A Bell Theorem with no locality assumption?

[DevilsAvocado]

I have been called a virus by some people...

Caroline H. Thompson?

 

[zonde]

There is so much confusion that I would like to start my participation in this thread by suggesting that we each define what we mean by "realism".

It should definitely help to follow this discussion.

To me, realism means, "elements of reality" exist independent of observation, or observability. To me realism has nothing to do with instrumental behaviour or whether these "elements" can be directly observed without disturbance or not. To me, when you say a photon is emitted but not detected, you are admitting to my definition as above. As far as I can tell from this thread so far, all participants believe realism as defined above is true even if they haven't explicitly admitted it. If anyone else thinks realism as defined above is false, please state it and I will show using your own quotes that you are lying. However, you may think "realism" means something else and it is important we all agree what we are arguing for or against to avoid confusion.

I would say that while this definition is "true" it is not restrictive enough to have some value.
Because you can arrive at situation where "elements of reality" are completely independent from results of observations.
I think that definition should include some statement how "elements of reality" are related to observations. Say "elements of reality" ascribed to particle together with "elements of reality" ascribed to measurement equipment (conditions) determine observed result.

Now some will argue that the EPR definition of realism is the idea that a single particle (or entangled pair) will have definite spin projections at 3 different angles. I do not agree that this is the EPR definition but I am willing to grant that definition for the sake of argument, so long as we are not later on drawing conclusions about the previous definition I gave above, based on this so called "EPR definition". In any case, I will suggest first that we present clearly the definition of realism we would like to argue, and then when all the parameters of this version of "realism" have been exposed, it will then make sense to question whether QM or Experiments in anyway tell us anything about the "realism" we are discussing.

This is not EPR definition. EPR definition covers only the case when say projection of spin is predictable with certainty. And because this definition involves "prediction" it can start a looong discussion.

 

[zonde]

This violation of "Effect After Cause Principle" seems quite paradoxical. I think I agree with Dmitry:

For me, Effect is in the lightcone of Cause, nothing more. (In CTL it could be laso vice versa). But then (in flat spacetime) Effect is always after the Cause - just by definition!

If we can relate event that has happened before (memory) with another event that just happened (senses) then event in memory is cause by definition and event reported by senses is effect by definition and to say that effect and cause can swap places means that we should alter memory and simulate sensory information. But in that case we can't be sure about anything and I prefer to be sure about something rather than nothing.

 

[DrChinese]

Caroline H. Thompson?

Probably worse...

 

[DrChinese]

Fair enough.

It is the spin which pre-exists the observation, not the "spin projection", yet it is the "spin projection" which is observable not the spin. So clearly, if the EPR definition is that "observables must pre-exist measurement", it is not a reasonable definition because as you have agreed in (1), realism simply means "elements of reality" (not "observables") pre-exist observation". In other words, it is possible for realism as defined and agreed in (1) to be true, in a completely contextual universe in which nothing can be directly observed, but in which pre-existing elements of reality always interact with instruments to reveal observables. But contextual observables are not allowed in a universe in which observables must pre-exist observation.


If the EPR definition is that "observables must pre-exist observation", then contextual observables are not allowed. But in my definition, contextual observables are fully consistent with pre-existing "elements of reality". But if you are willing to agree that underlined text above is not the EPR definition, and will rather say that my original definition which you agreed to is the EPR definition, then that is a good point to start, and we can proceed to discuss the burden of proof required to disprove it.

I'm pretty much OK with that as a working definition.

I don't really see the distinction though. EPR does not insist that the spin "projection" preexist the measurement, merely that there is an element which does. Since the result is certain, there is little point in distinguishing the two. 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).

Now of course this is true only in the case where there is an undisputed element of reality. Where my dispute arises is in the definition of simultaneous elements of reality which cannot be individually predicted with certainty. That is what Bell attacked.

 

[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.

...[/color]

 

[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?