A classical challenge to Bell's Theorem?

[DrChinese]

Re the correlations: Since the HVs are generally unknown random variables, it figures that correlations must arise from other sources (since "random" is hardly the sort of correlation we are looking for). But the A and B outcomes (from particle-device interactions), knock the HVs into shape (as it were), and so the HVs may be eliminated from the correlation functions (as we see). Thus the correlations, deriving from the distribution of the outcomes, are independent of the HVs.

...and thus leaving the (future) relative angle settings of the observation devices as the only relevant quantities in the outcomes. We live in an observer dependent universe.

 

[Gordon Watson]

...and thus leaving the (future) relative angle settings of the observation devices as the only relevant quantities in the outcomes. We live in an observer dependent universe.

..
DrC, I would welcome and appreciate your expanding on the point that you seek to make. It is not at all clear to me. Thanks. GW
..

GENERAL NOTE TO READERS (in passing):

Where I write cos2(a, b) I mean cos[2(a, b)] and NOT cos²( a, b).​

..

 

[Gordon Watson]

I can verify that this is correct as follows:

$P(B^+|W,\,{A^+}) + P(B^-|W,\,{A^+}) = 1, \; \; P(B^+|W,\,{A^-}) + P(B^-|W,\,{A^-}) = 1$
$P(B^+|W,\,{A^+}) = P(_B^-|W,\,{A^-}) = \frac{1}{2}cos^2(a-b) + \frac{1}{4}$
therefore
$P(B^-|W,\,{A^+}) = P(B^+|W,\,{A^-}) = -\frac{1}{2}cos^2(a-b) + \frac{3}{4}$
from V-4:
$E(AB)_w = \int dx \, \rho (x) \frac{1}{2}\left [ P(B^+|W,\,{A^+}) - P(B^-|W,\,{A^+}) - P(B^+|W,\,{A^-}) + P(B^-|W,\,{A^-}) \right ]$
$= \int dx \, \rho (x) \frac{1}{8}\left [ \left [2cos^2(a-b) + 1 \right ] - \left [-2cos^2(a-b) + 3 \right ] - \left [-2cos^2(a-b) + 3 \right ] +\left [2cos^2(a-b) + 1 \right ] \right ]$
$= \int dx \, \rho (x)\left [ cos^2(a-b) - \frac{1}{2} \right ] = cos^2(a-b) - \frac{1}{2} = \frac{1}{2}cos(2\theta), \;\;\; for \; \theta = a - b$

Many thanks, Bill, much appreciated: with a small point for the future.

Note that a and b are detector orientations: often defined as unit-vectors in a 2-space orthogonal to the line-of-flight; or in 3-space.

The latter is important in considering the spherically-symmetric singlet-state.

So, in Bell-studies, the most general way to represent the angle between these vectors (in the argument of a trig-function) is (a, b).

PS: My apologies if this sounds like a lecture, rather than an explanation of what I do!

 

[billschnieder]

Many thanks, Bill, much appreciated: with a small point for the future.

Note that a and b are detector orientations: often defined as unit-vectors in a 2-space orthogonal to the line-of-flight; or in 3-space.

The latter is important in considering the spherically-symmetric singlet-state.

So, in Bell-studies, the most general way to represent the angle between these vectors (in the argument of a trig-function) is (a, b).

That's right.

 

[billschnieder]

Aspect (2004) -- http://arxiv.org/abs/quant-ph/0402001 -- represents an optical Bell setup. Designating its general conditions by Y, and applying Bell's protocol as part of the form that you request, we proceed from (V-4) above as follows:

(Y-1) E(AB)_{Aspect (2004)} = E(AB)_Y =

(Y-2) ∫dx ρ(x) [P(B+|Y, A+) - P(B-|Y, A+) - P(B+|Y, A-) + P(B-|Y, A-)]/2 =

(Y-3) ∫dx ρ(x) [cos²(a, b) - sin²(a, b) - sin²(a, b) + cos²(a, b)]/2 = cos2(a, b):

which is the correct result for Aspect (2004); see his equation (6).

It appears you have classically reproduced the QM result E(AB) for the Aspect experiment. However, I'm not sure how you obtained $P(B^+|Y, A^+) = \cos^2(a,b)$

In other words, why is $P(B^+|Y, A^+) = \cos^2(a,b)$ for Aspect 2004 (Y), different from $P(B^+|W, A^+) = \frac{1}{2}cos^2(a,b) + \frac{1}{4}$ for the the classical case in the OP (W)? Thanks to Delta Kilo, we do have a locally causal derivation of the W case. Do you have a derivation of the Aspect case that is locally causal? Is it a straightforward application of Malus?

Also since
$P(B^+|W,\,{A^+}) + P(B^-|W,\,{A^+}) = 1, \; \; P(B^+|W,\,{A^-}) + P(B^-|W,\,{A^-}) = 1$
and $P(B^+|W,\,{A^+}) = P(B^-|W,\,{A^-})$

Your condition V-4 can be reduced to:

$E(AB)_V= \int dx \, \rho (x) \left [ 2 \cdot P(B^+|V,\,A^+) - 1 \right ]$

 

[DrChinese]

..
DrC, I would welcome and appreciate your expanding on the point that you seek to make. It is not at all clear to me. Thanks. GW

Why sure...

As you point out, all of the input parameters (initial conditions) essentially cancel out. That leaves the output parameters (essentially the observation conditions) as the only remaining variables in the equation, those being A and B in the cos^2() coincidence function. It is those settings and those alone that determine coincidence. Bell showed us that each A, B pairing is unique in the sense that others cannot simultaneously exist (at least in some combinations). Ergo our final results are uniquely dependent on the observer.

We live in an observer dependent universe. All of the major interpretations of QM agree on this point in some fashion: Copenhagen, MWI, dBB/BM, TS (Time Symmetric).

