Questioning assumptions behind Bell's and related theorems

[DevilsAvocado]

This quote does not answer my question.

Oops sorry, bad interpretation on my side.

My question was how you do away with spooky action at a distance by assuming that measurements are just random.

DrC can speak for himself, but to me it looks like he is talking about that the only way to have determined entangled particle spin, is thru some non-local function, i.e. de Broglie-Bohm theory.

On the other hand, if we interpret your way; i.e. what happens in EPR-Bell if we keep locality and exclude realism (in the “Three Amigos” above)?

That’s a good question, and the most important answer is that Bell’s theorem is a no-go theorem – i.e. it states that that a particular situation is not physically possible. In Bell’s theorem this impossible situation is LHV compatible with the predictions of QM.

This means that to refute Bell’s theorem you must also prove QM wrong.

This will, with no doubt, be the biggest task in history of science (certainly not compatible with the rules of this forum), and if this (against all odds in the observable universe) will ever happen – your computer and every other electronic gadget on this planet will stop working in a fraction of a second, and we will be thrown back to the dark ages of nineteenth century, using telegraphs and steam engines.

Back to your question; Are there any attempts to explain how locality & non-realism would work?

Yes there are, where non-realism is implemented by means of nonseparability, in for example a relational blockworld.

Realism and free will are very basic assumptions behind scientific method. You could simply state that QM is either non-scientific or it violates locality IMHO.

I think Lawrence Krauss said – "the universe isn't designed for us" – and QM has proven that this is at least true regarding the human brain.

You could easily replace QM for My computer, and say; “My computer is either non-scientific or it violates locality IMHO”.

What fits best in the mouth, I leave to you and any other reader out there...

 

[stevendaryl]

This quote does not answer my question. My question was how you do away with spooky action at a distance by assuming that measurements are just random.

Besides it does not seem like Erwin Schrödinger is explaining solution but rather a problem in that paragraph. After all the paragraph ends with this sentence: "Best possible knowledge of a whole does not include best possible knowledge of its parts - and that is what keeps coming back to haunt us."

Realism and free will are very basic assumptions behind scientific method. You could simply state that QM is either non-scientific or it violates locality IMHO.

Personally, I find the terms "free will" and "realism" to be too fuzzy to reason about. I think it's more useful to think in terms of possible models that are ruled out by invoking "free will" or "realism".

As for "free will", a sort of model that is local, deterministic and compatible with the QM prediction is a "superdeterministic" model. 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. In some GR cosmologies, that might not be the case for really distant detectors.) I think it would be really difficult to reason about such a superdeterministic theory, but not impossible.

I don't really know what people mean by "realism". What is an example of a non-realistic theory? Well, I suppose one could explain the EPR correlations by assuming that the world is just a dream.

 

[stevendaryl]

DrC can speak for himself, but to me it looks like he is talking about that the only way to have determined entangled particle spin, is thru some non-local function, i.e. de Broglie-Bohm theory.

The problem I have with Dr. C's either/or is that I don't see how a nondeterministic local realistic theory can reproduce the predictions of QM, either. So what's ruled out is local realistic models, and determinism is irrelevant.

 

[Nugatory]

Let me re state and clarify to show that measurement at t₁ at detector A is first. And a non - local effect in second measurement , t₂ at detector B : Suppose both detectors are in same frame or in comoving frames.
The source of the entangled photons is 9/20 of total distance (d) from A and 11/20 of total distance (d) from B on AB axis

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.

 

[DevilsAvocado]

The problem I have with Dr. C's either/or is that I don't see how a nondeterministic local realistic theory can reproduce the predictions of QM, either. So what's ruled out is local realistic models, and determinism is irrelevant.

Interesting, I have never thought of this... nondeterministic local realistic theory... is that even possible? Let's see:

1. The entangled particles are in a superposition of correlated random outcomes.
2. Non-locality is not present to assist.
3. Realism is a fact.

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??

AFAIK, Einstein spent a lot of time debating randomness vs realism, and I don't dare to enter these deep waters, but this setup will have serious problems just combining 1 & 2, which means it's not compatible with the predictions of QM.

I think many do put an equal sign between determinism and realism so when realism goes, so does determinism. We can at least be sure that if we exclude non-locality, determinism is the only way to get perfect correlations in EPR-Bell, which then is refuted by the full predictions of QM (i.e. all the other correlations/settings).

 

[DrChinese]

The problem I have with Dr. C's either/or is that I don't see how a nondeterministic local realistic theory can reproduce the predictions of QM, either. So what's ruled out is local realistic models, and determinism is irrelevant.

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.

You are asking "how is that possible physically?" or similar (what is the mechanism etc). I can't say I know any more than I can answer a lot of "how" questions. I choose (and this is consistent with Bell) to think of such a model in terms of time symmetry. The full experimental setup includes future variables (which include information about Alice and Bob's choice of measurement). I wouldn't speculate as to whether there is a root cause to the outcome of a quantum spin flip. And since there is still an element of randomness in the outcome, this is a non-deterministic model. It is also local because nothing is happening faster than c.

 

[DrChinese]

I think many do put an equal sign between determinism and realism so when realism goes, so does determinism.

That is how I see it too. I know there are others who draw a distinction between determinism and realism. That there is no distinction is best seen simply by referring to the EPR definition, which is what was used by Bell:

a) An element of reality exists if a prediction can be made with certainty.
b) Elements of reality do not need to be simultaneously demonstrable.

If you then define both realism and determinism around that, they must be the same thing for purposes of the EPR/Bell/Aspect line of reasoning.

 

[DrChinese]

And in my post above, I would add that requirement b) goes directly against QM's HUP. Therefore it is the weak link. No b) means Bell's realism assumption is invalid. And Bell's Theorem is satisfied because: No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. You could also say: No physical theory featuring local pre-determination can ever reproduce all of the predictions of quantum mechanics. Or: No EPR-like physical theory can ever reproduce all of the predictions of quantum mechanics.

 

[stevendaryl]

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.

What I'm saying is that Bell's argument goes through perfectly well without assuming determinism. The assumption of deterministic hidden variables is that there is a hidden variable \lambda that determines the outcomes at both detectors:

F(\hat{A}, \lambda) = the outcome at Alice's detector when the hidden variable has value \lambda and Alice's detector is at orientation \hat{A}

G(\hat{B}, \lambda) = the outcome at Bob's detector when the hidden variable has value \lambda and Bob's detector is at orientation \hat{B}

But if you started with a more general assumption (not assuming determinism), then there would be additional probabilities involved:

P_A(\hat{A}, \lambda) = the probability that Alice will measure spin-up at orientation \hat{A} when the hidden variable has value \lambda

P_B(\hat{B}, \lambda) = the probability that Bob will measure spin-up at orientation \hat{B} when the hidden variable has value \lambda

The perfect correlations that occur when \hat{A} = \pm \hat{B} imply that
P_B(\hat{B}, \lambda) = 0 or 1
P_B(\hat{A}, \lambda) = 0 or 1

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

 

[audioloop]

Personally, I find the terms "free will" and "realism" to be too fuzzy to reason about. I think it's more useful to think in terms of possible models that are ruled out by invoking "free will" or "realism".


I don't really know what people mean by "realism". What is an example of a non-realistic theory? Well, I suppose one could explain the EPR correlations by assuming that the world is just a dream.

counterfactual definiteness, absence of definite values of quantum objects or process.
just that, but some wish more, i.e no existence, absence of anything.

but how can someone make science without anything ?

.

 

[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.