A Bell Theorem with no locality assumption?

[billschnieder]

1) Since the result is certain, there is little point in distinguishing the two.

2)You call that a contextual measurement, and I do not define as such. Because the result is certain, it is non-contextual. I view contextual as meaning that the entire context, including spacelike separated components, is relevant. That would not be possible in a classically local world (but would in a quantum local world).

1) Well I think there is an important distinction. In modal logic, the certainty of a counter-factual statement can not be transferred to the events implied in the statement. The truth-value of an event can not pre-exist the event. The prediction is true, but the result is not certain until the event of measuring it actually occurs.

The counter-factual statement "if the Netherlands had scored 5 goals against Spain without conceding any, then they would have won the world-cup" is true, but the truth value of the statement can not be transferred to the events embodied in it. In fact, Netherlands lost and it is impossible to undo the event, but the counter-factual statement is still true even though the implied events will never be true. So it is possible to make a prediction of a counterfactual nature, even if it is impossible to actually realize it.

Similarly, the statement "If I had measured the projection along axis c, I would have obtained result C" is a perfectly valid statement, even when it is impossible to measure along axis c. The prediction, therefore is simply a clear description of the context, and what would be obtained in that context. The distinction above prevents us from erroneously assuming that not being able to measure "c" implies the counter-factual statement is wrong.

2) I don't know where you got your definition of contextual as I have never seen it defined as such. Essentially, you are saying contextual observables means they can not be predicted, or you are saying if it can be predicted definitely, then it is not contextual. I do not agree with this definition, but in any case I will keep it in mind that when you say contextual, that is what you mean.

Now continuing with the discussion about realism, since we have a working definition to continue with, I have a question:

If a single particle is real and has a pre-existing spin, according to realism, we would say measuring the spin-projection in a completely specified context, will result in a definite outcome. We can therefore define three or any number of different contexts "a", "b", "c", ... for the single particle for which we will obtain a definite result if we measure the single particle in that context. Do you agree that, this paragraph accurately. represents what a realist will say about the particle?

Non-realism will respond that it is not possible to predict what will be obtained even by completely specifying a contexts for the single particle, since it will not result in a definite outcome. Is this a correct representation of what a non-realism may say about the situation described in the previous paragraph? If not please could you rephrase it to your liking?

 

[DrChinese]

Now continuing with the discussion about realism, since we have a working definition to continue with, I have a question:

If a single particle is real and has a pre-existing spin, according to realism, we would say measuring the spin-projection in a completely specified context, will result in a definite outcome. We can therefore define three or any number of different contexts "a", "b", "c", ... for the single particle for which we will obtain a definite result if we measure the single particle in that context. Do you agree that, this paragraph accurately. represents what a realist will say about the particle?

Non-realism will respond that it is not possible to predict what will be obtained even by completely specifying a contexts for the single particle, since it will not result in a definite outcome. Is this a correct representation of what a non-realism may say about the situation described in the previous paragraph? If not please could you rephrase it to your liking?

I would say that the realist would agree, so yes. They would say the same even if these are not predictable.

The non-realist would say that the context would include the nature of a measurement, and there is no reality outside of that. They would say the same even if a, b and c were individually predictable but not simultaneously predictable.

 

[Pio2001]

So I suggest we discuss around these:

http://arxiv.org/abs/quant-ph/0608008
We prove here a version of Bell Theorem that does not assume locality. As a consequence classical realism, and not locality, is the common source of the violation by nature of all Bell Inequalities.

Hello, thanks for the links.

I read the above paper, and there is a point that I don't follow very well.

Page 3 § New Bell inequality, it is said "it follows from the EACP that the three sequences E, E' and P involved in (**) make sense".

For me, this is not true, for the obvious reason that the E' sequence does not exist.
In part C, it is said that E' is inferred to make sense, i.e. [...] (to [...] have well defined (albeit unknown) values) by using the augmentation of QM by A.

But since the orientations of E and P are not parallel, nor the ones of P and E', no definite value can be inferred for E'i.

I'd rather say "it follows from the EACP that the three probabilities p(Pi=Ei), p(Ei=E'i), and p(E'i=Pi) involved in (**) make sense".