 

[Gordon Watson]

It appears you have classically reproduced the QM result E(AB) for the Aspect experiment. However, I'm not sure how you obtained $P(B^+|Y, A^+) = \cos^2(a,b)$

See below, noting that I've changed the order of your questions.

Thanks to Delta Kilo, we do have a locally causal derivation of the W case. Do you have a derivation of the Aspect case that is locally causal? Is it a straightforward application of Malus?

Thanks indeed to Delta Kilo! It being understood that the classical analysis essentially proceeds on the basis that there is at least one physically significant formulation of Bell's functions A(a, λ) = ±1 and B(b, λ) = ±1.

The derivation in both W and Y is locally causal to the same (and essential) extent that Bell's protocol (see OP) is locally causal. That is, we capture Einstein-locality (an essentially classical concept) via Bell's functions A(a, λ) = ±1 and B(b, λ) = ±1: which we are happy to restrict to classical functions, in keeping with our classical analysis.

The application of Malus is straight-forward, bearing in mind that Malus examined the results of "one-sided" experiments and gave us his famous classical Malus' Law (ML) -- see below. He did not have double-sided experiments (involving Alice and Bob), but we easily follow him by examining and generalising Alice and Bob's classical results (+1 and -1 and their correlation) just as Malus did with his own classical results.

In other words, why is $P(B^+|Y, A^+) = \cos^2(a,b)$ for Aspect 2004 (Y), different from $P(B^+|W, A^+) = \frac{1}{2}cos^2(a,b) + \frac{1}{4}$ for the the classical case in the OP (W)?

Since the sources in W and Y differ, we allow that the HVs differ too: Let ∅ be the pair-wise common HV in W (i.e., ∅ is the linear polarisation; replacing x); let λ (replacing x) be the pair-wise common HV in Y (where, following Bell, we allow that the particles are unpolarised); let s denote the relevant intrinsic spin; let δ_a∅ → a denote the interaction of a particle (its HV ∅) with a test-device oriented a such that the result is the transition ∅ → a, etc. Then, with a little study, and noting that s = 1 in W and Y:

ML: P(δ_b∅ → b|W, ∅, s) = cos²[s(b, ∅)]; etc.


ML-W: $P(B^+|W, A^+)$ =

(ML-W1) P(δ_b∅ → b|W, ∅, s, δ_a∅ → a) =

(ML-W2) [P(δ_b∅ → b, δ_a∅ → a|W, ∅, s)]/[P(δ_a∅ → a|W, ∅, s)] =

(ML-W3) 2∫d∅ ρ(∅){cos²[s(b, ∅)]}{cos²[s(a, ∅)]} =

(ML-W4) (1/2) cos²(a, b) + 1/4.


ML-Y: $P(B^+|Y, A^+)$ =

(ML-Y1) P(δ_bλ → b|Y, λ, s, δ_aλ → a) = cos²[s(b, a)].

Each Malus Law arises from the classical analysis of classical outcomes in experiments. The differing results for W and Y that you ask about arise because of the differing sources: all else being the same. (You have already checked the W result, so you should be able to discern ML-W in play. You can check Aspect 2004 to see ML-Y in play; it falls out of the experimental results, essentially by observation.)

Also since
$P(B^+|W,\,{A^+}) + P(B^-|W,\,{A^+}) = 1, \; \; P(B^+|W,\,{A^-}) + P(B^-|W,\,{A^-}) = 1$
and $P(B^+|W,\,{A^+}) = P(B^-|W,\,{A^-})$

Your condition V-4 can be reduced to:

$E(AB)_V= \int dx \, \rho (x) \left [ 2 \cdot P(B^+|V,\,A^+) - 1 \right ]$

Correct, with many similarly instructive re-workings. For example: The product AB can only take values from the set {+1, -1}, so we need only assess the probabilities for these two AB values.

However, imho, we need to maintain the expository value of the version given in (V-1) - (V-4) above (at POST #100) ... perhaps with re-formatted maths. For it is easy to lose sight of the respective Einstein-local outcomes (+1, -1) and their origin in Bell's A(a, λ) = ±1 and B(b, λ) = ±1.

Note that, for EPRB (say condition Z; s = 1/2):

$E(AB)_Z= - \int dx \, \rho (x) \left [ 2 \cdot P(B^+|Z,\,A^+) - 1 \right ]$,

since B(b, λ) = - A(b, λ) ... after Bell (1964).

PS: I appreciate your engagement with the classical maths here, and am happy to rely on you (alone, it seems) spotting any errors. DrC has a comment that I've yet to study. If he is saying that Einstein-locality holds, then he and I agree. :!) Which would be nice!

How does all this, including DrC's comment, sit with your own views?

In conclusion: For me, maths is the best logic: so I'd like to reduce any disagreements to maths. The important point here being that every relevant element of the physical reality is included in the equations.

As the Accountants say: E. and O.E. (With apologies: I'm still way from my office, on a borrowed mini-screen computer.)

 

[billschnieder]

We live in an observer dependent universe. All of the major interpretations of QM agree on this point in some fashion: Copenhagen, MWI, dBB/BM, TS (Time Symmetric).

DrC et al,
Gordon has now shown that he can obtain classically the result that agrees with QM for the Aspect experiment in a local-realistic manner, which implies a violation of Bell's inequalities and a refutation of Bell's theorem. I'm surprised this is all you have to say in return. Besides, it is not clear to me how what you say above is relevant to the issue here especially since you already agreed earlier that the OP experiment was entirely classical and local realistic and yet E(AB) contains only the angular settings. Thus, the fact that E(AB) for any experiment contains only the angular settings means squat as far as locality or realism is concerned, no?

Do you see any problem in his analysis?

 

[bohm2]

Gordon has now shown that he can obtain classically the result that agrees with QM for the Aspect experiment in a local-realistic manner, which implies a violation of Bell's inequalities and a refutation of Bell's theorem.

