Bell's theorem & Bell's argument: Who is right, Fred or me?

[Gordon Watson]

Bell's theorem and Bell's argument: Who is right, Fred or me?

A certain Fred likes to say: "It's mathematically impossible for anything to violate an inequality of Bell's type (BI)."

I think Fred's wrong, and here's why; imho: EVERY BI and EVERY Bell-supporting work is infected with a BUG! Thus:

A recent draft of mine -- http://vixra.org/pdf/1511.0035v1.pdf -- titled "Bell's theorem is silly, false, misleading, interesting" -- starts with 2 simple formulations [(1),(2) in my draft] that define EPRB.

Written in Bell's terms, (1)-(2) are: (i) consistent with Bell's acceptance of discrete λ. (ii) as one with his goal of "restoring causality and locality" to QM. (iii) as one with his initial acceptance of Einstein-locality. (As is well-known, he later wimps out big-time on locality -- see para. #4.15 in the draft -- when all he had to do was fix the bug.)

The next equation [(3) in my draft] defines Bell's first BI, and I claim to refute it!

That's because, imho, this (the first) BI is established via a LATER analytical-error by Bell: an error that is NOT in those first 2 defining formulations.

In other words: Bell starts with FACTS consistent with EPRB, then errs by introducing NAIVE-REALISM in his subsequent analysis.

Clearly, EPRB is not such an experiment. So EPRB violates BI. So Fred is wrong (in the nicest possible way)!

QED?

PS: My essay attempts to make a NOVEL -- but is it? -- point. Bell's theorem, every BI (including CHSH) -- in fact all Bellian work -- is INFECTED with a BUG. And that bug is as simple as this -- and therefore easily fixed -- the inappropriate use of NAIVE-REALISM! But I digress.

Gordon

[FrediFizzx]

The next equation [(3) in my draft] defines Bell's first BI, and I claim to refute it!

Your eq. (3) is not strictly Bell's first inequality though it is somewhat compatible with his argument. Yes, we know that there is a "bug" in Bell's argument. Basically it is "rigged" against both LHV models and QM models. I suppose that is essentially what your argument is.

[Gordon Watson]

The next equation [(3) in my draft] defines Bell's first BI, and I claim to refute it!

Your eq. (3) is not strictly Bell's first inequality though it is somewhat compatible with his argument. Yes, we know that there is a "bug" in Bell's argument. Basically it is "rigged" against both LHV models and QM models. I suppose that is essentially what your argument is.

Fred, we appear to differ here; quite a bit. I think your comments miss "essentially what my argument is". But maybe I'm the one missing something?

In my terms, Bell's argument is not "rigged", it's just a blunder. And we find the source of his blunder in naive-realism, "Bell's error" -- see his (14b) = (14a) error -- ie, an error in the context of EPRB. (And we find the same error in CHSH; see their first equation.)

Now, re this: "Your eq. (3) is not strictly Bell's first inequality though it is somewhat [???] compatible with his argument."

A: Bell says it's a matter of indifference whether λ is discrete or continuous. (I presume he thought all bases were covered.) So, thanks to his indifference and with λ discrete, his integral in his (2) becomes a sum: and he remains indifferent. [Q: But you do not remain indifferent?]

B: He then says that this sum should equal the QM expectation, as in his (3).

C: He then promises to show that this is impossible ... then blunders!

D: What am I missing? Or adding? Thanks; G
.

[FrediFizzx]

Fred, we appear to differ here; quite a bit. I think your comments miss "essentially what my argument is". But maybe I'm the one missing something?

In my terms, Bell's argument is not "rigged", it's just a blunder. And we find the source of his blunder in naive-realism, "Bell's error" -- see his (14b) = (14a) error -- ie, an error in the context of EPRB. (And we find the same error in CHSH; see their first equation.)

Now, re this: "Your eq. (3) is not strictly Bell's first inequality though it is somewhat [???] compatible with his argument."

A: Bell says it's a matter of indifference whether λ is discrete or continuous. (I presume he thought all bases were covered.) So, thanks to his indifference and with λ discrete, his integral in his (2) becomes a sum: and he remains indifferent. [Q: But you do not remain indifferent?]

