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

"The Copenhagen interpretation is actually a refusal to interpret - that is why I am against it. It is not physics but metaphysics." We are in agreement there.

"Your vixra paper reaches its conclusions by saying that noise is unavoidable and then exploiting its properties." Exactly - something Bell's theorem and all similar theorems and thought experiments fail to correctly account for.

"Noise would mean in this context that they cannot hear exactly what their interrogators say to them." That is not required. The issue is what the interrogators perceive, when presented with only a single bit response, which by definition in Shannon's theory, cannot exist in the absence of noise - if there is no noise, then it is ALWAYS possible to extract more than just one bit. The problem does not even exist in your scenario, precisely because your scenario cannot possibly be implemented with only a single bit message (speech always encodes far more than a single bit)- the only type of message that Bell failed to account for; and that is a most curious state of affairs, given the fact that the actual physical experiments, are always performed with entities that only yield a single bit result, such as spin-up or spin-down.

Rob McEachern

"Yes/No binary type" has nothing to do with information content. The printed response "Yes" requires far more than a single bit of information to form the letters. The same is true of speaking the word. What I am talking about is setting Shannon's Capacity C = (Time*Bandwidth*log(1+S/N) = 1. In other words, the maximum number of bits of information that can ever be reliably recovered, from whatever message is being perceived by the interrogators, is equal to one. If N (the noise) =0, then C cannot be equal to 1, in any physically realizable system (non-infinite time-bandwidth product). C=1 demands the presence of noise. No naturally occurring, macroscopic entity that I am aware of, has such a small information content. But they can be created. And when they are created and subsequently observed, as in Bell tests, they exhibit behaviors unlike any other object in the macroscopic world - they behave just like quantum objects, such as polarized photons, being observed in Bell tests. The noise is not "intruding" into the measurement of such an object; it is intrinsic to their very existence, as one-bit entities - such identical particles are not identical in the classical sense of possessing an infinite number of identical bits of information. As a crude analogy, think of all the coins that you, by convention, treat as though they are all exactly the same value, even though they are visibly different. You can determine the ONLY value, in spite of the noise/differences. In similar fashion, the 1-bit entities all have the same exact value (like spin-up), when properly measured, in spite of the fact that they are otherwise not identical. They are not hiding any other value - they have no other value - nothing that can be reliably recovered from any sort of measurement.

Rob McEachern

In my previous post, I meant to say "(non-infinitesimal time-bandwidth product)" rather than "(non-infinite time-bandwidth product)" - I do wish they would allow editing of these posts.

Rob McEachern

"By what physical mechanism do you believe that noise must intrude into the interrogation scenario?" Reality - A no noise state may exist in a thought experiment, but not in reality. But that is beside my point. I freely acknowledge that noise can be reduced to being irrelevant in your scenario. But doing so also renders that scenario irrelevant to anything pertaining to Bell's theorem and the associated tests and claims, as far as I can tell. Would you care to explain what you think I am missing?

Rob McEachern

From your essay:

"Neo: 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."

My rewording, substituting "third arm on Anton's body" for "particle":

Neo: Suppose that the result of measuring some variable for a (third arm on Anton's body) is determined by the value of a variable that is internal to the (third arm on Anton's body) - a hidden variable. I am being careful not to say that the (third arm on Anton's body) 'had' the value of the variable that was measured; that is a stronger statement.

This is my concern regarding d'Espagnat's "subtle but important extension of the mean足ing..." that I noted previously. So, does Anton have a third arm or not? If not, then why are we even talking about what it may or may not have internally? And why are we deriving theorems about the nature of such a non-existent entity? The experimentally observed correlations are indicative of an attempt to measure some value associated with the "third arm on Anton's body" - and the world wonders why it all seems so weird - because it all seems so non-local - because no one can determine the location of the "third arm on Anton's body" that they so blissfully assumed they were measuring.

Rob McEachern

I will be happy to assume responsibility for the logic of a classical model, that demonstrates, prevailing wisdom notwithstanding, that such a model can indeed reproduce quantum correlations; and that there is nothing anymore mysterious going on, than a subtle but dubious assumption, in all the claims to the contrary.