Given the recent PBR theorem (see 2 of many links below), isn’t non-locality implied by any “realistic” model by PBR theorem itself, irrespective of Bell’s. For instance Leifer writes:

It (PBR) provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell’s theorem...Nevertheless, the PBR result now gives an arguably simpler route to the same conclusion by ruling out psi-epistemic theories, allowing us to infer nonlocality directly from EPR.

The quantum state cannot be interpreted statistically
http://lanl.arxiv.org/abs/1111.3328

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

 

[DrChinese]

DrC et al,
Gordon has now shown that he can obtain classically the result that agrees with QM for the Aspect experiment in a local-realistic manner, which implies a violation of Bell's inequalities and a refutation of Bell's theorem. I'm surprised this is all you have to say in return. Besides, it is not clear to me how what you say above is relevant to the issue here especially since you already agreed earlier that the OP experiment was entirely classical and local realistic and yet E(AB) contains only the angular settings. Thus, the fact that E(AB) for any experiment contains only the angular settings means squat as far as locality or realism is concerned, no?

It is really impossible at this point to comment, other that to repeat what has already been stated: his classical thought experiment yields classical probabilities (I gave those) that don't violate a Bell Inequality. Unless there is something serious offered forward, I do not plan to comment further on the example itself as I have indicated.

In cases where a Bell Inequality does not matter (as in a classical example), the observer angular settings would not imply failure of realism (observer independence).

Your pushing the idea that Gordon has disproved Bell here is particularly sad. I consider your comments either born of insincerity or ignorance or perhaps a strange form of humor, really cannot figure out what you are trying to do here.

Unless there is a new question or example put forth, I personally think this thread has reached the end of its useful life.

 

[billschnieder]

It is really impossible at this point to comment, other that to repeat what has already been stated: his classical thought experiment yields classical probabilities (I gave those) that don't violate a Bell Inequality.

Sure, we agree about that. I'm referring to his reproduction of the QM expectation value in post #102. Maybe you missed it. Check it out.

Your pushing the idea that Gordon has disproved Bell here is particularly sad.

That is strange given that all I'm asking is for someone else to verify the math in post #102 to make sure it is correct because I did not find any errors in it, and it appeared to reproduce the QM expectation classically. So check and explain why you think it is wrong *if* you think it is wrong.

Unless there is a new question or example put forth, I personally think this thread has reached the end of its useful life.

If the thread is no longer useful for you, feel free to not read it anymore. Clearly there are issues remaining to be clarified for those still participating. I assumed that if you believe Bell's theorem, you would be alarmed anytime the QM expectation values for the EPRB are reproduced in a local-realistic manner, and would seize the opportunity to point out where the error is if there was an error at all! But instead, you start dropping hints/suggestions that the thread should be closed. I wonder why ...

I consider your comments either born of insincerity or ignorance or perhaps a strange form of humor, really cannot figure out what you are trying to do here.

right back at ya!

 

[Gordon Watson]

It is really impossible at this point to comment, other that to repeat what has already been stated: his classical thought experiment yields classical probabilities (I gave those) that don't violate a Bell Inequality. Unless there is something serious offered forward, I do not plan to comment further on the example itself as I have indicated.

In cases where a Bell Inequality does not matter (as in a classical example), the observer angular settings would not imply failure of realism (observer independence).

Your pushing the idea that Gordon has disproved Bell here is particularly sad. I consider your comments either born of insincerity or ignorance or perhaps a strange form of humor, really cannot figure out what you are trying to do here.

Unless there is a new question or example put forth, I personally think this thread has reached the end of its useful life.

DrC, I am hoping that these questions might bring you back to this thread, for it is not yet clear (to me) the critical point that you are making:

Could you clarify your point by comparing how your criticism applies to the OP case and how it applies to Aspect 2004, please?

The similarity in the equivalent equations leads me to stick to my view that Einstein-locality rules OK. On what basis are you opposing that position, please?

 

[Gordon Watson]

Sure, we agree about that. I'm referring to his reproduction of the QM expectation value in post #102. Maybe you missed it. Check it out.That is strange given that all I'm asking is for someone else to verify the math in post #102 to make sure it is correct because I did not find any errors in it, and it appeared to reproduce the QM expectation classically. So check and explain why you think it is wrong *if* you think it is wrong.If the thread is no longer useful for you, feel free to not read it anymore. Clearly there are issues remaining to be clarified for those still participating. I assumed that if you believe Bell's theorem, you would be alarmed anytime the QM expectation values for the EPRB are reproduced in a local-realistic manner, and would seize the opportunity to point out where the error is if there was an error at all! But instead, you start dropping hints/suggestions that the thread should be closed. I wonder why ...
right back at ya!

..
Bill and DrC, I would be pleased if your ancient antagonisms do not disrupt the train of this thread.

Bill, I am still unsure of the case that you have long been making against DrC's position*** re locality and realism. So, if my stuff here helps you sharpen your view, maybe you should open another thread? Which, of course, does not mean that you desert this thread: just that you stay on focus.

DrC, please provide the comparison requested earlier. I truly want to understand (and hopefully respond to) the point that you are making. Are you just saying that our interaction with Nature influences the future trend of of events? Or just that reality is veiled from us? For I see the possibility of us being close to a serious point of agreement (along such lines). Or else I'm displaying how much I do not understand your point? Thanks in advance.

***EDIT: I am not saying that I understand DrC's position. I may be wrong in thinking that he has moved from being a non-localist (seeing some of his recent discussions with ttn); maybe he never was. Rather, I'm hoping that seeing your position will make both positions clearer to me. THAT I would welcome and appreciate. Thanks.
..

