Can grandpa understand the Bell's Theorem?

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The discussion centers on the challenges of understanding Bell's Theorem, particularly from the perspective of someone with a limited mathematical background. The theorem illustrates the discrepancies between quantum mechanics and classical physics, especially regarding correlations observed in entangled particles. Key points include the unexpected correlation results predicted by quantum mechanics, which differ from classical expectations, and the implications of these results for our understanding of measurement and communication at a distance. The conversation also touches on the need for clearer explanations of these complex concepts in physical terms, rather than relying solely on mathematical formalism. Ultimately, the discussion highlights the ongoing struggle to reconcile intuitive understanding with the counterintuitive nature of quantum phenomena.
  • #121
JesseM said:
Bell's proof was a theoretical one, therefore it is purely mathematical and just as unlikely to be disproven [..].

You did not comment on Nelson's counter proof of Bell's proof; for the application in the real world there is always an aspect of definition and interpretation involved.

Harald
 
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  • #122
DrChinese said:
I have 2 web pages which give separate proofs of Bell's Theorem. So yes, I consider Bell both correct and authoritative.

What does Bell have to do with Nelson? (Or vice versa?) Why would I care? Nelson's paper is about locality and stochastic mechanics, which I am unlikely to see as a good pairing anyway.

Nelson's paper has everything to do with Bell's theorem as you would have seen if you had clicked on the link. It starts as follows:

"Stochastic mechanics is a theory of quantum phenomena described in terms of classical random processes. An immediate objection is that such a theory is impossible due to Bell’s inequalities and their violation in experiment. Let us begin by confronting this problem."

It may be useful to start a thread on Nelson and "passive locality".

Harald
 
  • #123
harrylin said:
You did not comment on Nelson's counter proof of Bell's proof; for the application in the real world there is always an aspect of definition and interpretation involved.

Harald
The paper doesn't seem to be freely available online so I can't judge it for myself, nor do I necessarily trust your claim that the paper is intended to refute Bell's theorem. (have you actually read the full paper, or did you just make a quick judgment about what you think it says based on looking at the first page?) https://www.physicsforums.com/showthread.php?t=171545 discussing this and some other related papers, post #5 claims:
Benjamin said:
In the language of Nelson:
> Theorem: Bell has shown, that active locality AND passive locality can not explain quantum mechanics.

That is, a theory which violates Bells inequality must violate active or
passive locality or both of them. The violation of active locality
would mean a spooky interaction at a distance. The violation of passive
locality would mean simply a correlation that existed since the past.

Nelsons work is mainly a mathematical analysis of Bells sloppy speaking
and does only strenghten the language of Bell with mathematical rigour.

In fact, Nelson discussed it extensively with Bell himself at this time!

His work:
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1749-6632.1986.tb12456.x

Is only not well known for one reason:

Nelson failed to modify his stochastic mechanics, that it would be a
passivly nonlocal theory. Instead he found out that his theory was
actively nonlocal.
Also, while I don't claim to understand what they're talking about, I came across this paper which says on p. 9:
However, while it is often claimed that Nelson’s theory is empirically equivalent
to quantum theory, unfortunately, as shown by Wallstrom [39], the two
theories are in fact not equivalent, because Nelson’s function S does not have
the specific multivalued structure required for the phase of a single-valued (and
continuous) complex field \psi. The Schr¨odinger equation is indeed derived, but
only for the exceptional set of wave functions with no nodes, for which the circulation
of ∇iS around all closed curves vanishes. Since almost all wave functions
have nodal points (where \psi = 0), quantum theory cannot be derived from Nelson’s
theory, or from any model that leads to Nelson’s theory. (Note that there
is no such problem in pilot-wave theory, where is regarded as a basic entity.)
And here is a paper by Nelson himself where he writes on the very last page:
Here we have an empirical difference between
the predictions of quantum mechanics and stochastic
mechanics. Measurements of the position
of the first particle at time t and of the second particle
at time 0 do not interfere with each other, and
the two theories predict totally different statistics.
Does anyone doubt that quantum mechanics is
right and stochastic mechanics is wrong?
 
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  • #124
JesseM said:
The paper doesn't seem to be freely available online so I can't judge it for myself, nor do I necessarily trust your claim that the paper is intended to refute Bell's theorem. (have you actually read the full paper, or did you just make a quick judgment about what you think it says based on looking at the first page?) [..]

Thanks for the quick feedback - regretfully I won't be able to give feedback for a few days. Yesterday I downloaded the paper, read it quickly and asked people here to explain it to me; it tackles the definitions of Bell's theorem. On purpose I did not use the word "refute"; Nelson uses the word "confront". Bell's theorem is a claim about interpretations of physics, not just mathematics. I asked people here to please explain "passive locality".

I found myself this thread, discussing a recent publication on modified stochastic mechanics:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4020/my-article-on-Bell-s-theorem-in-Ann-Phys

As this is probably important for understanding Bell's theorem, I think we should start a thread on this.

Harald
 
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  • #125
harrylin said:
...As this is probably important for understanding Bell's theorem, I think we should start a thread on this.

Harald

You are free to do what you want. But if we started a thread for every paper that claims to refute Bell, we would be adding about 5 per month. Such critiques are soundly rejected because they end up modifying the Bell/EPR definitions beyond the point where they are meaningful. So basically, no one cares. There are NO generally accepted refutations of the main Bell conclusion. Despite claims to the contrary.

There is work being done to try to find ways to get around Bell using SM and various algebra. Peter Morgan's work comes to mind, which involves Lie algebra. There are tremendously complex issues involved, none of which really belong in discussions here. Peter publishes in this area regularly, and is also a member here. The point is that as you soften one element of Bell slightly, you open up opportunities/issues elsewhere. That may help us to better probe things. But it doesn't change Bell per se.
 
  • #126
I also want to add that many of the Bell "refuters" are hopelessly lost in the past in the sense that there have been many experiments in the past 10 years which dramatically change the landscape. For example, entanglement of particles which have never shared a common past is a very powerful counterexample to ANY traditional local theory.

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

Thus in the modern post-Bell/Aspect world, the requirements have been raised substantially for any LR theory.
 
  • #127
..
A thought-experiment shows grandpa can understand Bell's theorem.

A grandpa came to visit last Saturday, so I showed him this thread. His reply follows:

<<<SNIP>

Further to Saturday's discussion of that web-thread on Bell's theorem, https://www.physicsforums.com/showthread.php?t=488690, here's my reply:


How grandpa understands Bell's theorem in the context of Aspect's experiment.

Aspect Abstract = http://arxiv.org/abs/quant-ph/0402001
Aspect PDF = http://arxiv.org/pdf/quant-ph/0402001

Notes re notation:

1. V (below) stands for the Greek "nu" in Aspect's article.

2. Where Aspect [page 8, eqn (15)] uses P+(a), I use P(a+|V1', a); etc.

3. Where Aspect [page 4, eqn (5)] uses P++(a, b), I use P(ab++|V1, a; V2, b); etc.

4. Since all probabilities are conditional, I have included the conditions for clarity. Such clarifications do not change Aspect's experimental results in any way.


Grandpa's thought-experiment:

0. For starters, Gordon, let yourself be "Alice-in-Wonderland" for a day.

1. In his article above, Aspect generically identifies the photons in an entangled pair as V1 and V2; Aspect's Fig. 1, page 3.

2. Take just one of Aspect's singlet-entangled photon-pairs, and identify these two photons as V1' and V2'.

3. Test V1' with a linear polarizer oriented a; Aspect's Fig. 1, page 3.

4. Say outcome is a+. This indicates that, after the photon-polarizer interaction, V1' is polarized in the a direction.

5. Now, Alice; please, very carefully: Retrieve V1', restore it to its pristine condition, and retest it at a again.

6. The result is a+ again. And so on; each re-test of the retrieved-and-restored V1' at orientation a yields a+ with certainty.

6a. Note this very important point: There is NO implication here (whatsoever) that pristine V1' -- or, which is the same, "retrieved-and-restored" V1' -- was polarized a+ prior to its first (or prior to any subsequent re-test) polarizer-photon interaction. It was not! It is not.

