OK Corral: Local versus non-local QM

[JesseM]

"Bellian realism" is the constrained realism that we may associate with Bell (1964; for example); where A+, originally a measurement outcome, is subtly changed to a property of the particle itself

Again, you are free to assume that A+ is not a property of the particle itself, but that the particle just has some properties P which, when the particle is disturbed by a measurement of type A, leads deterministically to the result +. I tried to explain the logic behind the need for determinism in particle properties and measurement setting in post #56, if you don't see the logic it might help if you answered my questions there. Note that the assumption here is not that the whole universe is deterministic--indeed, the particular properties P of the particle sent out on each trial may be randomly created by the source, and the experimenter's choice of measurement setting may be random too--just that, if we know the complete properties of the particle and the measurement setting on a given trial, that is enough to uniquely determine the result on that trial.

 

[wm]

Ah ha!

You continue to ignore Bell's Theorem conveniently as if it does not exist. There is no substantive difference between your "common-sense" definition of realism (per your page) and Bell's. Even if there were, no one would care because Bell's maps to the debate of concern to Einstein, Bohr, and everyone who follows EPR's argument.

Bell's theorem (1964) is ever in my thoughts; so why do you say this?

You should quit confusing people with your statements, and acknowledge as follows:

1. You believe in locality.
2. You believe in your version of realism, which is slightly different than Bell's but you are not sure how so mathematically.
3. You do not accept Bell's Theorem as valid.
4. You accept 3. as a matter of faith because you believe 1. and 2., and you think other folks should too.
5. You have no actual plan for developing your pet theory, but hope that those of us here at Physicsforums will help you.

I would like to point out that this discussion belongs in Theory Development, and not quantum physics.

1. Yes.

2. Yes, re my realism. Then, No; I am sure now that I have seen vanesch's addendum (which I repeatedly requested of you) that mathematically I will be similar in deriving the EPR-Bohm correlation.

3. Just to be careful here: If you would define it, I would expect to give you a definite answer. Please define.

4. See 3 above. When it comes to maths, I'm not a faith-based person. So you are dead wrong again and again. (Why not follow JesseM and ask questions rather than promote lies and error (as you here do)?

5. (a) No! This is quite false and you must know that it is false!

Evidence: How would you know that it is false?

(a) I wrote to you off-PF and you replied that you were going to look at a matter and get back to me. You have not.

(b) So I am tending to read your question as an attempt to bias helpful communications from others with me. I take it you too can see where we're heading mathematically, thanks to vanesch. Put it another way: I see no theory of mine under threat.

SO why don't you ask an upfront question instead of non-locally reading my mind! Or should I rather say: Your non-locality fails again! (Many expletives deleted. But are you a PhD? By any chance, DrtC?)

5. (b) The PF communications have helped me greatly, especially JesseM, vanesch, hurkyl, DocAl +++

If I were familiar with LaTeX I would be more expansive.

PS-1. As to ''theory development'': This confirms my view that you can see where vanesch's maths (not yet mine) takes us.

PS-2. I hope the authorities will see that you are wrong (once again).

PS-3. Please provide evidence: What is the new theory that I am developing, please. (Please do not misunderstand or misrepresent the hidden-variables revealed on my website -- I should have picked you up on this before.)

PS-4. Finally: How many refereed papers do you want shoved down your fabricacious mouth?

wm

 

[JesseM]

PS-1. As to ''theory development'': This confirms my view that you can see where vanesch's maths (not yet mine) takes us.

If you think vanesch's math somehow shows QM is compatible with common-sense local realism, then you have totally misunderstood it (it would help if you explained why you think there is anything 'local' about his math).

And if you are not at least open to the possibility that Bell's theorem is valid and that common-sense local realism is definitively ruled out by quantum results such as the -cos(a-b) expectation value, then I agree this should go in theory development. If you are hoping to find a hole in Bell's theorem, but admit the fault may be in your understanding and are trying to improve your understanding through these discussions, then I think it's OK to continue the discussion here. So which is it?