 

[DrChinese]

DrC, I am hoping that thes question might bring you back to this thread, for it is not yet clear (to me) the critical point that you are making:

Gordon, it is not appropriate to take a classical example, run a few formulas and say "Voila! Bell is wrong." I have already provided the math to show you your example is classical and does not violate Bell. I believe zonde and Mark M both showed the same thing. Sadly, billschnieder is using you in some strange way and is egging you on. I do not know his reason, but again I implore you to go back to ground zero in learning about the math of Bell.

The idea of this thread - see title - is absurd. You have never done anything so far to show otherwise despite the time I have taken to assist you. Which is why I don't think further discussion here is warranted.

And I respect de Raedt and Michielsen too much to recommend you send your classical example to them so they can analyze your ground-breaking work. So perhaps you might send it to Joy Christian instead.

 

[Gordon Watson]

Gordon, it is not appropriate to take a classical example, run a few formulas and say "Voila! Bell is wrong." I have already provided the math to show you your example is classical and does not violate Bell. I believe zonde and Mark M both showed the same thing. Sadly, billschnieder is using you in some strange way and is egging you on. I do not know his reason, but again I implore you to go back to ground zero in learning about the math of Bell.

The idea of this thread - see title - is absurd. You have never done anything so far to show otherwise despite the time I have taken to assist you. Which is why I don't think further discussion here is warranted.

And I respect de Raedt and Michielsen too much to recommend you send your classical example to them so they can analyze your ground-breaking work. So perhaps you might send it to Joy Christian instead.

..
If our posts have crossed; pleased reconsider my requests. Thanks.

 

[DrChinese]

..
If our posts have crossed; pleased reconsider my requests. Thanks.

I can respond on this point:

Bell says, in essence: No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

So my position is simply that either there are no hidden variables, or locality is violated, or both. I think that most physicists would agree with both of these statements, which I also agree with:

a) We live in an observer dependent world, i.e. there is no observer-independent reality.
b) We live in a quantum non-local world, i.e. there are physical dependencies between some pairs of events which defy the normal limits of c. (Accepting this does not make you a Bohmian though.)

 

[Gordon Watson]

Gordon, it is not appropriate to take a classical example, run a few formulas and say "Voila! Bell is wrong." I have already provided the math to show you your example is classical and does not violate Bell. I believe zonde and Mark M both showed the same thing. Sadly, billschnieder is using you in some strange way and is egging you on. I do not know his reason, but again I implore you to go back to ground zero in learning about the math of Bell.

The idea of this thread - see title - is absurd. You have never done anything so far to show otherwise despite the time I have taken to assist you. Which is why I don't think further discussion here is warranted.

And I respect de Raedt and Michielsen too much to recommend you send your classical example to them so they can analyze your ground-breaking work. So perhaps you might send it to Joy Christian instead. [Emphasis added by GW.]

I'm happy to defend the thread title. It seems that I should have been clearer about the challenge for it was meant to be exactly what you now ask for: A return to basics!

To that end now: Some (sources not recalled) say that Bell presented no theorem. I take a different view: Bell's Theorem is one of the most succinct in history. Beginning with a neat protocol (my term), he concludes with an impossibility (de Broglie's dictum notwithstanding).

So the challenge (?) was there for me to learn how you (and others) applied Bell's protocol to a clearly classical (and therefore Einstein-local) experiment: for I had already done the sums (contrary to earlier counter-claims that I had not). As a supporter of Einstein-locality (EL), it follows for me that Bell's theorem reflects on Bell's realism assumption: NOT on EL.

The challenge (aimed at Herbert's Proof initially) also questions "classicist-types" like de Raedt, etc., whose cases thus far (it might surprise you) I do not support. So the chosen title was equally a challenge (?) to all who study Bell.

PS: I doubt BillS will ever egg me on or stir me up as much as you have in the past. Could it be unrequited love or jealousy on your part? :!) I love your being back here: AND I love Bill's entering into the maths here, leaving me personally with some formatting challenges to address! So please don't fret: as well as a good sharer I'm also a great lover.

 

[Gordon Watson]

I can respond on this point:

Bell says, in essence: No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

So my position is simply that either there are no hidden variables, or locality is violated, or both. I think that most physicists would agree with both of these statements, which I also agree with:

a) We live in an observer dependent world, i.e. there is no observer-independent reality.
b) We live in a quantum non-local world, i.e. there are physical dependencies between some pairs of events which defy the normal limits of c. (Accepting this does not make you a Bohmian though.) [Emphasis added by GW.]

..

DrC, Many thanks. Defending Einstein-locality, I'll address the emphasised piece here. More anon.

Bell (1964) states (in essence): "In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another such device, however remote. ..."

Do I misrepresent Bell (above), or the challenge itself (this thread, as it has developed), if I write:

1. In the challenge, as it emerges here: Parameters are added to QM to determine the results of individual measurements; NO changes are made to the statistical predictions.

2. In the experiment W (wholly classical): The added parameters are the pair-wise identical linear-polarisations ∅. ∅ = ∅'.

3. In experiment Y (Aspect 2004): The added parameters are the pair-wise conserved total angular momenta λ. λ + λ' = 0.

4. In experiment Z (EPRB, Bell 1964): If it were given here, the added parameters would be the pair-wise conserved total angular momenta λ. λ + λ' = 0.

5. And so on, through GHZ, GHSZ, CRB, etc.

6. In every case, parameters ARE ADDED TO QM to determine the results of individual measurements; NO changes are made to the statistical predictions.

6. The deeper point of the challenge is this: Accepting the validity of Einstein-locality, and accepting that Bell-style experiments yield definite dichotomic outcomes (Bell's A and B, represented by +1 and -1), we classically proceed to physically significant conclusions. NO changes are made to the statistical predictions.

7. To put it another way, defending Einstein-locality: Where is the mystery in Aspect (2004) when I can deliver exactly half its correlation [over every (a, b) combination] with a simple classical W-source: made in an hour, for a few dollars?

8. Is it not clear (to be expected, and without mystery) that Aspect's expensive singlet-source should deliver a higher correlation than my few dollars?