6b. For a similar view, see Bell: Speakable and Unspeakable in Quantum Mechanics, 1987, 2004, page 82, though in a different setting: "... and each particle, considered separately, is unpolarized here ... ." [Bell's emphasis.]

7. Now, Alice; with added confidence in your retrieve-and-restore technique: Test and re-test retrieved-and-restored V1', at orientation b, many times.

8. Outcome: P(b+|V1', b) = cos^2 (a, b). P(b–|V1', b) = sin^2 (a, b).

[NB: What if you had been working with a different photon-pair; say V1" and V2". And (say) V1" at orientation a had given the result a–? No problem. That a– notation says that the post-test polarization of V1" is orthogonal to orientation a. Then the multi-test outcomes of that photon (V1") at orientation b would be:

P(b+|V1", b) = sin^2 (a, b). P(b–|V1", b) = cos^2 (a, b).]

9. Outcome-consequence that we will now use: Since V2' is correlated with V1' via the conservation of total angular momentum at their creation, the behavior of pristine V2' under test is the same as the behavior of pristine V1' (which is the same as "recovered-and-restored" V1' under test by you, as Alice).

10. So there is no mystery that we obtain the following results for Aspect's experiments (now over many trials, on many entangled pairs, with no photon now recovered). That is, with the photons generically identified by Aspect as V1 and V2, we have (just as Aspect says; but now introducing the conventional Alice and Bob of EPR-Bohm fame):

Alice (single detections, polarizer oriented a): P(a+|V1, a) = P(a–|V1, a) = 1/2.

Bob (single detections, polarizer oriented b): P(b+|V2, b) = P(b–|V2, b) = 1/2.

11. Joint expectation, Aspect's correlation coefficient (page 5):

E(a, b) = P(a+, b+|V1, a; V1, b) – P(a+, b–|V1, a; V2, b) – P(a–, b+|V1, a; V2, b) + P(a–, b–|V1, a; V2, b)

= [cos^2 (a, b)]/2 – [sin^2 (a, b)]/2 – [sin^2 (a, b)]/2 + [cos^2 (a, b)]/2

= cos^2 (a, b) – sin^2 (a, b) = cos 2(a, b)] = QM result; see Aspect page 4, eqn (6).

12. QED. In this way I understand Bell's theorem in accord with my own (and Einstein's) locally causal world-view. In my opinion, Bell's theorem arises from a very narrow interpretation of the EPR definition of an element of reality. In my opinion -- viewed narrowly in the context of EPR's term "corresponding" -- the EPR definition is a classical concept; so Bell's theorem applies to classical systems.

(I think that it was you that told me that Einstein never used this "EPR-expression" in his own writings?)

Now we know that we can never get to QM from classical concepts: that move is blocked by the finite value of Planck's constant, etc. On the other hand, we can always get to classical concepts from QM. Thus, above, each real-local-causal element of quantum reality (my element of physical reality; the orientation of the total spin of each particle) is perturbed by the interaction of each carrier-particle (here, each Aspect photon) with the polarizer.

Aspect's experiment confirms the above derived correlations. Such correlations arise from the conservation of total spin when each pair of photons is created. This has nothing to do with non-locality, FTL, or similar ideas.

Rather, recognizing that we live in a quantum world, and using quantum thinking, we by-pass Bell's classical block on understanding. In this way we better understand the local-causal-realistic marvels associated with quantum-entanglement.

...............

Explanatory note re a common question:

Why did you measure the "recovered-and-restored" V1' at b.

1: Because (seeking to ensure that no non-local "influence" can be brought into the discussion), you seek to understand how one photon responds to varied tests. This must be done via a thought-experiment, since any real test perturbs the photon and effectively destroys it. (The above thought experiment is not much different to that one done by Einstein, where he traveled with a photon.) When you understand the V1' response to b, you then also understand how its twin V2' responds at b; via their pristine spherically-symmetric singlet-state correlation. So, after those repeated tests, testing "recovered-and-restored" V1' at b, you now understand how the pristine correlation of Aspect's V1 and V2 delivers the QM outcome statistics: locally, causally and realistically.

2: Because you need to circumvent the following "possibility": Suppose you test V2' at b, AND suppose your critics insisted that "non-locality", "FTL", "collapse of wave-function", etc., were (somehow) physical and real. Then your critics could say that the measurement on V1' had influenced V2' "non-locally ++". So the above thought-experiment eliminates all such loop-hole claims from the "non-local + "FTL" + ..." community.

3: Because you can then understand Bell's theorem in accord with my own (and Einstein's) locally causal and realistic world-view.

4: Because, most importantly, the above locally-causal-and-realistic thought-experiment eliminates the need for any other explanatory mechanism re entangled-particle dynamics and outcomes.

5. Because Aspect's experiment is then the physically-possible, the real experiment that confirms the validity of your thought-experiment. QED.


Hoping this all makes sense re this Grandpa's understanding of Bell's theorem, please get in touch re any matter that's not clear, etc.

Yours, etc.,

>>
 
  • #128
Gordon Watson said:
9. Outcome-consequence that we will now use: Since V2' is correlated with V1' via the conservation of total angular momentum at their creation, the behavior of pristine V2' under test is the same as the behavior of pristine V1' (which is the same as "recovered-and-restored" V1' under test by you, as Alice).
First of all, according to QM this is simply wrong, if you do two successive measurements with angles a and b on photon V1', the result of the second measurement with angle b is not expected to automatically be the same as a single measurement of V2' with angle b. Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V1', b) = cos^2 (a-b) and P(b–|V1', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V1', b) = sin^2 (a-b) and P(b–|V1', b) = cos^2 (a-b).

2. If you measure V2' only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation

The reasoning for why this is impossible is exactly the same as the reasoning behind the normal version of Bell's theorem, again the critical thing to realize is that in order to have perfect correlations in a locally causal theory, it would have to be true that photon V1' had predetermined results for any possible choice of a and b even before it reached the polarizers, and photon V2' had identical predetermined results. Do you agree with this point? I'm not sure because you never answered my last question in the [post=3239888]other thread[/post] when I asked you about it, and have also avoided the subject when I asked you on earlier occasions. This issue is central to Bell's whole argument, if you're not interested in actually thinking about Bell's proof but just want to trumpet the fact that you believe you've disproved him by finding a locally causal theory that reproduces QM predictions, without actually giving enough of a detailed model to demonstrate that the equations you write for correlations are even possible under local causality, you shouldn't be doing so on this forum.
 
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  • #129
JesseM said:
First of all, according to QM this is simply wrong, if you do two successive measurements with angles a and b on photon V1', the result of the second measurement with angle b is not expected to automatically be the same as a single measurement of V2' with angle b. Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V1', b) = cos^2 (a-b) and P(b–|V1', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V1', b) = sin^2 (a-b) and P(b–|V1', b) = cos^2 (a-b).

2. If you measure V2' only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation

The reasoning for why this is impossible is exactly the same as the reasoning behind the normal version of Bell's theorem, again the critical thing to realize is that in order to have perfect correlations in a locally causal theory, it would have to be true that photon V1' had predetermined results for any possible choice of a and b even before it reached the polarizers, and photon V2' had identical predetermined results. Do you agree with this point? I'm not sure because you never answered my last question in the [post=3239888]other thread[/post] when I asked you about it, and have also avoided the subject when I asked you on earlier occasions. This issue is central to Bell's whole argument, if you're not interested in actually thinking about Bell's proof but just want to trumpet the fact that you believe you've disproved him by finding a locally causal theory that reproduces QM predictions, without actually giving enough of a detailed model to demonstrate that the equations you write for correlations are even possible under local causality, you shouldn't be doing so on this forum.

..

Jesse, I'll get back to you re all of this.

BUT please note: In Grandpa's thought experiment the situation that you refer to does not arise. At least as I understand the situation:-

There are no successive measurements on a single photon (as generally understood by these terms) because the photon, after one test, is retrieved and RESTORED to its pristine state.

