for this supposedly surprising "violations" of the inequality are then proposed, based on the notion of quantum entanglement. But all these latter parts of Bell's argument hides and obscures the original asinine boo-boo made at the start of his argument --- that of considering three or four physically impossible experiments simultaneously. No one with a sane and rational mind, free of mystical proclivities, should be surprised that Nature does not respect the unphysical bounds on Boole's inequality, derived by considering the said unphysical scenario.

As to understanding the local-realistic origins and strengths of ALL quantum correlations, a comprehensive framework is on offer for the past eleven years. But this framework and its author have been viciously, maliciously, unethically and unjustly attacked by some fanatic Bell-believers, with all kinds of dirty political maneuvering, both online and behind the scenes, because acceptance of this framework by the physics community would threaten the vested interests of those who are drooling for a Nobel prize for experimentally confirming "non-locality."

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Tue Nov 20, 2018 1:26 am

There is no need to perform all experiments simultaneously - instead, the proper way to see it is that you have identical copies, independently perform measurements on them, and count statistics.

For example, performing 1000 flips of "standard 3 coins", you would get ~125 results for each ABC setting, asymptotically leading to Pr(ABC) = 1/8.
Having some "correlated 3 coins" and independently performing 1000 flips on their identical copies, you might get some different proportions, with asymptotically different probability distribution Pr(ABC).
However, whatever this probability distribution is, it needs to satisfy Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.

So please propose a model of something allowing to ask for 3 binary properties, such that independently asking many times (for two of them) we can get proportions with Pr(A=B) + Pr(A=C) + Pr(B=C) < 1 ?
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Tue Nov 20, 2018 1:45 am

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In any physically realizable EPR-Bohm type experiment Pr(ABC) = 0, identically, not 1/8, even in a large N limit.

As I mentioned above, a comprehensive framework explaining the local-realistic origins of ALL quantum correlations already exists: http://rsos.royalsocietypublishing.org/ ... 5/5/180526

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Tue Nov 20, 2018 3:28 am

Indeed standard setting of two entangled photons does not allow to measure three binary properties at once.

However, the main question is if there can be some local realistic physics behind QM.
Having an object with any probability distribution among these 8 possibilities, it would need to satisfy Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.
The question is how to model a local realistic object which, as QM ( https://arxiv.org/pdf/1212.5214.pdf ), can give Pr(A=B) + Pr(A=C) + Pr(B=C) < 1 ?
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Tue Nov 20, 2018 4:14 am

Jarek wrote:Indeed standard setting of two entangled photons does not allow to measure three binary properties at once.

However, the main question is if there can be some local realistic physics behind QM.
Having an object with any probability distribution among these 8 possibilities, it would need to satisfy Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.
The question is how to model a local realistic object which, as QM ( https://arxiv.org/pdf/1212.5214.pdf ), can give Pr(A=B) + Pr(A=C) + Pr(B=C) < 1 ?

As I have noted, such a local-realistic model for the singlet state already exists: https://arxiv.org/pdf/1405.2355.pdf

This model reproduces all the predictions of QM for the singlet (or EPRB) state, including all the probabilities predicted by QM that are said to "violate" Bell inequalities.

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Tue Nov 20, 2018 5:40 am

I see you require " Friedmann-Robertson-Walker spacetime with constant spatial curvature" cosmological assumption ... while asking about microscopic statistics, what is quite surprising.
What would change if your assumption was not satisfied?

Could you maybe give a simple intuition for the basic property of QM (allowing for Bell violation) - Born rule?
That probability of alternative of disjoint events is proportional to square of sum of their amplitudes?
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Tue Nov 20, 2018 6:24 am

Jarek wrote:I see you require " Friedmann-Robertson-Walker spacetime with constant spatial curvature" cosmological assumption ... while asking about microscopic statistics, what is quite surprising.
What would change if your assumption was not satisfied?

Could you maybe give a simple intuition for the basic property of QM (allowing for Bell violation) - Born rule?
That probability of alternative of disjoint events is proportional to square of sum of their amplitudes?