It seems to me that this article just proves that Heisenberg's inequality is true. Not that realism is incompatible with quantum mechanics predictions.

The difference with Bell's inequality is that Bell's inequality applies to actual measurements, while this one applies to measurements that can't be done in practice (measuring both Ei and E'i).
Thus, EPR-Bell experiments show the incompatibility between experimentation and local hidden variable models, while this paper shows the incompatibility between measuring Ei and E'i.

Or am I missing something ?

 

[jk22]

Thus, EPR-Bell experiments show the incompatibility between experimentation and local hidden variable models

This is what I understood, about the local variables.But how to make a no local assumption ? Does it is the case if we had made a 2-level variable system, by iterating the same approach :

a) local one k : C(A,B, g)=int[ A(thetA, k, g)B(thetB, k, g) ]dk (g left untouched)

the latter in fact equals C(A,B, g), where

b) g would remain as a kind of "non-localisable" variable, but seems not very physical.

then

CHSH = |C(A, B, g1) + C(A, B', g2)| + |C(A', B, g3) - C(A', B', g4)|

we could hide (under the moto : there will be always sthg hidden, the truth is somewhere else) the g's by setting values in function of some experimental parameter or results (but this seems not very physical)

does then the theorem hold : CHSH <= 2 forall g1,..g4

 

[Pio2001]

Hello jk22,
I was about to answer yes, but you made me read again CHSH's demonstration, and now I don't understand anything anymore.

I don't know how they can write such a thing as

$$\int d\lambda \, \rho (\lambda) \, \overline{A}(\alpha, \lambda) \, \overline{B}(\beta, \lambda)$$

(taken from [1])

While lambda can depend on the measuring device. The lambdas in A and B should be able to be different.

[1] J.S.Bell, Introduction to the hidden-variable question, Societa Italiana di Fisica. Rendiconti della scuola internazionale di fisica "`Enrico Fermi"', Il corso fondamenti di mecanica quantistica, Academic Press, New York and London, 1972.

 

[charlylebeaugosse]

1) The quasi-triviality of the EACP is what made the set of hypothesis (i.e., EACP+ Locality) weaker, hence the overall result stronger. The price of the weaker hypothesis is a smaller set of Boole-Bell-like inequalities, but GHZ works without changing much of the proof (just using Lorentz observers the right way o get the needed spin projections, observed or for hidden variables. The main goal is to "prove" (this is not math) that hidden variable do not exist, at least the way Bell used them, but the proof is by contradiction, so that these variables are used in the proof of their non-existence, so to speak.

2) The EACP being causality extended to work on hidden variables if any existed, it is essentially only causality. Thus the contradiction coming from the inequalities is almost a complete proof that locality, the other a priori questionable part of the hypotheses.

3) Both papers are now published in the same journal (Eur. Phys. J. D 58, 385–396 (2010) and Eur. Phys. J. D 62, 139–154 (2011): in the first paper, see the GHZ part, the second paper being much more complete on the EPR-Bohm-Bell setting and more precise on the analysis of basic facts).

 

[charlylebeaugosse]

1) A bit surprising that one of the participants manipulates integrals but does not seem to understand what is a proof by contradiction. Assuming true what one hopes to prove false is well known practice since at least the proof that there are infinitely many prime numbers.

2) Besides, Bell's inequalities also use HVs, irreducibly for the proof of them, in an almost tautological way. Now, using extra hypotheses one can deduce an inequality relating measurable quantities, but then one only prove experimentally a correlation between two spins or polarizations for the members of a EPRB pair. To get deeper conclusions from these experiments, one has again to assume many things and the result is that locality and realism (in the sense of preexistence of observables to measurement, or HVs according to preference but the HVs statements are weaker).

3) Using the EACP, that is indeed almost only causality, one has almost a full proof that realism by itself is false (no HV's). The "almost" are there to cover the fact that there could be HVs that would not obey causality the way observables do. I do not know many physicists ready to swallow such pathologies, even among people inclined to believe in HVs.

4) Truth is: these papers are hard to read and the second should be read first, using the first one only for the GHZ part. But the issues are hard. Very deep and hard and dangerously close to philosophy, but philosophy is always there in the way we understand physics (and create it), even if we do not always see it.

