Bell's Theorem, EPRB, QM, spin-1/2 particles, basic arithmetic: In reply

[Gordon Watson]

..
This thread is intended to focus on arithmetic issues, mainly raised by JesseM, vanesch, DrChinese, ThomasT, in the context of: "What's wrong with this local realistic counter-example to Bell's theorem?" https://www.physicsforums.com/showthread.php?t=475076 :

For newcomers to the issues, I am committed to reply to each and every question that arises in the above context. So further arithmetic questions, arising from that context, will also be answered here.

Thus, to be clear, this thread focusses on the arithmetic associated with quantum-entangled spin-1/2 particles in the EPR-Bohm experiment (Bohm 1951) and its analysis in Bell (1964).

(If the need arises, I'd propose to answer spin-1 questions in another thread -- to avoid arithmetic confusion.)

PS: I will attempt to answer each question in a separate Post, to facilitate follow-up questions. And I would very much appreciate ONE question per Post -- because it's difficult to reply to long Posts on my small-screen computer. Thanks!
.........

The main terms and equations are defined in PDF2 [post=3191024]attached here[/post], with partial-errata in https://www.physicsforums.com/showpost.php?p=3191819&postcount=86
.........

The main equations that we'll be discussing are similar to those which follow -- "etc." to be understood after each equation.

The OP-style identification is intended to lead back to this OP; the identifier on the Right is that found in PDF2 [post=3191024]attached here[/post], Appendix A:


From PDF2 ([post=3191024] attached here[/post]), Appendix A:

(OP-A) P(a+|a) = P(a–|a) =1/2. (A4).

(OP-B) P(ab++|ab) = P(ab++|a)/2 + P(ab++|b)/2. (A0a).

(OP-C) P(ab++|abc) = P(ab++|a)/3 + P(ab++|b)/3 + P(ab++|c)/3

= 2P(ab++|ab)/3 + P(ab++|c)/3. (A0b).


(OP-D) ∴ P(ab++|ab) = 3P(ab++|abc)/2 – P(ab++|c)/2.


From PDF2 ([post=3191024]attached here[/post]), Table A3.c, eqn. (A3.3a):

(OP-E) P(ab++|ab) = 3P(ab++|abc)/2 – (Cac.Sbc/2 + Sac.Cbc/2)/2.


From PDF2 ([post=3191024]attached here[/post]), Table 1:

(OP-F) P(ab++|abc) = P3 + P4 = Sab/3 + (Cac.Sbc/2 + Sac.Cbc/2)/3.


From (OP-E) and (OP-F):

(OP-G) P(ab++|ab) = Sab/2; (A0c); and PDF2, Table 2;

in full accord with QM.

.......

My next Posts will be replies to arithmetic questions from JesseM and vanesch.

 

[JesseM]

In the normal notation used by Bell and other physicists, something like P(ab++|ab) would mean "the probability Alice gets result + with setting a and Bob gets + with setting B, given that Alice chose setting a and Bob chose setting b". Are you using a different meaning for what it means to condition on "ab", i.e. in your notation the "|ab)" part is not just telling us that Alice chose detector setting a and Bob chose detector setting b? Because I have no idea what you are conditioning on when you write terms like P(ab++|a) or P(ab++|abc). Please explain in words what it means, physically, to have the condition "a" or the condition "abc".

 

[JesseM]

Also, as a separate question, regardless of what your own notation means, would you agree that by the very definitions of P1-P8 the following must be true?

P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4

P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting c) = P2 + P4

P(Alice gets + and Bob gets + | Alice chose setting c and Bob chose setting b) = P3 + P7

If you disagree with any of these equations, it seems to me you fundamentally misunderstand what the probabilities P1-P8 on the Bell inequality page[/url] are supposed to represent the probabilities of...

 

[Gordon Watson]

..
Jesse, your arithmetic error can be seen by comparing your arithmetic [[post=3228834]here[/post]] with that in the OP.

Please note the following:


From the OP, or from PDF2 ([post=3191024]attached here[/post]), Table 1:

(OP-F) P(ab++|abc) = P3 + P4 = Sab/3 + (Cac.Sbc/2 + Sac.Cbc/2)/3.

So you correctly derive the RHS.


But you clearly misstate the LHS; attributing it to PDF2 ([post=3191024]attached here[/post]), Table 1.


Clearly, from Table 1, the LHS should read: P(ab++|abc) = P3 + P4.

NOT P(ab++|ab) = P3 + P4; as you assume.


If you want P(ab++|ab), then you can proceed as follows (from the OP):


From (OP-E) and (OP-F):

(OP-G) P(ab++|ab) = Sab/2;

see PDF2 [post=3191024]attached here[/post], Table 2; ALSO equation (A0c) in Appendix A there.


As it must be, the above result is in full accord with QM.


.......
As I repeatedly insist:

1. L*R would not be offered here for discussion IF it any-where disagreed with QM.

2. For that reason, ALL the QM results are derived, in detail, in PDF2 [post=3191024]attached here[/post], Appendix A:
.......


I will expand on this and address you other questions ASAP.

With best regards, Gordon

 

[JesseM]

Clearly, from Table 1, the LHS should read: P(ab++|abc) = P3 + P4.

NOT P(ab++|ab) = P3 + P4; as you assume.

As I said I have no idea what your notation |ab) and |abc) even mean, but I did not make an "arithmetic error" in [post=3228834]the post you referred to[/post] because when I wrote P(a+,b+|ab) I did not claim to be replicating your own notation, I was just assuming the standard meaning used by Bell and other physicists, in which something like P(a+,b+|ab) is shorthand for P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b). If you don't agree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) would be equal to P3 + P4, then as I said you are simply badly confused about what the probabilities P1-P8 are supposed to represent. But when I asked if you agreed that P(a+,b+|ab)=P3+P4, that's what I was asking about, I don't care if you have some bizarre notation where P(ab++|ab) means something totally different from P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b).

Please, taking precedence over all other comments/answers, I would like an answer to the question of whether you agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4.

 

[Gordon Watson]

As I said I have no idea what your notation |ab) and |abc) even mean, but I did not make an "arithmetic error" in https://www.physicsforums.com/showthread.php?p=3228834#post3228834the post you referred to because when I wrote P(a+,b+|ab) I did not claim to be replicating your own notation, I was just assuming the standard meaning used by Bell and other physicists, in which something like P(a+,b+|ab) is shorthand for P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b). If you don't agree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) would be equal to P3 + P4, then as I said you are simply badly confused about what the probabilities P1-P8 are supposed to represent. But when I asked if you agreed that P(a+,b+|ab)=P3+P4, that's what I was asking about, I don't care if you have some bizarre notation where P(ab++|ab) means something totally different from P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b).

