OK Corral: Local versus non-local QM

[wm]

ps

Vanesch's math does not in any way support your conclusion that commonsense local realism (which is what I meant by the word 'classical') is compatible with QM, if you think it does, you need to explain why you think so (see my previous post #147). In fact, the probabilities vanesch calculates are absolutely incompatible with common-sense local realism, the only way for common-sense local realism to be true would be if the probabilities he calculated were incorrect. Bell's theorem shows this.

If you disagree that Bell's theorem proves that the quantum predictions derived by vanesch's math are absolutely incompatible with commonsense local realism (a conclusion I am sure vanesch and Doc Al and DrChinese would all agree with), then if you are interested in learning why everyone disagrees with you rather than just declaring everyone wrong, you need to cooperate with our attempts to try to walk you through Bell's theorem. If you're not interested in learning, but just in promoting your incorrect ideas, you should take it to theory development.

1. This is truly getting a bit silly:

2. Are you afraid of my new learning, seriously?

3. For I will sure have some better info to discuss.

4. When I say somewhere here or all the time to friends and firmly believe: WE ARE quantum machines in a quantum world! Does this sound that CLR is CLASSICAL.

5. Do you seek a straw-man to destroy for fun? Otherwise how can it be so opposite to what I affirm?

6. I am less concerned with who is wrong than me having a coherent world-view that I can live with CONSISTENT with QM formalisms.

7. I guess you have no idea whatsoever what vanesch has done favourably for me in 6 lines. (Did you know how to do it?)

8. Define Bell's theorem so that I may confess and be shot? Or give you pause for thort.

9. Now that I understand QM maths a bit better; I'd be happy to be walked quietly and slowly through BT. Seems like we need that definition?

PS: Could you possibly convert vanesch maths to out of mathematica please?

wm

 

[wm]

Vanesch's math does not in any way support your conclusion that commonsense local realism (which is what I meant by the word 'classical') is compatible with QM, if you think it does, you need to explain why you think so (see my previous post #147). In fact, the probabilities vanesch calculates are absolutely incompatible with common-sense local realism, the only way for common-sense local realism to be true would be if the probabilities he calculated were incorrect. Bell's theorem shows this.

If you disagree that Bell's theorem proves that the quantum predictions derived by vanesch's math are absolutely incompatible with commonsense local realism (a conclusion I am sure vanesch and Doc Al and DrChinese would all agree with), then if you are interested in learning why everyone disagrees with you rather than just declaring everyone wrong, you need to cooperate with our attempts to try to walk you through Bell's theorem. If you're not interested in learning, but just in promoting your incorrect ideas, you should take it to theory development.

+ emphasis

PLEASE: What incorrect idea do I now hold? wm

 

[JesseM]

vanesch gives me much personal comfort BECAUSE his QM maths I will be able to happily understand and live with.

Even though they are logically incompatible with commonsense local realism?

Please, me not being rude; define Bell's theorem that you want me to swear to. I am not avoiding here but I have no idea how to answer.

I've already given this to you in post #140. Here's a slightly modified one that takes into account the clarifications I added in that post:

do you agree or disagree that IF we have:

1. two experimenters, call them "Alice" and "Bob", who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like)
2. On each trial Alice and Bob choose their measurement settings randomly, and there is a spacelike separation between the events (Alice choosing her measurement setting) and (Bob making his measurement), along with a spacelike separation between the events (Bob chooses his measurement setting) and (Alice makes her measurement)
3. they always get opposite answers when they make the same measurement on any given trial

And we make the following 3 assumptions about the laws of physics:

4. no violations of locality allowed
5. no possibility of future events affecting past ones, or "conspiracies" in the initial conditions of the universe that could create a correlation between an experimenter's choice of measurement setting and the properties of the object/signal sent to them by the source even when the source sends them out before the experimenters make their choices
6. each experiment yields a single definite result (no splitting into multiple copies with measurement)

THEN it must be true that:

7. The perfect correlation between results when they choose the same setting can only be explained by some event or events in the past light cone of both measurements (like the event of the source sending out objects/signals with correlated properties), such that knowing what happened at this past event/s + knowing what measurement an experimenter makes is enough to uniquely determine the outcome of their measurement. For example, if the past event is that of the source sending out a particle with a set of properties {P1, P2, ..., Pn}, and Alice measures the spin using angle A, then it must be true that the outcome of this measurement was completely determined by the particle's properties plus the measurement angle A.

8. Assuming conditions 1-3 are met, assumptions 4-6 about the laws of physics are valid, and you accept that 7 is logically necessary given 1-6, then the following inequalities MUST be respected:

8a. Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures B and gets +) plus Probability(Experimenter #1 measures B and gets +, Experimenter #2 measures C and gets +) must be greater than or equal to Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures C and gets +)

8b. On the trials where they make different measurements, the probability of getting opposite answers must be greater than or equal to 1/3

So, there you have it. Presumably you disagree with either 7 or 8, since commonsense local realism requires that 4-6 be true, and yet quantum physics requires that the inequalities in 8 be violated. So, do you disagree with both 7 and 8, or just 8?

I believe in LOCAL QM; shall I be thrown out for that?

If you aren't willing to try to follow the argument as to why this belief is incompatible with the probabilities vanesch calculated, you might be. But if you are willing, please address my questions above.

 

[JesseM]

4. When I say somewhere here or all the time to friends and firmly believe: WE ARE quantum machines in a quantum world! Does this sound that CLR is CLASSICAL.

As I mentioned earlier, I just use the word to "classical" to mean "compatible with commonsense local realism". Sorry if this usage causes confusion, but that's why I said in the post you quoted:

Vanesch's math does not in any way support your conclusion that commonsense local realism (which is what I meant by the word 'classical') is compatible with QM

7. I guess you have no idea whatsoever what vanesch has done favourably for me in 6 lines. (Did you know how to do it?)

I actually haven't looked at his derivation (the first time I tried to download it my computer didn't recognize the file type, I haven't yet gone back to download the reader from the wolfram website), but I'm familiar with the type of calculation he described in the non-attachment part of post #122.

8. Define Bell's theorem so that I may confess and be shot? Or give you pause for thort.

9. Now that I understand QM maths a bit better; I'd be happy to be walked quietly and slowly through BT. Seems like we need that definition?

See the last post. But Bell's theorem doesn't depend on the details of the procedure for calculating probabilities in QM, it just depends on taking those probabilities and showing they are absolutely incompatible with commonsense local realism.

PS: Could you possibly convert vanesch maths to out of mathematica please?

Sure, I'll give it a shot.

PLEASE: What incorrect idea do I now hold? wm

The idea that the probabilities predicted by QM are compatible with commonsense local realism.

 

[wm]

My learning QM maths

Even though they are logically incompatible with commonsense local realism? I've already given this to you in post #140. Here's a slightly modified one that takes into account my clarifications:

do you agree or disagree that IF we have:

1. two experimenters, call them "Alice" and "Bob", who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like)
2. On each trial Alice and Bob choose their measurement settings randomly, and there is a spacelike separation between the events (Alice choosing her measurement setting) and (Bob making his measurement), along with a spacelike separation between the events (Bob chooses his measurement setting) and (Alice makes her measurement)
3. they always get opposite answers when they make the same measurement on any given trial

And we make the following 3 assumptions about the laws of physics:

4. no violations of locality allowed
5. no possibility of future events affecting past ones, or "conspiracies" in the initial conditions of the universe that could create a correlation between an experimenter's choice of measurement setting and the properties of the object/signal sent to them by the source even when the source sends them out before the experimenters make their choices
6. each experiment yields a single definite result (no splitting into multiple copies with measurement)

THEN it must be true that:

7. The perfect correlation between results when they choose the same setting can only be explained by some event or events in the past light cone of both measurements (like the event of the source sending out objects/signals with correlated properties), such that knowing what happened in this past event/s + knowing what measurement an experimenter makes is enough to uniquely determine the outcome of the measurement. For example, if the past event is that of the source sending out a particle with a set of properties {P1, P2, ..., Pn}, and Alice measures the spin using angle A, then it must be true that the outcome of this measurement was completely determined by the particle's properties plus the measurement angle A.

8. Assuming conditions 1-3 are met, assumptions 4-6 about the laws of physics are valid, and you accept that 7 is logically necessary given 1-6, then the following inequalities MUST be respected:

8a. Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures B and gets +) plus Probability(Experimenter #1 measures B and gets +, Experimenter #2 measures C and gets +) must be greater than or equal to Probability(Experimenter #1 measures A and gets +, Experimenter #2 measures C and gets +)

8b. On the trials where they make different measurements, the probability of getting opposite answers must be greater than or equal to 1/3

So, there you have it. Presumably you disagree with either 7 or 8, since commonsense local realism requires that 4-6 be true, and yet quantum physics requires that the inequalities in 8 be violated. So, do you disagree with both 7 and 8, or just 8? If you aren't willing to try to follow the argument as to why this belief is incompatible with the probabilities vanesch calculated, you might be. But if you are willing, please address my questions above.

I am willing to put quite some time into this; and it may take awhile; but first I would need to be comfortable with the vanesch maths.

Also, with respect: Could I be assured that the senior physicists, who know much more than me, that communicate here, have to assent to the same test.

Reason because: As a student here, I'd like some comfort that there may be others who would see some deep verbal and philosophical difficulties here. Example: I thought Peres +++ ... said some of this was not part of QM.

And I'm here to learn about QM maths; not philosophy.

Given my current stage of learning, it would be far better for me to study (with you) vanesch's maths in the light of 4-6? I said words aren't my strength; and such discussion would help me to understand the definitive QM maths better.

Would this latter be acceptable as a first step? After you have reprocessed his sheet? That way we could start discussing very soon.

You also need recall that I have yet to study those maths; to disentangle the version that comes thru my computer; to study matrices and Pauli vectors; etc. etc.

Is there any problem with the vanesch math starting point please?

wm

 

[wm]

As I mentioned earlier, I just use the word to "classical" to mean "compatible with commonsense local realism". Sorry if this usage causes confusion, but that's why I said in the post you quoted:
I actually haven't looked at his derivation (the first time I tried to download it my computer didn't recognize the file type, I haven't yet gone back to download the reader from the wolfram website), but I'm familiar with the type of calculation he described in the non-attachment part of post #122. See the last post. But Bell's theorem doesn't depend on the details of the procedure for calculating probabilities in QM, it just depends on taking those probabilities and showing they are absolutely incompatible with commonsense local realism. Sure, I'll give it a shot.

The idea that the probabilities predicted by QM are compatible with commonsense local realism.

This is good; (+ we have some common difficulties):

It will probably be a clarification of the realism for me that comes out of it all. I can't see LOCALITY going, for me; and we should agree about probability. And once I understand something; that's all I mean by common-sense.

Big PS: Know that I accept QM calculations and the Aspect-style Bell tests; I'm not into faulty weaseling outs; and hope you never think that.

I then look forward to discussing realism and VEM (new code word vanesch maths) with you (and others if they wish).

Thanks heaps, wm

 

[JesseM]

I am willing to put quite some time into this; and it may take awhile; but first I would need to be comfortable with the vanesch maths.

Why? I think you're misunderstanding the logic of Bell's theorem here--it has nothing to do with the methods of making calculations in QM, it only depends on the final results of those calculations, and shows that these probabilities are incompatible with commonsense local realism.

Also, with respect: Could I be assured that the senior physicists, who know much more than me, that communicate here, have to assent to the same test.

What test are you referring to?