B: He then says that this sum should equal the QM expectation, as in his (3).

C: He then promises to show that this is impossible ... then blunders!

D: What am I missing? Or adding? Thanks; G
.

I pretty much think that you are showing that Bell's blunder is that his argument is "rigged" against both LHV and QM models since using +/-1 outcomes, -a.b cannot be achieved by either one. You say Bell is silly when equating eq. (14a) with (14b). That is where the "rigging" happens.

It is true that the result of your eq. (3) is part of what Bell was claiming. However, his first inequality claimed/showed more than just that. So... using the strict form of his first inequality, it is true when I say that nothing can violate it.

[Gordon Watson]

Fred, we appear to differ here; quite a bit. I think your comments miss "essentially what my argument is". But maybe I'm the one missing something?

In my terms, Bell's argument is not "rigged", it's just a blunder. And we find the source of his blunder in naive-realism, "Bell's error" -- see his (14b) = (14a) error -- ie, an error in the context of EPRB. (And we find the same error in CHSH; see their first equation.)

Now, re this: "Your eq. (3) is not strictly Bell's first inequality though it is somewhat [???] compatible with his argument."

A: Bell says it's a matter of indifference whether λ is discrete or continuous. (I presume he thought all bases were covered.) So, thanks to his indifference and with λ discrete, his integral in his (2) becomes a sum: and he remains indifferent. [Q: But you do not remain indifferent?]

B: He then says that this sum should equal the QM expectation, as in his (3).

C: He then promises to show that this is impossible ... then blunders!

D: What am I missing? Or adding? Thanks; G
.

I pretty much think that you are showing that Bell's blunder is that his argument is "rigged" against both LHV and QM models since using +/-1 outcomes, -a.b cannot be achieved by either one. You say Bell is silly when equating eq. (14a) with (14b). That is where the "rigging" happens.

It is true that the result of your eq. (3) is part of what Bell was claiming. However, his first inequality claimed/showed more than just that. So... using the strict form of his first inequality, it is true when I say that nothing can violate it.

Fred,

1: If I accidentally/carelessly put too much lead in my saddle-bags, I blunder! I don't rig the race. Bell accidentally/carelessly put naive-realism in his argument. He blundered and rigged nothing. Rigging to me requires intention! Bell blundered and got carried away: blundering on (adding blarney) when CHSH followed suit. ...

2: My LHV model uses ±1 outcomes and achieves -a.b. But you say that cannot be achieved. Who blunders here? And where? Or is my model not LHV?

Thanks; G

[FrediFizzx]

Fred,

1: If I accidentally/carelessly put too much lead in my saddle-bags, I blunder! I don't rig the race. Bell accidentally/carelessly put naive-realism in his argument. He blundered and rigged nothing. Rigging to me requires intention! Bell blundered and got carried away: blundering on (adding blarney) when CHSH followed suit. ...

2: My LHV model uses ±1 outcomes and achieves -a.b. But you say that cannot be achieved. Who blunders here? And where? Or is my model not LHV?

Thanks; G

1: That is just semantics. I never said that Bell intentionally rigged it. I am just saying that his argument is "rigged" against both LHV and QM. That is why "rigged" is in quotes.

2: Where is your simulation using +/-1 outcomes that produces the negative cosine curve?

[Gordon Watson]

2: Where is your simulation using +/-1 outcomes that produces the negative cosine curve?

You mean on two separate computers?

[FrediFizzx]

2: Where is your simulation using +/-1 outcomes that produces the negative cosine curve?

You mean on two separate computers?

The simulation doesn't have to be on two computers. Bell's argument is right in that using +/-1 outcomes a LHV model cannot produce the negative cosine curve. But he missed that quantum theory can't do it either. Only non-local hidden variable models can do it. However, that only applies to R^3. A LHV model can do it in S^3. With the implication that QM can do it in S^3 also.

[Joy Christian]

Gordon,

I looked at your paper. As far as I can see you do not have a model for what is observed in the experiments. The following is observed in the experiments:

< A(a) B(b) > = -a.b ,

< A(a) > = 0 ,

and

< B(b) > = 0 .