 

[wm]

Well, if the long sentences are hard to follow, just ask for clarification, it's usually pretty easy to break them up into a list of distinct statements or assumptions...in the quote above, I could rewrite the assumptions like this:

do you agree or disagree that IF we have:

1. two experimenters with a spacelike separation
2. 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)
3. then if they always get opposite answers when they make the same measurement on any given trial
4. and we try to explain this in terms of some event in both their past light cone which predetermined the answer they'd get to each possible measurement
5. with no violations of locality allowed
6. and also with the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial, so their measurements are not having a backwards-in-time effect on the original predetermining event
7. as well as the assumption that the experimenters are not splitting into multiple copies as in the many-worlds interpretation)

THEN the following inequalities must hold:

1. 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 +)

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

I would say your old model, where the source knows what detector setting Alice will use before it sends out a signal, is violating condition 6 above, "the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial". In your "yoked" experiment, the angle that Alice measures the polarization is not independent of the polarization of the light sent out (and knowing both Alice's measurement angle and the polarization of the light does predetermine the result).

Of course my condition 6 also talked about a "backwards-in-time influence", which isn't true in your yoked scenario, since you assume there is enough time between Alice choosing her measurement angle and Alice actually making a measurement for a signal to have gotten back to the source and told it what the angle would be before it sent out the polarized light. I guess in condition 1 I was implicitly assuming that each experimenter's choice of detector setting was immediately before they actually made a measurement, so that there is also a spacelike separation between these two pairs of events:

1. (Alice randomly choosing her measurement angle) AND (Bob measuring the signal/object sent to him from the source)
2. (Bob randomly choosing his measurement angle) AND (Alice measuring the signal/object sent to her from the source)

So, if you add this condition explicitly to my list, then it would be impossible for the source's choice of what signals/objects to be sent out to be correlated with Alice and Bob's choice of detector settings, unless somehow the information was traveling backwards in time (or unless there was a weird cosmic conspiracy in the initial conditions of the universe which caused the source's output to be correlated with Alice and Bob's choices on each trial even though no signal could travel between them).
Yes. Nope, as long as you obey my conditions 1-7 above (including the clarification of what I meant by condition 1), then it is impossible for the inequalities to be violated by any experiment whatsoever. Therefore, since the inequalities are empirically violated in QM, it must be that QM violates one of the assumptions 5-7...either QM allows nonlocality, or QM allows backwards-in-time signalling, or QM allows experimenters to split into multiple copies (I suppose QM could also just violate the rules of logic, but I was assuming traditional logic must be obeyed). Not at all--where did you get that idea? Vanesch just shows that when you use the conventional quantum rules to make predictions, you get the prediction that the expectation value is -cos(a-b). But the conventional quantum rules themselves do not say anything about locality or nonlocality, that's a matter for interpretation.

Jesse, Do the following short-answers answer most of your questions:

1. vanesch has enabled me to clearly see that your last sentence is one that I can now wholeheartedly endorse!

2. You have been equally helpful in that important (for me, crucial) process; for which I thank you too.

3. Given the number of believers in non-locality, I had been searching for the origin of such a strange belief (which is totally alien to my present world-view).

4. I see now that I can happily persist with my concrete thinking-style; and bring more powerful arguments as to why non-locality is ...

5. I'm sorry if my slow-learning style upsets you. If I'm allowed to stay here (refer DrC prior post) then I think my arguments against non-locality will be be improved; coming from a more enlightened student.

Cheers, wm

 

[JesseM]

1. vanesch has enabled me to clearly see that your last sentence is one that I can now wholeheartedly endorse!

But I'm sure vanesch would also agree that "the conventional quantum rules themselves" + Bell's theorem do imply that common-sense local realism is ruled out, and that the only local options involve noncommonse interpretations like the many-worlds interpretation or perhaps the transactional interpretation (in which future events can effect past events that lie in their past light cone). Obviously you do not endorse this conclusion, so if you're open to the possibility that this might be due to an error in your understanding, it would help if we discussed the reasoning behind Bell's theorem more carefully.

4. I see now that I can happily persist with my concrete thinking-style; and bring more powerful arguments as to why non-locality is ...

No you can't, not unless you wish to persist in your confused understanding of Bell's theorem.

Again, to get around this confusion, please address the following:

1. Do you agree that none of the classical experiments you've presented so far (the "yoked" polarizer experiment and the experiment sending two classical vectors) both satisfy my conditions above (including the clarifications I added) and show a violation of any Bell inequality?