Reason because: As a student here, I'd like some comfort that there may be others who would see some deep verbal and philosophical difficulties here. Example: I thought Peres +++ ... said some of this was not part of QM.

Some of what is not part of QM? My assumptions #4-6 were not meant to be part of QM in general, they are meant to be part of commonsense local realism. There are certainly nonlocal or non-"commonsense" interpretations of QM which would disagree with one or more of those three assumptions.

And I'm here to learn about QM maths; not philosophy.

Again, Bell's theorem has nothing to do with "QM maths", only with the final probabilities predicted by QM, and showing that these probabilities are incompatible with commonsense local realism.

Given my current stage of learning, it would be far better for me to study (with you) vanesch's maths in the light of 4-6?

No, it would not really help you in understanding Bell's theorem or why QM is incompatible with commonsense local realism. But if you're just interested in learning more about the mathematics of quantum physics independent of these issues, you could start a new thread for help with that.

 

[wm]

Must go for awhile ... but want not

Why? I think you're misunderstanding the logic of Bell's theorem here--it has nothing to do with the methods of making calculations in QM, it only depends on the final results of those calculations, and shows that these probabilities are incompatible with commonsense local realism. What test are you referring to? Some of what is not part of QM? My assumptions #4-6 were not meant to be part of QM in general, they are meant to be part of commonsense local realism. There are certainly nonlocal or non-"commonsense" interpretations of QM which would disagree with one or more of those three assumptions. Again, Bell's theorem has nothing to do with "QM maths", only with the final probabilities predicted by QM, and showing that these probabilities are incompatible with commonsense local realism. No, it would not really help you in understanding Bell's theorem or why QM is incompatible with commonsense local realism. But if you're just interested in learning more about the mathematics of quantum physics independent of these issues, you could start a new thread for help with that.

Quick reply so you know where I'm coming from: I'd like to have some good hand-holding on this thread as we discuss VEM in line with OP.

PS: I will seek good book for broader QM studies: any that would be compatibel with your views please? wm

 

[JesseM]

Quick reply so you know where I'm coming from: I'd like to have some good hand-holding on this thread as we discuss VEM in line with OP.

Your OP was about issues of locality vs. nonlocality. Again, the techniques for calculating probabilities in QM really have nothing to do with this; it is Bell's theorem that is used to justify the claim that QM is incompatible with commonsense local realism, and Bell's theorem is just based on taking the final probabilities and showing (using arguments unrelated to the math of QM) that commonsense local realism can't possibly explain them.

If you want to just learn about the math of QM in general, without any relation to locality vs. nonlocality, you should start another thread. I'd like to discuss Bell's theorem on this thread.

PS: I will seek good book for broader QM studies: any that would be compatibel with your views please? wm

My introductory textbook in college was by Griffiths, but his E&M textbook was good, and the amazon reviews are pretty positive and say it's very good for beginners.

But I don't remember that either of the ones I read discussed Bell's theorem, and I wouldn't be surprised if this was absent from the Griffiths textbook too, introductory textbooks usually focus on developing one's skills at making calculations, not with interpretational issues that are irrelevant to making calculations.

 

[JesseM]

But there are some odd looking symbols: like

o/oo. = i?

And it starts:

pauli1 = ::0, 1<, :1,0<<. = Pauli matrix in mathematica notation?

That's very strange. I re-downloaded the notebook and it looks ok for me. (ok, I don't use the MathReader, but mathematica 4.1, but at least, the file is not corrupt)

Yes, I have the same problem with the file in mathreader, it seems to be in some kind of internal mathematica code rather than with the symbols displayed however they are supposed to look.

 

[JesseM]

1. Hmm, but when you say "QM=correct predictions", you're talking about some subset of its predictions rather than all possible predictions made by QM, right? After all, one of QM's predictions is that the inequality will be violated in certain experiments! Are you just talking about the prediction that whenever both experimenters measure their particles at the same angle, they always get opposite results? If my guess about what you meant in the "correct predictions" step is right, then no dispute...but if it isn't, could you clarify?

1. Sure, we are talking about the situation where QM makes a prediction. In this case, the prediction is not that the Inequality is violated, it is the "cos theta" relationship. That the Inequality is violated is applicable only when local realism is also present. There is no A, B and C in QM of course, only A and B.

Well, this may be the source of the confusion between us--I think we both agree that Bell showed that IF (a certain specific prediction of QM is correct) AND (local realism is correct) THEN (a certain inequality must hold for all experiments meeting certain conditions). But I understood the "certain specific prediction of QM" differently than you--I thought the QM prediction used in the Bell inequality was the one that says the experimenters always get opposite results when they choose the same detector setting, while you're saying that it's the "cos theta" relationship (though of course the opposite-result prediction is a special case of the cos theta prediction, but I thought it was the only assumption from QM that Bell used in deriving the inequalities). Now, I admit I haven't yet tried to follow Bell's paper step-by-step, I'm just going by proofs of Bell's theorem that I've seen elsewhere. But looking at the first section, I notice that after equation (2), where he shows a probability distribution for (a,b) under the assumption that the outcome of each measurement is determined by some hidden variables lamda, Bell then writes:

This should equal the quantum mechanical expectation value, which for the singlet state is

<sigma_1.a sigma_2.b> = - a.b

But it will be shown that this is not possible.

So if he's showing that it's "not possible" that the probability distribution based on the assumption that outcomes are determined by local hidden variables could equal -a.b = -cos(a-b), doesn't that mean that he's showing the cos theta relationship is a prediction incompatible with local realism and the inequalities, rather than using cos theta + local realism to derive the inequalities?

I also note that in the first page in the "Formulation" section, Bell does make use of the quantum-mechanical prediction that when both experimenters measure on the same axis, knowing the result of one measurement allows you to predict the result of the other measurement with 100% certainty:

If measurement of the component sigma_1.a, where a is some unit vector, yields the value +1 then, according to quantum mechanics, measurement of sigma_2.a must yield the value -1 and vice versa. Now we make the hypothesis, and it seems at least worth considering, that if the measurements are made at places remote from one another the orientation of one magnet does not affect the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of sigma_2, by previously measuring the same component of sigma_1, it follows that the result of any such measurement must actually be predetermined.

Finally, I note that the cos theta relationship is itself absolutely incompatible with local realism, because it leads to a violation of an inequality based on the assumption of local realism, the CHSH inequality. As I said in post #81:

For example, look at the CHSH inequality. This inequality says that if the left detector has a choice of two arbitrary angles a and a', the right detector has a choice of two arbitrary angles b and b', then the following inequality should be satisfied under local realism:

-2 <= E(a, b) - E(a, b') + E(a', b) + E(a', b') <= 2

Now, suppose wm were correct that he had a classical experiment satisfying the conditions of Bell's theorem such that the expectation value E(a, b) would equal -cos(a - b). In this case it we could pick some specific angles a = 0 degrees, b = 0 degrees, a' = 30 degrees and b' = 90 degrees; in this case we have E(a, b) = - cos(0) = -1, E(a, b') = -cos(90) = 0, E(a', b) = -cos(30) = -0.866, and E(a', b') = -cos(60) = -0.5. So E(a, b) - E(a, b') + E(a', b) + E(a', b') would be equal to -1 - 0 - 0.866 - 0.5 = -2.366, which violates the inequality.

Of course, I don't think anyone had discovered this inequality in 1964, so I suppose it's possible Bell could have used cos theta + local realism to derive his original inequality without realizing the two premises were inherently contradictory. But if you do think Bell used the cos theta relationship in deriving the inequality, as opposed to in proving that the full theory of QM violates the inequality, could you point to which step in his derivation of the inequality he uses it?

2. As I pointed out, such an attempt will not work using the path described. The logic statement I showed was equivalent to Bell's Theorem is:

IF Inequality=fails AND Local Realism=demonstrated, THEN QM=Limited Validity

Again, this is not how I would understand Bell's theorem, or at least the versions I've seen derived elsewhere (look at the discussion here, for example). I thought Bell's theorem said IF experimenters always get opposite results on same measurement setting AND Local realism=true, THEN Inequality must always be obeyed in experiments meeting Bell's conditions (which would also mean that QM has limited validity, since the full theory of QM predicts the inequality can be violated in these kinds of experiments). In my version, you can see that if someone produced a way of violating the inequality that was compatible with local realism and which still ensured experimenters get opposite results on the same setting, then this would demonstrate a flaw in Bell's theorem; this is what I think wm was trying to do with his example of sending vectors with definite angles to the experimenters, although he seems to have abandoned this tack now that the error in his math was pointed out.

 

[vanesch]

Yes, I have the same problem with the file in mathreader, it seems to be in some kind of internal mathematica code rather than with the symbols displayed however they are supposed to look.

I don't know how to solve this. At the office, where I have also mathematica, but on a different computer and all that, the file opens correctly too.

I will try to upload it in another format (such as pdf).

EDIT: I really don't understand what's going on. I installed mathreader too (even though I have mathematica). I downloaded the file from PF, saved it on my desk, and opened it with mathreader and everything is fine...

(I had to reboot my computer after the installation of mathreader, though).

 

[vanesch]

Ok, here is the pdf converted file from my notebook.
(mind you, you might need the mathematica fonts, which are normally
also installed if you have installed the mathreader - but then funny things go
on).

 

[wm]

Ok, here is the pdf converted file from my notebook.
(mind you, you might need the mathematica fonts, which are normally
also installed if you have installed the mathreader - but then funny things go
on).

Sorry to trouble you, but for me it's newly-garbled with many 8-s now appearing. wm

 

[wm]

<SNIP>In my version, you can see that if someone produced a way of violating the inequality that was compatible with local realism and which still ensured experimenters get opposite results on the same setting, then this would demonstrate a flaw in Bell's theorem; this is what I think wm was trying to do with his example of sending vectors with definite angles to the experimenters, although he seems to have abandoned this tack now that the error in his math was pointed out.

Re last line, last phrase: no; not correct. Did you see my post re Pauli matrices; and s and s' being ''unit-vectors associated with angular momentum''? That is s and s' are axial-vectors (= bi-vectors).

wm

 

[vanesch]

Mmm, wm not being with us anymore, I don't know if this is still of any use. But as the argument I posted has been cited and quoted in all thinkable ways, here's the thing. There's a priori no such thing as a local or a non-local "calculation". The expression taken from the Bell paper, which gives us the quantum prediction of the correlation, is only that: a calculation. The result is independent of any interpretation.

However, a calculation can be suggestive or not of a local mechanism. Now, if we had the following:

RESULT AT ALICE is given by a mathematical operation:
F(alice-settings, alice-particle,other-stuff-local-to-alice's place)

RESULT AT BOB is given by a mathematical operation:
G(bob-settings, bob-particle, other-stuff-local-to-bob's place)

and the correlation would be calculated to be < F.G >
(where the expectation is an expectation over all possible stochastic variables which occur in this business), then that would be evidence that there CAN be a local mechanism that produces the results at Alice and at Bob.

Indeed, one should then just try to make sense out of the mathematical description of F and G, and interpret it as some process that actually goes on. As they only depend on quantities local to Alice, resp. Bob, this would in principle be possible.

Now, and this is where the quantum expression (3) of Bell is both confusing and suggestive, Bell writes:

correlation = < (sigma_1.a) (sigma_2.b) >

At first sight, this looks exactly like our < F.G >. Indeed, (sigma_1.a) seems to be a mathematical expression local to Alice, and (sigma_2.b) seems to be a mathematical expression at Bob.