Here

A(a) = +/-1 ,

B(b) = +/-1 ,

< ... > represent averages,

and a and b are the directions about which the spins (or photons) are observed.

Whatever you have in your paper does not reproduce these results --- even non-locally.

You do not have to produce a simulation. Just reproduce the above results analytically to convince us that you have a model. At the moment you don't have a model.

[Gordon Watson]

Thanks Joy,

Referring to http://vixra.org/pdf/1511.0035v1.pdf and seeking to clarify our differences, I'll put my response beside your key points and after a colon.

The following is observed in the experiments;

< A(a) B(b) > = -a.b: Doesn't my (3) meet this specification?

< A(a) > = 0: Doesn't my #3.7 meet this specification?

and

< B(b) > = 0: Doesn't my #3.7 meet this specification?

Here

A(a) = +/-1: Agreed.

B(b) = +/-1: Agreed.

< ... > represent averages: Agreed.

and a and b are the directions about which the spins (or photons) are observed: Fixing a minor typo (changing "spins" to spin-half particles), I agree.

I look forward to further comments. Thanks again; G

[Joy Christian]

Gordon, I am unable to make any sense of your (3) or #3.7. As far as I can see, you do not have a model, let alone a local model.

[FrediFizzx]

Gordon, I am unable to make any sense of your (3) or #3.7. As far as I can see, you do not have a model, let alone a local model.

#3.7 is OK. If you get A to be +1 half the time, <A> will be close to zero.

[Gordon Watson]

Gordon, I am unable to make any sense of your (3) or #3.7. As far as I can see, you do not have a model, let alone a local model.

#3.7 is OK. If you get A to be +1 half the time, <A> will be close to zero.

As I see it:

My (3) is OK. That's how my experimental results are obtained; via summations over coincident discrete outcomes; coincident to ensure properly-paired lambdas. The equating to -a.b, to an adequate accuracy, comes via the appropriate (high) number of coincidences n.

Clarifying Fred's remark: (3.7) is fine. If you get A^+ half the time then <A> = 0. Same for B^+.

In that I use classical probability theory in a local realistic manner, my essay provides an epistemological model. My ontological model (with particles, detectors and event-by-event interactions) is based on the epistemic one; probably best incorporated in some detail in an Appendix (when I address the "interesting" part of BT).

Thanks for taking the time to comment: In that my writing tends to be "short and sweet" -- with most details covered sweetly but maybe too tersely -- this an area where I can always benefit from tough feedback! And I always appreciate it (despite my habitual defending; only when justified, I hope) .

[FrediFizzx]

My ontological model (with particles, detectors and event-by-event interactions) is based on the epistemic one; probably best incorporated in some detail in an Appendix (when I address the "interesting" part of BT).

Yeah, you need to have some A and B functions that can produce at least analytically what Joy said above. You can't just state the results and call it a model. But you don't need a LHV model to show that Bell was wrong as you have already seen. Though it does help. So far Joy's model is the best and is based on a very simple common sense postulate. And leads to some other very remarkable new physics. You should use it in your work if you can.

[Mikko]

Gordon, I am unable to make any sense of your (3) or #3.7.

The text is not as clear as it should be. (3) should be split and each part explained separately.
First two different notations are given for the average value <AB>. Then the value is expressed in terms of observations at the two detectors. The use of λ' is unnecessary but not wrong although λ+λ' = 0 is more restrictive than necessary (there is no reason to require that + be a valid operation for the type of λ).
The next expression is equivalent as a consequence of the perfect anticorrelation when the same measurement direction is chosen.
The last inequality expresses that the quantum mechanical result is impossible (although it should add that certain angles are exceptions.

[FrediFizzx]

The use of λ' is unnecessary but not wrong although λ+λ' = 0 is more restrictive than necessary (there is no reason to require that + be a valid operation for the type of λ).

You can see in paragraph 1.3 that his λ is tied to angular momentum so he is just conserving angular momentum. As λ defined as a unit vector in 3-space, then λ = -λ'. I don't think there has been any success in making that the hidden variable. Though it is physical.