Rob McEachern

I do not dispute your claim that "if they can't overhear each other's interrogations then you will never get correlations beteen their answer sets...". As I have stated previously (Jan. 3, 2018 @ 23:29 GMT) "But doing so also renders that scenario irrelevant to anything pertaining to Bell's theorem..." I have simply been trying to point out, that the correlations are critically dependent on the information content of "their answer sets"; specifically, on whether or not their answer sets enable the interrogator to make independent measurements of one, or more than one, bits of information, per entangled pair.

"You reckon it must contain a mistake:" The mistake is that your scenario, like Bell's theorem, only models the latter case, with multiple bits of information, but not the former. But the former seems to be the only one that has any known relevance to explaining what is happening in the QM case, without having to resort to some "weird", non-classical mechanism. In other words, your scenario provides a good model, for the wrong type of thing.

Rob McEachern

"The logic of the two situations is identical..." I have no reason to doubt that. However, if it is identical, then somewhere or other, it must contain the identical "loophole" that d'Espagnat identified 40 years ago - the very loophole I deliberately exploited, to reproduce the quantum correlations with a classical system. There is no need to read your paper, in order to find it, given that you yourself have informed me that it is, in fact, the identical logic (and thus with the identical, subtle loophole) that was analyzed by d'Espagnat.

Rob McEachern

"Why say that only now?" Because you claimed that "It is not legitimate to deny that without reading it." But think of the principle of reduction to an absurdity; if you can correctly identify a conclusion as being absurd, and you are willing to concede that the conclusion does indeed follow from the premise and thus contains no error in logic, then it is highly likely that there is an error in the premise. The existence of an error, is thus a deduction that can be made without reading the analysis. In fact, if the error is an unstated assumption, reading the analysis will not even be able to detect it, except by its omission.

I am hardly the first to point out the absurdity of many standard interpretations of QM and the EPR paradox. The entire reason Einstein et. al. introduced the EPR paradox, was precisely to attempt to demonstrate that the absurd conclusion must result from a faulty premise. d'Espagnat correctly identified the premise responsible. Unfortunately, neither he nor anyone else at the time, could imagine how to actually exploit it, in order to produce the observed correlations. But that has now been resolved.

"you are not willing to follow it through and show me where you consider I am wrong" I have already said that I am, but I do not have ready access to your paper. Post a copy where it is accessible.

"The partition between signal and noise is up to the observer." Exactly. And Bell's and all similar theorems seem to have partitioned it incorrectly, by attributing correlations to components, for which there is no signal, but there is noise. This is my point. And you have heard it many times before in connection with QM, and you just repeated it yourself: "It is up to the observer." It does not matter what the observed is doing, if the observer makes the incorrect partition. This is why what the observer does, matters so much in QM. In Information Theory, the observer has to know, a priori, how to make the correct partition; it cannot be deduced from the information content of the thing being observed. The observer has to make a decision (misidentified as the collapse of a wavefunction) - and if the observer frequently gets it wrong and decides (due to noise) that the cat is "dead", when it was actually "alive", then the statistics he computes are going to be "weird". And it has now been demonstrated that the precise character of these "weird" correlations, are identical to those observed in quantum experiments. I am reminded of the practice in the middle ages, of sometimes burying the dead in a coffin with a string attached to a bell above the ground, so that the misidentified dead could signal their own decision to the contrary, in regards to where the partition between life and death should be placed.

Rob McEachern

Anton

Yes, of course you cannot handle everything on 9 pages. Thanks.

John-Erik

Dear Dr. Anton Garrett,

You wroye: "Neo: Some people suggest that reality is operator-valued and our perplexities arise because of our obstinate insistence on thinking in - and therefore trying to measure - scalars."

My research has concluded that Nature must have devised the only permanent structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

Dear Anton Garrett,

I greatly enjoyed your essay [I use the same "conversational" vehicle in my essay, which I hope you will read.]

Literally thousands of comments have been spent on FQXi concerning Bell's theorem, which, as you state, "is about logic, not quantum mechanics". Bell's first statement defining the problem is his equation (1) in which he defines measurements A and B to have +/- unit values. The logical outcome is completely determined from this point!

Bell essentially asks for a "classical" explanation [the 'hidden variable'] while insisting on a "quantum" result. Stern-Gerlach did not find "quantum" results. Their deflection data is smeared over an upper "lip" and a lower "lip" which are arbitrarily called +1 and -1 to fit the naïve quantum picture of spin. But which picture? Pauli's, Dirac's, Feynman's? As you obviously spent time and effort on this topic I hope you might look at Spin: Newton, Maxwell, Einstein, Dirac, Bell.