BUT! Let us not forget that in < F.G >, F had to be the OUTCOME at Alice, and G had to be an outcome at Bob. Moreover, < > was supposed to be a statistical average.
This is where the superficial comparison goes wrong. (sigma_1.a) is NOT the outcome at Alice, if we require that outcome to be +1 or -1. sigma_1.a is an OPERATOR. Same at Bob. Moreover, < > is a hilbert space operation, not the usual "integration over stochastical variables" operation.

As such, the superficial formal equivalence between < F.G > and < (sigma_1.a)(sigma_2.b) > is misleading and confusing. The quantum calculation is hence not an indication that a local mechanism is at work.

At least, if we require that the outcomes at Alice and Bob are genuine, objective (observer-independent) physical outcomes (which is a tacit but obvious assumption in the derivation of Bell's theorem).

The only way to interpret the quantum-mechanical computation < (sigma_1.a)(sigma_2.b) > as a suggestion for a local mechanism, would be when we interpret (sigma_1.a) as the OUTCOME at Alice, and we interpret (sigma_2.b) as the outcome at Bob. But that's almost too crazy to consider. And some people leave out the "too"
It would mean that there is no objective result at Bob, and no objective result at Alice, which would be a list of {+1,-1,-1,...} The result would be "an operator" and NOT a +1 or a -1.

If you are mentally capable of stretching your imagination so far as to claim that there IS no outcome at Alice, that looks like a -1 or a +1, but that it is an operator, AND ONLY IN THAT CASE, then you CAN interpret the quantum expression as being of the kind < F.G >. This is the MWI view on things, and the only way to keep a local mechanism compatible with the quantum-mechanical predictions. Moreover, the local mechanism is then given exactly by the formal expression that was thought not to stand for any mechanism (but "just a calculation"). But one should really realize the stretch of imagination that is needed for that case: there is no objective outcome at Alice which takes on a +1 or -1 value
Nevertheless, to be able to make this crazy view compatible with the obvious fact that Alice HAS SEEN a +1 or a -1, the trick is to consider that there are now TWO ALICEs, one who has seen +1 and another who has seen -1. The "overall state" of Alice is then described not by a +1 or a -1, but by, exactly, an operator which is sigma_1.a.
When this "superposition of Alices" meets the "superposition of Bobs" (he will suffer a similar fate), then upon meeting, they will get together in SEVERAL DISTINCT COUPLES Alice/Bob (this time described by (sigma_1.a)(sigma_2.b) ). The statistics of this set of couples is then given by the quantum-mechanical expectation value < >, and gives us the correct correlations.

This is what the formalism suggests. It is also the IMO only way in which a local mechanism can be preserved. But it is of course totally crazy. That's MWI.

 

[vanesch]

BTW, ttn, I moved your post, and my answer, to the thread of "what we see is bogus" in MWI.

 

[DrChinese]

1. I had understood that there were POWERFUL arguments for NON-LOCALITY.

2. vanesch shows me (us all, surely) that there are not.

WHOA, you are again throwing the baby out with the bath water!

There ARE powerful arguments for non-locality. ttn is our standard bearer on this, but he has chosen not to chime in. So I will point out that the standard interpretation of Bell + Aspect is that either locality or realism must be rejected. ttn makes a very strong argument that is is locality that must be rejected.

Vanesch, on the other hand, takes a different approach. Both of their views are interpretations which are consistent with Bell. Your interpretation is not, and requires you to change something if you want to be consistent with the facts.

 

[vanesch]

There ARE powerful arguments for non-locality. ttn is our standard bearer on this, but he has chosen not to chime in. So I will point out that the standard interpretation of Bell + Aspect is that either locality or realism must be rejected. ttn makes a very strong argument that is is locality that must be rejected.

Vanesch, on the other hand, takes a different approach. Both of their views are interpretations which are consistent with Bell. Your interpretation is not, and requires you to change something if you want to be consistent with the facts.

Indeed. I think these are about the two "ontology" positions one can take: non-local mechanism (Bohmian), or a MWI-type mechanism.

Next to that, there are still a few possibilities:

- superdeterminism (the settings at Alice and Bob are pre-determined by a common origin in the (far) past, and you don't really have any statistically independent choice)

- shut-up-and-calculate

- I don't know where to put signaling from the future.

But in all these cases, some explicit or implicit assumption by Bell has been violated.

In Bohm, that's clear (locality). In MWI, "realism" (although there is a kind of realism, but not one in which there are objectively real and unique outcomes, which is what Bell needed).

In superdeterminism, the independence of choice was a necessary (though implicitly assumed) condition in Bell's derivation.

In the "shut up and calculate" approach, given that one doesn't consider any reality, or any mechanism, Bell's hypotheses don't hold necessarily.

Signaling from the future was also not considered, because by a front-and-back loop, the outcome at Alice can be influenced by the result at Bob's. I tend to think that "signaling from the future" should be some kind of non-locality, though in principle potentially compatible with relativity.

BTW, ttn DID chime in of course, but as his discussion was not on the topic of Bell's theorem, but just another attack on MWI, I moved it to the thread where his previous attack on MWI is housed.

 

[DrChinese]

1. Well, I think may be the source of the confusion between us--we both agree that Bell showed that IF (a certain specific prediction of QM is correct) AND (local realism is correct) THEN (a certain inequality must hold for all experiments meeting certain conditions). But I understood the "certain specific prediction of QM" differently than you--I thought the QM prediction used in the Bell inequality was the one that says the experimenters always get opposite results when they choose the same detector setting, while you're saying that it's the "cos theta" relationship. Now, I admit I haven't yet tried to follow Bell's paper step-by-step, I'm just going by proofs of Bell's theorem that I've seen elsewhere. But looking at the first section, I notice that after equation (2), where he shows a probability distribution for (a,b) under the assumption that the outcome of each measurement is determined by some hidden variables lamda, Bell then writes:

2. So if he's showing that it's "not possible" that the probability distribution based on the assumption that outcomes are determined by local hidden variables could equal -a.b = -cos(a-b), doesn't that mean that he's showing the cos theta relationship is a prediction incompatible with local realism and the inequalities, rather than using cos theta + local realism to derive the inequalities?

3. I also note that in the first page in the "Formulation" section, Bell does make use of the quantum-mechanical prediction that when both experimenters measure on the same axis, knowing the result of one measurement allows you to predict the result of the other measurement with 100% certainty: Finally, I note that the cos theta relationship is itself absolutely incompatible with local realism, because it leads to a violation of an inequality based on the assumption of local realism, the CHSH inequality. As I said in post #81: Of course, I don't think anyone had discovered this inequality in 1964, so I suppose it's possible Bell could have used cos theta + local realism to derive his original inequality without realizing the two premises were inherently contradictory. But if you do think Bell used the cos theta relationship in deriving the inequality, as opposed to in proving that the full theory of QM violates the inequality, could you point to which step in his derivation of the inequality he uses it?

4. Again, this is not how I would understand Bell's theorem, or at least the versions I've seen derived elsewhere (look at the discussion here, for example). I thought Bell's theorem said IF experimenters always get opposite results on same measurement setting AND Local realism=true, THEN Inequality must always be obeyed in experiments meeting Bell's conditions (which would also mean that QM has limited validity, since the full theory of QM predicts the inequality can be violated in these kinds of experiments). In my version, you can see that if someone produced a way of violating the inequality that was compatible with local realism and which still ensured experimenters get opposite results on the same setting, then this would demonstrate a flaw in Bell's theorem; this is what I think wm was trying to do with his example of sending vectors with definite angles to the experimenters, although he seems to have abandoned this tack now that the error in his math was pointed out.

A bit of good ground to cover here, so let's see what we get:

1. Bell actually shows both:

a) You get opposite results when the detector settings are the same - see his (8) for the various cases of 0, 90, 180 degrees. This is a subset of the general case b).
b) The -cos(\theta) relationship, which is "net correlation" basis (ranges from -1 to 1, matches less mismatches), or: sin^2(\theta/2) which is the &quot;gross correlation&quot; basis (ranges from 0 to 1, matches). I realize that these bases (gross and net) can be very confusing and I probably shouldn&#039;t mention them, but you often see them interchanged without being labelled (and I am often guilty of this too).<br /> <br /> In the net basis:<br /> <br /> 1=completely correlated.<br /> -1=completely anti-correlated<br /> 0=no correlation (due completely to chance, in other words)<br /> <br /> This matches Bell&#039;s (8) exactly. You can easily see this because sin^2(0 degrees/2)=0 (gross basis) or -cos(0) degrees=-1 (net basis). So what I am saying is this: historically, after EPR, it was generally accepted that the a) case worked for both classical explanations and was consistent with QM as well. The inequality had NOT yet been discovered of course.<br /> <br /> 2. Well, yes and no. You can read it a couple of different ways, but there is really only one meaning. The inequality comes from the following:<br /> <br /> a) Assume the QM predictions for the singlet state of an entangled spin 1/2 pair must hold.<br /> b) Apply those same predictions to 3 angle settings and require that they be internally consistent as well, so you expand the relationships that work OK for unit vectors a and b to a, b and c.<br /> <br /> So the Inequality does hold if QM and local realism are both valid. Keep in mind that you can derive many different forms of the Inequality using particle spin/polatization attributes, and all essentially lead down the same path - incompatibility with experimental results at some settings, but not at others. <br /> <br /> 3. The cos theta relationship is not incompatible with QM if you only look at 2 settings (a and b) as EPR did. And as you say, Bell discovered the Inequality as that is the core of his paper. The Inequality uses a, b and c, and yes Bell absolutely knows <b>and uses</b> the cos theta relationship in his paper. Unfortunately, he did not see that as very important to point out the step but <b>I can show it to you</b> (it is indirect):<br /> <br /> Look at (22) and the next line: a.c=0, a.b=b.c=1/sqrt(2)<br /> <br /> You must make the substitution Bell makes: a.c=0 because a and c are crossed, i.e. 90 degrees apart. b is midway between a and c so ab=bc=135 degrees. And of course -cos(ab)=-cos(bc)=1/sqrt(2)=.707. <br /> <br /> He is saying that the realistic assumption at these angles is violated but he is using (22) to show it. I always use (15) to get to the same point, because I get confused trying to manipulate the signs.<br /> <br /> So I will do a separate post to more readily show the angle setting violations.<br /> <br /> 4. Again, yes and no. The showing of the opposite results is needed for calibration and to show that you have entangled pairs. It alone does not violate any inequality nor does it support or refute local realism in any way. This was assumed to be the case in 1935 and did not pose a problem at that time. As I mention, the opposite results is a simple extension of the general QM correlation function, and there historically was never any worry about the fact that the same function might apply at any 2 angle settings. Of course, that ignores the realism assumption which changes everything. As I have said many times, a and b alone don&#039;t lead to inequalities. It is adding c into the picture that creates the Inequalities, and QM does NOT postulate a, b and c exist. Only realistic theories add this.

 

[DrChinese]

...Signaling from the future was also not considered, because by a front-and-back loop, the outcome at Alice can be influenced by the result at Bob's. I tend to think that "signaling from the future" should be some kind of non-locality, though in principle potentially compatible with relativity.

BTW, ttn DID chime in of course, but as his discussion was not on the topic of Bell's theorem...

Yes, effects from the future - or otherwise traversing the direction of time in feedback loops, is a possibility. But I can't figure out if they tend to be "non-realistic" or "non-local". Suppose the effect propagates at c (so relativity is respected) but the direction of movement through time was reversed. Now the definition of locality gets blurred as we normally assume a single direction of movement.

