Is Bell's Theorem a Valid Solution to the Locality Versus Nonlocality Issue?

[Rap]

But by definition when we ask if local realism might be true, we are asking about models that include hidden parameters that (at least if QM is empirically correct) can never be measured. If you don't even want to imagine what the objective reality beyond what we can measure might be like (and what might be deducible by a hypothetical being who knew the values of some of these nonmeasurable quantities), I don't see how the question of local realism vs. not local realism can even be meaningful to you, unless you are expecting an experimental violation of QM.

But Bell's theorem states that if you accept counterfactual definiteness, then no hidden variable theory can reproduce the results of QM. I don't expect an experimental violation of QM and I expect that Bell's theorem is correct, so I think the issue is settled for the case in which CFD is accepted - i.e. there can be no local realism (i.e. there are superluminal effects). However, my point was that maybe the resolution to Bell's paradox is not that there are superluminal effects, but rather that CFD is invalid.

 

[JesseM]

Apparently you have not read any of the papers listed by Bill Schneider. These simulations have already been published and shown to violate Bell's inequalities. You simply refuse to acknowledge their relevance to EPRB experiments.

I don't "refuse to acknowledge" anything, but I'm not going to waste my time wading through a lot of papers, I already read one of the papers Bill Schnieder mentioned, "Possible Experience: From Boole to Bell" and found it to contain nothing that refuted Bell (see Bill Schnieder's post [post=2766980]here[/post] which quoted extensively from that paper, and my responses [post=2780659]here[/post] and [post=2781956]here[/post]), nor did it contain a "simulation". If one of those papers has a simulation that meets the conditions of a Bell experiment that I mentioned, and finds consistent violations of some inequality, can you tell me which one. Note that most papers giving computer simulations are not actually denying Bell's theorem but rather are trying to model theories which exploit experimental loopholes like the one listed here, see for example this discussion of a model by de Raedt that DrChinese wrote up. If you think there are papers that have given simulations that violate Bell inequalities even in simulated loophole-free experiments, I suspect you're either misunderstanding something or else the simulated test conditions don't actually match those assumed by Bell in deriving the same inequality, but again feel free to point me in the direction of a specific example.

In any case, are you going to avoid answering my question #1 about whether you disagree that the "Bell inequalities" that are believed by physicists to follow from local realism but to conflict with QM always involve probabilities or expectation values, and my question #2 about whether you disagree that in your model where Alice and Bob are choosing randomly from a set of three coins on each trial, the probability of a violation of nab(HT) + nbc(HT) ≥ nac(HT) gets increasingly tiny the more trials are performed?

 

[JesseM]

But Bell's theorem states that if you accept counterfactual definiteness, then no hidden variable theory can reproduce the results of QM. I don't expect an experimental violation of QM and I expect that Bell's theorem is correct, so I think the issue is settled for the case in which CFD is accepted - i.e. there can be no local realism (i.e. there are superluminal effects). However, my point was that maybe the resolution to Bell's paradox is not that there are superluminal effects, but rather that CFD is invalid.

But are you trying to use the hypothetical violation of CFD to save local realism? If so I think you need a model which postulate physical facts beyond those measurable in quantum theory, quantum theory itself does not clearly satisfy the criteria for a local realistic model (for example there is a single quantum state for an entangled 2-particle system where the particles may be measured very far apart, and a measurement at either location instantaneously changes the whole state according to the formalism).

 

[Rap]

But are you trying to use the hypothetical violation of CFD to save local realism? If so I think you need a model which postulate physical facts beyond those measurable in quantum theory, quantum theory itself does not clearly satisfy the criteria for a local realistic model (for example there is a single quantum state for an entangled 2-particle system where the particles may be measured very far apart, and a measurement at either location instantaneously changes the whole state according to the formalism).

I'm just trying to follow the consequences of rejecting CFD, and it does remove the problem of superluminal effects. Also, as in Copenhagen, I consider the wave function to be an encoding of measurement-produced knowledge rather than an objective entity, so that the collapse of the wave function is a collapse of our uncertainty, not of some objective field. Thus there are no superluminal effects when the whole state collapses.

 

[DrChinese]

There is not any communication between Alice and Bob in the Example 2 activity in OP. Alice randomly generates her own coin selections and measured outcomes without the knowledge of Bob’s coin selections or outcomes. Your suggestion that there is communication comes from not actually performing the activity as described in my posts.

Flip the three coins on the glass table. These are your three values that you request. Let Alice randomly choose a coin and record the coin selection (a,b,c) and the outcome (H,T) while viewing from the top from a defense satellite. Now let Bob randomly choose a coin while viewing from the bottom of the table and again record the coin selection and outcome for Bob. This is trial #1. No communication! Now repeat the trials 50 or more times. Decide on which Bell inequality you would like to test, I will suggest a different one from the OP.
...