Please, taking precedence over all other comments/answers, I would like an answer to the question of whether you agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4.

..
Jesse, Your arithmetic error* continues here; above.

In meeting your request for precedence, please note: NOT now, NOR ever, has there been any difference between our interpretations of P(ab++|ab)!

(I truly trust that you are not in the process of inventing a non-arithmetic black-hole, through which to escape?)

As to your claim to have been manipulating terms that you do not understand, that's another matter: But, clearly, the Conditioning Space (CS) in P(...|ab) is NOT the same as in P(...|abc).

To equate them here, as you do, is to err.
..........

Note to the Reader: PDF2 (referred to below) is attached as a pdf at https://www.physicsforums.com/showthread.php?p=3191024#post3191024.

Some essentials are addressed in the OP: https://www.physicsforums.com/showpost.php?p=3233997&postcount=1
..........

Jesse, You need to understand that my completion of PDF2, Table 1, is based on our mutually-agreed acceptance of the 8 equivalence classes that Sakurai lists. But all the |abc) conditioned Probabilities (all 8 of them; in Table 1, PDF2), relate to results derived from local realism (L*R). THEY are not derived from QM!

THUS, to equate Table 1 to QM -- to thereby derive P(ab++|ab) from Table 1 -- the CS must be reduced from |abc) to |ab).

The consequent L*R predictions THEN equate to quantum-mechanical predictions -- in full accord with QM. THIS IS DONE, for the Reader, correctly: See PDF2, Table 2, & Appendix A therein, & equations therein; with questions most welcome.So, in answer to you question: "DO I agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4?"A1: P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P(ab++|ab) = (equals) P(ab++|a) = P3 + P4, as specified in PDF2, Table A1. We agree; Yes?

A2: P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P(ab++|ab) ≠ (does not equal) P(ab++|abc) = P3 + P4, as specified in PDF2, Table 1. We agree; Yes? PS: If you disagree, please try to express your disagreement in mathematical terms only.

All terms are defined in PDF2, and their physical significance is evident from the numerical predictions that they deliver -- all in full accord with QM.

......
* Termed an "arithmetic" error because of your claim: "The basic laws of arithmetic show it's impossible to meet DrChinese's challenge in a way that gives results "in full accord with QM." " https://www.physicsforums.com/showpost.php?p=3228834&postcount=2 (Though that challenge has not yet been formalized, at PF, by DrChinese.)

 

[JesseM]

..
Jesse, Your arithmetic error* continues here; above.

In meeting your request for precedence, please note: NOT now, NOR ever, has there been any difference between our interpretations of P(ab++|ab)!

(I truly trust that you are not in the process of inventing a non-arithmetic black-hole, through which to escape?)

As to your claim to have been manipulating terms that you do not understand

No, I never "manipulated" any of your terms. I understand what P(a+,b+|ab) means in my notation (which is basically identical to the standard notation used by Bell and other physicists), as I said it is just meant to be shorthand for P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b). When someone is making far-fetched claims to have disproven a long-standing result in physics, I think it's their responsibility to take to the time to learn the standard theory and the standard notation, not to make up their own novel notation and expect everyone else to learn it.

But, clearly, the Conditioning Space (CS) in P(...|ab) is NOT the same as in P(...|abc).

To equate them here, as you do, is to err.

Stop misrepresenting me, I don't "equate" them at all, I said I have no idea what "conditioning space" you are referring to when you write "|abc)" (and I'm also not sure if when you write "|ab)" you mean the same as what I mean by it), and you ignored the request in my first post on this thread to explain in words what it means, physically, to have the condition "a" or the condition "abc", analogous to how I explained in words that when I write "|ab)", in my notation that is intended to be a shorthand for the condition "Alice chose setting a and Bob chose setting b".

But in any case, I never used your terms in any of my arguments, the meaning of your terms is irrelevant to my own summary of Sakurai's argument which I am trying to get you to actually address. I asked you to give precedence to answering a simple question, namely do you agree or disagree with the following:

P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4

And your response was:

So, in answer to you question: "DO I agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4?"A1: P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P(ab++|ab) = (equals) P(ab++|a) = P3 + P4 -- FROM PDF2, Table A1. We agree; Yes?

A2: P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P(ab++|ab) ≠ (does not equal) P(ab++|abc) = P3 + P4 -- FROM PDF2, Table 1. We agree; Yes?

Um, how is this not a blatant self-contradiction? In A1 you say P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "equals" P3 + P4, then in A2 you say P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "does not equal" P3 + P4. Are you trying to claim both can be true? Do you deny that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) is a well-defined expression that, for any specific experimental setup, must have some unique unchanging value, and that similarly P3 and P4 are supposed to have unique unchanging values for a given experimental setup?

 

[Gordon Watson]

No, I never "manipulated" any of your terms. I understand what P(a+,b+|ab) means in my notation (which is basically identical to the standard notation used by Bell and other physicists), as I said it is just meant to be shorthand for P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b). When someone is making far-fetched claims to have disproven a long-standing result in physics, I think it's their responsibility to take to the time to learn the standard theory and the standard notation, not to make up their own novel notation and expect everyone else to learn it.

Stop misrepresenting me, I don't "equate" them at all, I said I have no idea what "conditioning space" you are referring to when you write "|abc)" (and I'm also not sure if when you write "|ab)" you mean the same as what I mean by it), and you ignored the request in my first post on this thread to explain in words what it means, physically, to have the condition "a" or the condition "abc", analogous to how I explained in words that when I write "|ab)", in my notation that is intended to be a shorthand for the condition "Alice chose setting a and Bob chose setting b".

But in any case, I never used your terms in any of my arguments, the meaning of your terms is irrelevant to my own summary of Sakurai's argument which I am trying to get you to actually address. I asked you to give precedence to answering a simple question, namely do you agree or disagree with the following:

P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4

And your response was:

Um, how is this not a blatant self-contradiction? In A1 you say P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "equals" P3 + P4, then in A2 you say P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "does not equal" P3 + P4. Are you trying to claim both can be true? Do you deny that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) is a well-defined expression that, for any specific experimental setup, must have some unique unchanging value, and that similarly P3 and P4 are supposed to have unique unchanging values for a given experimental setup?

JesseM, this interim response is designed to clarify, and resolve, an evident difference between us:

I raise the matter directly (not being fond of "dog-whistling" at PF) because your final comment (above) is unbelievable (to me):

Quoting JesseM (above): "Um, how is this not a blatant self-contradiction?"

GW replies: In all the discussions at PF, relating to PDF2,

attached as a pdf at https://www.physicsforums.com/showthread.php?p=3191024#post3191024,

P3 and P4 can refer to FOUR (4) different PDF2 Tables (i.e., Tables 1, A1, A2, A3). So your "Um" statement refers to no contradiction whatsoever.