Yes, I had seen that and felt you guys were better off without me in the mix. Of course ttn supports Bell strongly, and I was dropping his name...

 

[enotstrebor]

My apologies for not getting back.

You can't give a classical example which satisfies all the conditions laid out in Bell's theorem ... and still violates an inequality. If you think you have one, please present it.

1) The reason that a classical example can violate Bell's is related to Bayes formula and as I pointed out cases two and seven are not classically valid in the case of correlated events. When one introduces the new "c" condition one needs to take into account that P(c,b) is not independent of P(a,b) when subtracting P(c,b). That is if P(a,b) is correlation dependent, then if one could also measure "c" at the same time as "a" the two probabilities P(a,b) and P(c,b) are not independent. One should be subtracting P(c,b) given "a" from P(a,b) given "a". Thus when one uses the average P(c,b) subtracting it from the average P(a,b) one gets the violation.

Note that taking the average "violation" over all angles (some above/positive Bells expected linear (versus angle) result and some below/negative) the average does not violate the inequality while at all specific angles, except 0,90,180, there is a violation. Thus one must be careful because the average probability is not the same as the individual event (or individual angle) probability.

For correlated events one can not deal with averages ( bar-P(c,b) ) but must subtract the specific P(c,b) given "a" from the specific P(a,b) given "a".

Thus although Bell appears to include correlated events, the P(c,b) is used as if (effectively assumes) there is no correlation in the physics process (Bayes chain rule is only specifically valid for independent events when averages are use or when bar-P(c,b)= P(c,b))

2) But there is also another error often used in "classical" approaches which use Malus Law probabilities (associate with integrals of some "probability of interaction", e.g. Malus Law cos^2(a-\phi), over all angles). That is that Malus Law is true for all potential causes of photon correlations. But this assumes! And there are reasons to believe that the photon, a bi-vectored object, has at least two (potentially three) "phase" type variables to describe its behavior, not the single phase of Malus Law (average behavior over the other phase variables). If correlated in the "hidden phase" then for example the actual probability for correlated photons could be some other relationship (.e.g cos(a-\phi)), rather than cos^2(a-\phi) which gives an entirely different answer.

If you're implying each particle could be a classical quadrupole, then no, this could not possibly explain quantum experiments which violate Bell inequalities.

This is related to item 2) above when using classical probabilities (associate with integrals of some "probability of interaction" over all angles to calculate probabilities) to show the violation of Bell type inequalities using the bi-state SM view rather than the quadrapole view. It again changes the probabilites traditionally associated with the SM single spin up/down state.

If you're implying each particle could be a classical quadrupole, .

Also note that Stern-Gerlach experiments make physics sense if the electron is magnetic quadrapole at 90 degrees.

 

[JesseM]

1) The reason that a classical example can violate Bell's

No, it really can't. If you think it can, you are either misunderstanding the conditions of Bell's theorem, or failing to understand the proof. But if you think it can, then please provide a specific classical example.

is related to Bayes formula and as I pointed out cases two and seven are not classically valid in the case of correlated events.

Cases 2 and 7 of what? If you're talking about the eight possible hidden states, i.e.

1. a+ b+ c+
2. a+ b+ c-
3. a+ b- c+
4. a+ b- c-
5. a- b+ c+
6. a- b+ c-
7. a- b- c+
8. a- b- c-

...then there is no assumption that the source must emit hidden states in such a way that each has a nonzero probability. It is quite possible that the probability of a+ b+ c- could be 0, and that the probability of a- b- c+ could be 0 as well; the only assumption is that every pair emitted is in one of these states on every trial.

When one introduces the new "c" condition one needs to take into account that P(c,b) is not independent of P(a,b) when subtracting P(c,b). That is if P(a,b) is correlation dependent, then if one could also measure "c" at the same time as "a" the two probabilities P(a,b) and P(c,b) are not independent.

What does P(a,b) represent in your notation, precisely? And can you be specific about which of the various Bell inequalities you think can be violated classically? For example, if you're talking about this Bell inequality:

P(a+, b-) + P(b+, c-) >= P(a+, c-)

then in this case P(a+, b-) means "the probability that experimenter 1 chooses detector setting a and gets result +, while experimenter 2 chooses detector setting b and gets -". Do you think this inequality can be violated classically, given all the conditions assumed in Bell's theorem? (and note that I'm assuming here that whenever both experimenters choose the same setting, they always get the same result, so P(a+, a-) and P(a-, a+) = 0) Or is it some other inequality you think can be violated? Can you explain in words what the notation P(a,b) represents, as I did for P(a+, b-)?

One should be subtracting P(c,b) given "a" from P(a,b) given "a".

Why "should" one be doing that?

Note that taking the average "violation" over all angles (some above/positive Bells expected linear (versus angle) result and some below/negative) the average does not violate the inequality

What specific inequality are you talking about? All the Bell inequalities I've seen involve some finite number of detector angles, I haven't seen any that involve taking an average over all angles. If you are going to claim Bell's theorem is wrong, you'd better show that some specific Bellian inequality which Bell's theorem says can never be violated classically actually is violated classically, you can't just make up some new inequality that Bell's theorem doesn't even address.

while at all specific angles, except 0,90,180, there is a violation.

What inequality is violated at angles 0, 90, 180? Can you give in detail a specific classical setup where a specific inequality will be violated using these angles?

For correlated events one can not deal with averages ( bar-P(c,b) ) but must subtract the specific P(c,b) given "a" from the specific P(a,b) given "a".

Again, why "must" one do this? If you understand what Bell's theorem is actually saying, you must understand that an expression like P(a+, b-) refers to the probability of experimenter 1 getting + and experimenter 2 getting - over many trials where experimenter 1 used setting a and experimenter 2 used setting b. This probability would be perfectly well-defined, and would depend on the probability of the source emitting different possible "hidden states" on each trial. For example, suppose the source emits identical particles in 3 possible hidden states (so on a given trial, both particles will always have the same hidden state) with the following probabilities:

A. a+ b- c+ (P=20%)
B. a- b+ c- (P=60%)
C. a+ b- c- (P=20%)

In this case, if experimenter 1 uses setting a and experimenter 2 uses setting b, then experimenter 1 is guaranteed to get + and experimenter 2 is guaranteed to get - if the hidden state is A or C, while experimenter 1 will get - and experimenter 2 will get + if the hidden state is B. So, since there is a 20% chance of A and a 20% chance of C, P(a+, b-) would be 40%. Do you disagree?

Thus although Bell appears to include correlated events, the P(c,b) is used as if (effectively assumes) there is no correlation in the physics process (Bayes chain rule is only specifically valid for independent events when averages are use or when bar-P(c,b)= P(c,b))

Again, I don't even know what P(c,b) means in your notation, so I don't know what you mean by "P(c,b) is used as if there is no correlation in the physics process". Correlation between what and what? There can certainly be a correlation between the variables of the possible hidden states...for example, in my above example if the hidden state includes a+ there's a 100% chance it also includes b- (cases A and C), and if the hidden state includes a- there's a 100% chance it also includes b+ (case B).

2) But there is also another error often used in "classical" approaches which use Malus Law probabilities (associate with integrals of some "probability of interaction", e.g. Malus Law cos^2(a-\phi), over all angles).

"Probability of interaction"? Malus' law gives the intensity of light polarized at a certain angle after it passes through a polarizer at a different angle, which is the same as the probability that a given photon makes it through the polarizer in the case of a beam where all the photons have the same frequency (since the intensity of a single-frequency beam is just proportional to the number of photons). You can test this experimentally to see that it does hold for any combination of angles.

Also note that Stern-Gerlach experiments make physics sense if the electron is magnetic quadrapole at 90 degrees.

Not sure what you mean by this, can you provide a calculation showing how this works? With a classical quadrupole, can you explain why no matter how you orient your Stern-Gerlach apparatus, you always get only two possible deflection angles (spin-up or spin-down) rather than a continuous range of them? (see this page for an explanation of how classical charged spinning objects would behave differently than electrons when passing through a Stern-Gerlach apparatus) Also, keep in mind that the Bell inequalities deal with pairs of entangled electrons which have the property that when the Stern-Gerlach apparatus of second experimenter is at a 180-degree angle from the Stern-Gerlach apparatus of the first experimenter, they always measure the same spin, regardless of what specific angle the first experimenter chose. In order to explain this in terms of quadrupoles, presumably you'd have to say that the source emits pairs of electrons in such a way that the quadrupole moment of the first is correlated to the quadrupole moment of the second, in such a way that you're guaranteed to get the same deflection when the two Stern-Gerlach apparatus are at 180 degree angles. But in this case you will not be able to violate any of the Bell inequalities when you choose any three angles for the first experimenter a, b, and c, and also label the corresponding 180-degree shifted angles for the second experimenter a, b, and c. For example, you will not find a violation of this inequality:

P(a+, b-) + P(b+, c-) >= P(a+, c-)

Do you disagree, and think you can violate this inequality using classical quadrupoles, given the correct understanding of what the symbols mean, and given the condition that experimenters always get the same spin when they choose the same setting, along with the condition that the source has no foreknowledge of what settings they'll choose on a given trial? If so, then once again I must ask you to provide some kind of detailed numerical example showing how it would work.

 

[enotstrebor]

I again apologize for not getting back to you in a timely manor.

Also I did make some statements that, after reflection, would not effect this specific situation.

No, it really can't. If you think it can, you are either misunderstanding the conditions of Bell's theorem, or failing to understand the proof. But if you think it can, then please provide a specific classical example.

Do you think this inequality can be violated classically, given all the conditions assumed in Bell's theorem?
.

Violation can occur when one does not have the full facts, correct model or one makes incorrect assumptions.

It has always been assumed that the "entangled'' photon is no different EM-wise than any other photon.

If one had a physical model of the photon one might see that there are actually two types of linear polarized photons. Regular and "entangled". The entangled photon has a electric vector which at maximum is twice (mag. 2) that of the normal photon (mag 1). Thus in fact rather than the correlation being <=2 (1+1) the result actually can be <= 4 (2+2).

What is actually occurring is that the larger maximum of the "entangled" photon E-vector produces a higher rate (than the cos^2) of passing through the polarizer between 0 and 45 and a higher rate of no-pass (sin^2) between 45-90. Basically, a sin(\theta/2) like modulation of the normal cos^2 curve. The observe correlation curve (cos(\theta/2) from +1 to -1) from 0 to 90 is the resultant.

Phenomenologically one can perform the ``classical'' local and realistic calculation of this probability using the cos(A-x)^2 and sin(B-x)^2 integrations (x is the angle of the photon polarization) for the product of A and B polarization angles. One can compute the ++ coincidence with the factor of 2 for the amplitude (2*int(cos(A-x)^2*cos(B-x)^2)dx) and -- coincidence (2*int(sin(A-x)^2*sin(B-x)^2)dx) where now the coincidence minus anti-coincidence is calculation based on the amplitude of 2 rather than 1, i.e. correlation= 2*coincidence-2 (rather than 2*(++ plus --) - 1 ).

Note that one can get photon/polarizer "probabilities" >1 which is why one gets negative probabilities also (though I prefer in this case and in QM not to use the term probabilities, at best relative probabilities).

This local realistic calculation produces the correct (experimental) results.

If this model is correct, although the average over 360 is the same the model predicts that if one put a second polarizer after the first (one only needs one side of the EPR experiment) that one will see a non-malus law function between the two polarizers, i.e. the modulation of cos(theta/2). I also have yet to find a way to circularly polarize this "entangled" photon.