FRW spacetime of constant spatial curvature is not an assumption. It is one of the solutions of Einstein's field equations of general relativity. We live in an FRW spacetime. That fact is not in dispute. But the open question is: whether the spatial part of the FRW spacetime we live in is S^3 or R^3. I have proposed an experiment to test that: https://arxiv.org/abs/1211.0784

According to my model, if we had been living in a flat space, R^3, then Bell inequalities would not have been "violated" in the experiments.

Born rule is a part of quantum mechanics. It relates probabilities to wavefunction. Born rule has no place in local-realism. Probabilities do not play a fundamental role in my model, just as they do not play a fundamental role in classical mechanics.

It is incorrect to think that Born rule is responsible for the "violations" of Bell inequalities. Only some correlations predicted by quantum mechanics "violate" Bell inequalities, but those which do not "violate" Bell inequalities are also predicted by quantum mechanics using the Born rule. Therefore Born rule cannot be the reason for the "violations."

According to my model, the real reasons for the "violations" of Bell inequalities are the algebraic, geometrical and topological properties of the physical space we live in. As a result, Bell inequalities would be "violated" even in the classical experiment I have proposed: https://arxiv.org/abs/1211.0784

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Tue Nov 20, 2018 7:32 am

Born rule has no place in local-realism.

The question is how to understand "locality" - usually it is seen through intuitive "evolving 3D" perspective: that there is some present moment which evolves in time.
There are many reasons that we should rather imagine Einstein's "block universe" instead - we live in some 4D spacetime ("4D jello") and travel through its time directions:
- in all scales from QFT to GRT we use Lagrangian mechanics, which is time (or CPT) symmetric, which allows to use Euler-Lagrange equations to evolve in both time directions, or using mathematically equivalent time symmetric action optimization formulation,
- QM unitary evolution is also time symmetric. Wavefunction collapse is seen as a result of interaction with environment - considering wavefunction of the Universe, there is no longer environment and so collapse - only unitary evolution,
- special relativity says that there is no objective present moment - it is skewed by changing velocity: boost,
- general relativity literally requires working on 4D spacetime, its 4D curvature.

Finally we have equivalent QM formulation through Feynman path integrals - in "4D spacetime" view particles are their entire paths - path ensemble is local model in "4D spacetime" view and leads to Born rules as in the diagram:
Image

It is incorrect to think that Born rule is responsible for the "violations" of Bell inequalities.

I disagree.
Standard probabilistic models have "probability of alternative of disjoint events is sum of their probabilities", what leads to Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1.
In contrast, QM "violates" this inequality and has Born rule: "probability of alternative of disjoint events is proportional to square of sum of their amplitudes".

Such square changes a lot - I gave example for using it for "violation" - choose:
psi000 = psi111 = 0,
psi001 = psi010 = psi100 = psi011 = psi101 = psi110 = 1/sqrt(6)

Now using Born rules, for example measuring only A and B:
Pr(A=B) ~ (psi000 + psi001)^2 + (psi110 + psi111)^2
what leads to Pr(A=B) + Pr(A=C) + Pr(B=C) = 3/5
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Re: Bell inequalities from the incompatibility of experiment

Postby Joy Christian » Tue Nov 20, 2018 8:23 am

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All of this is completely irrelevant to the question of local causality within the context of Bell's theorem. Bell mathematically formalized Einstein's conception of local causality in his 1964 paper by defining local functions of the form A(a, h) and B(b, h), where a and b are experimental parameters, freely chosen by Alice and Bob, and "h" is shared randomness between them.

The correlations between the results A(a, h) and B(b, h) observed by Alice and Bob are then computed as E(a, b) = (1/n) Sum_i A(a, h_i) B(b, h_i) = -cos(a, b). All the rest is irrelevant.

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Re: Bell inequalities from the incompatibility of experiment

Postby Jarek » Tue Nov 20, 2018 10:55 am

Having Born rule it is not a problem to "violate" also the original Bell inequalities: viewtopic.php?f=6&t=318&p=7838#p7832

I prefer working on Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1 instead because it is simpler, "drawing three coins, at least two are equal" - seeming to leave no hope for "violation" ... but it can be done using Born rules/path ensembles.

Can you find Pr(A=B) + Pr(A=C) + Pr(B=C) < 1 with your model?
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