 

[JordanL]

DrC: Does your personal inclination to reject objective realism lead you to any other assumptions or hypotheses?

Or, I suppose, does the collected work that has been done on that point of view have any other conclusions that might be testable? I would think that observational dependence in realism would imply a more fundamental interconnectedness of things that we observe to exist within our concept of reality. Would QM be sufficient to explain this greater connection? Or would a greater connection be unnecessary? If such a fundamental interdependence of existence were posited, how would it be tested?

I ask because this is an area I have not ventured very far into, and it seems you have given it more consideration.

 

[DrChinese]

DrC: Does your personal inclination to reject objective realism lead you to any other assumptions or hypotheses?

Or, I suppose, does the collected work that has been done on that point of view have any other conclusions that might be testable? I would think that observational dependence in realism would imply a more fundamental interconnectedness of things that we observe to exist within our concept of reality. Would QM be sufficient to explain this greater connection? Or would a greater connection be unnecessary? If such a fundamental interdependence of existence were posited, how would it be tested?

I ask because this is an area I have not ventured very far into, and it seems you have given it more consideration.

Welcome to PhysicsForums, JordanL!

I don't see rejecting realism as requiring any other assumptions. Keep in mind that there are several different interpretations that reject realism. I would say that "most" physicists reject realism in one fashion or another.

As to testing: there are "some" experiments which appear to support rejection of realism. There are a number of papers on the subject. I would say nothing to date is absolutely conclusive but that seems to be the direction. A lot of Bohmians reject realism too, or at a minimum reject non-contextuality (which to me is the same as objective realism).

 

[JordanL]

Welcome to PhysicsForums, JordanL!

I don't see rejecting realism as requiring any other assumptions. Keep in mind that there are several different interpretations that reject realism. I would say that "most" physicists reject realism in one fashion or another.

As to testing: there are "some" experiments which appear to support rejection of realism. There are a number of papers on the subject. I would say nothing to date is absolutely conclusive but that seems to be the direction. A lot of Bohmians reject realism too, or at a minimum reject non-contextuality (which to me is the same as objective realism).

Interesting. So ideas have been proposed that stop at simply rejecting realism, and ideas have also gone further than that? I'm opening up the links you provided in the first post now to give them a look through.

If observation itself presents a change in reality, there is some kind of information exchange between the observer and the observed. Is this a reasonable statement?

I have studied the ideas behind QM, GR and SR for a while, but I'm just teaching myself about the underlying math. Or rather, I'm just starting the process of teaching myself about the underlying math. I'm trying to check the understanding I have about the abstract ideas so that I have more context for the math I'm trying to learn.

EDIT: Also, thank you for the welcome. :) My first post got deleted because I guess I posted it in the wrong forum, but it was actually inspired by a similar thread about Bell's theorem that you posted on over a year ago.

 

[Demystifier]

A lot of Bohmians reject realism too, or at a minimum reject non-contextuality (which to me is the same as objective realism).

I would put it this way. Strong theorems (such as Kochen-Specker) rule out SIMULTANEOUS non-contextual/objective realism of non-commuting quantum observables. E.g., if spin in z-direction is real, then spin in x-direction is not. The Bohmian interpretation exploits the fact that at most one quantity may be real in the NON-CONTEXTUAL/OBJECTIVE sense, and this quantity is (usually) taken to be the particle position. Thus, in Bohmian mechanics spin indeed is not non-contextually/objectively real, but the particle position is. So when we measure spin, we don't really measure spin (because it is not real); what we really measure are some particle positions in the Stern-Gerlach apparatus.

Thus, it is not correct to say that Bohmians reject non-contextual realism. Instead, they reject non-contextual realism for almost all quantum observables, except one.