So, in terms of any photon in Grandpa's thought-experiment, it is always a first test on a pristine photon (not a succession of tests). For example, Grandpa could have said (as another thought-experiment): Just select another photon that yields a+ when tested at orientation a. [This could be done, in a thought-experiment which admitted no non-locality, FTL, etc., by testing a string of V2 photons at orientation a (at Bob's end). When the outcome a+ is there observed, you then subject its pristine twin V1 to test at b (at Alice's end).

This second thought-experiment would equally go through. AND deliver the same mathematical relations.

That's the essence of the thought-experiment, as I see it. But I'll check further.

PS-1: Do you not see that these thought-experiment scenarios differ (markedly) from your (and the common) expression for "successive real tests on real photons"?

PS-2: As for Grandpa's thought-experiment delivering the same results at the same settings in Aspect's experiment:-

P(a+, a+|V1, a; V2, a) = P(aa++|V1, a; V2, a) = cos^2 (a, a) = 1.

GW
 
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  • #130
Gordon Watson said:
There are no successive measurements on a single photon (as generally understood by these terms) because the photon, after one test, is retrieved and RESTORED to its pristine state.
There is no "restoring" procedure in QM.
Gordon Watson said:
For example, Grandpa could have said (as another thought-experiment): Just select another photon that yields a+ when tested at orientation a. [This could be done, in a thought-experiment which admitted no non-locality, FTL, etc., by testing a string of V2 photons at orientation a (at Bob's end). When the outcome a+ is there observed, you then subject its pristine twin V1 to test at b (at Alice's end).
How is this different from just doing a normal Bell test and looking only at the subset of trials where a+ was observed at the V2 location, throwing out all the other trials where that didn't happen? Either way, if you have a 100% chance of b+ for V1 whenever you get a+ for V2 when the same angle is chosen (a = b), then (if the measurements are made at a spacelike separation, and the experimenters choose the angle at random) under local realism implies predetermined results for all possible angles. Which leads to the rest of Bell's argument, and proves that local realism is incompatible with the relation cos^2(a-b)
Gordon Watson said:
PS-1: Do you not see that these thought-experiment scenarios differ (markedly) from your (and the common) expression for "successive real tests on real photons"?
No, I don't see any marked difference, Bell's argument would seem to apply either way, unless you are claiming the measurements on V1 and V2 are not made at a spacelike separation.
Gordon Watson said:
PS-2: As for Grandpa's thought-experiment delivering the same results at the same settings in Aspect's experiment:-

P(a+, a+|V1, a; V2, a) = P(aa++|V1, a; V2, a) = cos^2 (a, a) = 1.
Yes, but you're just asserting that the cos^2 relationship for getting the same result is possible, when in fact it is impossible under local realism if the measurements are at a spacelike separation. You need to actually address the basics of Bell's argument, not just make empty assertions.
 
  • #131
I wrote:

Gordon Watson said:
9. Outcome-consequence that we will now use: Since V2' is correlated with V1' via the conservation of total angular momentum at their creation, the behavior of pristine V2' under test is the same as the behavior of pristine V1' (which is the same as "recovered-and-restored" V1' under test by you, as Alice).

In reply, you wrote:

JesseM said:
First of all, according to QM this is simply wrong, ...

So you are saying that Grandpa's Thought Experiment (GTE) is contradicted by Quantum Theory (QT); and presumably Aspect's experiment? Since I accept both GTE and QT, I'd welcome a more detailed explanation (with special reference to QT) of why you take this view. To be very clear: IMHO, GTE and QT are as one -- allowing of course for the fact that (evidently) QT has never before contemplated GTE. (But see below re the importance of thought-experiments.)

Please also note that your continuation [... next, below] is invalid and misleading. GTE does not do "successive measurements" as that phrase is commonly understood. I prefer to use the word "test", not "measurement"; and here's what we find:


GTE has this sequence: Test, retrieve, restore to pristine condition, re-test.

Your implication has this sequence: Test, test.


So if your reference is to your sequence and QT, we will probably agree.

But the question you need to answer is this: Can you show me where, precisely, GTE and QT disagree?

JesseM said:
... if you do two successive measurements with angles a and b on photon V1', ...


Well, of course, if you do something different with QM tests, you generally do get something different re QM outcomes. But, as noted above, GTE does NOT do as you suggest.


JesseM said:
... the result of the second measurement with angle b is not expected to automatically be the same as a single measurement of V2' with angle b.

Of course, under your sequence of "successive tests" [Test, test], we agree.

But you must here address the GTE sequence [Test, retrieve, restore to pristine condition, re-test]. In which case the outcomes are identical. This identity is confirmed by QT and by Aspect's experiment (the latter being a practical outworking, a proxy, a surrogate for GTE).


JesseM said:
Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V1', b) = cos^2 (a-b) and P(b–|V1', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V1', b) = sin^2 (a-b) and P(b–|V1', b) = cos^2 (a-b).

2. If you measure V2' [sic] only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation


This part of your response continues with reference to "successive" tests" -- see also (presumed) typo marked [sic]. However: If you rephrase the above, consistent with the GTE sequence and QT, the correct conclusion is the diametric opposite to yours.

JesseM said:
The reasoning for why this is impossible is exactly the same as the reasoning behind the normal version of Bell's theorem, ...

But GTE is a quantum-based experiment, involving quantum events. As eaglelake said in that earlier post:

eaglelake said:
<SNIP>
Essentially, Bell’s theorem describes a classical experiment, not a quantum one. ... ... In that sense, Bell’s theorem is about classical physics. It is about an experiment that has several possible outcomes, which are mutually exclusive. ... ... we do not simultaneously perform the experiments for the other components and “unperformed experiments have no results.” Thus, we have no values from the unperformed experiments to be used in our calculations! If we insist on using the inferred values from unperformed experiments we often get contradictions and paradoxes. That is what happens in Bell’s theorem. Several results are used to obtain his inequality. But the experiment he describes can yield only one of those values. The other results are from unperformed experiments, and are, therefore meaningless in quantum mechanics, but Bell uses them as we would in a classical calculation. Consequently, quantum events violate Bell’s inequality while classical experiments satisfy it.


GTE involves quantum events, and quantum events violate Bell’s inequality while classical experiments satisfy it. That, as I see it, is the whole point of GTE: GTE involves quantum events and GTE suggests an underlying local realism. [Which views are not taken to be those of eaglelake.]


JesseM said:
... again the critical thing to realize is that in order to have perfect correlations in a locally causal theory, it would have to be true that photon V1' had predetermined results for any possible choice of a and b even before it reached the polarizers, and photon V2' had identical predetermined results. Do you agree with this point?


Do I agree that the results are determined? Yes. And I accept that the results of unperformed tests can be statistically predicted.

But since I take the view (promulgated by Peres), that unperformed experiments have no results, what could it POSSIBLY mean for a photon to "have" an infinity of "predetermined results"? For that infinity arises from the fact that a and b are just two arbitrary orientations from the infinity of orientations in 2-space.

As you know: I take a very different, QM-based, view. The paired-photons in GTE (and hence each Aspect pair), are correlated by the conservation of total angular momentum. If we consider the orientation of such (in 3-space), there are an infinity of such. So I take the view that no two pairs have the same orientation: so every pair is different.

Further, that orientation in 3-space is the local realistic hidden-variable; no two pairs the same, and our tests not revealing any of them! So what could it mean, in QT terms, for each photon to "have" an infinity of "predetermined results"? It seems to me that is how you would describe the diameters of a classical sphere?

Note that, if every Aspect-photon in the world were tested at orientation a, there are just two (2) equivalence classes under such a test: The class that yields the a+ result, and the class that yields the a– result. Similarly for Bob's test at orientation b. So we find in GTE, no requirement for "predetermined results of unperformed experiments". Rather, a requirement (as specified) to understand how the four (4) equivalence classes relate under determinism.