Leaving no doubts about the validity of Einstein-locality?

GW
..

 

[Gordon Watson]

Given the recent PBR theorem (see 2 of many links below), isn’t non-locality implied by any “realistic” model by PBR theorem itself, irrespective of Bell’s. For instance Leifer writes:

(A). The quantum state cannot be interpreted statistically
http://lanl.arxiv.org/abs/1111.3328

(B). Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

bohm2, thanks for these. I trust Bill will address them in typical detail, my focus being elsewhere at the moment. But I wonder if your "Given" follows correctly? (Me finding no evidence to advance non-locality over Einstein-locality.)

From (A) abstract: "If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality."

I expect quantum predictions to be confirmed. So it seems to me that their conclusion must follow. Which (to me) looks like a move toward the "Classical Quantum Mechanics (CQM)" that I'm interested in.

Question: Am I missing something, in such a view?

Re (B): Note by its author, via your link: "Due to the appearance of this paper [link not given here, GW], I would weaken some of the statements in this article if I were writing it again. The results of the paper imply that the factorization assumption is essential to obtain the PBR result, so this is an additional assumption that needs to be made if you want to prove things like Bell’s theorem directly from psi-ontology rather than using the traditional approach. When I wrote the article, I was optimistic that a proof of the PBR theorem that does not require factorization could be found, in which case teaching PBR first and then deriving other results like Bell as a consequence would have been an attractive pedagogical option. However, due to the necessity for stronger assumptions, I no longer think this."

Comment: As I see it, CQM operates with classical factoring.

Thus, overall (and at the moment), I'm not sure PBR impacts here in favour of non-locality?

With thanks again,

GW

 

[bohm2]

Re (B): Note by its author, via your link: "Due to the appearance of this paper [link not given here, GW], I would weaken some of the statements in this article if I were writing it again...Thus, overall (and at the moment), I'm not sure PBR impacts here in favour of non-locality?

Good point. I'm still a bit confused if PBR implies non-locality directly with respect to any "realistic" model but I've asked Matt and if he responds, I will post his response on here.

 

[DrChinese]

Good point. I'm still a bit confused if PBR implies non-locality directly with respect to any "realistic" model but I've asked Matt and if he responds, I will post his response on here.

If you accept the basic premise of the PBR paper, they demonstrate there are NO realistic solutions (because the wave function itself is as "real" as it gets). Therefore, non-locality is NOT a deduction of PBR.

Keep in mind that a realistic model posits that there ARE definite values for observables at all times. If the wave function itself is real, by definition there are NOT definite values for observables until an observation context appears (at which point there is collapse to an eigenstate).

 

[bohm2]

I'm stil confused about the implications of PBR. But here's Matt's answer in his blog:

Do you still believe that PBR directly implies non-locality, without Bell’s as I think you argued in a section of Quantum Times article?

“It (PBR) provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell’s theorem. ”

Matt's response:

mleifer | 25 April, 2012 at 5:20 am |
Yes, but this requires the factorization assumption used by PBR. At the time of writing, I was hopeful that we could prove the PBR theorem without factorization, but now I know that this is not possible. Therefore, the standard Bell-inequality arguments are still preferable as they involve one less assumption. BTW, this is not something I “believe”, but rather something that Spekkens and Harrigan have proved.

 

[gill1109]

..

7. To put it another way, defending Einstein-locality: Where is the mystery in Aspect (2004) when I can deliver exactly half its correlation [over every (a, b) combination] with a simple classical W-source: made in an hour, for a few dollars?

8. Is it not clear (to be expected, and without mystery) that Aspect's expensive singlet-source should deliver a higher correlation than my few dollars?

Leaving no doubts about the validity of Einstein-locality?

GW
..

Exactly. It is easy to get half way. Fix two directions a, a'; b, b'. Suppose that the choices to measure in direction a or a', and in direction b or b', are taken independently and completely randomly in both sides of the experiment, many times in succession.

Your "half-way" satisfies CHSH. Any set of four correlations rho(a,b), rho(a,b'), rho(a',b), rho(a'b') satisfying all the CHSH inequalities is easy to generate in a completely classical way.

But any set such that one of the CHSH inequalities is violated cannot be generated in a classical way.

Proof. Suppose we accept Einstein reality. In each of N runs, there exist alongside one another "out there in reality", potential outcomes A, A', B and B', each with value +/-1. In each run, the experimenter has essentially tossed two coins. Depending on the first coin he gets to see A or A'. Depending on the second coin he gets to see B or B'. And of course he knows which one he is seeing.

Arrange the 4N numbers +/-1 in an Nx4 table. Note that per row, AB+AB'+A'B-A'B'=A(B+B')+A'(B-B')=+/-2 since B and B' are either equal or different. Either B-B'=0 and B+B'=+/-2, or B-B'=+/-2 and B+B'=0. Since A and A' equal +/-1 the value, row-wise, of AB+AB'+A'B-A'B, is +/-2.

Therefore the average over all the rows of AB+AB'+A'B-A'B lies between -2 and +2 (inclusive). But the average of a sum is the sum of the averages. So

Ave(AB)+Ave(AB')+Ave(A'B)-Ave(A'B') lies between -2 and +2.

Now the experimenter does not get to see these averages, since per row of the table, he only gets to see A or A', and B or B'. His experimental correlations are computed from from four random samples from this table. With probability 1/4, on the n'th run, he measures in directions a and b, and only then gets to observe A and B. With probability 3/4 he gets to observe A and B', or A' and B, or A' and B'. Same thing for all the other rows, independently of one another. Unless he is very unlucky, the average of the values of A times B over the approximately N/4 measurements in which the directions chosen are a and b, will be close to the average of the values of A times B over all N measurements.