 

[Zarqon]

Haven't read the whole thread yet, but since the OP contained only refs to preprints, I though I would note that a PRL appeared on the subject a few days ago:

http://prl.aps.org/abstract/PRL/v107/i9/e090401"

Quantum nonlocality has been experimentally investigated by testing different forms of Bell’s inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constraint on the system’s time correlations. In this Letter, we report on the experimental violation of a temporal Bell’s inequality using a nitrogen-vacancy (NV) defect in diamond and provide a novel quantitative test of quantum coherence. Such a test requires strong control over the system, and we present a new technique to initialize the electronic state of the NV with high fidelity, a necessary requirement also for reliable quantum information processing and/or the implementation of protocols for quantum metrology.

Is it true that since the temporal Bell inequalities do not depend on locality, a violation of the inequalities in this frame directly disproves realism? Or is it rather that there exists an equivalent notion of locality for time correlations instead, such that realism could still not be singled out even in this case. What's your thoughts on this?

 

[Demystifier]

Is it true that since the temporal Bell inequalities do not depend on locality, a violation of the inequalities in this frame directly disproves realism?

No, it doesn't disprove realism. It only disproves non-contextual realism, but the violation of original Bell inequalities also does that. Bell and many others emphasize nonlocality rather than contextuality because contextuality does not look so surprising to them, not because they thought contextuality could be avoided.

 

[DrChinese]

I would put it this way. Strong theorems (such as Kochen-Specker) rule out SIMULTANEOUS non-contextual/objective realism of non-commuting quantum observables. E.g., if spin in z-direction is real, then spin in x-direction is not. The Bohmian interpretation exploits the fact that at most one quantity may be real in the NON-CONTEXTUAL/OBJECTIVE sense, and this quantity is (usually) taken to be the particle position. Thus, in Bohmian mechanics spin indeed is not non-contextually/objectively real, but the particle position is. So when we measure spin, we don't really measure spin (because it is not real); what we really measure are some particle positions in the Stern-Gerlach apparatus.

Thus, it is not correct to say that Bohmians reject non-contextual realism. Instead, they reject non-contextual realism for almost all quantum observables, except one.

Thanks for clarifying that point, I wasn't certain I was getting it entirely correct.

 

[nikman]

A very recent interview with the Z of GHZ wherein he talks about local realism, progress in loophole closing and related stuff.

http://discovermagazine.com/2011/jul-aug/14-anton-zeilinger-teleports-photons-taught-the-dalai-lama

 

[jk22]

Is the detection loophole the fact that the experimental correlation function does not give -1 at angle 0, and a value of CHSH which is 2.38 and not 2.82 ?

This can be seen on the graph at the end of this paper :

http://arxiv.org/PS_cache/quant-ph/pdf/9806/9806043v1.pdf ?

 

[jk22]

If you want can we say in the formula used :
<AB> counts the matching pairs,
whereas <A><B> counts the non detected as pair, hence the loophole, so that the experimental result should give : <AB>-<A><B> if we take into account the detection loophole ?

 

[zonde]

Detection loophole is the fact that interpretation of Bell tests that use photons should relay on fair sampling assumption. This assumption means that correlations in photon pairs where one of two is not detected would be the same (if they would be detected) as for the pairs where both photons were detected.
If that is not so then correlations can be affected by detection of different subsamples under different settings of analyzer.

 

[DevilsAvocado]

http://discovermagazine.com/2011/jul-aug/14-anton-zeilinger-teleports-photons-taught-the-dalai-lama/article_view

So does that mean Einstein was wrong?

There are still some technical loopholes in the experiments testing Bell’s theorem that could allow for a local realistic explanation of entanglement. For instance, we don’t detect all the particles in an experiment, and therefore it is conceivable that, were we to detect every single particle, some would not be in agreement with quantum mechanics. There is *a very remote chance* that nature is really vicious and that it allows us to detect only particles that agree with quantum mechanics. If so, and if we could ever detect the others, then local realism could be saved. But I think we are close to closing all of these loopholes, which would be a significant achievement with practical implications for quantum technologies.

...

 

[zonde]

April 13, 2010:
http://www.nist.gov/pml/div686/detector_041310.cfm"
So we are waiting ...

 

[DevilsAvocado]

... for that 1% to turn everything upside down ...

 

[zonde]

... for that 1% to turn everything upside down ...

Who is talking about 1%?
I am talking about 90% turning it into something slightly more classical.

Didn't you know that there are no reports about experiments that would aim for increased coincidence rates?