Nevertheless, pleased that you have captured what I originally wrote (and which I stand by), I have edited the phrasing in my original post to be absolutely clear how my maths and my words are to be understood.

QUESTION: In that a simple mathematical sequence is so badly misinterpreted by you, would you please specify explicitly what it is that you find (to use your terms) "crackpot" or "far-fetched" about anything that I have written in relation to PDF2?

Thanks.

 

[JesseM]

P3 and P4 can refer to FOUR (4) different PDF2 Tables (i.e., Tables 1, A1, A2, A3). So your "Um" statement refers to no contradiction whatsoever.

You seem to be incapable of explaining the physical meaning of any of your terms, you just refer me to mathematical definitions in tables without explaining what the probabilities actually are the probabilities of. In any case, if P3 and P4 do not have fixed values for a given experimental setup, then it's obvious that they can no longer mean what they were supposed to have meant on the Bell inequality page[/url], where P3 simply referred to the probability that the source will emit a pair of particles whose hidden variables imply the following predetermined results:

If Alice chooses detector setting a, the hidden variables on her particle imply she is predetermined to get result +
If Alice chooses detector setting b, the hidden variables on her particle imply she is predetermined to get result -
If Alice chooses detector setting c, the hidden variables on her particle imply she is predetermined to get result +
If Bob chooses detector setting a, the hidden variables on his particle imply he is predetermined to get result -
If Bob chooses detector setting b, the hidden variables on his particle imply he is predetermined to get result +
If Bob chooses detector setting c, the hidden variables on his particle imply he is predetermined to get result -

Likewise P4 refers to the probability that the source will emit a pair whose hidden variables give it these predetermined results:

If Alice chooses detector setting a, the hidden variables on her particle imply she is predetermined to get result +
If Alice chooses detector setting b, the hidden variables on her particle imply she is predetermined to get result -
If Alice chooses detector setting c, the hidden variables on her particle imply she is predetermined to get result -
If Bob chooses detector setting a, the hidden variables on his particle imply he is predetermined to get result -
If Bob chooses detector setting b, the hidden variables on his particle imply he is predetermined to get result +
If Bob chooses detector setting c, the hidden variables on his particle imply he is predetermined to get result +

Any time the source is about to emit a particle pair, there must be two unique probabilities P3 and P4 that the hidden variables will be associated with these two groups of predetermined results. If you think P3 can have multiple possible values in the context of a single experiment, and likewise P4, then you obviously are not defining them to just mean the probability the source will emit a particle pair with a given set of predetermined results, and so your arcane math is completely irrelevant to Bell's argument.

QUESTION: In that a simple mathematical sequence is so badly misinterpreted by you, would you please specify explicitly what it is that you find (to use your terms) "crackpot" or "far-fetched" about anything that I have written in relation to PDF2?

It's crackpot to write a bunch of probabilistic terms that no longer have the same meaning as identical-looking terms in Bell's proof, if your intent is to somehow refute his proof. It also seems rather crackpot to just write a bunch of abstract math and say "voila! I refuted Bell!" and yet refuse to answer simple questions about what your mathematical terms actually mean, physically. What does P3 refer to the probability of in one table vs. another? What is being conditioned on when you write terms like P(...|abc) or P(...|a)? These questions shouldn't be so hard for you to answer, if in fact there are any coherent physical conceptions behind your math at all.

 

[JesseM]

P3 and P4 can refer to FOUR (4) different PDF2 Tables (i.e., Tables 1, A1, A2, A3). So your "Um" statement refers to no contradiction whatsoever.

Incidentally Gordon, looking at your pdf I see that the tables A1, A2, A3 refer to different "reference orientations". Do the different reference orientations imply different ways of labeling the angles of the three allowed orientations of the polarizer/SG apparatus? If so, I already told you I wanted to define all angles relative to a fixed coordinate system, and you agreed to do so in future discussions with me--remember my comment from [post=3223794]post #158 on the other thread[/post]:

Your response below doesn't actually answer my primary question, can you please give a simple yes/no answer to whether you are willing, for the sake of discussion with me (what you do with others is your business), to phrase your arguments in terms of a single fixed coordinate system where each possible orientation of the polarizer/Stern-Gerlach device is assigned a fixed angle which doesn't change from one trial to another? Again, a yes/no answer to this question should take precedence over all other responses, such as responses to my other comments below.

And your response in [post=3223941]post #162[/post]:

YES: I am willing, for the sake of discussion with you (JesseM) (what I do with others is my business), to phrase my arguments in terms of a single fixed coordinate system where each possible orientation of the polarizer/Stern-Gerlach device is assigned a fixed angle which doesn't change from one trial to another.

So relative to a fixed coordinate system, would you still say that P3 can take multiple different values in the same experiment (and likewise P4), or would you agree that fixing both the coordinate system and the experimental setup should fix the value of P3 (and P4) to a unique value?

 

[Gordon Watson]

Jesse, this "QUOTE" of your post is giving a surprising result; as if revealing hidden content? I'll answer all the matters as they appear here.

PS: It would help me if you post questions in smaller posts. I believe that we are moving toward some important agreements.

No, I never "manipulated" any of your terms. I understand what P(a+,b+|ab) means in my notation (which is basically identical to the standard notation used by Bell and other physicists), as I said it is just meant to be shorthand for P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b).

As to our understandings re the meaning of P(a+,b+|ab), which equals P(ab++|ab) in my notation, we agree.

When someone is making far-fetched claims to have disproven a long-standing result in physics, I think it's their responsibility to take to the time to learn the standard theory and the standard notation, not to make up their own novel notation and expect everyone else to learn it.

Novel notations are required when "standard" notations miss or neglect important or new facts or insights. Perhaps such notations over-reach, and (in doing so) miss their (anticipated) far-reaching consequences; which is different to being a "far-fetched". (At least in so far as I understand Wheeler's Dictum.)

Stop misrepresenting me, I don't "equate" them at all, I said I have no idea what "conditioning space" you are referring to when you write "|abc)" (and I'm also not sure if when you write "|ab)" you mean the same as what I mean by it), and you ignored the request in my first post on this thread to explain in words what it means, physically, to have the condition "a" or the condition "abc", analogous to how I explained in words that when I write "|ab)", in my notation that is intended to be a shorthand for the condition "Alice chose setting a and Bob chose setting b".

P(ab++|abc) is defined in equation (A0b), PDF2.

In L*R we take Bell's triple of test settings (a, b, c) seriously, and conduct an analysis across all three. This, THE new idea, needs new notation.

The analytical significance is the equiprobable representation of each frame of reference.

A similar equiprobable distribution is seen in (A0a).P(a+|a) is defined in equation (A4), PDF2.