2. Do you agree that in a classical universe obeying locality, if experimenters always get the same (or opposite) result when using the same setting, and there is no possibility the source can know their choice of settings in advance (see my clarification of condition 1), then the only way to explain this correlation is to assume the complete properties of the object/signal sent out by the source + the choice of detector setting -> a deterministic result for that measurement? If you don't agree, please address my questions 1-3 in post #56, or provide an alternate classical explanation for the correlation.

 

[wm]

Thanks for asking questions!

If you think vanesch's math somehow shows QM is compatible with common-sense local realism, then you have totally misunderstood it (it would help if you explained why you think there is anything 'local' about his math).

And if you are not at least open to the possibility that Bell's theorem is valid and that common-sense local realism is definitively ruled out by quantum results such as the -cos(a-b) expectation value, then I agree this should go in theory development. If you are hoping to find a hole in Bell's theorem, but admit the fault may be in your understanding and are trying to improve your understanding through these discussions, then I think it's OK to continue the discussion here. So which is it?

Jesse; more misunderstandings; is my writing that bad?

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

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

3. My world-view is common-sense local realism (CLR).

4. I would call that my interpretation of the QM and its formalisms.

5. Does my CLR interpretation cause any problems here on PF?

6. For it seems to be a fairly-mild mid-range belief compared to others and extremes that I find here on PF.

7. vanesch enables me to discuss my view in the light of QM maths; with no need to dispute the maths.

8. vanesch enables me to bring better arguments to my view in the light of QM maths.

8. I think it more like that I am more here to find any holes in my world-view. (PS: While I am doing that, Am I permitted to poke holes in other views; especially using maths as my main argument now.)

9. I think I am very happy: and mostly due to about 6 lines of vanesch maths: 6 lines that you know I've been asking for for quite a while.

10. Is this above acceptable, please?

wm

 

[JesseM]

Jesse; more misunderstandings; is my writing that bad?

What exactly have I "misunderstood"?

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

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

WHY DO YOU THINK THIS? Vanesch just gave a recipe for calculating things in QM, the recipe itself is not based on local or nonlocal signals between events, it doesn't explain anything about why you see the correlations you do between measurements on entangled particles. However, if you take the results given to you by the recipe, and then you take Bell's theorem, it is clear that logically the results DO absolutely rule out common-sense local realism.

You seem to be confusing these two statements:

-Vanesch's calculations do not in themselves say anything either way about nonlocality vs. locality

-Vanesch's calculations are equally compatible with nonlocality and (common-sense) locality

But they are NOT equivalent--the first is true while the second is totally false! Logically the results are completely incompatible with common-sense local realism, it's just that this is not immediately obvious from looking at the calculations, you have to provide some additional logical arguments which go by the name of "Bell's theorem".

3. My world-view is common-sense local realism (CLR).

4. I would call that my interpretation of the QM and its formalisms.

But it is an invalid interpretation, definitively ruled out by quantum predictions. Bell's theorem shows this.

5. Does my CLR interpretation cause any problems here on PF?

Yes, no mainstream physicist would accept it as a valid "interpretation", because it does not make logical sense. You would see this if you actually made an effort to understand Bell's theorem, which is why I have been trying to walk you through it. If you're not trying to understand it, then this is equivalent to advancing the "interpretation" that perpetual motion is possible without listening to people's attempts to explain why it is ruled out by the laws of thermodynamics.

9. I think I am very happy: and mostly due to about 6 lines of vanesch maths: 6 lines that you know I've been asking for for quite a while.

10. Is this above acceptable, please?

No, because you have given no explanation for why you think vanesch's math somehow supports your idea. It doesn't, all vanesch's math gives is a recipe for calculating the probabilities, and then Bell's theorem proves that these probabilities are absolutely incompatible with common-sense local realism.

 

[wm]

Maybe too many questions now?

But I'm sure vanesch would also agree that "the conventional quantum rules themselves" + Bell's theorem do imply that common-sense local realism is ruled out, and that the only local options involve noncommonse interpretations like the many-worlds interpretation or perhaps the transactional interpretation (in which future events can effect past events that lie in their past light cone). Obviously you do not endorse this conclusion, so if you're open to the possibility that this might be due to an error in your understanding, it would help if we discussed the reasoning behind Bell's theorem more carefully. No you can't, not unless you wish to persist in your confused understanding of Bell's theorem.

Again, to get around this confusion, please address the following:

1. Do you agree that none of the classical experiments you've presented so far (the "yoked" polarizer experiment and the experiment sending two classical vectors) both satisfy my conditions above (including the clarifications I added) and show a violation of any Bell inequality?