To my knowledge neither of these aspects have been looked at. I believe it has always been assumed that the "entangled'' photon is no different EM-wise.

If you know of published or unpublished (but documented) sources on these two "predicted" aspects of the "entangled" photon. Please quote me the sources.

With a classical quadrupole, can you explain why no matter how you orient your Stern-Gerlach apparatus, you always get only two possible deflection angles (spin-up or spin-down) rather than a continuous range of them?
.

First don't confuse the ``spinning charge'' concepts with anything that follows. It does not apply. The particle does not have a spinning charge. It does have a spinning vector potential (like) force which has nothing to do with charge but results in a magnetic (like) interaction.

Having two spin planes at 90 degrees it also has two magnetic interactions orientated at 90 degrees. The magnetic field of the Stern-Gerlach orients one of the two spin planes (50/50 chance where the other being normal is not effected - this is not a bar magnet type interaction, i.e. no true north south, just orientational to the magnetic field) is oriented field normal (field vertically through the spin plane).

This oriented plane can be spin spin up or spin down with respect to the magnetic field. The spin plane at 90 degrees is un-oriented.

As long as the magnetic field is kept normal to this oriented plane the particle stays oriented. When passing onto a second magnetic orientation, this new magnetic orientation, not being normal to the oriented plane interacts with both spin planes (unless of course it is normal to the first magnetic field).

The case, the second SG-magnet being normal to the first is more straight forward so I will deal with this only. In this case this second SG-magnet does not effect the originally oriented plane (the magnetic field lines are parallel to the plane) but orients the second plane which can be rotated by the magnetic interaction to be normal to the second SG-magnets field lines. Again, depending on the specific relative rotational angle of this plane's spin with respect to the field the plane, this second spin plane is now either oriented spin up or spin down with respect to this plane (while the first spin plane is now un-oriented). As this second plane was rotationally unoriented by the first magnet then the result is again 50/50 mix of spin up or spin down. The first SG-magnet is irrelevant to the probabilities of the second 90 degree SG-magnet.

Note that calculations of probabilities for a quadrapole also introduces a "hidden" factor of two.

There ARE powerful arguments for non-locality.

In deed there are, but only if one assumes that one can have a complete understanding of the physics of the particle by modelling its behavior and without having a model of the particle, the source and cause of the behavior.

"The map is not the territory." and "The behavior is not the particle."

 

[JesseM]

Violation can occur when one does not have the full facts, correct model or one makes incorrect assumptions.

No, it is impossible to violate Bellian inequalities classically, provided you respect all the conditions in the proof of Bell's theorem. If you disagree, please provide a specific numerical example which you think shows a violation of one of the inequalities in a classical context, but still respects all the conditions of the proof.

It has always been assumed that the "entangled'' photon is no different EM-wise than any other photon.

There is no such assumption made in the proof of Bell's theorem, every photon can be in a completely different state for its "hidden variables". Where did you get this idea? Have you actually studied the proof, and if so, what was your source?

If one had a physical model of the photon one might see that there are actually two types of linear polarized photons. Regular and "entangled". The entangled photon has a electric vector which at maximum is twice (mag. 2) that of the normal photon (mag 1). Thus in fact rather than the correlation being <=2 (1+1) the result actually can be <= 4 (2+2).

What correlation are you talking about? Are you referring to the correlation in the CHSH inequality? If so, do you understand that when the inequality says that S <=2, S refers to the sum of E(a, b) - E(a, b') + E(a', b) + E(a', b'), where each E is the expected value of the product of the two measurements given the stated settings (for example, if I use setting a and you use setting b', and I get the result +1 and you get -1 on that trial, (a,b') for that trial is 1*-1, and E(a,b') is the average of this product (a,b') over a large number of trials on which I use setting a and you use setting b').

If you are interpretating the correlation in the correct way, then are you saying you have a specific example in mind where E(a, b) - E(a, b') + E(a', b) + E(a', b') is larger than 2? What are the individual values of E(a,b) and E(a, b') and E(a',b) and E(a', b') in your example? What angles have you chosen for a, a', b and b'?

What is actually occurring is that the larger maximum of the "entangled" photon E-vector produces a higher rate (than the cos^2) of passing through the polarizer between 0 and 45 and a higher rate of no-pass (sin^2) between 45-90.

"Larger maximum" of what quantity, exactly? Please give more specifics...what are the exact characteristics of these classical versions of "entangled" photons which determine the probability they pass through a given filter angle? You said something about them having a larger "electric vector" but I'm not clear what you mean. So again, it would help if you describe the specific variables which characterize each photon (and what range of values these variables can take, and the probability distribution for different possible values over multiple trials), and give an equation for the probability they pass through the filter as a function of these variables. If it helps, imagine that we were just trying to simulate the situation you're imagining, by sending a data packet representing a particular entangled photon to a computer, and the computer using some algorithm to determine the probability the simulated photon makes it through its simulated filter, based on the filter angle and on the properties of the simulated photon given in the data packet...what would need to be in the data packet, and what algorithm should the computer use?

 

[DrChinese]

It has always been assumed that the "entangled'' photon is no different EM-wise than any other photon.

If one had a physical model of the photon one might see that there are actually two types of linear polarized photons. Regular and "entangled". The entangled photon has a electric vector which at maximum is twice (mag. 2) that of the normal photon (mag 1). Thus in fact rather than the correlation being <=2 (1+1) the result actually can be <= 4 (2+2).

etc.

OK, let's test your hypothesis against Bell's Theorem. For the 8 cases
below, please give your expectation probabilities for a specific a, b and c:

1. a+ b+ c+ : ?
2. a+ b+ c- : ?
3. a+ b- c+ : ?
4. a+ b- c- : ?
5. a- b+ c+ : ?
6. a- b+ c- : ?
7. a- b- c+ : ?
8. a- b- c- : ?

If they add to 100% and none are less than 0%, then your hypothesis is realistic (as this is the precise definition of realism). Try settings a=0, b=67.5, c=45 for your entangled photons.

You see, a model does not become realistic simply because you say it is. It must meet a very specific condition, one that Bell found was too difficult for local realistic theories to achieve.

Unless you are willing to share your predictions, I don't think we will be able to evaluate your idea.

 

[Mentz114]

It has always been assumed that the "entangled'' photon is no different EM-wise than any other photon.

If one had a physical model of the photon one might see that there are actually two types of linear polarized photons. Regular and "entangled". The entangled photon has a electric vector which at maximum is twice (mag. 2) that of the normal photon (mag 1). Thus in fact rather than the correlation being <=2 (1+1) the result actually can be <= 4 (2+2).

Robert, can you point me to any reference where this is explicated, I'm very interested to find out more.

Interesting thread. Has anyone read this ?

 

[QuantunEnigma]

Robert, can you point me to any reference where this is explicated, I'm very interested to find out more.

Interesting thread. Has anyone read this ?

Attached Files: Clifford alg values and Bell quant-ph. 0703179.pdf (131.3 KB, 1 views)

Please. The attached files, are they accessible by clicking, or by how?

 

[Mentz114]

Yes. I can click on that link and download from arXiv.

It does not work for you, go to the xxx.lanl.gov and download it.

 

[QuantunEnigma]

Yes. I can click on that link and download from arXiv.

It does not work for you, go to the xxx.lanl.gov and download it.

Is this Bell's theorem refuted? Expert comment please?

From abstract quant-ph/0703179

Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables

Joy Christian, Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada, and Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, England

It is shown that Bell’s theorem fails for the Clifford algebra valued local realistic variables. This is made evident by exactly reproducing quantum mechanical expectation value for the EPR-Bohm type spin correlations observable by means of a local, deterministic, Clifford algebra valued variable, without necessitating either remote contextuality or backward causation. Since Clifford product of multivector variables is non-commutative in general, the spin correlations derived within our locally causal model violate the CHSH inequality just as strongly as their quantum mechanical counterparts.

 

[JesseM]

Is this Bell's theorem refuted? Expert comment please?

From abstract quant-ph/0703179

Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables

I don't know anything about Clifford Algebra so I can't follow it myself, but I came across a short critical response here:

http://www.arxiv.org/abs/quant-ph/0703218

Christian also has a "reply to critics" here:

http://www.arxiv.org/abs/quant-ph/0703244

 

[DrChinese]

Is this Bell's theorem refuted? Expert comment please?

From abstract quant-ph/0703179

Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables

Joy Christian, Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada, and Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, England

It is shown that Bell’s theorem fails for the Clifford algebra valued local realistic variables. This is made evident by exactly reproducing quantum mechanical expectation value for the EPR-Bohm type spin correlations observable by means of a local, deterministic, Clifford algebra valued variable, without necessitating either remote contextuality or backward causation. Since Clifford product of multivector variables is non-commutative in general, the spin correlations derived within our locally causal model violate the CHSH inequality just as strongly as their quantum mechanical counterparts.

I have previously read this. In my opinion, it will never be accepted as being of substance sufficient to change minds about Bell's Theorem. It is highly technical, and I don't believe it addresses any of the elements Bell has laid out.

There are new "disproofs" of Bell being published in the archives every month or so. These are rejected regularly for publication in peer reviewed journals.

I have a simple test for any disproof - I have posted it here many times. So far, I have no takers. (All I ask is that someone provide their predictions for a pair of entangled particles when at observation settings a, b and c - where the outcomes are independent of which a/b/c are to be observed. The predictions need only add to 100% and none should be less than zero, which is of course the requirement of Bell Realism.)

Because most of these disproofs hinge on technical issues, they miss the entire point Bell made. Bell used the definition of reality associated with Einstein, that particle observables must have values independent of the act of observation. This is directly opposed to the Heisenberg Uncertainty Principle, as Einstein was acutely aware. Disproofs provide different definitions, so it becomes a "straw man" argument to tear it down.

This paper's argument attempts to show that a local realistic theory will also violate a Bell Inequality - something that presumably can only be accomplished by a non-local or non-realistic theory such as Quantum Mechanics. This is a flawed logic model, as the issue is to demonstrate that a local realistic theory can both match experiment AND meet (not violate) the standard set by a Bell Inequality. If it were capable of this, it could pass my little test. Note that Quantum Mechanics does NOT need to address my test, since it does not claim to be realistic (and local).

In summary: it is NOT true that a purported classical (local & realistic) theory which violates a Bell Inequality will render Bell's Theorem invalid. Therefore, Christian's paper ultimately fails. Bell provided a specific set of settings for a/b/c to consider for any local realistic theory, and I note that these were not addressed.

 

[ueit]

This paper's argument attempts to show that a local realistic theory will also violate a Bell Inequality - something that presumably can only be accomplished by a non-local or non-realistic theory such as Quantum Mechanics. This is a flawed logic model, as the issue is to demonstrate that a local realistic theory can both match experiment AND meet (not violate) the standard set by a Bell Inequality. If it were capable of this, it could pass my little test. Note that Quantum Mechanics does NOT need to address my test, since it does not claim to be realistic (and local).

A local realistic theory, in order to predict the observed correlations, must be deterministic. If it is stochastic it needs non-locality.

Bell's theorem rejects from the start any deterministic theory because of its "free-choice" assumption.

What you are asking with your test is a logical impossibility. Any local theory that tries to "beat" Bell's theorem and does not deny the "free choice" assumption is doomed because it is logically contradictory (deterministic and non-deterministic in the same time).

 

[JesseM]

A local realistic theory, in order to predict the observed correlations, must be deterministic. If it is stochastic it needs non-locality.