JesseM said:
I'm not sure because you never answered my last question in the [post=3239888]other thread[/post] when I asked you about it, and have also avoided the subject when I asked you on earlier occasions. This issue is central to Bell's whole argument, if you're not interested in actually thinking about Bell's proof but just want to trumpet the fact that you believe you've disproved him by finding a locally causal theory that reproduces QM predictions, without actually giving enough of a detailed model to demonstrate that the equations you write for correlations are even possible under local causality, you shouldn't be doing so on this forum.

Well: I'm here to learn. And I try to learn from what is invariably true, or close thereto. And from my mistakes, and those of others. Since I've done much thinking about BT, and since the issue central to "Bell's whole argument" is a classical one, and since I live in a quantum world - I seek to understand that which is central to that quantum world ... and "Einstein's arguments". To that end, my PF-signature alerts students to that interest of mine. And in that context, my probings, fumblings, mumblings, etc., re my point of view lead to questions for discussion, correction, etc.

I'd therefore hope that there would not be a pattern here, of getting close to the nitty-gritty of an issue and finding the thread locked. So that still leaves us discussing GTE in its terms; a fairly detailed model, as I see it, with a specific question to you:

Where does GTE breach QT, having in mind that Aspect's experiment is a valid surrogate for GTE?

In that regard, I wrote:

Gordon Watson said:
..
BUT please note: In Grandpa's thought experiment the situation that you refer to does not arise. At least as I understand the situation:- There are no successive measurements on a single photon (as generally understood by these terms) because the photon, after one test, is retrieved and RESTORED to its pristine state.

So, in terms of any photon in Grandpa's thought-experiment, it is always a first test on a pristine photon (not a succession of tests).

The GTE sequence is: Test, retrieve, restore to pristine condition, re-test.

You replied:

JesseM said:
There is no "restoring" procedure in QM.

Of course. And, in STR, there is no "pursuing a beam of light with velocity c" when one is aged 16. However, that story continues: "One sees that in this paradox the germ of the special relativity theory is already contained." Einstein, "Autobiographical Notes", in Schilpp (1954: p. 53).

Re GTE, we are discussing a thought-experiment that delivers results in accord with QT and Aspect's experiments.
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  • #132
JesseM said:
There is no "restoring" procedure in QM.

See response above.

JesseM said:
How is this different from just doing a normal Bell test and looking only at the subset of trials where a+ was observed at the V2 location, throwing out all the other trials where that didn't happen? Either way, if you have a 100% chance of b+ for V1 whenever you get a+ for V2 when the same angle is chosen (a = b), then (if the measurements are made at a spacelike separation, and the experimenters choose the angle at random) under local realism implies predetermined results for all possible angles. Which leads to the rest of Bell's argument, and proves that local realism is incompatible with the relation cos^2(a-b)
My emphasis.

It seems to me that your "local realism" is of the classical kind - akin to Mermin's "instruction sets". That the predetermined test-results are pre-existing, and not the product of each photon-polarizer interaction.

Here's a typical example of that genre: Kuttner & Rosenblum (The Physics Teacher, 48, 2010, p. 125) write: "Bell's theorem in a nutshell: Suppose that unobserved objects in our world have physically real properties that are NOT created by their observation."

GTE proceeds from a different supposition: We know that we cannot get to QM from classical concepts: that move is blocked by the finite value of Planck's constant, etc. On the other hand, we can always get to classical concepts from QM. In GTE, each real-local-causal element of quantum reality (an element of physical reality; the orientation of the total spin of each particle) is perturbed by the interaction of each carrier-particle with the polarizer.

Aspect's experiment confirms the GTE correlations. Such correlations arise from the conservation of total spin when each pair of photons is created. So, recognizing that we live in a quantum world, and using quantum thinking, we by-pass Bell's classical block on understanding. In this way we better understand the local-causal-realistic marvels associated with quantum-entanglement.

So GTE employs a real element of physical reality (total-spin orientation) and shows how it manifests: in full accord with QT and Aspect's experiment.

JesseM said:
No, I don't see any marked difference, Bell's argument would seem to apply either way, unless you are claiming the measurements on V1 and V2 are not made at a spacelike separation.

This has been addressed before: The Alice and Bob tests are space-like separated.

JesseM said:
Yes, but you're just asserting that the cos^2 relationship for getting the same result is possible, when in fact it is impossible under local realism if the measurements are at a spacelike separation. You need to actually address the basics of Bell's argument, not just make empty assertions.

The cos^2 relation emerges from GTE. Not much different to the emergence of the cos^2 relation in QT? As for the basics of Bell's argument: see Kuttner & Rosenblum above. In my view, this is the naive (narrow) interpretation of "EPR elements of physical reality". GTE rejects this view and those EPR elements.
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  • #133
Gordon Watson said:
So you are saying that Grandpa's Thought Experiment (GTE) is contradicted by Quantum Theory (QT); and presumably Aspect's experiment? Since I accept both GTE and QT, I'd welcome a more detailed explanation (with special reference to QT) of why you take this view.
Since my response was specifically about what would happen if you did multiple measurements on V1' via your notion of "recovering and restoring", I think it was clear that I was talking specifically about this notion when I said the thought-experiment is contradicted by QM. In QM there is no way to "recover and restore" an already-measured photon V1' in such a way that a subsequent measurement on V1' would show the same correlations with its entangled twin V2' as the first measurement. But I already explained this in my response, so I'm not really sure what you're confused about.
Gordon Watson said:
Please also note that your continuation [... next, below] is invalid and misleading. GTE does not do "successive measurements" as that phrase is commonly understood. I prefer to use the word "test", not "measurement"; and here's what we find:GTE has this sequence: Test, retrieve, restore to pristine condition, re-test.

I would say "test ... re-test" is commonly understood as "successive measurements", regardless of what happens in between ("successive" just means the two happen in a sequence, it doesn't say anything about what happens in between). Again, QM simply doesn't allow any intermediate procedure between successive measurements that would "restore to pristine condition" and cause the same correlations between V1' and V2' to occur on the "re-test" as on the first "test". This would be a clear violation of the uncertainty principle, as you could "test" V1' for its spin on one axis a, then "restore to pristine condition" and "re-test" for spin on a different axis b (spin on different axes have uncertainty relations just like position and momentum), and then via the "test" and "re-test" you could predict with 100% certainty what the result of a measurement of V2' would reveal on either a or b, so there'd be no sense in which knowledge of one gives uncertainty in the other.
Gordon Watson said:
[But you must here address the GTE sequence [Test, retrieve, restore to pristine condition, re-test]. In which case the outcomes are identical. This identity is confirmed by QT and by Aspect's experiment (the latter being a practical outworking, a proxy, a surrogate for GTE).
You think there is any notion of "restoring to pristine condition" in the Aspect's experiment? If so you're completely misunderstanding something, this isn't possible at all in QM with one member of an entangled pair.
JesseM said:
Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V1', b) = cos^2 (a-b) and P(b–|V1', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V1', b) = sin^2 (a-b) and P(b–|V1', b) = cos^2 (a-b).

2. If you measure V2' [sic][/color] only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation
Gordon Watson said:
This part of your response continues with reference to "successive" tests" -- see also (presumed) typo marked [sic].
There was no typo where you put "[sic]" above, I meant V2', not V1'. Again the idea you seem to be expressing is that if we do a measurement #1 on V1', the "recover and restore" V1', then do a second measurement on V1' (which I call "successive" since I don't think that word implies anything about what happens in between), then you think the second measurement on V1' will show the same correlations with the first measurement on V2' as the first measurement on V1' would have. For example, you would say that if our second measurement on V1' was on angle b and gave result b+, then if our first measurement on V2' had also been at angle b, we'd be guaranteed to see b+ with V2' as well--am I misunderstanding?
Gordon Watson said:
But GTE is a quantum-based experiment, involving quantum events.
Unless I have misunderstood your notion of "recover-and-restore" (see above), the experiment is not possible in QM.
Gordon Watson said:
Do I agree that the results are determined? Yes. And I accept that the results of unperformed tests can be statistically predicted.