2. Do you agree that in a classical universe obeying locality, if experimenters always get the same (or opposite) result when using the same setting, and there is no possibility the source can know their choice of settings in advance (see my clarification of condition 1), then the only way to explain this correlation is to assume the complete properties of the object/signal sent out by the source + the choice of detector setting -> a deterministic result for that measurement? If you don't agree, please address my questions 1-3 in post #56, or provide an alternate classical explanation for the correlation.

I personally DO NOT NEED A CLASSICAL EXPLANATION OF ANYTHING :::: NOW THAT I HAVE VANESCH'S MATHS.

NB: THAT IS NOT me SHOUTING AT YOU. THAT IS ME SHOUTING TO THE ROOF-TOPS AND MY (sorry -- meant to turn caps off) friends that I have learned something good.


PS: I am making a big mistake in rushing all this stuff when i am so busy. I do feel that I owe you answers. But please consider them in the spirit of community dialogue and my personal learning. There is not a question I will not answer honestly; just maybe not good wording, especially when rushing.

Is this now OK please?

wm

 

[JesseM]

I personally DO NOT NEED A CLASSICAL EXPLANATION OF ANYTHING :::: NOW THAT I HAVE VANESCH'S MATHS.

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.

 

[wm]

Gosh!

What exactly have I "misunderstood"? WHY DO YOU THINK THIS? Vanesch just gave a recipe for calculating things in QM, the recipe itself is not based on local or nonlocal signals between events, it doesn't explain anything about why you see the correlations you do between measurements on entangled particles. However, if you take the results given to you by the recipe, and then you take Bell's theorem, it is clear that logically the results DO absolutely rule out common-sense local realism.

You seem to be confusing these two statements:

-Vanesch's calculations do not in themselves say anything either way about nonlocality vs. locality

-Vanesch's calculations are equally compatible with nonlocality and (common-sense) locality

But they are NOT equivalent--the first is true while the second is totally false! Logically the results are completely incompatible with common-sense local realism, it's just that this is not immediately obvious from looking at the calculations, you have to provide some additional logical arguments which go by the name of "Bell's theorem". But it is an invalid interpretation, definitively ruled out by quantum predictions. Bell's theorem shows this. Yes, no mainstream physicist would accept it as a valid "interpretation", because it does not make logical sense. You would see this if you actually made an effort to understand Bell's theorem, which is why I have been trying to walk you through it. If you're not trying to understand it, then this is equivalent to advancing the "interpretation" that perpetual motion is possible without listening to people's attempts to explain why it is ruled out by the laws of thermodynamics. No, because you have given no explanation for why you think vanesch's math somehow supports your idea. It doesn't, all vanesch's math gives is a recipe for calculating the probabilities, and then Bell's theorem proves that these probabilities are absolutely incompatible with common-sense local realism.

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

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

I think my saints (my co-conspirators) might be Bell, Einstein, Cramer (bit re-interpreted), Peres, Rovelli, Ballentine, Griffiths, Haag, Froehner, Kracklauer, Mayants, Jaynes, Hestenes, Harrison, Gottfried, parly vanesch (because I think we might be able to agree, due his maths) +++++++++ (though I know little of them and I'm not a full-member of MWI -- see hurkyl comment early on; it seems to fit me ok but I'm not studied it much). Some gurus here seem to be ok in ideas too.

Am I fallen into a group of terrorists? Should I head voluntarily for Guantanamo Bay?

wm

 

[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: [tex]sin^2(\theta/2) which is the "gross correlation" basis (ranges from 0 to 1, matches). I realize that these bases (gross and net) can be very confusing and I probably shouldn't mention them, but you often see them interchanged without being labelled (and I am often guilty of this too).

In the net basis:

1=completely correlated.
-1=completely anti-correlated
0=no correlation (due completely to chance, in other words)

This matches Bell'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.

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:

a) Assume the QM predictions for the singlet state of an entangled spin 1/2 pair must hold.
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.

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.

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 and uses the cos theta relationship in his paper. Unfortunately, he did not see that as very important to point out the step but I can show it to you (it is indirect):

Look at (22) and the next line: a.c=0, a.b=b.c=1/sqrt(2)

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.

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.

So I will do a separate post to more readily show the angle setting violations.

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'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?