Questioning assumptions behind Bell's and related theorems

[stevendaryl]

But... afaik, realism requires that “the Moon is there even when nobody looks”... which means the particles assembling the Moon must have definite states all the time, i.e. superposition is out of the question. If this also excludes “classical randomness”, I don’t know... how would a “stochastic Moon” look like??

I don't see how being in a definite state at each moment in time implies that there is a unique future state.

 

[DrChinese]

So determinism is a consequence of the assumption of local realism, not an additional assumption.

I never said otherwise. I have said repeatedly that I use those terms interchangeably, that it is the EPR definition I follow (as does Bell). Realism = simultaneous elements of reality. Those determine measurement outcomes, there being no random element.

And I don't believe we live in such a realistic universe.

 

[stevendaryl]

counterfactual definiteness

I don't see that counterfactual definiteness is that important, conceptually. If you take classical mechanics and add a random number generator, you still have a theory that's not all that mysterious. You can still make predictions and do experiments, etc. It might be weird (and Einstein may not have liked such a theory) but it's not anywhere near as weird as QM. I wouldn't call such a theory "non-realistic". It's just nondeterministic.

 

[DevilsAvocado]

This is a typical example of the relativity of simultaneity at work; there is no way of deciding which of two spacelike-separated events "really" happened first. It's also why the apparent faster-than-light propagation of entanglement effects is so perplexing.

Agreed 100% :thumbs:

This was also a big dilemma for John Bell, who just a few month before he died, said that "this doesn't work, or it's just me, being silly", i.e. he was even prepared to dump his theorem as silliness, facing the problem of SR vs QM.

Many seem to sweep this question under the rug, saying "Well, there is NO usable information transmitted, therefore this is not an issue" or "What issue?? I have rigorously shown that with this equation, in the 11^th dimension, everything works as expected!".

Still we have correlations between the entangled particles, which shows that they 'knows' what happened to the other, even if the outcome (as always in QM) is random. And the outcome is definitely not in any 11^th dimension, it's right in front of our nose.

To me, the sign saying "STOP! VERY INTERESTING!" can't possibly be any larger than this...

 

[DrChinese]

This is a typical example of the relativity of simultaneity at work; there is no way of deciding which of two spacelike-separated events "really" happened first. It's also why the apparent faster-than-light propagation of entanglement effects is so perplexing.

I would disagree that "relativity of simultaneity" has anything to do with the perplexing ftl effects. You can see that quantum ordering is irrelevant in many cases in which ordering is absolute. An example is entanglement swapping such as this:

http://arxiv.org/abs/quant-ph/0201134

The decision to swap can be made anytime: before, after or between detection of pair members. This is true in any reference frame, relative or absolute. The results never vary.

 

[DevilsAvocado]

You could also say: No physical theory featuring local pre-determination can ever reproduce all of the predictions of quantum mechanics.

This is very nice, says it all. And in case of objections regarding pre-determination, all you have to say is "perfect correlations", which is then disputed by 'ordinary' correlations. Sweet!

 

[billschnieder]

And therefore you, at rest relative to the source and both detectors, are quite clear that $t_1 < t_2$ and that the detection at A happens before the detection at B. I, however, am watching from a spaceship moving along the AB axis at a speed of .1c relative to your lab and I will observe that $t_1 = t_2$ so the two detections were simultaneous. At any greater speed, I would find that $t_1 > t_2$ so the detection at B came first.

(Someone check my math, please - I did the algebra in my head so .1c may not be right for this particular combination of distances).

This is a typical example of the relativity of simultaneity at work; there is no way of deciding which of two spacelike-separated events "really" happened first. It's also why the apparent faster-than-light propagation of entanglement effects is so perplexing.

This is a red herring. If Alice an Bob have synchronized clocks, as they should/do in any such experiment, then according to their clocks (not any third-party) it makes sense to talk of a before/after/simultaneous. You could even eliminate clocks and talk of time as measured by the entangled pair themselves (e.g. distance traveled at c) and still it would make sense to talk of before/after/simultaneous. In EPR experiments, each station records the time of each detection event using synchronized clocks. The third-party analyzing the results uses those timestamps, not their own, so this issue you talk about is irrelevant.

You could change the before-/after-/simultaneous-"ness" by changing the path length traveled by the particles to get to each station and you will still obtain the correlations; so the question of direction of communication remains for those who hold to non-locality.

 

[DevilsAvocado]

I don't see how being in a definite state at each moment in time implies that there is a unique future state.

Maybe you’re right, but I think it will be hard to combine indefinite states with unique future states... i.e. indefinite states could hardly be a part of “classical realismâ€... and then we’re back to Einstein’s “classical randomnessâ€, which I interpret as “definite states that are real but not predictableâ€, and if this interpretation is correct, it is excluded by Bell’s theorem – if, and only if – locality is also required.

And this is due to definiteness, not randomness.

 

[billschnieder]

If one of Bell's assumptions (such as deterministic hidden variables) is wrong, then there could be a nondeterministic local model that can reproduce the predictions of QM. I don't claim it to be realistic, however, so I don't follow that part.

The paper which started this thread PROVED (without any doubt), that only two assumptions are required to obtain Bell's inequalities

(i) that the random variables take values in the interval [−1;+1]
(ii) that the random variables are dened on the same probability space

Notice the absence of "determinism, or realism, or locality in those assumptions?

Bell's implicit assumption of the single probability space is equivalent to the postulate that, for each j = 1...N
pjI = pjII (3)
Physically this means that:
the hidden parameter in the first experiment is the same as the hidden parameter in
the second experiment. This is surely a very implausible assumption.
Notice however that, without this assumption, Bell's argument cannot be carried over
and we cannot deduce the inequality because we must stop at equation (3).