But since I take the view (promulgated by Peres), that unperformed experiments have no results, what could it POSSIBLY mean for a photon to "have" an infinity of "predetermined results"?
Peres is not a local realist! A local realist must necessarily say that the local variables associated with the particle immediately prior to encountering the measuring device (polarizer, Stern-Gerlach) must have already predetermined what results it would give to any possible setting it might encounter at the measuring-device. This is necessary in order to explain how the two particles are guaranteed with probability 1 to always give the same results if they encounter devices with the same setting, despite the fact that neither particle can causally influence one another. After all, if the particles' responses to any possible setting were not predetermined by the value of local variables prior to measurement, that would imply some random element in what result each one would give when it encountered the measuring-device, so there would always be a nonzero probability the two members of the pair would give different results.

If you don't understand this very basic aspect of Bell's reasoning, then after all this time you really haven't understood the first thing about the theorem you are trying so hard to overturn. As I said in my last post on the other thread:
it must nevertheless be true that the results for each detector setting are predetermined by the hidden variables of the two particles after they have been emitted but prior to the moment when Alice and Bob make a choice of detector settings (at least this must be true in any Bell experiment where Alice and Bob are guaranteed to get opposite--or identical--results each time they choose the same setting). If you don't understand why this must be the case, we should probably go back to my basic definition of local realism offered in [post=3196744]post #94[/post] from the other thread (also see my response to your question about the meaning of my phrase "irreducibly nonlocal" in [post=3213709]post #135[/post])
We could also discuss the paper where I think Bell gives the clearest argument for why local realism (what he calls "local causality") implies predetermined results, using an argument about the past light cones of each measurement, see [post=3248153]this post[/post] where I link to and discuss his paper La nouvelle cuisine. But I would rather not derail this thread to discuss your misconceptions about Bell's theorem and I already asked you not to spread out the same arguments over multiple threads, so for further discussion of the "local realism implies predetermined results" idea, please respond on the other thread.
Gordon Watson said:
As you know: I take a very different, QM-based, view. The paired-photons in GTE (and hence each Aspect pair), are correlated by the conservation of total angular momentum. If we consider the orientation of such (in 3-space), there are an infinity of such. So I take the view that no two pairs have the same orientation: so every pair is different.
QM does not say that each pair has a well-defined angular momentum vector prior to measurement, but OK, in a local realist theory you're free to make such an assumption.
Gordon Watson said:
Further, that orientation in 3-space is the local realistic hidden-variable; no two pairs the same, and our tests not revealing any of them! So what could it mean, in QT terms, for each photon to "have" an infinity of "predetermined results"?
It would just mean that the orientation of the angular momentum vector is sufficient to determine whether the particle gives + or - in response to each possible detector setting.

To put it another way, suppose we imagine a godlike being who just knows the value of all hidden variables associated with the particles (under your suggestion, an angular momentum vector) without having to interact physically with anything. Suppose this being also knows the complete equations of the fundamental laws of physics, and can calculate perfectly the answer to any sufficiently well-defined problems involving these laws. In this case, if the being sees a particular particle rushing towards a detector with a known angular momentum vector, then if she doesn't yet know what angle the detector is going to be set at (perhaps because this decision has not yet been made, and is going to be made in a truly random fashion), but she does know it's going to be set to one of three possible angles a, b, and c, then with her knowledge of the angular momentum vector and the basic laws of physics she can at least predict with 100% certainty whether the particle will give + or - if angle a is chosen, and likewise for b and c. Whichever one actually ends up chosen, her prediction for that angle is guaranteed to be correct based on her knowledge of the angular momentum vector and the basic laws of physics, even though she didn't know in advance which of the three was going to be chosen. In this case, her three predictions about the result at each angle would be the "predetermined results" for each angle, results which are "predetermined" by the value of the particle's hidden variables (its angular momentum vector) and the basic laws of physics governing how the particle interacts with the detector.

Again, if you don't see the need for such predetermined results even in a local realist theory where the particles can't communicate, feel free to quote the above and respond to it on the other thread, I don't want to derail this one.
Gordon Watson said:
The GTE sequence is: Test, retrieve, restore to pristine condition, re-test.

You replied:
JesseM said:
There is no "restoring" procedure in QM.
Of course. And, in STR, there is no "pursuing a beam of light with velocity c" when one is aged 16. However, that story continues: "One sees that in this paradox the germ of the special relativity theory is already contained." Einstein, "Autobiographical Notes", in Schilpp (1954: p. 53).
But Einstein did not claim that this thought-experiment should have any well-defined answer in his finished theory of relativity, it was just something he thought about when young that made him realize a problem with some earlier non-relativistic views of electromagnetism (see this page for an excellent discussion of the meaning of the role of this thought-experiment in his thinking). If you agree that "of course" there is no possible restoring procedure in QM, why do you keep asking me why the thought-experiment is incompatible with QM? Einstein would not have disagreed that the thought-experiment of a normal observer (one made of massive particles, and who had a clock that could measure time) traveling along with a light beam was incompatible with relativity! Neither SR nor GR can give you an answer to what the outcome of this thought-experiment would be, because they both judge the basic premise to be impossible. Similarly QM can say nothing about what would happen under your thought-experiment because the premises are incompatible with QM, the thought-experiment is only meaningful if you want to explore some non-QM theory (like my suggestion of a hidden variables theory which is meant to give the same result as QM if only a single measurement is made on each particle, but which differs from QM in allowing your "recover and restore" procedure).
 
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  • #134
Gordon Watson said:
Do I agree that the results are determined? Yes. And I accept that the results of unperformed tests can be statistically predicted.

But since I take the view (promulgated by Peres), that unperformed experiments have no results, ...

This is absurd (and that is being kind). You say the results are (pre)determined, which is a realistic stance, and then reject that by saying that what you can't measure isn't real. Well, which is it?

Further, you say that the results of unperformed tests CAN be statistically predicted. Well, perhaps you care to back this up by showing us your predictions for a dataset of photons, at settings 0/120/240. Put up!

(JesseM, sometimes I wonder... know what I mean?)
 
  • #135
..
Jesse, many thanks for the nice reply above. I'll be happily addressing all the points that you raise; but maybe you could save me from addressing some unimportant side-issues re BT. SO: In the interim, could you comment on the following, please. I think it might short-cut and by-pass the need to discuss many irrelevancies:

AS I understand BT: Bell based his argument on two primary assumptions. Let me call them (hopefully with your approval and agreement) "Einstein-locality" and "EPR-realism".

In my world-view, the view that is behind all my PF posts, I accept "Einstein-locality" but I totally reject "EPR-realism" in quantum situations.

I have done so from my first reading of EPR; it is a stand-out silliness, imho; and it was well-known to the founding-fathers of QT that a test perturbed the tested system. (In private discussions, one close to those fathers scathingly agreed that it was often wrongly-overlooked or misunderstood later on.) So I believe that I am in good company with this rejection of "EPR-realism".

To take just one example of that company: From my readings, I believe that Einstein also rejected "EPR-realism". He was cranky with Podolsky's editing of EPR. And while there's much discussion about what made him cranky, all that I can say is that I too would be cranky about the naive realism associated with "EPR-realism". Moreover, I can find no reference to it anywhere in Einstein's writings.

So if Bell is a refutation of "EPR-realism", well I'm on his side. And your side. So the question then arises: Is Bell limited to a refutation of "EPR-realism" or of "realism" in general?

Imho, BT is not a rejection of "realism" in general because many leading commentators and professors use the naive "EPR-realism" in their discussions; note: they make no mention of the more general one. They make no mention of that early, more-general and properly realistic QM view. Examples (from hundreds): Throughout Mermin we find "instruction sets" -- "EPR-realism" if I ever saw it. In Zeilinger et al. (roughly, as I recall) we find "EPR-realism" expressed something like this: "Bell's realism assumption assumes that the outcome of a test on a pristine particle reflects properties that the particle had prior to and independent of the test," -- again, "EPR-realism" if I ever saw it.

Can I make it any clearer: It is this NR (naive-realism, or "EPR-realism") that I object to, and reject. And surely we do not need to discuss BT to reject it! For it seems to me to be a carry-over from classical theory -- and, imho, we cannot understand quantum-reality if we allow ourselves to be bound by classical or naive-realism or "EPR-realism".