Bell's theorem rejects from the start any deterministic theory because of its "free-choice" assumption.

It doesn't reject deterministic theories, it just rejects bizarre "conspiracy" theories where somehow the initial conditions of the universe determine both the state of the particles emitted by the source on a given trial and the brain state of the experimenter on the same trial in just the right way to give the required correlations. As long as you assume the brain state of the experimenter before making a choice on a given trial is statistically independent of the hidden states of the particle emitted by the source on the same trial, then Bell's theorem can rule out local realism, it doesn't matter whether the universe is fundamentally deterministic or not.

In any case, although I don't understand the details of what Christian is proposing in his Clifford Algebra paper, I didn't get the impression he was proposing this sort of "conspiracy" explanation.

 

[DrChinese]

A local realistic theory, in order to predict the observed correlations, must be deterministic. If it is stochastic it needs non-locality.

Bell's theorem rejects from the start any deterministic theory because of its "free-choice" assumption.

What you are asking with your test is a logical impossibility. Any local theory that tries to "beat" Bell's theorem and does not deny the "free choice" assumption is doomed because it is logically contradictory (deterministic and non-deterministic in the same time).

You imply that Bell's requirements are too strict, and possibly unnecessary as well.

IF...*you* postulate a local realistic theory, THEN Bell applies. If you don't like the results, that is your problem, and I cannot help you. Bell does not apply to a non-realistic theory such as QM, nor does it apply to non-local theories such as BM.

I mean, it is not like Bell randomly came up with his theory just to confound you!

 

[ueit]

It doesn't reject deterministic theories, it just rejects bizarre "conspiracy" theories where somehow the initial conditions of the universe determine both the state of the particles emitted by the source on a given trial and the brain state of the experimenter on the same trial in just the right way to give the required correlations. As long as you assume the brain state of the experimenter before making a choice on a given trial is statistically independent of the hidden states of the particle emitted by the source on the same trial, then Bell's theorem can rule out local realism, it doesn't matter whether the universe is fundamentally deterministic or not.

I think there are two types of deterministic theories:

1. theories that lack long-range forces (Newtonian billiard balls that interact only when collisions take place)

2. GR type theories, where each particle (in the case of GR-each massive body) interacts with every other particle.

I agree with you that "billiard balls" theories are pretty much rejected by Bell's theorem, not because they cannot possibly work, but because, in order for them to work, "bizarre conspiracies" must be postulated about the initial state of the universe.

However, the second type theories need not to posit such conspiracies. The assumption of statistical independence between distant parts of a system is highly questionable. A change in one part of the system requires a change of the whole. You cannot, say, move Mars on a different orbit while keeping the other bodies in place. Of course, with a more complex system, like two distant galaxies, it is not so obvious that a change in one is not possible without a corresponding adjustment of the second so one might be fooled to think that there are two statistically independent systems.

The bottom line is that local-deterministic theories are not ruled out by the experimental evidence but by the assumption of statistical independence used for the derivation of Bell's theorem.

 

[ueit]

IF...*you* postulate a local realistic theory, THEN Bell applies.

Not if I deny statistical independence between the source and detectors.

 

[JesseM]

I think there are two types of deterministic theories:

1. theories that lack long-range forces (Newtonian billiard balls that interact only when collisions take place)

2. GR type theories, where each particle (in the case of GR-each massive body) interacts with every other particle.

But objects don't interact instantaneously--GR still has a light cone structure, so if you foliate spacetime into a stack of spacelike surfaces, everything going on in one region of space in a given surface should be determined by what was going on in the complete set of points in space in an earlier surface that lie in the later region's past light cone, and nothing outside that region of the earlier surface should have an effect on the chosen region of the later surface (There are weird spacetimes that apparently can't be foliated in this way, like ones containing closed timelike curves, but I think this is true as long as you assume a globally hyperbolic spacetime).

So, it seems to me the situation is no different with GR than with billiard balls--if the event of the experimenter choosing what measurement setting to use and the event of the source generating the two particles are each outside the other's future and past light cone (a spacelike separation), the only way they could fail to be statistically independent is if you assume that some event or events in their mutual past light cone determined these two events in just the right way to create the correlations--the "conspiracy" assumption.

However, the second type theories need not to posit such conspiracies. The assumption of statistical independence between distant parts of a system is highly questionable. A change in one part of the system requires a change of the whole. You cannot, say, move Mars on a different orbit while keeping the other bodies in place.

If you set off a bunch of nuclear bombs or something on Mars to shift its orbit, we wouldn't feel any gravitational effects of this event any sooner than we'd receive light waves from the event--gravitational waves travel at c just like electromagnetic waves.

The bottom line is that local-deterministic theories are not ruled out by the experimental evidence but by the assumption of statistical independence used for the derivation of Bell's theorem.

As I understand it, "local" means "having a light cone structure", and you can use the type of argument I made above to show that no local theory where each event has a single definite outcome (as opposed to a many-worlds type theory) can explain the violation of Bell inequalities without positing a "conspiracy" where events in the past light cone of both the source's particle emission and the experimenter's choosing of setting always causes them to be correlated in just the right way to give the observed results. If you don't posit such a conspiracy, how can you explain a correlation between two events with a spacelike separation?

 

[DrChinese]

Not if I deny statistical independence between the source and detectors.

Again, you speak in generalities when you imply such a connection. The source is a polarized laser beam. The detectors are polarized as well. Exactly how do you propose that the results depend on the source? The usual formula, Cos^2(a-b), relates the results of the detector settings but lacks a term for the source setting. This formula has substantial experimental validation.

In my scientific opinion: unless you can predict the results of specific cases in advance or otherwise improve the accuracy of the usual formula by adding a term for a source setting, you may as well be asserting that the results are a function of the phase of the moon.

Or perhaps - gasp - it is a hidden variable. But haven't we been down that road before? Isn't that exactly what Bell started with?

 

[ueit]

But objects don't interact instantaneously--GR still has a light cone structure, so if you foliate spacetime into a stack of spacelike surfaces, everything going on in one region of space in a given surface should be determined by what was going on in the complete set of points in space in an earlier surface that lie in the later region's past light cone, and nothing outside that region of the earlier surface should have an effect on the chosen region of the later surface (There are weird spacetimes that apparently can't be foliated in this way, like ones containing closed timelike curves, but I think this is true as long as you assume a globally hyperbolic spacetime).

I agree.

So, it seems to me the situation is no different with GR than with billiard balls--if the event of the experimenter choosing what measurement setting to use and the event of the source generating the two particles are each outside the other's future and past light cone (a spacelike separation), the only way they could fail to be statistically independent is if you assume that some event or events in their mutual past light cone determined these two events in just the right way to create the correlations--the "conspiracy" assumption. If you set off a bunch of nuclear bombs or something on Mars to shift its orbit, we wouldn't feel any gravitational effects of this event any sooner than we'd receive light waves from the event--gravitational waves travel at c just like electromagnetic waves.

There is a subtle error in your above line of reasoning. It is true that if we change Mars orbit by using a nuke, the effect will manifest on Earth at the same moment we see the explosion. However, in this case we do not deal with a deterministic theory anymore. While GR is deterministic, the nuclear explosion is not governed by GR and therefore, from GR's "point of view" it is a true unpredictable event. We have a mixture of a deterministic theory with random events and this is not what I propose as a local realistic explanation of EPR.

Now, let's make a correct analogy, by letting a stray planet, coming from a distant galaxy, to alter the orbit of Mars. In this case we deal with a true deterministic system and the effect will be felt instantaneously on Earth, as Newton's law of gravity (which is a good approximation for this case) predicts, before the light from Mars will reach us. This is because the stray planet does not interact only with Mars, but with Earth, and Jupiter, and all other bodies at once.

If we return to Bell's theorem we see that we are in the "stray planet" case and not in the "nuke" case. The mechanism behind the decision to move the detector on a different axis is entirely covered by QM (unless you do not propose a mind/body dualism) so it does not and cannot "inject" randomness into the quantum system in the way the nuke does for the gravitational system.

The difference between the "billiard ball" theory and GR is that in the former the particles are not aware of each other (a particle in a distant place has no effect on another) while in the later such awareness exists even beyond the light cone (if no non-deterministic events like nukes are allowed). For example, in the solar system Earth accelerates towards the future position of the Sun, and not towards its retarded position (the place we see the Sun).

As I understand it, "local" means "having a light cone structure", and you can use the type of argument I made above to show that no local theory where each event has a single definite outcome (as opposed to a many-worlds type theory) can explain the violation of Bell inequalities without positing a "conspiracy" where events in the past light cone of both the source's particle emission and the experimenter's choosing of setting always causes them to be correlated in just the right way to give the observed results. If you don't posit such a conspiracy, how can you explain a correlation between two events with a spacelike separation?

I think I've provided an explanation why your above argument does not apply to EPR. If QM is deterministic there is no source of randomness that can be used to "fool" the PDC about the future detector orientation. The light cone structure is not a problem because the information about the past is enough to perfectly predict the future.

A local, realistic, non-conspiracy type mechanism for EPR would be as follows:

1. every particle in the experimental setup sends a signal, at light speed towards the PDC source. (this is in fact true for every particle in the visible universe)

2. The calcium atom "reads" from those signals the position/momentum for each particle and "computes" their future evolution (including how the detector will be oriented at the time of detection). This might resemble the way Earth "reads" from the space curvature around it the position/momentum of other massive bodies and then "decides" how to accelerate.

3. When a suitable future detector orientation is detected (suitable in the sense that it must conform with Malus's law and conservation laws) a pair of "entangled" particles is emitted, "laughing" about the futile attempts of the experimenter to "beat the system".

 

[ueit]

Again, you speak in generalities when you imply such a connection. The source is a polarized laser beam. The detectors are polarized as well. Exactly how do you propose that the results depend on the source? The usual formula, Cos^2(a-b), relates the results of the detector settings but lacks a term for the source setting. This formula has substantial experimental validation.

Please take a look at my above post to JesseM

In my scientific opinion: unless you can predict the results of specific cases in advance or otherwise improve the accuracy of the usual formula by adding a term for a source setting, you may as well be asserting that the results are a function of the phase of the moon.

I do not need to provide a physically plausible local-realistic mechanism for EPR, only a logically consistent one (without appealing to conspiracies as these are extremely non-parsimonious). That is enough to prove that your assertion regarding the applicability of Bell's theorem (in spite of what Bell himself said) is false.

 

[JesseM]

There is a subtle error in your above line of reasoning. It is true that if we change Mars orbit by using a nuke, the effect will manifest on Earth at the same moment we see the explosion. However, in this case we do not deal with a deterministic theory anymore. While GR is deterministic, the nuclear explosion is not governed by GR and therefore, from GR's "point of view" it is a true unpredictable event. We have a mixture of a deterministic theory with random events and this is not what I propose as a local realistic explanation of EPR.

I didn't assume the nuclear explosion was random, though. You are free to assume that whatever non-gravitational forces are involved are also governed by deterministic laws, like classical electronmagnetism, which can certainly be incorporated into GR.

The point is just that no matter what your complete set of fundamental laws are, as long as they have a light cone structure, then there should be no statistical correlation between events A and B with a spacelike separation unless there's some event or events in the past light cone of A and B which predetermines them in the right way to create the correlation. And if A is the event of the source emitting particles in a certain state, and B is the event of an experimenter's brain making a choice of which setting to use on a given trial, then explaining the violation of Bell inequalities in terms of such a predetermining event in A and B's past light cone amounts to the "conspiracy" assumption discussed earlier. Do you disagree with any of this? If so, what specifically do you disagree with?