In L*R, this simple test yields the correct QM result; (A4) being processed "robot-like", and not with one eye on the QM result.

These are "analytic" considerations in L*R, leading to physically significant predictions.

But in any case, I never used your terms in any of my arguments, the meaning of your terms is irrelevant to my own summary of Sakurai's argument which I am trying to get you to actually address. I asked you to give precedence to answering a simple question, namely do you agree or disagree with the following:

P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4

And your response was:

Um, how is this not a blatant self-contradiction? In A1 you say P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "equals" P3 + P4, then in A2 you say P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "does not equal" P3 + P4. Are you trying to claim both can be true? Do you deny that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) is a well-defined expression that, for any specific experimental setup, must have some unique unchanging value, and that similarly P3 and P4 are supposed to have unique unchanging values for a given experimental setup?

Your claim of "blatant self-contradiction" was shown (in earlier post) to be false.

In L*R we allow you (or any critic), to select any three (3) Bell-test orientations (a, b, c) that you like.

If you check EVERY Probability in PDF2, every one of them is a fixed number; a specified function of your choice of a, b, c. Is this somehow different to your requirement that Probabilities "are supposed to have unique unchanging values for a given experimental setup"?

I believe that it is NOT different.

You seem to be incapable of explaining the physical meaning of any of your terms, you just refer me to mathematical definitions in tables without explaining what the probabilities actually are the probabilities of.

Jesse, I am reluctant to get into the physical significance of L*R terms until we at least agree on what the L*R analysis and maths says. Once we agree that they correctly deliver EVERY possible QM result correctly -- THEN -- it seems to me -- we need to assess L*R's physical significance and hence, whether L*R is truly "local and realistic."

For the record: Nothing here so far points to L*R being in error. Much points to many misunderstandings.

In any case, if P3 and P4 do not have fixed values for a given experimental setup, then it's obvious that they can no longer mean what they were supposed to have meant on the Bell inequality page[/url], where P3 simply referred to the probability that the source will emit a pair of particles whose hidden variables imply the following predetermined results:

If Alice chooses detector setting a, the hidden variables on her particle imply she is predetermined to get result +
If Alice chooses detector setting b, the hidden variables on her particle imply she is predetermined to get result -
If Alice chooses detector setting c, the hidden variables on her particle imply she is predetermined to get result +
If Bob chooses detector setting a, the hidden variables on his particle imply he is predetermined to get result -
If Bob chooses detector setting b, the hidden variables on his particle imply he is predetermined to get result +
If Bob chooses detector setting c, the hidden variables on his particle imply he is predetermined to get result -

Likewise P4 refers to the probability that the source will emit a pair whose hidden variables give it these predetermined results:

If Alice chooses detector setting a, the hidden variables on her particle imply she is predetermined to get result +
If Alice chooses detector setting b, the hidden variables on her particle imply she is predetermined to get result -
If Alice chooses detector setting c, the hidden variables on her particle imply she is predetermined to get result -
If Bob chooses detector setting a, the hidden variables on his particle imply he is predetermined to get result -
If Bob chooses detector setting b, the hidden variables on his particle imply he is predetermined to get result +
If Bob chooses detector setting c, the hidden variables on his particle imply he is predetermined to get result +

Any time the source is about to emit a particle pair, there must be two unique probabilities P3 and P4 that the hidden variables will be associated with these two groups of predetermined results. If you think P3 can have multiple possible values in the context of a single experiment, and likewise P4, then you obviously are not defining them to just mean the probability the source will emit a particle pair with a given set of predetermined results, and so your arcane math is completely irrelevant to Bell's argument.

Note that, in L*R, the hidden variables (HV) are real but hidden -- we can never know the orientation of an entangled particle's total spin. In L*R, the Probabilities are predicting the distribution of test outcomes. Test outcomes are determined by the interaction of the HV with the test device.

It's crackpot to write a bunch of probabilistic terms that no longer have the same meaning as identical-looking terms in Bell's proof, if your intent is to somehow refute his proof.

In my terms, it would be wrong to do as you suggest; so I do not do it! PS: "Crackpot" is a popular 'dog-whistle' in the Academy.

However, since my "bunch of probabilistic terms have EXACTLY the same meaning as identical-looking terms in Bell's proof, specifically terms having the form P(ab++|ab)," it should be clear to you that I am neither wrong nor crack-pot.

Further: Where I have different terms, they are defined in terms of simpler expressions which are equally valid in "Bell's proof". Thus P(ab++|a) and P(ab++|b) are shown to be equivalent to P(ab++|ab); see equation (A0a).

It also seems rather crackpot to just write a bunch of abstract math and say "voila! I refuted Bell!" and yet refuse to answer simple questions about what your mathematical terms actually mean, physically. What does P3 refer to the probability of in one table vs. another? What is being conditioned on when you write terms like P(...|abc) or P(...|a)? These questions shouldn't be so hard for you to answer, if in fact there are any coherent physical conceptions behind your math at all.

Trusting that the maths questions are answered satisfactorily above, let's resolve what the L*R mathematics mean, and what it is that they deliver, before attempting to address their physical significance.

Consequent discussions re physical significance and the underlying and coherent conceptualizations will then have added cogency.

PS: If the L*R maths does not deliver the L*R claims, then no arguments about physical significance or concepts will correct or save it.

 

[Gordon Watson]

Incidentally Gordon, looking at your pdf I see that the tables A1, A2, A3 refer to different "reference orientations". Do the different reference orientations imply different ways of labeling the angles of the three allowed orientations of the polarizer/SG apparatus?

No.

If so, I already told you I wanted to define all angles relative to a fixed coordinate system, and you agreed to do so in future discussions with me--remember my comment from [post=3223794]post #158 on the other thread[/post]:

And your response in [post=3223941]post #162[/post]:

So relative to a fixed coordinate system, would you still say that P3 can take multiple different values in the same experiment (and likewise P4), or would you agree that fixing both the coordinate system and the experimental setup should fix the value of P3 (and P4) to a unique value?

Yes; see my last post here; recalling that PDF2 contains four (4) P4-s, with varied Conditioning Spaces.

Table 1 is the key L*R result; Table 2 shows all the QM results correctly flowing from Table 1 -- as detailed in Appendix A.

If you want to move to the physical significance of L*R, are we now in agreement re L*R notation?

NOTE: It occurs to me that you keep referring to Sakurai's table.

I have been focussed on PDF2. That was the "counter-example" referred to in the original post:

Sakurai has P1-P8, with no numbers and no conditioning spaces. I simply took the wholly local and realistic L*R, accepted Sakurai's 8 equivalence classes, then allocated 8 probabilities (one each) to them, via L*R: PDF2, Table 1 is the result.

As expected (by me) the QM results drop (readily) from Table 1: Witness PDF2, Table 2.