 

[DevilsAvocado]

Who is talking about 1%?

There must be something wrong with my calculator because I can’t even get the basic math right...

NIST Detector Counts Photons With 99 Percent Efficiency
...
Who is talking about 1%?
...
I am talking about 90%​

So, are you saying (for real) that there is 90% chance for Local Reality to survive?

 

[zonde]

There is no problem with math.
The fact that we have detectors with 99% detection efficiency does not automatically solve question about detection loophole free photon Bell test.
Bell test still has to be performed using these detectors and should give high coincidence count rate while violating Bell inequalities by significant amount at the same time.

For example you can take a look at this experiment:
http://arxiv.org/abs/quant-ph/9810003"
It says:
"After passing through adjustable irises, the light was collected using 35mm-focal length doublet lenses, and directed onto single-photon detectors — silicon avalanche photodiodes (EG&G #SPCM’s), with efficiencies of ∼ 65% and dark count rates of order 100s⁻¹."
and:
"The collection irises for this data were both only 1.76 mm in diameter – the resulting collection efficiency (the probability of collecting one photon conditioned on collecting the other) is then ∼ 10%."

So while detector efficiency is around 65% coincidence rate was only around 10%. And it is this coincidence rate that is important if we want to speak about closing detection loophole.

 

[DevilsAvocado]

... coincidence rate was only around 10%

Okay, so I’m asking you again:

So, are you saying (for real) that there is 90% chance for Local Reality to survive?

 

[zonde]

Make it 100%. I have no doubt that local realism holds at least as far as quantum entanglement is concerned.

 

[ThomasT]

Make it 100%. I have no doubt that local realism holds at least as far as quantum entanglement is concerned.

That would mean that the qm predictions for all optical Bell tests are incorrect.

That's hard to accept, especially since the qm predicted correlation between the angular difference of the crossed polarizers and the rate of coincidental detection is also intuitively in line with classical optics principles, whereas that of the archetypal local realistic model isn't.

 

[DevilsAvocado]

Hey TT! Welcome back! I’m sorry for that terrible "silly joke"... pleeeeeeeeease tell me that this had absolutely nothing to do with your 'pause'...

 

[DevilsAvocado]

Make it 100%. I have no doubt that local realism holds at least as far as quantum entanglement is concerned.

zonde, you’re refuting the most precise theory we got, thousands of experiments, consensus in the global scientific community, the work and words by Anton Zeilinger et al., etc, etc, ...

How does it feel to be a heretic? Left all alone out in the cold?

 

[zonde]

That would mean that the qm predictions for all optical Bell tests are incorrect.

No, it doesn't mean that. QM predictions are tested and they work for inefficient detection case. Experiments with efficient detection can not change that.

But it would mean that QM predictions are incorrect for the limit of single photon.

That's hard to accept, especially since the qm predicted correlation between the angular difference of the crossed polarizers and the rate of coincidental detection is also intuitively in line with classical optics principles, whereas that of the archetypal local realistic model isn't.

I am not saying that "archetypal local realistic model" used by Bell is correct. It was successfully used to make mathematical argument but it is very poor as description of physical reality.

 

[zonde]

zonde, you’re refuting the most precise theory we got, thousands of experiments, consensus in the global scientific community, the work and words by Anton Zeilinger et al., etc, etc, ...

How does it feel to be a heretic? Left all alone out in the cold?

I can say the same as in the replay to Thomas.
Experiments with efficient detection can not change results of experiments with inefficient detection.

And I don't see that I am alone.
Idea that QM does not apply to single particles is quite common.

 

[DevilsAvocado]

And I don't see that I am alone.

In mainstream science you are, or you have to show me a least one reputable professor working at a reputable institute, preferably with one or two awards, accepted by the community – who agrees with you that local realism has 100% chance to survive.

And while you’re at it, you could maybe also explain to me why Zeilinger, Aspect and Clauser has won the http://www.wolffund.org.il/cat.asp?id=25&cat_title=PHYSICS" (one of the most prestigious in the world) along with 100,000 Euros "for their fundamental conceptual and experimental contributions to the foundations of quantum physics, specifically an increasingly sophisticated series of tests of Bell’s inequalities or extensions there of using entangled quantum states"...?