Now, let's make a correct analogy, by letting a stray planet, coming from a distant galaxy, to alter the orbit of Mars. In this case we deal with a true deterministic system and the effect will be felt instantaneously on Earth, as Newton's law of gravity (which is a good approximation for this case) predicts, before the light from Mars will reach us. This is because the stray planet does not interact only with Mars, but with Earth, and Jupiter, and all other bodies at once.

Are you sure about that? I believe it is true that if a body is moving at a constant velocity then we'll feel the pull from its current position. This is analogous to the situation in classical electromagnetism, where if you have a charge moving at constant velocity, other charges will be attracted to its current position rather than its retarded position; but this is in effect because the electromagnetic field has a built-in ability to "extrapolate" linear movement, there's no actual signals moving faster than light, and if the charge were to accelerate other charges would continue to be attracted to where the original charge would have been had it continued to move in a straight line, until they receive an "update" on its position in the form of electromagnetic waves. Because electromagnetic waves depend on a dipole moment while gravitational waves depend on a quadrupole moment, the gravitational field can "extrapolate" some more general types of movement than the electromagnetic field, like a spherically symmetric collapsing star, but in any situation where gravitational waves are generated, other objects do not anticipate all the motions, and continue to be attracted to the "wrong" positions until the gravitational waves reach them. And wouldn't one planet smashing into another and knocking it off course generate gravitational waves? See Sources of gravitational waves on wikipedia.

In any case, it seems to me the argument about the light cone structure is pretty airtight. In electromagnetism there is a correlation between the direction one charge A is being pulled at a given moment and the current position of another charge B moving at constant velocity, and these events have a spacelike separation, but this could be explained in terms of the position of the charge B at some previous time, an event in the past light cone of charge A, plus the electromagnetic field's ability to naturally "extrapolate" the position of charge B as long as it keeps moving at constant velocity. But any such dependence on events in the past light cone for Bell experiments would either involve a "conspiracy" in the initial conditions, or it would involve ridiculously complex laws of nature that were somehow "extrapolating" the precise future brain state of the experimenter at the moment of choice using only events in the past light cone of the event of the source emitting particles (and even if you are willing to allow such ridiculously complex laws of nature, this probably doesn't make sense anyway since the brain is a chaotic system and the choice would probably depend on everything in the past light cone of the experimenter's choice at a given time, but at any given time some of the events which lie in the past light cone of the choice-event are outside the past light cone of the event of the source emitting the particles, so even Laplace's demon couldn't predict the choice using only the set of events in the past light cone of the emission-event).

The difference between the "billiard ball" theory and GR is that in the former the particles are not aware of each other (a particle in a distant place has no effect on another) while in the later such awareness exists even beyond the light cone (if no non-deterministic events like nukes are allowed). For example, in the solar system Earth accelerates towards the future position of the Sun, and not towards its retarded position (the place we see the Sun).

But again, the type of motions that GR can "extrapolate" in this way are pretty limited, I think it may just be constant-velocity motion and spherically or cylindrically symmetric acceleration; any type of motion complicated enough to result in gravitational waves cannot be extrapolated in this way, so objects will not be pulled in exactly the direction of other object's current position in these circumstances.

A local, realistic, non-conspiracy type mechanism for EPR would be as follows:

1. every particle in the experimental setup sends a signal, at light speed towards the PDC source. (this is in fact true for every particle in the visible universe)

2. The calcium atom "reads" from those signals the position/momentum for each particle and "computes" their future evolution (including how the detector will be oriented at the time of detection). This might resemble the way Earth "reads" from the space curvature around it the position/momentum of other massive bodies and then "decides" how to accelerate.

But like I said, the more complicated the types of motion you want objects to be able to "extrapolate", the more complicated your fundamental laws have to be; and I think my parenthetical comment about how even Laplace's demon probably couldn't predict the experimenter's choice using only information about events in the past light cone of the source's emission event suggests that even ridiculously complicated laws couldn't do what you're suggesting without "conspiracy-like" restrictions on the initial conditions of the universe.

 

[ueit]

I didn't assume the nuclear explosion was random, though. You are free to assume that whatever non-gravitational forces are involved are also governed by deterministic laws, like classical electromagnetism, which can certainly be incorporated into GR.

Yeah, but introducing additional complexity in my analogy does no good.

The point is just that no matter what your complete set of fundamental laws are, as long as they have a light cone structure, then there should be no statistical correlation between events A and B with a spacelike separation unless there's some event or events in the past light cone of A and B which predetermines them in the right way to create the correlation.

I agree with this. More, I think there is good evidence (the uniformity of microwave background radiation) that all the visible universe passed a period when all its particles were able to "make contact" with each other:
http://en.wikipedia.org/wiki/Inflationary_theory"

In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density.[1] As a direct consequence of this expansion, all of the observable universe originated in a small causally-connected region. Inflation answers the classic conundrums of the big bang cosmology: why does the universe appear flat, homogeneous and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the big bang, a highly curved, inhomogeneous universe.

(emphasis mine)

And if A is the event of the source emitting particles in a certain state, and B is the event of an experimenter's brain making a choice of which setting to use on a given trial, then explaining the violation of Bell inequalities in terms of such a predetermining event in A and B's past light cone amounts to the "conspiracy" assumption discussed earlier. Do you disagree with any of this?

I disagree with "predetermining event in A and B's past light cone" formulation. All the particles in the universe are correlated with each other from the time of big-bang. Even if those particles are now far from each other, the correlation between their motion remains.

Are you sure about that?

Of course I'm not. It's just one of many possible scenarios.

I believe it is true that if a body is moving at a constant velocity then we'll feel the pull from its current position. This is analogous to the situation in classical electromagnetism, where if you have a charge moving at constant velocity, other charges will be attracted to its current position rather than its retarded position; but this is in effect because the electromagnetic field has a built-in ability to "extrapolate" linear movement, there's no actual signals moving faster than light, and if the charge were to accelerate other charges would continue to be attracted to where the original charge would have been had it continued to move in a straight line, until they receive an "update" on its position in the form of electromagnetic waves. Because electromagnetic waves depend on a dipole moment while gravitational waves depend on a quadrupole moment, the gravitational field can "extrapolate" some more general types of movement than the electromagnetic field, like a spherically symmetric collapsing star, but in any situation where gravitational waves are generated, other objects do not anticipate all the motions, and continue to be attracted to the "wrong" positions until the gravitational waves reach them. And wouldn't one planet smashing into another and knocking it off course generate gravitational waves? See Sources of gravitational waves on wikipedia.

I didn't think about the planet "smashing into" Mars, only passing close enough to significantly alter its orbit. In a collision, a lot of energy is lost as heat, and the analogy wouldn't work (the error introduced by gravity waves is negligible though). Now, GR is only an analogy. I do not claim that the mechanism behind EPR is exactly like GR. In any case, the accelerated motion is "extrapolated" very well by GR so that a non-local mechanism as the one proposed by Newtonian gravity works very well for all but extreme situations like the merging of black holes or neutron stars. I know that it doesn't work perfectly and that's why I specified that for the case I gave you, Newtonian theory is a good approximation. I see no reason to assume that a better or even perfect "extrapolation" of accelerated motion (which is the only possible motion of a point particle except the uniform one) cannot be accomplished by a theory. At least, I know of no proof of that.

In any case, it seems to me the argument about the light cone structure is pretty airtight. In electromagnetism there is a correlation between the direction one charge A is being pulled at a given moment and the current position of another charge B moving at constant velocity, and these events have a spacelike separation, but this could be explained in terms of the position of the charge B at some previous time, an event in the past light cone of charge A, plus the electromagnetic field's ability to naturally "extrapolate" the position of charge B as long as it keeps moving at constant velocity. But any such dependence on events in the past light cone for Bell experiments would either involve a "conspiracy" in the initial conditions, or it would involve ridiculously complex laws of nature that were somehow "extrapolating" the precise future brain state of the experimenter at the moment of choice using only events in the past light cone of the event of the source emitting particles (and even if you are willing to allow such ridiculously complex laws of nature, this probably doesn't make sense anyway since the brain is a chaotic system and the choice would probably depend on everything in the past light cone of the experimenter's choice at a given time, but at any given time some of the events which lie in the past light cone of the choice-event are outside the past light cone of the event of the source emitting the particles, so even Laplace's demon couldn't predict the choice using only the set of events in the past light cone of the emission-event).

When you are speaking about “ridiculously complex laws of nature that were somehow "extrapolating" the precise future brain state of the experimenter at the moment of choice” you are referring to a high level description of facts. The mechanism I propose works at the lowest level. A calcium atom doesn’t “know” anything about brains, computers or experiments; it only “looks” for two suitable absorbers (other atoms) for the entangled photons. When such absorbers are found, a pair of photons is send towards their extrapolated position. That’s all. The chain of events by which those absorbers arrive at their position is irrelevant. You may have a human pushing a button that hits a monkey; then the monkey starts a computer running a random number generator that in turn commands an engine to change the polarizer’s position. If, at low level, the “extrapolation” mechanism works perfectly, or at least with a good enough accuracy the calcium atom would not be “fooled” and Bell’s inequality would be violated.

But again, the type of motions that GR can "extrapolate" in this way are pretty limited, I think it may just be constant-velocity motion and spherically or cylindrically symmetric acceleration; any type of motion complicated enough to result in gravitational waves cannot be extrapolated in this way, so objects will not be pulled in exactly the direction of other object's current position in these circumstances. But like I said, the more complicated the types of motion you want objects to be able to "extrapolate", the more complicated your fundamental laws have to be; and I think my parenthetical comment about how even Laplace's demon probably couldn't predict the experimenter's choice using only information about events in the past light cone of the source's emission event suggests that even ridiculously complicated laws couldn't do what you're suggesting without "conspiracy-like" restrictions on the initial conditions of the universe.

From my answer above I conclude:

1. It should be enough to extrapolate accelerated motion. Other types are not possible for a point particle. Probably even the imperfect extrapolation of GR is enough to explain all experiments to date.
2. “all of the observable universe originated in a small causally-connected region”. This is the event that “links” the whole experimental setup. Since then all particles are correlated with each other because of the “extrapolation” effect.
3. No complicated laws must be postulated to deal with brains or different experimental tricks. Conservation laws, the microscopic equivalent of Mallus’ law plus the extrapolation mechanism will do.

 

[Demystifier]

Is this Bell's theorem refuted? Expert comment please?

From abstract quant-ph/0703179

Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables

Joy Christian, Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada, and Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, England

It is shown that Bell’s theorem fails for the Clifford algebra valued local realistic variables. This is made evident by exactly reproducing quantum mechanical expectation value for the EPR-Bohm type spin correlations observable by means of a local, deterministic, Clifford algebra valued variable, without necessitating either remote contextuality or backward causation. Since Clifford product of multivector variables is non-commutative in general, the spin correlations derived within our locally causal model violate the CHSH inequality just as strongly as their quantum mechanical counterparts.

Let me make a comment on the Clifford-valued local realistic variables.
Although I have not completely understood the paper, it is not a surprise to me that local Clifford-valued realistic variables may simulate QM. This is because, in a sense, non-commuting variables are never truly local, even if they are local formally. Let me explain what I mean by this:
A formally local quantity is a quantity of the form A(x) or B(y), where x and y are positions of the first and the second particle, respectively. Now, if they are not commuting, then
A(x)B(y) \neq B(y)A(x)
But how two quantities A and B know that they should not commute if x is very far from y? This knowledge is a sort of nonlocality as well.