What about computer simulations like those of de Raedt and Michielsen? They exploit an easy trick called the detection loophole. It has been known since a well known paper by P. Pearle (1970). Bell later explained in more detail how to set up the experiment in such a way that this loophole cannot be invoked to explain what has happened (see especially the "Bertlmann's socks" paper.

Let me explain the detection loophole through an extreme example. Imagine two photons about to leave a source and fly to two detectors, where one will be measured in direction a or a' (but it doesn't know which it will be), and the other will be measured in direction b or b' (and similarly, doesn't know which it will be). Suppose these two photons want to contribute to generating correlations rho(a,b)=rho(a,b')=rho(a',b)=+1, rho(a',b')=-1. Going to be difficult, right?

But if they also have the option of "not being detected" they can do it easily.

Imagine the two photons start at the source by tossing three fair coins. One of them is their own preference to be measured in direction a or a', the second encodes their own preference for b or b', and the third encodes the outcome which they would generate, if they are both measured as they both want to be measured. Equal to one another and equally likely +1 or -1 for three pairs of settings, opposite to one another and each equally likely to be +1 or -1 for the fourth pair.

Now they fly to their respective measurement stations and see if they are about to be measured, on this particular run, in the way they want. Each one separately of course. If Alice's photon wants to be measured in direction a', but Alice's detector has been set to direction a, it chooses to vanish. Similarly on Bob's side. They only *both* get measured, when they are *both* measured how they *both* want to be measured. And in that case they have arranged using their third shared coin toss, whether to be both +1, or both -1, in the three cases ab, a'b,ab'; but whether to deliver the outcomes +1,-1 or -1,+1 in the fourth case a'b'.

Half the photons on each side of the experiment will fail to be detected. Only a quarter of the photon pairs will survive with both getting detected and measured. These ones will exhibit perfect correlation for three of the four pairs of measurement settings, and perfect anti-correlation for the fourth.

There are mathematical theorems that in a CHSH experiment one can achieve QM's "2 sqrt 2", quite some way above the CHSH local realism bound of 2 by such trickery, as long as at least 5% (or something like that) of the photons on each side of the experiment can go undetected. Weihs et al experiment actually only detected 5% of the photons on each side of the experiment, ie 1 only in 400 photon pairs got both measured. One has to assume that those 1 in 400 are representative of the whole collection, in order that the Weihs experiment proves something conclusive. If just a small proportion of the other pairs were undetected for reasons correlated with the hidden variables generating the A, A', B and B' values, they could easily reproduce 2 sqrt 2 in a completely locally realistic way.

Well, no one believes that nature is do devious, so most people are happy to take Weihs experiment as proof that Einstein realism is not valid.

 

[Gordon Watson]

Exactly. It is easy to get half way. Fix two directions a, a'; b, b'. Suppose that the choices to measure in direction a or a', and in direction b or b', are taken independently and completely randomly in both sides of the experiment, many times in succession.

Your "half-way" satisfies CHSH. Any set of four correlations rho(a,b), rho(a,b'), rho(a',b), rho(a'b') satisfying all the CHSH inequalities is easy to generate in a completely classical way.

But any set such that one of the CHSH inequalities is violated cannot be generated in a classical way.

Proof. Suppose we accept Einstein reality. In each of N runs, there exist alongside one another "out there in reality", potential outcomes A, A', B and B', each with value +/-1. In each run, the experimenter has essentially tossed two coins. Depending on the first coin he gets to see A or A'. Depending on the second coin he gets to see B or B'. And of course he knows which one he is seeing.

Arrange the 4N numbers +/-1 in an Nx4 table. Note that per row, AB+AB'+A'B-A'B'=A(B+B')+A'(B-B')=+/-2 since B and B' are either equal or different. Either B-B'=0 and B+B'=+/-2, or B-B'=+/-2 and B+B'=0. Since A and A' equal +/-1 the value, row-wise, of AB+AB'+A'B-A'B, is +/-2.

Therefore the average over all the rows of AB+AB'+A'B-A'B lies between -2 and +2 (inclusive). But the average of a sum is the sum of the averages. So

Ave(AB)+Ave(AB')+Ave(A'B)-Ave(A'B') lies between -2 and +2.

Now the experimenter does not get to see these averages, since per row of the table, he only gets to see A or A', and B or B'. His experimental correlations are computed from from four random samples from this table. With probability 1/4, on the n'th run, he measures in directions a and b, and only then gets to observe A and B. With probability 3/4 he gets to observe A and B', or A' and B, or A' and B'. Same thing for all the other rows, independently of one another. Unless he is very unlucky, the average of the values of A times B over the approximately N/4 measurements in which the directions chosen are a and b, will be close to the average of the values of A times B over all N measurements.

What about computer simulations like those of de Raedt and Michielsen? They exploit an easy trick called the detection loophole. It has been known since a well known paper by P. Pearle (1970). Bell later explained in more detail how to set up the experiment in such a way that this loophole cannot be invoked to explain what has happened (see especially the "Bertlmann's socks" paper.

Let me explain the detection loophole through an extreme example. Imagine two photons about to leave a source and fly to two detectors, where one will be measured in direction a or a' (but it doesn't know which it will be), and the other will be measured in direction b or b' (and similarly, doesn't know which it will be). Suppose these two photons want to contribute to generating correlations rho(a,b)=rho(a,b')=rho(a',b)=+1, rho(a',b')=-1. Going to be difficult, right?

But if they also have the option of "not being detected" they can do it easily.

Imagine the two photons start at the source by tossing three fair coins. One of them is their own preference to be measured in direction a or a', the second encodes their own preference for b or b', and the third encodes the outcome which they would generate, if they are both measured as they both want to be measured. Equal to one another and equally likely +1 or -1 for three pairs of settings, opposite to one another and each equally likely to be +1 or -1 for the fourth pair.