Apparently, you want to be a realist without giving any meaning or definition to it. If you look at your example 1, which is classical, you get results which are experimentally refuted by a Bell test. If you relax the realism requirement to match your example 2, then you get results which match the predictions of QM. This is Bell at work.

P.S. I wouldn't reference billschnieder's comments if I were you, his name is mud to me.

In fact, he can't even spell his last name correctly.

 

[DrChinese]

I'm just trying to follow the consequences of rejecting CFD, and it does remove the problem of superluminal effects. Also, as in Copenhagen, I consider the wave function to be an encoding of measurement-produced knowledge rather than an objective entity, so that the collapse of the wave function is a collapse of our uncertainty, not of some objective field. Thus there are no superluminal effects when the whole state collapses.

If you reject CFD, then it is somewhat meaningless to declare yourself as occupying a position other than the standard one. And you are free to pick an interpretation.

 

[harrylin]

Per EPR (1935), the following is sufficient:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

Thanks! Apparently you (and Bell?) interpret "then" as "only then"... I'll look up the original to see if it was just formulated in an awkward way. If so, "EPR reality" is much more narrow than the common concept of "reality"!

 

[Rap]

If you reject CFD, then it is somewhat meaningless to declare yourself as occupying a position other than the standard one. And you are free to pick an interpretation.

Hmm - I don't understand - what is the "standard position"? And why am I free to pick an interpretation? I'm not saying you are wrong, I'm just trying to understand.

 

[DrChinese]

Thanks! Apparently you (and Bell?) interpret "then" as "only then"... I'll look up the original to see if it was just formulated in an awkward way. If so, "EPR reality" is much more narrow than the common concept of "reality"!

The originals:

http://www.drchinese.com/David/EPR_Bell_Aspect.htm

And yes, because it was so formulated, it has been well accepted as being fairly stringent. Which led to Bell being all the more respected.

 

[DrChinese]

Hmm - I don't understand - what is the "standard position"? And why am I free to pick an interpretation? I'm not saying you are wrong, I'm just trying to understand.

Most scientists do not accept that there is a value to unmeasured particle observables. They reject CFD. That is mainline QM. There are the various interpretations such as MWI, BM, Copenhagen, etc. which all make the same predictions.

 

[harrylin]

Thanks! Apparently you (and Bell?) interpret "then" as "only then"... I'll look up the original to see if it was just formulated in an awkward way. If so, "EPR reality" is much more narrow than the common concept of "reality"!

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken:

"We shall be satisfied with the following criterion [..] far from exhausting all possible ways of recognizing a physical reality [...]." and "Regarded not as a necessary, but merely a sufficient condition of reality, this criterion [...]". -EPR1935.

Thus their predictibility criterion was for them (of course!) not a necessary condition of reality. If Bell's theorem would be based on the assumption that it is a necessary condition for EPR, then his theorem would be wrong. However, I'm not aware that such is the case.

Regards,
Harald

 

[JesseM]

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken

It depends if by "no element of reality" you just mean "we are not justified in concluding there is an element of reality in that case, though there could be" or "there is definitely no element of reality in that case". I think EPR (and DrChinese, and Bell) would say the first, but not the second.

 

[harrylin]

It depends if by "no element of reality" you just mean "we are not justified in concluding there is an element of reality in that case, though there could be" or "there is definitely no element of reality in that case". I think EPR (and DrChinese, and Bell) would say the first, but not the second.

This is about what EPR meant (and with less importance what DrChinese meant); and I think that everyone meant what they wrote:

"not as a necessary, but merely a sufficient condition of reality". -EPR

Which is exactly how I understood it in post #36. Then I asked:

" Just to be sure: does EPR according to Bell also assume that if I can not predict Alice's result in advance, there may still be an element of reality? I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

"No element of reality if the observable cannot be predicted with certainty, according to EPR."

Harald

 

[JesseM]

This is about what EPR meant (and with less importance what DrChinese meant); and I think that everyone meant what they wrote:

"not as a necessary, but merely a sufficient condition of reality". -EPR

Which is exactly how I understood it in post #36. Then I asked:

" Just to be sure: does EPR according to Bell also assume that if I can not predict Alice's result in advance, there may still be an element of reality? I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

"No element of reality if the observable cannot be predicted with certainty, according to EPR."

Hmm, I suspect there was some miscommunication there and DrChinese thought you were just asking if according to EPR's argument we are justified in inferring an element of reality in that case. But perhaps DrChinese can comment...