Comments and critique, please. And thanks again.

GW
 
  • #136
DrChinese said:
This is absurd (and that is being kind). You say the results are (pre)determined, which is a realistic stance, and then reject that by saying that what you can't measure isn't real. Well, which is it?

Further, you say that the results of unperformed tests CAN be statistically predicted. Well, perhaps you care to back this up by showing us your predictions for a dataset of photons, at settings 0/120/240. Put up!

(JesseM, sometimes I wonder... know what I mean?)

..

Dearest DrC, I do not wonder; I know! :smile:

You were recently caught out, very badly, misrepresenting my position. :smile:

And, as I understand the PF guidance, with respect to the following, you're being naughty again. :smile:

Please: Do not high-jack this thread -- with "The DrChinese Challenge" -- just open a new one. :smile:

Just put it up! :smile:

You know what I mean! :smile:

Just let me know; OK? :smile:

GW
 
  • #137
DrChinese said:
I also want to add that many of the Bell "refuters" are hopelessly lost in the past in the sense that there have been many experiments in the past 10 years which dramatically change the landscape. For example, entanglement of particles which have never shared a common past is a very powerful counterexample to ANY traditional local theory.
As I understand all these experiments observe the cos^2 correlation. This result is predicted by the 200 year-old Malus law. Does it mean that non-locality and FTL communication could be derived from the Malus law? If it is, why do we need Bell’s theorem?

***

I just finished reading BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST by Alain Aspect. This paper convinced me that in Bell’s theorem, the EPR correlation is presented as the classical deterministic corpuscular model of the photons. It is hard to believe that this model is proclaimed as a “reasonable” Supplementary Parameters Theory in the “spirit of Einstein’s ideas.” This deterministic corpuscular EPR model is completely foreign to QM and also doesn’t have any wave like properties. Of course this “reasonable dummy” mechanical model was found to be incompatible with QM.
Aspect characterized this finding as a discovery. I found this discovery laughable.

I also don’t understand how Bell and Aspect could believe that this model is in the “spirit of Einstein’s ideas.” In his paper, Aspect admitted that for Einstein “fields rather than particles are at the bottom of everything.” Bell in his article mentioned that “determinism is not a presupposition for Einstein in his analysis, regardless of a widespread and erroneous conviction that for Einstein determinism was always the sacred principle.”

However Bell didn't see any problem with this “dummy” EPR model and after knocking it down Bell proclaimed that that the search for alternative realistic models is hopeless and that the local realistic model that would explain the cos^2 correlation does not exist. This opinion was widely accepted within the scientific community.

I am not sure about the scientific approach to non-existence and impossibility, but among us grandpas and grandmas, we don’t believe in proof of non-existence UNLESS in the ABSOLUTELY defined area of knowledge. For example I may prove to myself the non-existence of a dime in my empty pocket, but only after thorough searching it; and even then I may have some reservations.

I don’t agree with Bell/Aspect that the search for realistic models is hopeless and can ofer one. For example, after separation, two correlated photons are represented by their own wave functions having hidden variables that determine antiparallel properties of these photons. However these photons are never perfectly correlated (this could be tested) because of a probability dictated by the respective wave functions. According to this model, if the photon is “retrieved and RESTORED to its pristine state” the second time it would have somewhat different polarization. This local realistic model isn’t helpful for the EPR argument because the absolute knowledge about the polarization of one “correlated” photon would not tell an exact polarization for another photon. However, as I understand the main reason for the EPR argument is to achieve a realistic understanding of physical reality (regardless of our ability to observe) and in this sense, I think that this simplified model is in agreement with the spirit of Einstein’s ideas.

While admitting the limitation of the EPR argument (exploited by Bell’s theorem) I can’t accept the alternative views in terms of "don't ask, don't tell policies” and can’t accept the absurdities of QM interpretation even though they are accepted as the norm within mainstream science.
I am planning (but not reday yet) to start the thread to discuss my views on this topic and already have a name for this thread: “Can a grandpa understand the QM?”
I am not sure if the rules of this forum tolerate the dilettante who is questioning the foundation of QM and may need to find another one.
 
  • #138
miosim said:
As I understand all these experiments observe the cos^2 correlation. This result is predicted by the 200 year-old Malus law.
No, it most certainly is not predicted by Malus' law which is not about multiple photons (or light beams) measured by separate polarizers, but rather about a single light beam going through two polarizers in succession (or a single pre-polarized beam going through a single polarizer) as I already explained in post #111 and you ignored:
JesseM said:
No, you misunderstand Malus' law here, it's a law in classical electromagnetism which only predicts what happens when the same electromagnetic wave is passed through two polarizers at different angles in succession (or when a single pre-polarized wave with known polarization angle passes through a single polarizer), whereas in Bell's theorem QM is being used two make a prediction about how two entangled particles behave when each is sent through a different polarizer. So while the equation is the same, the physical meaning of the equation is rather different in the two cases.
miosim said:
I just finished reading BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST by Alain Aspect. This paper convinced me that in Bell’s theorem, the EPR correlation is presented as the classical deterministic corpuscular model of the photons.
Big surprise, you've been "convinced" of the ignorant opinion you've kept repeating from the very beginning, even though others have already told you, over and over again, that this is complete nonsense (Bell's argument does not assume anything specific about the nature of particles, including whether they behave deterministically, it only uses the basic premises of local realism which I outlined [post=3245651]here[/post]). You continually ignore all the explanations and questions people put to you (like my repeated question about whether you understand why local realism implies that there are predetermined results for each measurement axis), so it kind of seems like you think you already know everything important about Bell's theorem and have no interest in actually learning anything about it from your dialogue here. If that's the case, the forum rules say this is a place to learn about mainstream physics, which may include open-minded questioning but doesn't include continual assertions that it's all wrong without accepting any possibility your understanding may be mistaken. If you continue to blithely repeat completely ignorant statements without listening to explanations of why they're wrong or answering questions, I'm just going to report further posts like this to the moderators because I don't think they belong on this forum.
 
  • #139
Gordon Watson said:
..
Jesse, many thanks for the nice reply above. I'll be happily addressing all the points that you raise; but maybe you could save me from addressing some unimportant side-issues re BT. SO: In the interim, could you comment on the following, please. I think it might short-cut and by-pass the need to discuss many irrelevancies:

AS I understand BT: Bell based his argument on two primary assumptions. Let me call them (hopefully with your approval and agreement) "Einstein-locality" and "EPR-realism".
I don't know what you mean by EPR-realism, please explain. If it implies that measurements simply reveal preexisting values of properties like spin (as opposed to the possibility that the measurement process alters the value, and so the measured value is not the same one the particle had immediately before measurement), then no, Bell certainly did not include that as one of his "primary assumptions". Remember that in my last post on the other thread I linked to an earlier post explaining my understanding of the basic premises of local realism (or what Bell called "local causality"):
JesseM said:
we should probably go back to my basic definition of local realism offered in [post=3196744]post #94[/post] from the other thread (also see my response to your question about the meaning of my phrase "irreducibly nonlocal" in [post=3213709]post #135[/post])
...please look these links over and explain (on the other thread) whether your term "EPR-realism" is meant to go beyond the assumptions I give (in which case I would disagree that Bell assumed "EPR realism"), or whether Einstein-locality + EPR-realism are equivalent to those assumptions.
 
  • #140
miosim said:
... For example, after separation, two correlated photons are represented by their own wave functions having hidden variables that determine antiparallel properties of these photons. However these photons are never perfectly correlated (this could be tested) because of a probability dictated by the respective wave functions. ...

As I have said any number of times, this hypothesis has been tested and rejected. The tests show perfect correlation to over 100 SD (depending on which version you look at) and rejects the idea that Product state statistics result. (Please note that all tests of perfect correlations are part and parcel of a standard Bell test.)

miosim, you have shown over and over that you have no desire to understand Bell's Theorem. After over 100 posts, I don't believe you have learned anything new. Your desire is clearly to disprove it (or find a reason to reject ot). In this regard, I can be of no service. Have a nice day, I am bowing out of this one.
 