I mean... you could hardly claim that they’re just "nice" to Zeilinger, Aspect and Clauser, right?

And why are there http://blogs.scientificamerican.com/observations/2011/09/21/annual-nobel-predictions-announced-but-forecasting-prizes-remains-a-tricky-business/" for "their tests of Bell’s inequalities and research on quantum entanglement", if there are a lot of people like you who have "found out" that this is just "mumbo-jumbo"...?

 

[ThomasT]

No, it doesn't mean that. QM predictions are tested and they work for inefficient detection case. Experiments with efficient detection can not change that.

Ok, but calculations assuming 100% efficient detection also indicate a measurable difference between qm predictions and LRHV predictions. So, I'm not sure what you're asserting wrt local realism.

But it would mean that QM predictions are incorrect for the limit of single photon.

I'm not sure what you mean by this. Afaik, wrt the way I learned what I remember of qm , it doesn't have to do with single photon detections, but only with photon flux wrt large number of trials. And isn't this is also what LRHV models of entanglement are concerned with predicting?

I am not saying that "archetypal local realistic model" used by Bell is correct. It was successfully used to make mathematical argument but it is very poor as description of physical reality.

Ok, I think we agree on this. So exactly what are you referring to when you speak of "local realism"?

 

[DrChinese]

Ok, but calculations assuming 100% efficient detection also indicate a measurable difference between qm predictions and LRHV predictions. So, I'm not sure what you're asserting wrt local realism.

With LR nowhere near those results, which are 100% consistent with QM.

Don't make me come and beat you up!

 

[No-where-man]

I am opening a new thread to continue discussion of some interesting ideas around EPR and Bell. Specifically, this is about the idea of realism, and whether it is tenable in light of Bell and other HV no-go theorems. Note: I usually use Hidden Variables (HV) and Realism interchangeably although some people see these as quite different. I also tend to use Realism as being an extension of EPR's "elements of reality" as a starting point for most discussions. After all, if a physical measurement can be predicted with certainty without disturbing what is measured... well, I would call that as real as it gets.

charlylebeaugossehad thrown out a few ideas in another thread - especially around some papers by Charles Tresser. So I suggest we discuss around these:

http://arxiv.org/abs/quant-ph/0608008
We prove here a version of Bell Theorem that does not assume locality. As a consequence classical realism, and not locality, is the common source of the violation by nature of all Bell Inequalities.

http://arxiv.org/abs/quant-ph/0503006
In Bohm's version of the EPR gedanken experiment, the spin of the second particle along any vector is minus the spin of the other particle along the same vector. It seems that either the choice of vector along which one projects the spin of the first particle influences at superluminal speed the state of the second particle, or naive realism holds true i.e., the projections of the spin of any EPR particle along all the vectors are determined before any measurement occurs). Naive realism is negated by Bell's theory that originated and is still most often presented as related to non-locality, a relation whose necessity has recently been proven to be false. I advocate here that the solution of the apparent paradox lies in the fact that the spin of the second particle is determined along any vector, but not along all vectors. Such an any-all distinction was already present in quantum mechanics, for instance in the fact that the spin can be measured along any vector but not at once along all vectors, as a result of the Uncertainty Principle. The time symmetry of the any-all distinction defended here is in fact reminiscent of (and I claim, due to) the time symmetry of the Uncertainty Principle described by Einstein, Tolman, and Podolsky in 1931, in a paper entitled ``Knowledge of Past and Future in Quantum Mechanics" that is enough to negate naive realism and to hint at the any-all distinction. A simple classical model is next built, which captures aspects of the any-all distinction: the goal is of course not to have a classical exact model, but to provide a caricature that might help some people.

http://arxiv.org/abs/quant-ph/0501030
We prove here a version of Bell's Theorem that is simpler than any previous one. The contradiction of Bell's inequality with Quantum Mechanics in the new version is not cured by non-locality so that this version allows one to single out classical realism, and not locality, as the common source of all false inequalities of Bell's type.

What implications this could have on modern thoughts?
Does it mean universe is random and unpredictable or is it still the opposite?