Pauli conveniently chose half integral eigenvalues, which Bell uses unquestioningly, while Dirac, who many think more fundamental, derived a four component equation that is no longer an eigenvalue equation. Indeed, it is only "converted into" an eigenvalue equation by the Foldy-Wouthuysen transformation which smears the particle with spin over a region of space. Only after this integration do we arrive at a Dirac-based eigenvalue equation.

Perhaps if Bell had thought more deeply about spin he would've had more reservations than he did about this issue. Unfortunately, about the same time Bell developed his theorem, Feynman, deeply in love with the two slit experiment, decided to apply the analogy to Stern-Gerlach-as-two-slit and [of course!] the two state "wave function" worked. [What a surprise -- Pauli invented a workable 'wave-function' when he used O|+> = +|+> and O|-> = -|->.] Thus deBroglie's linear momentum-based wave function, with wavelength proportional to inverse momentum, compatible with experimental tests, was conceptually extended to angular momentum, with no logical justification for associating a wavelength with electron spin. [Spin waves in condensed matter or solid-state physics are not spin wave functions.] But, like Einstein, it is today verboten to question Feynman, so we are stuck with "wave functions" for spin analogous to wave functions for particles with momentum. This leads to superposition concepts for particles going through non-homogeneous fields that are entirely inappropriate but unquestioned, although never demonstrated.

Nino says: "I presume physicists... are now looking for a theory that predicts what happens each time you put a particle through successive Stern-Gerlach apparatuses."

Neo answers: "Actually we are not."

Actually we are. Or were. Two other physicists and myself [one received the National Medal of Technology at the White House in 2014] began this experiment in 2015. We produced fine healthy silver atomic beams but finally decided that single atom detectors were far beyond our resources.

If the first SG detector is used to prepare atoms from the oven in a particular state, say + (up), and the second SG detector is offset at angle theta from the first, then the deflection of the particle from the second device will be a factor of theta.

Here's the kicker: according to my theory (which does violate Bell's theorem classically) only + particles will be detected from the second SG device. According to Feynman's two slit spin analogy, the wave function will predict some - states will be found.

If spin is actually 3D, then the deflection of SG can be shown to depend on the angle between the spin and the field. This is what is actually seen in the SG data. But as you imply, no one wants to test this. Even suggesting it is to be drummed out of the corps.

But if spin is actually 3D, then the measured deflection is not +1 or -1 but is ~cos(theta). This conflicts with Bell's definition A,B= +/-1. Using real theta-based measurement results (i.e., deflection) it is easy to show the correlation cos(a.b). Using Bell's +1 or -1 constraints it is logically (not physically) impossible.

In Modern Classical Spin Dynamics see figure 6 on page 20 wherein the classical model overlays SG data almost exactly, and in Bell was simply wrong see page 6 where the energy-exchange model is shown to yield cos(a.b) while the Bell-constrained version cannot accomplish this.

So, to repeat, if one accepts Bell's requirement that measurements be +1 or -1 , instead of actual deflection seen in the SG data, then one is logically bound to fail. If one allows actual deflection data the classical model obtains the quantum correlation cos(a.b) violating Bell's theorem and removing even the suggestion of "entanglement".

This is further complicated by loose thinking, such as Nino's statement "but nevertheless only one of the detectors actually goes off." If this is applied to Stern-Gerlach, it means only that every particle is deflected up or down based on initial state, but does not imply A,B= +/-1. On the other hand, Bell is not tested with SG atoms but with photons which are detected (+1) or not (0).

Due to Feynman's beloved two-slit-spin-analogy, people consider atomic spin wave functions and photon wave functions to be the same, thus on/off photon detection results are conflated with the SG deflection results.

Confusion reigns.

Nino says "quantization is indeed a mental rather than a physical procedure." Bell forces classical physics into a quantized mold that is mental rather than physical. When this artificially constrained logical problem leads to the conclusion that classical physics cannot yield the measured correlation we invented "entanglement". This nonlocality that has ruled physics for fifty years is a farce, but one which cannot be challenged without forfeiting one's establishment position. The natives should be restless.

Congratulations on a very fine essay,

My very best regards,

Edwin Eugene Klingman