Hidden Variables: Just a little shy? by Anthony John Garrett

Thank you, Anton, for posting this enjoyable and thought-provoking essay. I too enjoyed the comment "Never be put off, for only seekers find. By doing this you become part of a great project.". Seekers should not be satisfied. We should be able to understand either how to predict what a single electron will do in an SG apparatus, or why such a prediction is not possible.

You know my take on this. I believe that there is an underlying model that can explain what we can and cannot predict and how to make such predictions. I will keep Seeking...

Dear Anton,

I welcome your essay and our many shared interests: eg, with my emphasis throughout, we are both for hidden variables at a deeper level of ontology. I'm guessing that we differ re this next? In my essay, I claim to have found them.

However, surprised by our differing approaches, please note that I here (as elsewhere) a receptive seeker for evidence that counters my classical views; firm, not aggressive. Thus:

Q-A: Nino, p.7: "Never be put off, for only seekers find. By doing this you become part of a great project."

From your 1990 FOOP essay, and your comments above: am I right in thinking that part of your part in that great project is to defend Bell's theorem and nonlocality?

Q-B: Neo, p.2: "Suppose that the result of measuring some variable for a particle is determined by the value of a variable that is internal to the particle - a hidden variable. I am being careful not to say that the particle 'had' the value of the variable that was measured; that is a stronger statement. The result of the measurement on the particle tells us something about the value of its internal variable. Suppose this particle is correlated with another - for example, if the pair had zero combined angular momentum when they were in contact previously. That correlation now tells you something about the internal variable of the second particle. ... ." [See my related comments on my FQXi essay-site.]

So, do you agree with this next statement? It follows that you and I can logically infer (from one result) to a correlated property of the other (twinned) particle.

Q-C: So why does our modern friend Neo infer to nonlocality?

Neo, p.2 continues: " ...In situations like this a man called Bell derived an inequality. You can't do better than an inequality because of the openness about how the internal variables govern the outcome of measurements. Bell's inequality is violated by observations on many pairs of particles, whose statistics are predicted correctly by quantum mechanics. The only physical assumption involved in the reasoning is that the result of a measurement on a particle is determined by the value of a variable internal to it - locality, in other words. So a measurement made on one particle alters what would have been seen if a measurement had been made on its partner. That's the operative meaning of nonlocality."

Q-D: In my essay, More realistic fundamentals: quantum theory from one premiss, at p.5, I derive the EPRB-expectation classically. At p.8, I advance a classical refutation of Bell's theorem.

So Neo might disagree, but how do you respond, please?

Q-E: We both like Mermin's version of GHZ. Would you like to see that result derived classically?

With best regards, and enough for now,

Gordon Watson

More realistic fundamentals: quantum theory from one premiss.

Anton,

Interesting. Have you read the essay (is it Phillips?) identifying that the Cos curve distributions are ubiquitous in all of nature?

Can you pass me a link to your finding/paper?

Mine shows non-locality isn't required in the case of Bob & Alice correlations, so on the face of it one or other may be flawed, or maybe not. Lets study each others. I'd like you to spot the flaw in mine if there is one. Plenty have tried but most aren't as well qualified as you may be.

Very best

Peter

Anton, if/when you reply to my post, please copy it to my essay-thread so that I'm alerted to it. I'm having trouble keeping abreast of many good discussions this year.

Many thanks; Gordon More realistic fundamentals: quantum theory from one premiss.

Anton, if/when you reply to my post, please copy it to my essay-thread so that I'm alerted to it. I'm having trouble keeping abreast of many good discussions this year.

Many thanks; Gordon More realistic fundamentals: quantum theory from one premiss.

Dear Anthony,

I highly appreciate your well-written essay in an effort to understand.

It is so close to me. «Regard all strange outworkings of quantum mechanics as information about the hidden variables. Purported no-hidden-v ariables theorems that are consistent with quantum mechanics must contain extra assumptions or axioms, so put such theorems to work by arranging that your research violates those assumptions». «Never be put off, for only seekers find. By doing this you become part of a great project».

I hope that my modest achievements can be information for reflection for you.

Vladimir Fedorov

https://fqxi.org/community/forum/topic/3080

Dear Anton; further to my earlier comments, please: Since we cannot both be right, would you mind commenting on my half-page refutation of Bell's theorem?

See ¶13 in More realistic fundamentals: quantum theory from one premiss.

NB: I clarify Bell's 1964-(1) functions by allowing that, pairwise, the HV (λ) heading toward Alice need no be the same as that (μ) heading toward Bob; ie, it is sufficient that they are highly correlated via the pairwise conservation of total angular momentum. Thus, consistent with Bell's 1964-(12) normalization condition:

[math]\int\!d\boldsymbol{\lambda}\:\rho(\boldsymbol{\lambda})=\int\!d\boldsymbol{\mu}\:\rho(\boldsymbol{\mu})=1.\;\;\;(1)[/math]

Further, in my analysis: after leaving the source, each pristine particle remains pristine until its interaction with a polarizer. Then, in that I allow for perturbative interactions, my use of delta-functions represents the perturbative impact of each such interaction.

My equation (26) then represents the distribution of perturbed particles proceeding to Alice's analyzer. Thus (with b and μ similarly for Bob):

[math]\int\!d\lambda\;\rho(\lambda)_{Alice}=\tfrac{1}{2}\int\!d\;\lambda[\delta\,(\lambda\sim a^{+})+\delta\,(\lambda\sim a^{-})]=1.\;\;\;(2)[/math]

PS: Bridging the continuous and the discrete -- and thus Bell's related indifference -- integrals are used here by me for generality. Then, since the arguments of Bell's 1964-(1) functions include a continuous variable λ, ρ(λ) in Bell 1964-(2) must include delta-functions. Thus, under Bell's terms, my refutation is both mathematically and physically significant.

PLEASE: When you reply -- or if you will not -- please drop a note on my essay-thread so that I receive an alert. Many thanks; Gordon

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