My opinion is that realistic variables (local or not) must be not only commuting, but represented by real numbers. This is because they are supposed to be measurable, while a measurable quantity must be a real number. Therefore, I believe that the Clifford-valued realistic variables are physically meaningless.

In fact, the claim that physical variables could be noncommuting numbers does not differ much from the claim that physical variables could be noncommuting operators or noncommuting matrices. But this is exactly what the realistic physical variables in QM are NOT supposed to be, because otherwise we deal with QM in the usual matrix/operator form.

 

[DrChinese]

I do not need to provide a physically plausible local-realistic mechanism for EPR, only a logically consistent one (without appealing to conspiracies as these are extremely non-parsimonious). That is enough to prove that your assertion regarding the applicability of Bell's theorem (in spite of what Bell himself said) is false.

Well, I'm not too sure how "logically consistent" your mechanism is if it can't meet my simple test (in which each possible outcome probability is non-negative).

I place your hypothesis in the bin with the other "proofs" that Bell is not applicable.

 

[DrChinese]

My opinion is that realistic variables (local or not) must be not only commuting, but represented by real numbers. This is because they are supposed to be measurable, while a measurable quantity must be a real number. Therefore, I believe that the Clifford-valued realistic variables are physically meaningless.

In fact, the claim that physical variables could be noncommuting numbers does not differ much from the claim that physical variables could be noncommuting operators or noncommuting matrices. But this is exactly what the realistic physical variables in QM are NOT supposed to be, because otherwise we deal with QM in the usual matrix/operator form.

Well said.

I am always amazed at new hypotheses (such as Christian's) which purport to show a local realistic scenario which agree with the predictions of QM - yet do not discuss the negative probabilities which result when the observer freely chooses between measurement settings. The entire realistic argument IS that the observer could do this! That is what everyone cares about - whether the results are observer dependent or not. So when the observer independence issue is magically dropped (in this case by having non-commutivity), it is no big surprise that Bell is bypassed in the results. Of course, that is why Bell's Theorem is so important. His assumptions are very straightforward and easy to agree with.

 

[JesseM]

I agree with this. More, I think there is good evidence (the uniformity of microwave background radiation) that all the visible universe passed a period when all its particles were able to "make contact" with each other

Unless I'm misunderstanding something, that doesn't mean that there was any time when all the events in the past light cone of the event of the experimenter making a choice of what to measure were also in the past light cone of the event of the the source sending out the particles. Again, if you don't place any special constraints on initial conditions, then even in a deterministic universe, a Laplacian demon with knowledge of everything in the past light cone of the source sending out the particles would not necessarily be able to predict the brain state of the experimenter at the time he made his choice of what to measure. Do you disagree?

I disagree with "predetermining event in A and B's past light cone" formulation. All the particles in the universe are correlated with each other from the time of big-bang. Even if those particles are now far from each other, the correlation between their motion remains.

"Correlated" is too vague. I think that inflationary theory would say that the past light-cones of the most widely-separated events we can see will partially overlap, so that the similarity of the CMBR in different regions can have a common past cause. But again, it doesn't mean that knowing the past light cone of one event would allow you to predict every other event, even in a perfectly deterministic universe, because any pair of spacelike separated events would have parts of their past light cones that are outside the past light cone of the other event. (This is assuming you don't try to define the past light cone of each event at the exact time of the initial singularity itself, since the singularity doesn't seem to have a state that could allow you to extrapolate later events by knowing it...for every time slice after the singularity, though, knowing the complete physical state of a region of space would allow you to predict any future event whose past light cone lies entirely in that region, in a deterministic universe.)

Are you sure about that?

Of course I'm not. It's just one of many possible scenarios.

I was asking if you were sure about your claim that in the situation where Mars was deflected by a passing body, the Earth would continue to feel a gravitational pull towards Mars' present position rather than its retarded position, throughout the process. This is a question about GR that would presumably have a single correct answer, so I'm not sure what you mean by "many possible scenarios"--perhaps you misunderstood what I was asking.

I didn't think about the planet "smashing into" Mars, only passing close enough to significantly alter its orbit.

That's fine, but like I said, my understanding is that GR can only "extrapolate" constant-velocity motion or situations involving acceleration which are spherically or cylindrically symmetric. I don't see how the situation of Mars being deflected from its orbit by a passing body could exhibit this kind of symmetry, so I'm pretty sure the Earth would not continue to be pulled towards Mars' present position throughout the process.

In any case, the accelerated motion is "extrapolated" very well by GR so that a non-local mechanism as the one proposed by Newtonian gravity works very well for all but extreme situations like the merging of black holes or neutron stars.

It only works as an approximation. If you're claiming that it works in the specific sense of objects continuing to be pulled towards other object's present positions rather than retarded positions, I believe you're wrong about that--again, the "extrapolation" only happens in the case of constant velocity or spherically/cylindrically symmetric motion AFAIK.

When you are speaking about “ridiculously complex laws of nature that were somehow "extrapolating" the precise future brain state of the experimenter at the moment of choice” you are referring to a high level description of facts. The mechanism I propose works at the lowest level. A calcium atom doesn’t “know” anything about brains, computers or experiments; it only “looks” for two suitable absorbers (other atoms) for the entangled photons. When such absorbers are found, a pair of photons is send towards their extrapolated position. That’s all.

By "complexity" I was referring to the mathematical complexity of the laws involved. We could say that in electromagnetism a charged particle "knows" where another particle would be now if it kept moving at constant velocity, and in GR a test particle "knows" where the surface of a collapsing shell would be if it maintains spherical symmetry; there isn't a literal calculation of this of course, but the laws are such that the particles act as if they know in terms of what direction they are pulled. In order for the source to act as though it knows the orientation of a distant polarizer which was fixed by the brain of a human experimenter, then even if we ignore the issue of some events in the past light cone of the experimenter's choice being outside the past light cone of the source emitting the particles, the "extrapolation" here would be far more complicated because of the extremely complicated and non-symmetrical motions of all the mutually interacting particles in the experimenter's brain which must be extrapolated from some past state, and presumably the laws that would make the source act this way would not have anything like the simplicity of electromagnetism or GR. We could think in terms of algorithmic complexity, for example--the local rules in a cellular-automata program simulating EM or GR would not require a hugely long program (although the actual calculations for a large number of 'cells' might require a lot of computing power), while it seems to me that the sort of rules you're imagining would involve a much, much longer program just to state the fundamental local rules.

1. It should be enough to extrapolate accelerated motion. Other types are not possible for a point particle. Probably even the imperfect extrapolation of GR is enough to explain all experiments to date.

You refer to "imperfect" extrapolation, but I'm pretty sure it's not as if GR can kinda-sorta extrapolate accelerations that aren't perfectly spherically or cylindrically symmetric, it's an all-or-nothing deal, just like with EM where the extrapolation is to where the other particle would be if it kept moving at an exactly constant velocity, not somewhere between a constant velocity and its true acceleration. GR wouldn't in any way begin to extrapolate the current positions of particles which are accelerating in all sorts of different directions in a non-symmetric way, with the direction and magnitude of each particle's acceleration always changing due to interactions with other particles (like all the different molecules and electrons in your brain).

And of course, even if you set things up so the detector angle was determined by some simple mechanism which GR could extrapolate, like the radius of a collapsing star at the moment the source emits its particles, the "extrapolation" just refers to where other objects will experience a gravitational pull, what sort of laws do you propose that would allow the source to "know" that the detector angle depends on this variable, and to modify the hidden variables based on the detector angles? Obviously there's nothing in GR itself that could do this.

2. “all of the observable universe originated in a small causally-connected region”. This is the event that “links” the whole experimental setup. Since then all particles are correlated with each other because of the “extrapolation” effect.

See above--like I said, this doesn't mean that knowing the past light cone of one event would allow you to automatically predict the outcome of another event with a spacelike separation from the first. The regions of the two past light cones will overlap in the very early universe, but there will be no finite moment after the singularity where the regions encompassed by the two past light cones at that moment are identical, there will always be some points in the past light cone of one that are outside the past light cone of the other. If the event we're talking about is the product of a nonlinear system exhibiting sensitive dependence on initial conditions like the brain, then it seems to me that even in a deterministic universe you'd need to know the complete state of the region of space inside the past light cone at an earlier time in order to predict the event. This is why I think that even Laplace's demon could not predict what the detector setting would be if he only knew about events in the past light cone of the source emitting the entangled particles. Do you disagree, and if so, why?

 

[Hurkyl]

Let me make a comment on the Clifford-valued local realistic variables.
Although I have not completely understood the paper, it is not a surprise to me that local Clifford-valued realistic variables may simulate QM. This is because, in a sense, non-commuting variables are never truly local, even if they are local formally. Let me explain what I mean by this:
A formally local quantity is a quantity of the form A(x) or B(y), where x and y are positions of the first and the second particle, respectively. Now, if they are not commuting, then
A(x)B(y) \neq B(y)A(x)
But how two quantities A and B know that they should not commute if x is very far from y? This knowledge is a sort of nonlocality as well.

Well, there are some problems with this. First, a RAA: let's suppose A and B are real-valued functions. How can A and B know that they should commute if x is very far from y?

Anyways, this is very simple. If A and B are Clifford-valued functions, (or if they are real-valued functions), then A(x) and B(y) are numbers. I repeat, they are not numbers located someplace in space-time: they are simply numbers.

OTOH, if A and B took values in a line bundle, so that A(x) is a number located someplace in space-time, then A(x)B(y) is nonsensical: we need a connection (and a path from x to y) to transport a value at x to the fiber at y before we can do any arithmetic with them. (This is true, even if our line bundle is of real numbers)

My opinion is that realistic variables (local or not) must be not only commuting, but represented by real numbers. This is because they are supposed to be measurable, while a measurable quantity must be a real number.

Just to be clear -- is "a measurable quantity must be a real number" your opinion, or are you claiming that as fact?

 

[Demystifier]

Just to be clear -- is "a measurable quantity must be a real number" your opinion, or are you claiming that as fact?

It is my opinion. But I am quite certain about it, so I would even dare to claim that it is a fact.

 

[ueit]

Well, I'm not too sure how "logically consistent" your mechanism is if it can't meet my simple test (in which each possible outcome probability is non-negative).

My mechanism is as follows:

The PDC source generates photon pairs that obey Malus’ law (n = cos^2(alpha)), where:

n = the probability that the two photons have the same spin on the two measurement axes.

alpha = angle between the polarizers.

The detectors' settings are not communicated non-locally but are "extrapolated" from the past state of the system.

This mechanism is therefore local, realistic (the photons had the measured spin all along) and gives the same predictions as QM, but would not pass your test. This is because your constraints are irrelevant as locality and realism are concerned. It is the statistical independence assumption that requires the probabilities to add to 100% and my mechanism denies this.

I place your hypothesis in the bin with the other "proofs" that Bell is not applicable.

There is nothing to prove. Bell himself clearly stated that the theorem depends of the assumption of statistical independence. You seem not to be able to accept this, for a reason I can't understand.

Bell J., Speakable And Unspeakable In Quantum Mechanics, p. 100:

It has been argued the QM is not locally causal and cannot be embedded in a local causal theory. That conclusion depends on treating certain experimental parameters, typically the orientations of polarization filters, as free variables

(emphasis mine)

Please read carefully the above quote and try to understand the irrelevance of your "test" in my case.