 

[JesseM]

P(ab++|abc) is defined in equation (A0b), PDF2.

You just give an equation, not a conceptual definition of what physical condition is being denoted by "abc" (again, "ab" is easy to define conceptually, it just means that we're talking about a trial where Alice chose setting a and Bob chose setting b. Are you unable to give an equivalent conceptual definition of what physical conditions the notation "abc" represent?). What's more, your equation (A0b) involves terms like P(ab++|a), I already told you several times I don't know what it means to condition on "a" either (does it mean that Alice chose setting a, without telling us what Bob chose? Or does it mean Bob chose setting a? Or something completely different?)

In L*R we take Bell's triple of test settings (a, b, c) seriously, and conduct an analysis across all three. This, THE new idea, needs new notation.

The analytical significance is the equiprobable representation of each frame of reference.

You already promised a while ago to drop the "frames of reference" nonsense in all future posts to me, see my post #10. I'm not willing to deal with any posts of yours that fail to state everything in terms of a single fixed coordinate system, it simply makes these issues needlessly confusing when they should be rather simple. So please keep your promise, and restrict yourself solely to notation and equations that you still feel would be correct if we were using a single fixed coordinate system.

P(a+|a) is defined in equation (A4), PDF2.

Again you offer no conceptual definition of what it means to condition on "a", and your equations defining P(a+|a) involve terms which condition on "abc", but your definition of P(ab++|abc) in (A0b) involves terms which condition on "a", as I noted above, so I still don't know what any of these conditions mean physically.

 

[JesseM]

Yes; see my last post here; recalling that PDF2 contains four (4) P4-s, with varied Conditioning Spaces.

Arrrrgggghhhh if you have different probabilities with "varied conditioning spaces" you can't refer to them all with the same notation P4, a given notation has to have a unique meaning or else your equations will be totally incoherent to anyone trying to understanding them! Are you really completely unfamiliar with that different probabilities should be denoted with different symbols? In your tables you do have different notation for different conditional probabilities like P(04|abc) and P(A4|a), but then you go and refer to both as "P4", a major no-no that no good math teacher would let you get away with. And are you really so lost in the fog of your own thinking that you didn't understand that when I asked you if you agreed or disagreed that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4, I obviously did not intend notation like P3 to have multiple inconsistent meanings? I've noticed this problem in the past, you seem to have no ability to put yourself in someone else's shoes and see how equations might most naturally be interpreted by someone not already completely steeped in your own odd notation and thinking.

Sakurai has P1-P8, with no numbers and no conditioning spaces.

Yes, of course, if he intended them to be conditional probabilities he would have included that in the notation. I'm asking you to pull your head out of your own tangle of equations for just a second and deal with the actual argument on the Sakurai page (show some basic intellectual humility and consider that if this argument has stood unchallenged for decades, reviewed by thousands of smart physicists, there might be something to it that would make it worth considering carefully on its own terms before you excitedly jump into your own attempt to disprove Bell). Given Sakurai's definition of P1-P8 where each must have a single fixed value for a given experimental setup, not your bizarre multi-definitions (which again are a recipe for confusion, please always denote distinct probabilities with distinct notation), do you agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4? Please answer this question again, with the understanding that I am defining P3 and P4 as Sakurai does, not in terms of your own notation. Again, for reference here is the physical meaning of P3 and P4:

P3 simply referred to the probability that the source will emit a pair of particles whose hidden variables imply the following predetermined results:

If Alice chooses detector setting a, the hidden variables on her particle imply she is predetermined to get result +
If Alice chooses detector setting b, the hidden variables on her particle imply she is predetermined to get result -
If Alice chooses detector setting c, the hidden variables on her particle imply she is predetermined to get result +
If Bob chooses detector setting a, the hidden variables on his particle imply he is predetermined to get result -
If Bob chooses detector setting b, the hidden variables on his particle imply he is predetermined to get result +
If Bob chooses detector setting c, the hidden variables on his particle imply he is predetermined to get result -

Likewise P4 refers to the probability that the source will emit a pair whose hidden variables give it these predetermined results:

If Alice chooses detector setting a, the hidden variables on her particle imply she is predetermined to get result +
If Alice chooses detector setting b, the hidden variables on her particle imply she is predetermined to get result -
If Alice chooses detector setting c, the hidden variables on her particle imply she is predetermined to get result -
If Bob chooses detector setting a, the hidden variables on his particle imply he is predetermined to get result -
If Bob chooses detector setting b, the hidden variables on his particle imply he is predetermined to get result +
If Bob chooses detector setting c, the hidden variables on his particle imply he is predetermined to get result +

Any time the source is about to emit a particle pair, there must be two unique probabilities P3 and P4 that the hidden variables will be associated with these two groups of predetermined results. If you think P3 can have multiple possible values in the context of a single experiment, and likewise P4, then you obviously are not defining them to just mean the probability the source will emit a particle pair with a given set of predetermined results, and so your arcane math is completely irrelevant to Bell's argument.

Also, if you don't see why it must be true in a local realist theory that every particle pair must have hidden variables that predetermine their results for the three measurement axes, and thus fall into one of the 8 categories of predetermined results on Sakurai's table (like the two categories I explain in words above), and why each of these 8 categories must have a single well-defined probability for a given experimental setup, please tell me that you have trouble understanding why this would have to be the case and I'll try to explain in more detail. But hopefully you already understand why this would have to be true in any local realist theory that purports to explain how Alice and Bob always get opposite results whenever they choose the same detector setting, in spite of the fact that they choose detector settings randomly at a spacelike separation. And if you don't give values for P1-P8 when they are defined this way, then you haven't met DrChinese's challenge and have no basis for saying that you are offering a "local realist" model.

 

[Gordon Watson]

Arrrrgggghhhh if you have different probabilities with "varied conditioning spaces" you can't refer to them all with the same notation P4, a given notation has to have a unique meaning or else your equations will be totally incoherent to anyone trying to understanding them!

Are you really completely unfamiliar with that different probabilities should be denoted with different symbols? In your tables you do have different notation for different conditional probabilities like P(04|abc) and P(A4|a), but then you go and refer to both as "P4", a major no-no that no good math teacher would let you get away with.

And are you really so lost in the fog of your own thinking that you didn't understand that when I asked you if you agreed or disagreed that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4, I obviously did not intend notation like P3 to have multiple inconsistent meanings?

I've noticed this problem in the past, you seem to have no ability to put yourself in someone else's shoes and see how equations might most naturally be interpreted by someone not already completely steeped in your own odd notation and thinking.

Yes, of course, if he intended them to be conditional probabilities he would have included that in the notation.