  • #141
JesseM said:
No, it most certainly is not predicted by Malus' law which is not about multiple photons (or light beams) measured by separate polarizers, but rather about a single light beam going through two polarizers in succession (or a single pre-polarized beam going through a single polarizer) as I already explained ...

There two differences between Aspect and Malus experiments. First difference is in intensity of light (light beam vs. individual photons). The second difference is that Aspect measures two “perfectly” correlated photons that mirror each other, but the result of this experiment should be the same (cos^2 correlation) as Malus’ experiments with one polarizer for consecutive polarized photons.

It is why the result of Aspect’s experiment is fully predictable from Malus law.

JesseM said:
Big surprise, you've been "convinced" of the ignorant opinion you've kept repeating from the very beginning, even though others have already told you, over and over again, that this is complete nonsense (Bell's argument does not assume anything specific about the nature of particles, including whether they behave deterministically, it only uses the basic premises of local realism which I outlined here).

From BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST (page 13)

“…The second considered hypothesis is determinism. As a matter of fact, the
formalism of section 3.1 is deterministic: once λ is fixed, the results A(λ,a) and B(λ,b) of the polarization measurements are certain.”

Please let me know if you have more questions.

JesseM said:
…You continually ignore all the explanations and questions people put to you (like my repeated question about whether you understand why local realism implies that there are predetermined results for each measurement axis)…
I do understand “your local realism” that implies that there are predetermined results for each measurement. Now, do you understand why this deterministic (predetermined results) model is in the “spirit of Einstein’s ideas? I don’t.

JesseM said:
…so it kind of seems like you think you already know everything important about Bell's theorem and have no interest in actually learning anything about it from your dialogue here. )…
Now I belief that I understand the most important about Bell's theorem, mostly by carefully reading Bell’s and Aspect’s original papers. At the same time I don’t think I can learn from you as long as you provide the explanation similar to one you gave for local realism in your post #55 (as shown below).
JesseM said:
1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic)
And I have no choice but ignore these explanations, partially because of your unfriendly mentoring attitudes.
 
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  • #142
miosim said:
There two minor differences between Aspect and Malus experiments. First difference is in intensity of light (light beam vs. individual photons). The second difference is that Aspect measures both “perfectly” correlated photons that mirror each other, but the result of this experiment should produce the same result (cos^2 correlation) as Malus’ experiments with one polarizer for consecutive polarized photons.

It is why the result of Aspect’s experiment is fully predictable from Malus law.
No, it would be impossible to produce the same correlations in classical electromagnetism. Specifically, imagine a situation where you send two electromagnetic waves in different directions from a common source (prepared in whatever manner you like, for example, you could initially send both through local polarizers that would give them the same polarization angle), then two experimenters at different locations measure them using a polarizer that is set to a random angle on each trial, along with a device which is programmed to give a binary + or - result depending in some way (anyway you like) on the result of the polarizer experiment (for example, the device might be programmed to give + if the intensity is reduced by more than 50%, - if the intensity is reduced by less than 50%. Another possible rule would be that if the reduction in intensity is by a fraction F, the device has a probability F of giving + and a probability 1-F of giving -. But you don't have to use either of those rules, the device can be programmed any way you like as long as it always gives one of two binary results). If there is a spacelike separation between the two measurements, then there is no possible way that this purely classical experiment could give the same result as in QM, namely that that if experimenter #1 sets his polarizer to angle a, and experimenter #2 sets her polarizer to angle b, then the probability that they will both get the same result (both + or both -) is cos^2 (a-b). This despite the fact that Malus' law is still quite operative in this scenario, so for example if the source emitted two beams polarized at angle c and with the same intensity I, experimenter #1 would see the intensity reduced to I*cos^2 (a-c) while experimenter #2 would see the intensity reduced to I*cos^2 (b-c).

If you think there is some way that a purely classical experiment of this type could give the same correlations as predicted by QM in Bell's experiment please give the details, if not you have no excuse to repeat the false claim that the correlations predicted by QM can be derived from the classical Malus' law.
JesseM said:
Big surprise, you've been "convinced" of the ignorant opinion you've kept repeating from the very beginning, even though others have already told you, over and over again, that this is complete nonsense (Bell's argument does not assume anything specific about the nature of particles, including whether they behave deterministically, it only uses the basic premises of local realism which I outlined here).
miosim said:
From BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST (page 13)

“…The second considered hypothesis is determinism. As a matter of fact, the
formalism of section 3.1 is deterministic: once λ is fixed, the results A(λ,a) and B(λ,b) of the polarization measurements are certain.”

Please let me know if you have more questions.
The snide final line suggests again that you have no interest in learning anything, and think you know everything already. But why are you quoting from Aspect's paper when my statement was about Bell's argument? Aspect was using a simplified and less rigorous version of Bell's proof, Bell's more general later proofs talked about the probabilities of getting a result A with setting a, just look at the Bertlmann's socks paper you directed us to earlier, where you can plainly see on p. 15 that he uses probabilistic expressions like P(A|a,λ) and P(B|b,λ), not simple functions like A(λ,a) which assume from the outset that there is only one possible value for A given the values of λ and a.

A subtlety here is that if you start with the basic assumptions of local realism I mentioned earlier:
1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).
Then even though these assumptions say nothing about whether the basic laws are determistic or probabilistic, it is possible to derive from these assumptions the conclusion that if there are perfect correlations whenever the experimenters randomly choose the same detector setting (and their choices are made at a spacelike separation), then the only way to explain this in a way consistent with 1) and 2) is to assume the variables associated with the particles already predetermined their results for all possible measurement settings at some time before the settings were chosen. If you change your mind and decide you're interested in learning something new, I can explain how this conclusion follows from the basic assumptions 1) and 2). But the fact that this conclusion does follow in a natural way from the basic premises of local realism means if you're not interested in full rigor it's OK as a shortcut to simply assume predetermined results from the outset (as Aspect did in his paper), rather than use conditional probabilities as Bell did in the Bertlmann's socks paper.
miosim said:
At the same time I don’t think I can learn from you as long as you provide the explanation similar to one you gave for local realism in your post #55.

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

And I have no choice but ignore these explanations, partially because of your unfriendly mentoring attitudes.
Why do you have "no choice" but to ignore my explanations? I didn't become unfriendly until you continually repeated the same statements over and over again, ignoring my repeated explanations as to why they were mistaken. Anyway you're a big boy, I'm sure if you actually had any interest in learning you could learn something from a slightly hostile person. If you just doubt that my assumptions are equivalent to Bell's but are willing to be proven wrong, I already recommended that you try looking at the La nouvelle cuisine paper I linked to and discussed in [post=3248153]this post[/post], if you read it you can see that Bell clearly does use the same assumptions as I do above--my talk of "local facts" in 1) is equivalent to his discussion in section 6.3 here of "local beables" (a "be"able is meant to express an objective fact about what exists, in contrast to QM "observables"), and then section 6.7 here, along with the diagram 6.3 at the top of the page (and diagram 6.4 on the next page), makes it clear that he is defining locality in terms of the idea that the values of local beables in a given region of spacetime can only be causally influenced by events in the past light cone of that region, same as my 2).

If you take the time to look over this paper and still disagree that Bell's assumptions are equivalent to mine, feel free to point out specifically where you think he introduces some additional assumption, but if you just continue to spout the same tired old false claims about Bell's assumptions (and about Malus' law) without giving any sort of specific and substantive response to my corrections, as I said I'll just be reporting your posts to the mods.
 
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  • #143
JesseM,

Let me think about your responds. I am slow.