 

[stevendaryl]

I never said otherwise. I have said repeatedly that I use those terms interchangeably.

Those terms being "determinism" and "local realism"? I wouldn't say that they are interchangeable. It just happens to be that for EPR correlations, there is no difference between the two.

 

[Nugatory]

This is a red herring.

Not for MorroBay's argument, where he suggests that there is a causal relationship between the observation at one station and the result at the other station.

 

[Nugatory]

I would disagree that "relativity of simultaneity" has anything to do with the perplexing ftl effects. You can see that quantum ordering is irrelevant in many cases in which ordering is absolute. An example is entanglement swapping such as this:

Ah, you're right, there's a bottomless supply of perplexity here

MorroBay was proposing a causal relationship between the observation at one station and the result at the other, and RoS is (for me, at least, and I expect some company here) a problem for that line of thinking.

 

[billschnieder]

In the reasoning that leads up to Bell's inequality, it is assumed that the choice of the hidden variable is independent of the choice of settings of distant measurement devices. That might not be the case. If the world is deterministic, then the settings of detectors is determined long in the past, and so it is possible to choose the hidden variable in a way that takes into account the future settings. (Actually, there's an interesting--to me--question about whether superdeterminism requires that twin-pair sources and detectors have an overlap in their backward lightcones.

As Accardi proves in the paper cited at the beginning of this thread, the assumption that "the choice of the hidden variable is independent of the choice of settings of distant measurement devices" is the same as the assumption "that the random variables are defined on the same probability space" and that is the only other assumption assumption required to obtain the inequalities together with the assumption of outcomes (+1, -1).
Note that what most people call the "realism assumption", or the "counterfactual definiteness" assumption, are simply variants of this assumption, albeit while using non-standard definitions of "realism" or "CFD". Accardi has distilled it down to the essential mathematical assumption and clearly reveals that you do not need any physical assumption to obtain the inequalities.

Superdeterminism is not the only way to violate the requirement of "the same probability space". QM violates this requirement because non-commuting measurements by definition do not have the same probability space. The authors discuss other mechanisms way more reasonable than superdetermism. See for example the discussion on page 16.

If I may summarize:
* Some λs may not be measurable at certain detector angles, which means non-detection of particles may not be a problem of "detection efficiency" but rather due to the mechanics of the particle detector interaction. In this case, you will never have the same probability space even with perfect detectors.

* The measurement time at given detector angles may a function of both the detector setting and the hidden variable λ, T(α,λ). If T is not a constant you could have a scenario in which for some combinations of setting and λ, the delays are too long that the pairing operation or (coincidence matching) eliminates some λs unfairly.

 

[billschnieder]

Ah, you're right, there's a bottomless supply of perplexity here

MorroBay was proposing a causal relationship between the observation at one station and the result at the other, and RoS is (for me, at least, and I expect some company here) a problem for that line of thinking.

What then does "non-locality" mean if it does not entail "causality"? What is the "mainstream-view" answer to this question?

 

[DevilsAvocado]

This is a red herring. If Alice an Bob have synchronized clocks, as they should/do in any such experiment,

And the reply is a blue parrot, synchronized clocks works only within a single inertial frame, unless you want to dispute SR also.

If one wants to do science, I believe one would like the theory to work in all, including difficult, situations. Not only in the living room.

 

[Maui]

And the reply is a blue parrot, synchronized clocks works only within a single inertial frame, unless you want to dispute SR also.

If one wants to do science, I believe one would like the theory to work in all, including difficult, situations. Not only in the living room.

Are you claiming that if I bury my head in the sand, the relativity of time will not go away?

 

[DrChinese]

Those terms being "determinism" and "local realism"? I wouldn't say that they are interchangeable. It just happens to be that for EPR correlations, there is no difference between the two.

Take out the word "local", and that's what I was saying...

 

[DrChinese]

Ah, you're right, there's a bottomless supply of perplexity here

MorroBay was proposing a causal relationship between the observation at one station and the result at the other, and RoS is (for me, at least, and I expect some company here) a problem for that line of thinking.

That's true too!

 

[DrChinese]

As Accardi proves in the paper cited at the beginning of this thread, the assumption that "the choice of the hidden variable is independent of the choice of settings of distant measurement devices" is the same as the assumption "that the random variables are defined on the same probability space" and that is the only other assumption assumption required to obtain the inequalities together with the assumption of outcomes (+1, -1).
Note that what most people call the "realism assumption", or the "counterfactual definiteness" assumption, are simply variants of this assumption, albeit while using non-standard definitions of "realism" or "CFD". Accardi has distilled it down to the essential mathematical assumption and clearly reveals that you do not need any physical assumption to obtain the inequalities.

You need another source for this statement. That paper is not acceptable by forum standards.

 

[audioloop]

I don't see that counterfactual definiteness is that important, .

i concur.
they bloated it to non realism.
realism is more than definite values.

 

[DevilsAvocado]

Are you claiming that if I bury my head in the sand, the relativity of time will not go away?

Ahh! The Stop Analyzing Next Difficulty experiment!
Of course you're right. Did a quick check and found the preliminary results from The Nevada Synchronized Counter Intuitive Experiment:

Bob (sponsored by Taco Bell) looking for the ground breaking results

 

[DevilsAvocado]

MorroBay was proposing a causal relationship

Who the h**l is MorroBay??

Googled Bell MorroBay causal and got Lolo's Mexican Food - Morro Bay, CA – Yelp??


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[Dale]

My apologies for not closing this sooner.