I'm asking you to pull your head out of your own tangle of equations for just a second and deal with the actual argument on the Sakurai page (show some basic intellectual humility and consider that if this argument has stood unchallenged for decades, reviewed by thousands of smart physicists, there might be something to it that would make it worth considering carefully on its own terms before you excitedly jump into your own attempt to disprove Bell).

Given Sakurai's definition of P1-P8 where each must have a single fixed value for a given experimental setup, not your bizarre multi-definitions (which again are a recipe for confusion, please always denote distinct probabilities with distinct notation),


do you agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4? Please answer this question again, with the understanding that I am defining P3 and P4 as Sakurai does, not in terms of your own notation. Again, for reference here is the physical meaning of P3 and P4:

Also, if you don't see why it must be true in a local realist theory that every particle pair must have hidden variables that predetermine their results for the three measurement axes, and thus fall into one of the 8 categories of predetermined results on Sakurai's table (like the two categories I explain in words above), and why each of these 8 categories must have a single well-defined probability for a given experimental setup, please tell me that you have trouble understanding why this would have to be the case and I'll try to explain in more detail.

But hopefully you already understand why this would have to be true in any local realist theory that purports to explain how Alice and Bob always get opposite results whenever they choose the same detector setting, in spite of the fact that they choose detector settings randomly at a spacelike separation.

And if you don't give values for P1-P8 when they are defined this way, then you haven't met DrChinese's challenge and have no basis for saying that you are offering a "local realist" model.

Jesse, I'll be answering all questions in due course, and correcting your errors.

Re the latter, and the accompanying "groan" above, let's see if we can sort this important point out first:

You emphasize above: You "can't refer to them all with the same notation P4, a given notation has to have a unique meaning or else your equations will be totally incoherent to anyone trying to understanding them!"

.....

Now the above relates to an earlier question from you: JesseM: "Um, how is this not a blatant self-contradiction?"

I replied: "In all the discussions at PF, relating to PDF2 [post=3191024]attached here[/post], with partial-errata [post=3191819]here[/post],

P3 and P4 can refer to FOUR (4) different PDF2 Tables (i.e., Tables 1, A1, A2, A3).

So your "Um" statement refers to no contradiction whatsoever."

.........

NOW, referring to your latest groan, above: When we check out each use of (just for now) P4, we find that P4 is only ever used as a compact short-form identifier for a fully specified Probability (including a full specification of the equivalence class to which that Probability applies).

The relevant compact short-form identifiers are then used (for convenience; and in these places only) as an appropriate short-hand in corollary Tables A1.a, A2.b, A3.c; each of which is immediately below (and refers to) the Table containing the relevant compact identifier and its complete specification.

THEN, wherever the short-form identifier is used in a corollary Table, there is given an accompanying equation-identifier.

Reference to each detailed equation shows no reference to the short-form identifier at all; it having served its purpose in the compact data tabulation.

Does this clarify the situation, and reduce your pain? On this one point?

And, please, while you're at it, so that I can correct them: Please identify the equations which might be totally incoherent to anyone trying to understanding them!?

Thanks.

 

[JesseM]

Now the above relates to an earlier question from you: JesseM: "Um, how is this not a blatant self-contradiction?"

I replied: "In all the discussions at PF, relating to PDF2 [post=3191024]attached here[/post], with partial-errata [post=3191819]here[/post],

P3 and P4 can refer to FOUR (4) different PDF2 Tables (i.e., Tables 1, A1, A2, A3).

So your "Um" statement refers to no contradiction whatsoever."

.........

NOW, referring to your latest groan, above: When we check out each use of (just for now) P4, we find that P4 is only ever used as a compact short-form identifier for a fully specified Probability (including a full specification of the equivalence class to which that Probability applies).

The relevant compact short-form identifiers are then used (for convenience; and in these places only) as an appropriate short-hand in corollary Tables A1.a, A2.b, A3.c; each of which is immediately below (and refers to) the Table containing the relevant compact identifier and its complete specification.

THEN, wherever the short-form identifier is used in a corollary Table, there is given an accompanying equation-identifier.

Reference to each detailed equation shows no reference to the short-form identifier at all; it having served its purpose in the compact data tabulation.

Does this clarify the situation, and reduce your pain? On this one point?

No, this doesn't reduce my "pain" at what a terrible, confusing communicator you are. A good communicator who wasn't completely blind to how other people think wouldn't respond to a question like "do you agree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4" by immediately assuming the questioner was intimately familiar with pages and pages of "tables" he had written, and a good communicator would understand that if you're going to use a completely crazy notational practice like having P3 and P4 refer to multiple different probabilities, you need to at least explain this explicitly in your answer to the question rather than giving a completely crazy-looking response like first saying that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "equals" P3+P4 and then immediately going on to to say it is "not equal to" P3+P4. But really, there is no excuse for using P3 and P4 to refer to multiple distinct probabilities in the first place, this is just a completely godawful notation. In addition, a good communicator might also consider the possibility that when we are discussing Sakurai's Bell inequality, a question about P3 + P4 might refer to the probabilities that are labeled P3 and P4 on the Sakurai's Bell inequality page rather than to his own "tables", especially since in post #3 I said:

Also, as a separate question, regardless of what your own notation means, would you agree that by the very definitions of P1-P8 the following must be true?

P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4

...

If you disagree with any of these equations, it seems to me you fundamentally misunderstand what the probabilities P1-P8 on the Sakurai's Bell inequality page are supposed to represent the probabilities of

Maybe the part in bold was a hint that when I used the notation P3, P4 etc. I was referring to the probabilities on the Sakurai's Bell inequality page? Ya think?

Then to add to the groan-worthiness of your arguments, there's also this recent comment from post #11:

It's crackpot to write a bunch of probabilistic terms that no longer have the same meaning as identical-looking terms in Bell's proof, if your intent is to somehow refute his proof.

In my terms, it would be wrong to do as you suggest; so I do not do it! PS: "Crackpot" is a popular 'dog-whistle' in the Academy.

However, since my "bunch of probabilistic terms have EXACTLY the same meaning as identical-looking terms in Bell's proof, specifically terms having the form P(ab++|ab)," it should be clear to you that I am neither wrong nor crack-pot.

But when it comes to P1-P8, you are doing exactly what you denied doing above--taking probabilistic terms that have a particular meaning on the Sakurai Bell inequality page, and then completely redefining the meaning in your "tables". If P1-P8 don't refer specifically to the non-conditional probabilities that the source will emit particle pairs with different sets of predetermined responses to the three detector settings, then you are engaging in exactly the type of crackpot move I referred to.

And, please, while you're at it, so that I can correct them: Please identify the equations which might be totally incoherent to anyone trying to understanding them!?

