Anton,

"the Bell analysis is capable of showing, by comparing their sets of answers, that they must have been overhearing each other's interrogations"

That conclusion follows from a false assumption - that they do not answer in the manner that I indicated - via a mechanism encoding only a single bit of information.

"please say where the error is in my "Bell's theorem..." I think I already did, but if you do not believe it, then read this Actual Construction of a Classical System that Exhibits "Quantum Correlations" It is only a few pages long, with no complicated math; and you can reproduce it yourself, with little effort, others already have.

I have not found a complete, free copy of your paper on-line, only the abstract and a preview that requests $40 for the entire paper, so I cannot be more specific about where in your paper you introduced the subtle, but dubious assumption, being exploited to reproduce "Quantum Correlations" classically, in the paper linked to above. But if you can direct me to a freely downloadable copy, I will look at it.

Rob McEachern

I'm not aware of where it is online but try your university library or its physics department for the relevant journal. I can't scan my copy because I'm away for a while - sorry! But you can surely find Mermin's "Is the moon there" article and say where you think *he* goes wrong in his technical analysis. (Let's not discuss his metaphysics!) I think he is right, you presumably think he is wrong, so that's the basis of a clearer discussion.

NB In my own paper I make no assumptions about the hidden variables other than that they are "onboard" a particle, ie local, and that they influence the outcome of a measurement made of an observable (using the word in the quantum sense). I deliberately do *not* require "the angular momentum to simultaneously have well defined components in 3 orthogonal directions. Are you aware of that?

From Mermin's paper

Page 9: "There is no conceivable way to assign such instructions sets..."

True, but irrelevant. The mechanism has to do with what the observer is doing, not what the particles being observed are doing - the particles are not doing anything - other than merely existing - as the physical manifestation of a single bit of information; NOT one bit per particle, NOT one bit per particle component, but one bit TOTAL - redundantly encoded into two particles. The observer however, is making decisions about what state he or she thinks the particles are in. But he or she made a fundamental mistake by even ATTEMPTING the experiment in the first place. There is NO POINT in even TRYING to compare the measurements of the two particles, if (1) they are entangled and (2) both particles only exhibit a single bit of information in total; because there are only two possible outcomes: (1) either the second measurements yield the same result (or negative, if anti-parallel) as the first or (2) you made a bad measurement and consequently FAILED to get the ONLY POSSIBLE A PRIORI KNOWN-TO-BE-CORRECT ANSWER, by making a measurement that FAILED to get the only possible correct answer - the same answer as the first measurement - that is what is meant by a single bit of information, redundantly encoded into two entities.

"I deliberately do *not* require "the angular momentum to simultaneously have well defined components in 3 orthogonal directions. Are you aware of that?" Yes. But you did assume that there is more than one component. That is the problem. Single bits of information do not have multiple components. When you assume they do (as Bell did) and then try to measure and compare them, you are destined to observe some rather weird correlations, if you believe you are measuring two different things/components.

Rob McEachern

Rob,

You wrote: "But you did assume that there is more than one component". That isn't true. In my FQXI essay I had Neo say, "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."

If you look at my full paper, to which the essay refers, you will see that this is indeed the case. If you doubt this, please read the full paper, which would therefore seem to overcome your objection. I don't see how you can make assertions about my analysis before you have read it.

Best

Anton

Your "Never be put off, for only seekers find. By doing this you become part of a great project." was the best bit for me. Good luck. Haven't read it in full, hope to be back. Kind regards Georgina

    Anton,

    "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."

    Suppose, that under certain specific measurement conditions, the underlying value was always identically equal to zero - not because there is a hidden variable with that value, but because there is no spin or polarization "variable that is internal to the particle" at all - like seeing a zero-thickness coin perfectly edge-on - there is nothing to see - no variable - just noise), but due to noise, it was "determined" by the observing apparatus to be either 1 or -1, because the nature of the detection apparatus is such that it must yield one of those two results, because it "knows", a priori, that no other result is valid, just like you know that a letter other than a-z is not a valid letter in the English alphabet. So you make your best guess, and the guess is *always* wrong.

    Rob McEachern

    You say "Suppose this and suppose that" and on that basis assert that I am wrong. But I make no such suppositions; *you* do. Please take the trouble to familiarise yourself with my detailed analysis, which you say you haven't yet read.

    I will, when I can obtain a copy of your paper; I do not live around the corner from any institution that might have one. In the meantime, please consider the fact that the basis upon which I am asserting that these types of therorems and thought experiments are flawed, is by simply taking note of the fact that their primary claim, that no Classical system can reproduce the observed correlations, has recently been EXPERIMENTALLY FALISIFIED and the experiments have been independently replicated; what they claim is an impossiblity, is now known to be possible. Something is rotten is Denmark - the Copenhagen Interpretation and all the other "standard" interpretations of what is going on, in these systems.

    Rob McEachern

    The Copenhagen interpretation is actually a refusal to interpret - that is why I am against it. It is not physics but metaphysics.

    Your vixra paper reaches its conclusions by saying that noise is unavoidable and then exploiting its properties. That is simply not so in the interrogation situation. The two subjects hear the questions accurately and they have an agreed strategy for replying, to which they faithfully adhere, whether their strategy is pre-agreement if they cannot overhear each other's interrogation or something smarter if they can. Noise would mean in this context that they cannot hear exactly what their interrogators say to them, but that is to do with the biology of their ears and has nothing to do with the logic of the situation.

    "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

    The subjects in the interrogation are asked binary questions and pre-agree their answers to every question that they might be asked, and pre-agree a strategy in the event that they can overhear each other's interrogations. These pre-agreements involve a lot more than one bit, although of course the questions they are asked are of Yes/No binary type. The entire scenario is noiseless in the sense that the subjects hear the questions accurately and stick exactly to their pre-agreed strategy. By what physical mechanism do you believe that noise must intrude into this scenario?

    "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

    Sorry, you haven't answered my question. By what physical mechanism do you believe that noise must intrude into the interrogation scenario?

    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

    If you are willing to take my question seriously then I think you would find out for yourself.

    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 meanč¶³ing..." 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

    If you are going to put words in my mouth then you are responisble for the resulting logic, not me. I am trying to simplify the issue as far as it can be, so as to clarify it, but I am not going to endorse analogies that might not turn out to be equivalent.

    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