Now they fly to their respective measurement stations and see if they are about to be measured, on this particular run, in the way they want. Each one separately of course. If Alice's photon wants to be measured in direction a', but Alice's detector has been set to direction a, it chooses to vanish. Similarly on Bob's side. They only *both* get measured, when they are *both* measured how they *both* want to be measured. And in that case they have arranged using their third shared coin toss, whether to be both +1, or both -1, in the three cases ab, a'b,ab'; but whether to deliver the outcomes +1,-1 or -1,+1 in the fourth case a'b'.

Half the photons on each side of the experiment will fail to be detected. Only a quarter of the photon pairs will survive with both getting detected and measured. These ones will exhibit perfect correlation for three of the four pairs of measurement settings, and perfect anti-correlation for the fourth.

There are mathematical theorems that in a CHSH experiment one can achieve QM's "2 sqrt 2", quite some way above the CHSH local realism bound of 2 by such trickery, as long as at least 5% (or something like that) of the photons on each side of the experiment can go undetected. Weihs et al experiment actually only detected 5% of the photons on each side of the experiment, ie 1 only in 400 photon pairs got both measured. One has to assume that those 1 in 400 are representative of the whole collection, in order that the Weihs experiment proves something conclusive. If just a small proportion of the other pairs were undetected for reasons correlated with the hidden variables generating the A, A', B and B' values, they could easily reproduce 2 sqrt 2 in a completely locally realistic way.

Well, no one believes that nature is do devious, so most people are happy to take Weihs experiment as proof that Einstein realism is not valid.

..

gill1109,

Many thanks for you response. But it seems to me that your first word -- "Exactly" -- does not to relate to the balance of your writing? "Exactly what, please?"

You write above: "But any set such that one of the CHSH inequalities is violated cannot be generated in a classical way."

So, please, to be clear, you do realize THAT:

1. I derive the results for both W (the classical OP experiment) and Y (the well-known Aspect (2004) experiment) in a classical way?

2. Analytically, via my way: Going the whole-way (100%, say, with Y) is as easy as going half-way (50%, with W)?

3. My analysis is based on idealised experiments, just like Bell (1964), so that NO "detection loop-hole", nor any other loop-hole, is invoked here?

Thanks,

GW
..

 

[harrylin]

[..] What about computer simulations like those of de Raedt and Michielsen? They exploit an easy trick called the detection loophole. [..]

At first sight your explanation is very good until that sentence (and I'll post a comment to Gordon about the foregoing).
If someone does a trick, it's reasonable to say that the one who designs the trick and does the operation, exploits it for creating an illusion. I find it a bit strange if you say that an onlooker who has seen the illusion and figures out how, perhaps, the illusionist has done the trick, is "exploiting" the trick; in any case, the performance isn't done by the onlooker.

[..] If Alice's photon wants to be measured in direction a', but Alice's detector has been set to direction a, it chooses to vanish. [...]

I may be mistaken of course but I'm nearly certain that their explanation is quite different, more related to where the experimenter chooses to look.

no one believes that nature is do devious [..] Einstein realism is not valid.

Experiments aren't designed by nature but by experimenters - and experimenters are not devious either, but by necessity they observe those things that they want to see, according to their expectations, and usually they suggest an interpretation that matches their prior thinking.

 

[harrylin]

..[..]
2. Analytically, via my way: Going the whole-way (100%, say, with Y) is as easy as going half-way (50%, with W) [..]

I'm sorry that I just couldn't spend the time to really follow it, but apparently you did not show that your way does produce the required result, and it isn't taken for granted either.

Also, if I see it correctly, the experimental conditions of Gill's reply closely match those of the presentation of Herbert. As you had in mind to challenge Herbert's proof, for me (and perhaps others) it would be very useful if you would explicitly present your mathematical argument in that context, which is simpler than Bell's and thus easier to follow (but in case you already did: please give the post number!).

 

[gill1109]

Quick response to Gordon. You said you could get half-way to the desired correlations, easily. I said "exactly", because half-way does not violate CHSH. Sorry, I have not found out exactly what you mean by Y, W, and I don't know what you mean by the classical OP experiment. My discussion was aimed at Aspect, done more recently, better still, by Weihs.

Quick response to harylin: I know that de Raedt et al does not think they are playing a trick on us. I call it a trick. I could easily write programs which do the same as theirs. Their simulation succeeds in reproducing the statistics of these famous experiments, but the point is that that is not difficult at all, because of the detection loophole. In effect they are using the detection loophole. If they would change the parameters of their simulation such that hardly any photons got lost any more, they would no longer be able to violate CHSH.

 

[Delta Kilo]

1. I derive the results for both W (the classical OP experiment) and Y (the well-known Aspect (2004) experiment) in a classical way?

No, you don't. You did not provide classical derivation for Y. Instead you just "borrowed" the result from Aspect paper. Aspect makes it very clear eq(6) was derived using QM rather than classical model.

2. Analytically, via my way: Going the whole-way (100%, say, with Y) is as easy as going half-way (50%, with W)?

No, it isn't. There is a big difference: one satisfies Bell's inequality, another violates it.

 

[harrylin]

[..]I know that de Raedt et al does not think they are playing a trick on us. I call it a trick. I could easily write programs which do the same as theirs. Their simulation succeeds in reproducing the statistics of these famous experiments, but the point is that that is not difficult at all, because of the detection loophole. In effect they are using the detection loophole. If they would change the parameters of their simulation such that hardly any photons got lost any more, they would no longer be able to violate CHSH.

Hi gill, as I said, I doubt that that is correct as they do not explain the trick as a conspiracy of disappearing photons*. And sorry if I wasn't clear: I similarly don't think that Weihs tried to play a trick on us. However, the one who designed, performed and presented that experiment was Weihs and not De Raedt. To me it's a distortion to describe an observer who thinks that it's a trick and who explains how exactly the trick may have been done, as a person who "exploits a trick". As I see it, instead the one giving the performance with long sleeves (even if he didn't notice it himself) is the one exploiting the trick - not the one who sees those long sleeves and sketches how the trick may be done. Next the performer will say "No problem, I can do the trick without such long sleeves"; the question is if the performance can be done without any tricks. Let's hope so!