Any and all that use a notation that is assigned multiple different meanings, your notion that this is OK for P1-P8 because they are (to use your made-up term) "short-form identifiers" is completely bizarre and no professional mathematician or physicists would ever do anything like this. Different probabilities must have different notations, period. Also, in the context of a discussion of Sakurai's Bell inequality which refers to the wikipedia page, it is incoherent to redefine any of the terms that appear on that page to mean something different in your equations from what they mean on the page; if you use the notation P1-P8, it must always refer to the non-conditional probabilities of different combinations of predetermined results, as defined on the table on the wiki page. If you want to have your own separate set of 8 probabilities on some table, make up your own new notation for them! It's really not that hard, the alphabet has a lot of letters besides "P"!

Now, please answer the question I put to you in post #14, the same question you were supposed to answer long ago:

Given Sakurai's definition of P1-P8 where each must have a single fixed value for a given experimental setup, not your bizarre multi-definitions (which again are a recipe for confusion, please always denote distinct probabilities with distinct notation), do you agree or disagree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4? Please answer this question again, with the understanding that I am defining P3 and P4 as Sakurai does, not in terms of your own notation.

With the additional request at the end of post #14 that you speak up if you don't understand why local realism demands that each particle pair have a set of predetermined results of the type appearing in the table on the wiki page:

Also, if you don't see why it must be true in a local realist theory that every particle pair must have hidden variables that predetermine their results for the three measurement axes, and thus fall into one of the 8 categories of predetermined results on Sakurai's table (like the two categories I explain in words above), and why each of these 8 categories must have a single well-defined probability for a given experimental setup, please tell me that you have trouble understanding why this would have to be the case and I'll try to explain in more detail. But hopefully you already understand why this would have to be true in any local realist theory that purports to explain how Alice and Bob always get opposite results whenever they choose the same detector setting, in spite of the fact that they choose detector settings randomly at a spacelike separation. And if you don't give values for P1-P8 when they are defined this way, then you haven't met DrChinese's challenge and have no basis for saying that you are offering a "local realist" model.

 

[Gordon Watson]

No, this doesn't reduce my "pain" at what a terrible, confusing communicator you are. A good communicator who wasn't completely blind to how other people think wouldn't respond to a question like "do you agree that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) = P3 + P4" by immediately assuming the questioner was intimately familiar with pages and pages of "tables" he had written, and a good communicator would understand that if you're going to use a completely crazy notational practice like having P3 and P4 refer to multiple different probabilities, you need to at least explain this explicitly in your answer to the question rather than giving a completely crazy-looking response like first saying that P(Alice gets + and Bob gets + | Alice chose setting a and Bob chose setting b) "equals" P3+P4 and then immediately going on to to say it is "not equal to" P3+P4. But really, there is no excuse for using P3 and P4 to refer to multiple distinct probabilities in the first place, this is just a completely godawful notation. In addition, a good communicator might also consider the possibility that when we are discussing Sakurai's Bell inequality, a question about P3 + P4 might refer to the probabilities that are labeled P3 and P4 on the Sakurai's Bell inequality page rather than to his own "tables", especially since in post #3 I said:

Maybe the part in bold was a hint that when I used the notation P3, P4 etc. I was referring to the probabilities on the Sakurai's Bell inequality page? Ya think?

Then to add to the groan-worthiness of your arguments, there's also this recent comment from post #11:

But when it comes to P1-P8, you are doing exactly what you denied doing above--taking probabilistic terms that have a particular meaning on the Sakurai Bell inequality page, and then completely redefining the meaning in your "tables". If P1-P8 don't refer specifically to the non-conditional probabilities that the source will emit particle pairs with different sets of predetermined responses to the three detector settings, then you are engaging in exactly the type of crackpot move I referred to.

Any and all that use a notation that is assigned multiple different meanings, your notion that this is OK for P1-P8 because they are (to use your made-up term) "short-form identifiers" is completely bizarre and no professional mathematician or physicists would ever do anything like this. Different probabilities must have different notations, period. Also, in the context of a discussion of Sakurai's Bell inequality which refers to the wikipedia page, it is incoherent to redefine any of the terms that appear on that page to mean something different in your equations from what they mean on the page; if you use the notation P1-P8, it must always refer to the non-conditional probabilities [SIC; emphasis added by GW] of different combinations of predetermined results, as defined on the table on the wiki page. If you want to have your own separate set of 8 probabilities on some table, make up your own new notation for them! It's really not that hard, the alphabet has a lot of letters besides "P"!

Now, please answer the question I put to you in post #14, the same question you were supposed to answer long ago:

With the additional request at the end of post #14 that you speak up if you don't understand why local realism demands that each particle pair have a set of predetermined results of the type appearing in the table on the wiki page:

Call me a slow learner, etc., or whatever, if you like.

I thought we were discussing the subject of the first post that relates to this matter:

PDF2 attached here https://www.physicsforums.com/showthread.php?p=3191024#post3191024,

with partial-errata here https://www.physicsforums.com/showpost.php?p=3191819&postcount=86

It is located in the thread entitled: "What's wrong with this local realistic counter-example to Bell's theorem?"

https://www.physicsforums.com/showthread.php?t=475076


Sakurai is hardly a counter-example to Bell's theorem. And I doubt we'd differ over what Sakurai claims.

BUT NOTE: In your terms, and in the interests of precision, Sakurai uses non-conditional probabilities.

WOW.

In PDF2, I specify the conditionals precisely.

More to come.

 

[JesseM]

It is located in the thread entitled: "What's wrong with this local realistic counter-example to Bell's theorem?"

As I said, unless you provide values for the probabilities P1-P8 as defined the way they are defined on the Sakurai page (probabilities of the source emitting particles whose hidden variables give them different combinations of predetermined results for the three detector settings), then you haven't actually provided a "local realistic" model at all.

Sakurai is hardly a counter-example to Bell's theorem. And I doubt we'd differ over what Sakurai claims.

It's not at all clear to me you have a good understanding of Sakurai's argument, which is exactly why I was trying to get you to go through it in a step-by-step manner and show me which step you first disagreed with. Remember, my argument was that if you look at Sakurai's argument then you see that "basic arithmetic" shows it's impossible for a local realistic theory to violate Bell inequalities, and you had some objection to this, including my words "basic arithmetic" in the thread title and saying in the opening post that you wanted to "focus on arithmetic issues". So it would be worth our time to go over Sakurai's argument, no? If your only purpose on this forum is to advertise a long pdf full of poorly-defined terms and equations whose relevance to Bell's argument is hardly apparent, and you have no intention of seriously engaging with the details of the actual derivation of the claim that local realism implies Bell inequalities (by going through the derivation in a step-by-step manner and saying where you first disagree with it), then you really shouldn't be posting here at all. This forum does allow people with questions about mainstream results to discuss those questions, but that doesn't extend to people who just want to advertise that they are a brilliant genius who has overthrown some mainstream result and who refuse to actually engage in thoughtful discussion of the reasoning/evidence for that mainstream result.