 

[DrChinese]

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken:

"We shall be satisfied with the following criterion [..] far from exhausting all possible ways of recognizing a physical reality [...]." and "Regarded not as a necessary, but merely a sufficient condition of reality, this criterion [...]". -EPR1935.

Thus their predictibility criterion was for them (of course!) not a necessary condition of reality. If Bell's theorem would be based on the assumption that it is a necessary condition for EPR, then his theorem would be wrong. However, I'm not aware that such is the case.

Regards,
Harald

I said it was sufficient as a definition when I quoted it. I also said that there is no element of reality without that. I meant that per the definition in use. Perhaps you have a better definition.

Strictly speaking, it is certainly possible there is an element of reality WITHOUT us being able to predict it in advance. For example, I had to pay when my son wrecked the car even though I could not predict the amount in advance with certainty. And believe me, that was very real to my pocketbook.

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality. But what can you do with this statement? I don't think too much, because you cannot prove the antecedent.

So my point is: Bell used the well accepted EPR definition. That definition is one which is easy to follow, and because it is sufficient it is enough for our examples. I.e. for entangled pairs. The only issue to Bell would be if you could prove convince folks that this was not a sufficient condition. That would be a tough hurdle. Keep in mind that was a cornerstone of EPR.

 

[DrChinese]

Hmm, I suspect there was some miscommunication there and DrChinese thought you were just asking if according to EPR's argument we are justified in inferring an element of reality in that case. But perhaps DrChinese can comment...

Yes, I think a slight miscommunication. Per EPR's definition, they would not have ascribed an element of reality without meeting this requirement. Not that they themselves believed as such. They simply used it for convenience. I think it was a brilliant touch, personally.

That was why I mentioned it as a sufficient condition. There could exist a less restrictive definition, I just cannot imagine such which is also useful.

 

[DrChinese]

I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

"No element of reality if the observable cannot be predicted with certainty, according to EPR."

Harald

The local realist wants a MORE restrictive definition of reality, not less. That way Bell wouldn't apply. So the way you are headed (i.e. towards a lesser definition) doesn't do too much.

 

[JesseM]

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality.

Why would that statement be true though? Let A=you can predict in advance with certainty, and B=there is an element of reality. A -> B is not logically equivalent to ~A -> ~B, so just because you believe the first there is no justification for believing the second.

 

[JesseM]

Yes, I think a slight miscommunication. Per EPR's definition, they would not have ascribed an element of reality without meeting this requirement. Not that they themselves believed as such. They simply used it for convenience. I think it was a brilliant touch, personally.

Right, if the requirement wasn't met then they wouldn't say there was any justification for believing there must be an element of reality (whereas if the requirement was met they would), but that doesn't mean they would definitely conclude there wasn't an element of reality either, they just wouldn't claim to know one way or another, and thus this scenario (where you can't predict with certainty) isn't useful to their argument. harrylin was interpreting you to mean they would say if you couldn't predict with certainty, then there is definitely no hidden element of reality that predetermines the measurement outcome, but that wouldn't be EPR's claim or Bell's.

 

[DrChinese]

Why would that statement be true though? Let A=you can predict in advance with certainty, and B=there is an element of reality. A -> B is not logically equivalent to ~A -> ~B, so just because you believe the first there is no justification for believing the second.

A-> B

implies

~B -> ~A

Too bad I reversed it.

 

[DrChinese]

Right, if the requirement wasn't met then they wouldn't say there was any justification for believing there must be an element of reality (whereas if the requirement was met they would), but that doesn't mean they would definitely conclude there wasn't an element of reality either, they just wouldn't claim to know one way or another, and thus this scenario (where you can't predict with certainty) isn't useful to their argument. harrylin was interpreting you to mean they would say if you couldn't predict with certainty, then there is definitely no hidden element of reality that predetermines the measurement outcome, but that wouldn't be EPR's claim or Bell's.

Yup. Somehow or another, he probably wants to draw some parallel to Bell tests where the angle settings lead to a fraction rather than certainty. But of course there is no connection there.

 

[JesseM]

A-> B

implies

~B -> ~A

Too bad I reversed it.

It's easy to get tripped up by these logic rules I can never keep them straight so I always have to think about examples, like A="an integer is prime and larger than 2", and B="the integer is odd"

 

[Rap]

Most scientists do not accept that there is a value to unmeasured particle observables. They reject CFD. That is mainline QM. There are the various interpretations such as MWI, BM, Copenhagen, etc. which all make the same predictions.

This is not my understanding of CFD. CFD means that, looking forward, if I can predict with 100% accuracy the outcome of a particular measurement, then I am justified in assuming, looking backward, that, not having made such a measurement, but if I had made such a measurement, it would have given the predicted results. Classically, this is so trivially true as to be not worth mentioning, but in QM, where one measurement may preclude another (e.g. measuring momentum precludes measuring position simultaneously), it needs to be examined.