[Gordon Watson]

My ontological model (with particles, detectors and event-by-event interactions) is based on the epistemic one; probably best incorporated in some detail in an Appendix (when I address the "interesting" part of BT).

Yeah, you need to have some A and B functions that can produce at least analytically what Joy said above. You can't just state the results and call it a model. But you don't need a LHV model to show that Bell was wrong as you have already seen. Though it does help. So far Joy's model is the best and is based on a very simple common sense postulate. And leads to some other very remarkable new physics. You should use it in your work if you can.

Correct Fred, re my lovely A and B; both true mathematical functions, as befits BT's premises (by my reading).

My model is based on GA in 3-space; with s = 1/2 and s = 1 in the same formulation: so I haven't kept pace with Joy's work.

And re that, in case you didn't know: I am one of Joy's earliest fans!

PS: Thanks again for SPF!!!

[FrediFizzx]

Correct Fred, re my lovely A and B; both true mathematical functions, as befits BT's premises (by my reading).

In eq. (2) you just state as a "Given" that A and B are +/-1. You should have actual functions for A and B that can produce the + or - one analytically. You really don't have any kind of good model until you can do that.

[Gordon Watson]

Gordon, I am unable to make any sense of your (3) or #3.7.

The text is not as clear as it should be. (3) should be split and each part explained separately.
First two different notations are given for the average value <AB>. Then the value is expressed in terms of observations at the two detectors. The use of λ' is unnecessary but not wrong although λ+λ' = 0 is more restrictive than necessary (there is no reason to require that + be a valid operation for the type of λ).
The next expression is equivalent as a consequence of the perfect anticorrelation when the same measurement direction is chosen.
The last inequality expresses that the quantum mechanical result is impossible (although it should add that certain angles are exceptions.

Mikko, thanks, and please do not hold back. You have some helpful comments here! Indeed: if you, a presumed (by me) Bellian, want to expand my essay to critique or refute it, I'd be very happy to check that the expansion was fair and devoid of Bellian oversights.

Alas, I have to say it all seems so clear to me: in that it is all there (pretty much). However (thank you Mikko): when I do the next revision I will start on a proper draft introduction. There I will spell out that the essay is a reply to Gill (2015) -- that is: Gill, R.G. (2015). Personal communication, 22 Sept. 2015. So it is written for a Bellian that is (one expects/hopes/prays) fair and open-minded and fully conversant with BT and the related experiments. Then, for the non-Bellian reader (NBR): every paragraph and equation is numbered so that they can join the discussion via specific focussed questions, criticism, etc. So when you correctly write -- "The next expression is equivalent as a consequence of the perfect anticorrelation when the same measurement direction is chosen" -- I take that to be instantly understood by a Bellian. And I also take it that a keen NBR will read Bell (1964) -- available online via my References -- and see that sort of stuff there. NB: I do not myself see that any of my material is beyond a questing and questioning NBR!

Re (3). I trust it is now clearer why I do not see two different notations in (3). And I trust you realise that it is fully equivalent to Bell (1964: eq. 3)? That it better reflects how the experimental values are determined?

Yes, the notation is different to Bell's. Indeed, if Bell had used mine he might not have blundered via Bell's error -- Bell's realism; BLNR = Bell's local naive-realism -- in his analysis with that erroneous (14a) = (14b): erroneous, with certainty, under EPRB. PS: I will also spell out that pristine λ is taken to be a Multivector in 3-space and show how that works (in an Appendix).

Thanks again! Gordon

[Gordon Watson]

Correct Fred, re my lovely A and B; both true mathematical functions, as befits BT's premises (by my reading).

In eq. (2) you just state as a "Given" that A and B are +/-1. You should have actual functions for A and B that can produce the + or - one analytically. You really don't have any kind of good model until you can do that.

I trust my reply to Mikko helps to make better sense of my essay. It is answering a Bellian's question: "What is your problem with BT?" So I don't put the actual functions in the early text since the focus is initially on my problem with BT. I'll put mathematically-correct functions of (a, λ) and (b, λ') in the Appendix.