*ADDENDUM. I now checked and found that you indeed completely misunderstood their explanation, as they specify: "we consider ideal experiments only, meaning that we assume that detectors operate with 100% efficiency, clocks remain synchronized forever, the “fair sampling” assumption is satisfied and so on." Their explanation is discussed in the following thread: https://www.physicsforums.com/showthread.php?t=597171

 

[DrChinese]

I know that de Raedt et al does not think they are playing a trick on us. I call it a trick. I could easily write programs which do the same as theirs. Their simulation succeeds in reproducing the statistics of these famous experiments, but the point is that that is not difficult at all, because of the detection loophole. In effect they are using the detection loophole. If they would change the parameters of their simulation such that hardly any photons got lost any more, they would no longer be able to violate CHSH.

I actually used their Fortran code to program (in Visual Basic) my own Excel simulation to mimic theirs. Sure enough, it worked exactly as they said. (I will be happy to share that if anyone wants it.) I have not yet dissected how their code pulls off this feat. I personally consider it is a pretty clever little algorithm (since I couldn't figure it out quickly - honestly didn't spend much time on it and I would have liked to). But of course ultimately you are correct; you always come back to what I call the "Unfair Sampling Assumption".

The Unfair Sampling Assumption is that there would need to exist a suppression mechanism (let's call this SupMech) whereby as more and more pairs are sampled as a % (let's called this detection efficiency, or DE), there is *progressively* more pairs suppressed unfairly. Because as DE has risen in actual experiments, the deviation from the local realistic bound (2) has increased! Therefore to have the true full universe respect Bell, and therefore contradict QM, SupMech works harder as DE rises. What a strange concept, that there is a mechanism tied to detection efficiency! You would absolutely expect - if you took the de Raedt et al argument seriously - that as DE rises, the results would approach 2 instead of the other way as has actually occurred. So the only way around it is the Unfair Sampling Assumption!

Of course, it is well known that once DE exceeds a certain point (perhaps 71% or something, there are a variety of papers on this) then there is no possible SupMech that could deliver the hypothesized local realistic outcome anyway. Further, no one has the slightest clue how SupMech could work (considering that is coupled to DE - this doesn't exist in the de Raedt et al simulation which clearly approaches product state statistics as more and more of the universe is presented which is contradicted by experiment). More importantly, how could QM be so completely wrong? And finally, it turns out that there are experiments in which DE=100% (although the locality loophole is open) and those don't support the local realistic hypothesis either.

 

[DrChinese]

...they specify: "we consider ideal experiments only, meaning that we assume that detectors operate with 100% efficiency, ...

Well yes and no. You can call it anything you want. They disappear (because are not matched), and it is a bit of a misnomer to say that detection efficiency is not the issue. The entire point is that the de Raedt detected sample looks different than the full universe and how that happens is irrelevant for a simulation.

Here is a specific example. At 30 degrees, 100,000 iterations (pairs), window size k=30, I get the following results in one typical run using Type II PDC (opposite polarizations):

Entangled state rule (which is the QM expectation) = .2500
Local realistic boundary = .3333
Product state rule = .3750

de Raedt detected sample = .3261 (violates Bell inequality but does not match QM)
de Raedt full universe = .3751 (closely matches product state)

So their simulation respects Bell, even though the full universe does not. Their sample does not match experiment however. Additionally, since it makes predictions different than QM, it is subject to verification/rejection on numerous other levels.

 

[harrylin]

I actually used their Fortran code to program (in Visual Basic) my own Excel simulation to mimic theirs. Sure enough, it worked exactly as they said. (I will be happy to share that if anyone wants it.) [..]

Yes please! It will be helpful for the discussion of different models.

Well yes and no. You can call it anything you want. They disappear, and it is a bit of a misnomer to say that detection efficiency is not the issue. Where are they if detector efficiency is 100%? The entire point is that the de Raedt detected sample looks different than the full universe. [..]

If the detector efficiency in your version is not 100%, obviously there must be an error somewhere -either in your version or already in theirs. That's certainly a point to discuss in the thread on that topic (I will now stop hijacking Gordon's thread).

 

[DrChinese]

Yes please! It will be helpful for the discussion of different models.

If the detector efficiency in your version is not 100%, obviously there must be an error somewhere...

See:

http://drchinese.com/David/DeRaedtComputerSimulation.EPRBwithPhotons.C.xls

Again it is a completely artificial mechanism, so what you call it is completely irrelevant. When talking about a suppression mechanism, I may call mention Detector Efficiency while they call it Coincidence Time Window. But nothing changes. There is no more one effect than the other. As you look at more of the universe, you get farther and farther away from the QM predictions and that never really happens in actual experiments. So the Suppression Mechanism must grow if you DO want it to match experiment! And THAT is the Unfair Sampling Assumption.

 

[DrChinese]

Here is the thread where we discussed this:

https://www.physicsforums.com/showthread.php?t=369286&page=2

 

[gill1109]

The important measure of efficiency is determined empirically. And it is not just about what goes on at the detectors. It is: what proportion of the observed events in Alice's side of the experiment are linked to an observed event on Bob's side. And the same thing, the other way round. Both of these two proportions have to be at least something like 95%, before a violation CHSH at 2 sqrt 2 actually proves anything. In Weihs experiment they are both about 5%.

Particles don't just get lost at the detectors. They also get lost "in transmission". Some even get reabsorbed in the same crystal where they were "born" by being excited with a lazer. I'm afraid de Raedt and his colleagues are rather confused and don't understand these issues. So many things they say are rather misleading. The experiment as a whole has an efficiency and it is measured by the proportion of unpaired events on both sides of the experiment. Big proportion unpaired, low efficiency.