In the case of Bell, you can illustrate the paradox with just one pair of measurements along with the statement "Although Alice and Bob did not align their detectors, had they aligned their detectors, they would have measured equal and opposite spins." This is an acceptance of CFD and produces the paradox. Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

 

[JesseM]

Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

But "superluminal effects" are only needed in a realistic model whose basic elements are localized "beables" (see Bell's paper The Theory of Local Beables), and predictions about experimental results are derived from the behavior of these beables. What Bell proves is that if you have such a model, there's no way to have it also be true that these local beables are only causally influenced by events in their past light cone. If you look at the definition of local realism I gave in [post=3231977]this post[/post], then the idea is that if you accept part 1) of my definition there, according to QM part 2) can't also be correct. But if you don't accept 1) in the first place, as your preference for pure QM with no hidden variables would suggest, then you're free to adopt some totally different definition of "locality" like one that just says that it's impossible to use measurements to transmit messages faster-than-light. The issue of QM being incompatible with locality only comes up when you use a definition of "locality" based on the realistic assumption that there must be a model that breaks up the state of a region at any given time into a collection of localized facts, as outlined in part 1) of my definition, and then says that causal influences between these localized facts shouldn't move faster than light.

 

[DrChinese]

This is not my understanding of CFD. CFD means that, looking forward, if I can predict with 100% accuracy the outcome of a particular measurement, then I am justified in assuming, looking backward, that, not having made such a measurement, but if I had made such a measurement, it would have given the predicted results. Classically, this is so trivially true as to be not worth mentioning, but in QM, where one measurement may preclude another (e.g. measuring momentum precludes measuring position simultaneously), it needs to be examined.

In the case of Bell, you can illustrate the paradox with just one pair of measurements along with the statement "Although Alice and Bob did not align their detectors, had they aligned their detectors, they would have measured equal and opposite spins." This is an acceptance of CFD and produces the paradox. Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

Counterfactual definteness does not require you be able to predict something in advance. That is more related to the EPR definition of elements of reality. They are related. This is certainly a classical concept regardless of where you draw the line.

The issue with Bell is quite different per your second paragraph. You don't really need the requirement that the spins be opposite. More that they have a value.

 

[yoda jedi]

Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

not necessarily, just postulating nonseparability is enough.


.

 

[yoda jedi]

"EPR reality" is much more narrow than the common concept of "reality"!

of course you are Right.
Reality is what exist, the state of things as they actually exist. "No Strings Attached".

with CFD or without CFD.


.

 

[billschnieder]

The issue with Bell is quite different per your second paragraph. You don't really need the requirement that the spins be opposite. More that they have a value.

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements. This is an unreasonable expectation and points to a naive understanding of simple modal logic. You can have a local realistic theory with hidden variables governing photons and still be limited by the fact that Bob and Alice can not repeat their measurement on the same two photons already measured and destroyed. You can even have non-locality with spooky action at a distance and still "x, y, r and s" will not have simultaneous reality for the same simple logical reasons.

Insisting that such a straw-man is the meaning of "realism", effectively renders impossible any experiment that could ever test it, no experimenter can ever recover their photons, restore them to their pristine condition and re-measure them.

 

[billschnieder]

The following highlights the modal error mentioned in my previous post. If you can see the error in the following argument, you will immediately see the logical error being made by Bell proponents:

A photon A is heading toward Alice's detector on a distant galaxy. They will interact tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of noncontradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be). Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hist her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then planning, or as Aristotle put it 'taking care', is illusory in its efficacy. The future will be what it will be, irrespective of our planning, intentions, etc. Free-will is an illusion."

Hint: admit the validity of CFD

 

[JesseM]

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements.

No, they don't. The notion of predetermined values prior to measurements is a deduction that physicists make in scenarios where both experimenters are guaranteed to get identical (or opposite) results whenever they measure the same property, and the deduction also depends on some other assumptions like the assumption of local realism, the no-conspiracy condition, and assumptions about the experimental setup like that the measurements are made at a spacelike separation. But as I pointed out to you in an [post=3275052]earlier post[/post], there are some inequalities like the CHSH inequality that don't depend on the condition that the experimenters always get identical results when they perform the same measurement. I haven't looked at the derivation of the CHSH inequality in a while but I'm fairly certain that here there is no assumption that the measurement results were predetermined prior to measurement, you're free to assume a local realist theory that contains a genuine random element, so that the outcome of any measurement could not have been predicted even with complete knowledge of all hidden and observable variables at some time just prior to measurement.