Thank you,
Mark
 
  • #144
I would like to clarify my position regarding Malus’ law before discussing the next issues you raised in the previous post.
JesseM said:
No, it would be impossible to produce the same correlations in classical electromagnetism. Specifically, imagine a situation where you send two electromagnetic waves in different directions from a common source (prepared in whatever manner you like, for example, you could initially send both through local polarizers that would give them the same polarization angle), then two experimenters at different locations measure them using a polarizer that is set to a random angle on each trial, along with a device which is programmed to give a binary + or - result depending in some way (anyway you like) on the result of the polarizer experiment (for example, the device might be programmed to give + if the intensity is reduced by more than 50%, - if the intensity is reduced by less than 50%. Another possible rule would be that if the reduction in intensity is by a fraction F, the device has a probability F of giving + and a probability 1-F of giving -. But you don't have to use either of those rules, the device can be programmed any way you like as long as it always gives one of two binary results). If there is a spacelike separation between the two measurements, then there is no possible way that this purely classical experiment could give the same result as in QM, namely that that if experimenter #1 sets his polarizer to angle a, and experimenter #2 sets her polarizer to angle b, then the probability that they will both get the same result (both + or both -) is cos^2 (a-b). This despite the fact that Malus' law is still quite operative in this scenario, so for example if the source emitted two beams polarized at angle c and with the same intensity I, experimenter #1 would see the intensity reduced to I*cos^2 (a-c) while experimenter #2 would see the intensity reduced to I*cos^2 (b-c)..

I think that a much simpler approach could be taken to compare the result of Malus law with Bell’s theorem.
The main goal of Bell’s theorem is to demonstrate a difference between the prediction of QM and “local realism” (the way Bell understood it).
The QM model predicts cos^2 (a-b) correlation while the “local realism” yields a linear (saw-like) function. To prove that the QM model is correct, Bell could justify that his theoretical setup is equivalent to Malus’ experimental setup in which both polarizers are placed on the same side of the light source (so the photons need to pass both polarizers in order to reach the target). In this case, the intensity of light that reaches the target is cos^2 (a-b), which proves the correctness of the QM model.
 
  • #145
miosim said:
The QM model predicts cos^2 (a-b) correlation while the “local realism” yields a linear (saw-like) function.
I don't think "local realism" yields any specific function, I think the saw-like function is just meant to represent the closest you can come to the cos^2 function in local realism, as I explained in [post=3240160]post #20[/post].
miosim said:
To prove that the QM model is correct, Bell could justify that his theoretical setup is equivalent to Malus’ experimental setup in which both polarizers are placed on the same side of the light source (so the photons need to pass both polarizers in order to reach the target).
You can't just declare two setups "equivalent" when they clearly aren't, Bell's setup involved two measurements with polarizers made at a spacelike separation, not two successive measurements with polarizers on the same light beam. As I said there is no way in classical electromagnetism to reproduce the QM prediction of the cos^2 relationship for the correlations of these two spacelike-separated measurements, despite Malus' law, so it would simply be false to claim that a completely different setup with non spacelike-separated measurements was "equivalent" and therefore that the QM prediction could be "derived" from Malus' law.
 
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  • #146
DrChinese said:
[..] Such critiques are soundly rejected because they end up modifying the Bell/EPR definitions beyond the point where they are meaningful.
As far as I know his critique has not been rejected but accepted*; and it appears to me that a refining of Bell's definitions as Nelson did after discussing it with Bell is very meaningful.
So basically, no one cares.
:rolleyes: Surely you mean that you don't care; for I do and so does Annalen der Physik! :wink:
[..] The point is that as you soften one element of Bell slightly, you open up opportunities/issues elsewhere. That may help us to better probe things. But it doesn't change Bell per se.

Indeed, that's the point!

*http://onlinelibrary.wiley.com/doi/10.1002/andp.200810345/abstract
 
  • #147
harrylin said:
As far as I know his critique has not been rejected but accepted...

If you think that is the definition of acceptance, then you are sadly mistaken. That alone counts for little, as I would expect you to know. I can cite any number of disproofs of Bell that have been published. I can also cite published disproofs of general relativity, evolution and the big bang.

Any way, start a thread if you want to discuss it rather than hijack another.
 
  • #148
harrylin said:
As far as I know his critique has not been rejected but accepted*; and it appears to me that a refining of Bell's definitions as Nelson did after discussing it with Bell is very meaningful.
As I mentioned in post #123, Nelson acknowledged that his stochastic model can't reproduce the predictions of QM. http://www.mth.kcl.ac.uk/~streater/lostcauses.html#II which says:
I believe that Nelson's reason for giving the theory up was the difficulty in preventing action at a distance and the transmission of information faster than light. Doubts were expressed in the beautiful book, Quantum Fluctuations, by Edward Nelson, Princeton Series in Physics, 1985. Morato and Petroni surmise (page 5833) that it was the study of entangled states which turned Nelson against it.
Entangled states are the foundation of almost all versions of Bell inequality violations, so if stochastic mechanics can't reproduce QM predictions for entangled states it would seem to have questionable relevance to Bell's theorem.
harrylin said:
Indeed, that's the point!

*http://onlinelibrary.wiley.com/doi/10.1002/andp.200810345/abstract
There's another paper here which responds to that one and claims to discount its conclusions:

http://onlinelibrary.wiley.com/doi/10.1002/andp.201010462/abstract
http://arxiv.org/abs/0910.4740

And then Schulz responds here:

http://arxiv.org/abs/0910.5660
 
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  • #149
JesseM said:
You can't just declare two setups "equivalent" when they clearly aren't, Bell's setup involved two measurements with polarizers made at a spacelike separation, not two successive measurements with polarizers on the same light beam. As I said there is no way in classical electromagnetism to reproduce the QM prediction of the cos^2 relationship for the correlations of these two spacelike-separated measurements, despite Malus' law, so it would simply be false to claim that a completely different setup with non spacelike-separated measurements was "equivalent" and therefore that the QM prediction could be "derived" from Malus' law.
As I understand, QM predicts the same probability function for a pair of correlated photons to pass the corresponding polarizers in Bell/Aspect experiment as for a single photon to pass both polarizers in Malus’ experiment. The fact that the logic and math in both experiments correlate tells me that they describes the very similar physical phenomena.

JesseM said:
I don't think "local realism" yields any specific function, I think the saw-like function is just meant to represent the closest you can come to the cos^2 function in local realism, as I explained in post #20.
I agree that different models of "local realism" may yield different specific functions. The critical part is that as long the particular function of "local realism" differs from the one predicted by QM, Bell’s inequity holds ground.

However, the supporters of Bell’s theorem are missing an elephant in the room because any model of "local realism" that yields a result that is different from QM cannot be in the “spirit of Einstein’s ideas” because he never questioned the correctness of QM, but its completeness and interpretation instead. Therefore Bell’s model of a "local realism" is a profound distortion of Einstein’s EPR argument
 
  • #150
miosim said:
As I understand, QM predicts the same probability function for a pair of correlated photons to pass the corresponding polarizers in Bell/Aspect experiment as for a single photon to pass both polarizers in Malus’ experiment. The fact that the logic and math in both experiments correlate tells me that they describes the very similar physical phenomena.
No, the "logic" is completely different in both experiments, even if the same equation is used. Again, Malus' law is derived from classical electromagnetism, but if you use the logic of classical electromagnetism to predict what will happen in a Bell type experiment where the two measurements are made at a spacelike separation, you can never reproduce the cos^2 relationship predicted by QM using the very different logic of a 2-particle wavefunction.
miosim said:
However, the supporters of Bell’s theorem are missing an elephant in the room because any model of "local realism" that yields a result that is different from QM cannot be in the “spirit of Einstein’s ideas” because he never questioned the correctness of QM, but its completeness and interpretation instead. Therefore Bell’s model of a "local realism" is a profound distortion of Einstein’s EPR argument
No, it isn't. You're missing the elephant in the room, which is that Einstein didn't know that it would be impossible for a local realistic theory to reproduce QM predictions, because Bell hadn't proved that while Einstein was alive. If you look at what Einstein was hoping for when he talked about a more complete explanation for QM, it seems he was thinking of a hidden variable theory based on exactly the same type of assumptions that physicists now call "local realism", the type of theory I was describing in 1) and 2) in [post=3245651]this post[/post]. I can give you quotes from Einstein's writings to support this, if you request.
 

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