 

[Gordon Watson]

As I said, unless you provide values for the probabilities P1-P8 as defined the way they are defined on the Sakurai page (probabilities of the source emitting particles whose hidden variables give them different combinations of predetermined results for the three detector settings), then you haven't actually provided a "local realistic" model at all.

It's not at all clear to me you have a good understanding of Sakurai's argument, which is exactly why I was trying to get you to go through it in a step-by-step manner and show me which step you first disagreed with. Remember, my argument was that if you look at Sakurai's argument then you see that "basic arithmetic" shows it's impossible for a local realistic theory to violate Bell inequalities, and you had some objection to this, including my words "basic arithmetic" in the thread title and saying in the opening post that you wanted to "focus on arithmetic issues". So it would be worth our time to go over Sakurai's argument, no? If your only purpose on this forum is to advertise a long pdf full of poorly-defined terms and equations whose relevance to Bell's argument is hardly apparent, and you have no intention of seriously engaging with the details of the actual derivation of the claim that local realism implies Bell inequalities (by going through the derivation in a step-by-step manner and saying where you first disagree with it), then you really shouldn't be posting here at all. This forum does allow people with questions about mainstream results to discuss those questions, but that doesn't extend to people who just want to advertise that they are a brilliant genius who has overthrown some mainstream result and who refuse to actually engage in thoughtful discussion of the reasoning/evidence for that mainstream result.

I understand the mainstream result well enough.

The issue we are discussing is a non-mainstream result (designated L*R) which delivers results in full accord with QM.

Its basis is outlined in PDF2.

In agreement with QM, the non-mainstream result (L*R) arrives at a similar conclusion to QM: Bell's theorem cannot be rationally constructed from within QM.

SO, equally: Bell's theorem cannot be rationally constructed from within L*R, which a wholly local and realistic theory.

My "questioning thread" ("What's wrong with this local realistic counter-example to Bell's theorem?") therefore sought to actually engage in thoughtful discussion of reasoning/evidence that might indicate that the non-mainstream result (L*R) is wrong.

More soon.

 

[JesseM]

I understand the mainstream result well enough.

You can assert that, but if you aren't willing to actually discuss the specific point in the mainstream result you disagree with it's not very convincing.

The issue we are discussing is a non-mainstream result (designated L*R) which delivers results in full accord with QM.

Its basis is outlined in PDF2.

If your pdf does not assign probabilities to the P1-P8 as defined on the Sakurai Bell inequality page, then there is no reason to think your equations qualify as a "local realistic" model at all. Again, you need to show whether you "understand the mainstream result", not just blithely assert it, by engaging with the derivation of the result, specifically answering my last question about whether you understand that local realism demands that each particle pair have some set of predetermined results for each of the three measurement settings:

Also, if you don't see why it must be true in a local realist theory that every particle pair must have hidden variables that predetermine their results for the three measurement axes, and thus fall into one of the 8 categories of predetermined results on Sakurai's table (like the two categories I explain in words above), and why each of these 8 categories must have a single well-defined probability for a given experimental setup, please tell me that you have trouble understanding why this would have to be the case and I'll try to explain in more detail. But hopefully you already understand why this would have to be true in any local realist theory that purports to explain how Alice and Bob always get opposite results whenever they choose the same detector setting, in spite of the fact that they choose detector settings randomly at a spacelike separation. And if you don't give values for P1-P8 when they are defined this way, then you haven't met DrChinese's challenge and have no basis for saying that you are offering a "local realist" model.

If you aren't willing to engage with these sorts of questions about the derivation of the mainstream result, but just want to continue to advertise your pdf as "local realist" without dealing with the mainstream understanding of what that implies, then I don't think this sort of thing belongs on these forums at all and I will just report these threads to the mods in hopes that they close them.

 

[Gordon Watson]

You can assert that, but if you aren't willing to actually discuss the specific point in the mainstream result you disagree with it's not very convincing.

If your pdf does not assign probabilities to the P1-P8 as defined on the Sakurai Bell inequality page, then there is no reason to think your equations qualify as a "local realistic" model at all. Again, you need to show whether you "understand the mainstream result", not just blithely assert it, by engaging with the derivation of the result, specifically answering my last question about whether you understand that local realism demands that each particle pair have some set of predetermined results for each of the three measurement settings:

If you aren't willing to engage with these sorts of questions about the derivation of the mainstream result, but just want to continue to advertise your pdf as "local realist" without dealing with the mainstream understanding of what that implies, then I don't think this sort of thing belongs on these forums at all and I will just report these threads to the mods in hopes that they close them.

Please clarify the phrasing emphasized by me above.

For example: Are you implying that local realism is restricted to Mermin's "instruction sets"?

If not: How does you "demand" differ from Mermin's well-published ideas about local realism?

 

[JesseM]

Please clarify the phrasing emphasized by me above.

For example: Are you implying that local realism is restricted to Mermin's "instruction sets"?

Not sure what you mean by "restricted to", the hidden variables may be vastly more complicated than a simple list of predetermined results, but it must nevertheless be true that the results for each detector setting are predetermined by the hidden variables of the two particles after they have been emitted but prior to the moment when Alice and Bob make a choice of detector settings (at least this must be true in any Bell experiment where Alice and Bob are guaranteed to get opposite--or identical--results each time they choose the same setting). If you don't understand why this must be the case, we should probably go back to my basic definition of local realism offered in [post=3196744]post #94[/post] from the other thread (also see my response to your question about the meaning of my phrase "irreducibly nonlocal" in [post=3213709]post #135[/post])

By the way, I wouldn't have expected you to dispute the notion of predetermined results under local realism, as [post=2794546]this post[/post] from "JenniT" seemed to agree with such a notion:

Also, do the polarizers reorient the spin vectors in a deterministic way, so that if both polarizers are at the same angle and both spin vectors start out at the same k before passing through the polarizer, they are guaranteed to both end up parallel or both end up orthogonal, with no chance of one ending up parallel to the polarizer and one ending up orthogonal?

This is Mermin's baby. In my view the answer here is Yes.

If it is something else, like a different singlet state, we just change the correlation and proceed.

If so we can say that at the moment the two particles first begin their journey from the source, their initial spin vectors should give them a predetermined answer to what direction they would end up if they met a polarizer at any given angle, right?

That is correct.

For example, we might have a situation where one particle's initial spin vector (the spin vector assigned to it by the source, prior to encountering the polarizers) is such that it if it encountered a polarizer at a=30 it would be predetermined to end up parallel to it, predetermined to come out orthogonal a polarizer at a=60, and predetermined to come out parallel to a polarizer at a=120. Is this how you see things,...

Yes.

Is your current opinion different from the one expressed in this post?