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

"Those who say quantum theory is the end of the line argue that the universe is not deterministic -- genuinely random." Kolmogorov's axiomatic foundations of probability theory are precisely defined in terms of Zermelo-Fraenkel set theory, but what is meant by "genuinely random" in the Copenhagen Interpretation is not precisely defined in mathematical terms. My guess is that Bell's theorem is philosophically wrong but empirically irrefutable. My guess is that string theory with the infinite nature hypothesis implies some version of the string landscape with some version of supersymmetry, while string theory with the finite nature hypothesis implies MOND and no supersymmetry. Google "witten fredkin milgrom".

Hello Anton.

In the tradition of the discussion I hope you will allow me to add this:

To speak of Brownian motion in the context of looking for an unseen communication channel between culprits dancing to the same tune in different rooms, rightly begs the question of whether choreography is prearranged or momentary via instantaneous communication. This question has two faces, but we only need to speak of one if we abandon the possibility that it started at the beginning of time, i.e., Big Bang. Non-local or spooky action at a distance implies instantaneous communication, and that brings to mind what happens when we introduce a wave into the water while observing Brownian motion. The wave 'unseen' suggests a communication channel between particles which appear to be behaving in choreographed fashion even though other aspects of their motion appear unpredictable; particles moved on mass by the wave may also have a tendency to align on the up and down slopes of the wave implying not only instantaneous communication but an action by their environment. Now, I am not asking whether the culprits being interrogated in different rooms are surfing or treading water in the same ideal pond, what I am getting at is the reason why no one wants to test for the existence of an ideal substance in which atoms tread water so to speak. Various notions of ideal substance have been misused by philosophers intent on inflicting substantial forms and occult qualities on science and the public for the sake of one aggrandisement or another for centuries if not millennia. Neither side today wants to look for empirical evidence because the evidence already suggests not just that this ideal substance is real but just like natural substances, ideal substance is composed of forms having spatial extension, i.e., discreta, and not points, simples or Monads without form which have been flogged to death and are still being flogged to death by philosophy to this day. For example, the black star at the centre of the galaxy, if composed of ideal discreta, may be the hardest rock in the galaxy with mountain ranges formed at the equator moving north and south in concentric circles. Who knows, maybe just like tree rings they will tells us when the black star last fed; just a thought which Nino brought to mind when speaking of Brownian motion. Notwithstanding that some scientists don't like looking out of unfamiliar windows, the question is, whose jail cell has fewer windows, Nino's or Neo's?

"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."

Actually, there are several other assumptions: and they turn out to be false: A critique of the assumptions in the paper "A Stronger Theorem Against Macro-realism

Rob McEachern

David Brown wrote : "My guess is that Bell's theorem is philosophically wrong but empirically irrefutable."

It has been refuted, both empirically and logically (a bad, but seldom discussed subtle assumption). See my post below. Other discussions can be found here on FQXi

Rob McEachern

The error in the logic was pointed out 40 years ago on the bottom of page 166: "These conclusions require a subtle but important extension of the mean足ing assigned to a notation..." In other words, you have to assume there is a one-to-one correspondence between two or more measurements and two or more attributes of the thing being measured. That is a logical impossibility, when the thing being measured only possesses a single bit of information, redundantly encoded (AKA entangled) into two objects.

"would you tell me where that same logic fails in its application to the interrogation of two persons in adjacent rooms, please, and the inference that they must have been overhearing each other's interrogation when answering their own questions?"

Sure. The entire conversation consists of uttering a sequence of single bits of information, being unreliably measured by the interrogator (naive measurements produce correlated measurement errors of the only existing bit's value). The two always only utter a single bit value, which the interrogator mishears, because it never occurred to him or her, that the correct value can ONLY ever be measured, by "listening" from two very specific phase angles, which differ for each of the two persons. Any attempt to listen at a different phase, is doomed to produce a high probability of a bit-error in the measurement, particularly when the measured phase is nearly orthogonal to the unique, required phase angle (the only measurement angle guaranteed to produce no intersymbol interference and thus a bit-error). The problem is related to avoiding intersymbol interference, in Quadrature Amplitude Modulated (QAM) signaling.

In the link from my previous post, I used the term "cross talk", since few physicists are familiar with the more technically correct concept of "intersymbol interference": measurements of one attribute (symbol) being mistaken for measurements of another, that happens to be "local".

This may be easier to visualize, if you think of the conversation as using visual symbols, rather than sounds. Each person presents a sequence of anti-parallel coins, for the interrogator to see. But the coins are noisy and are not identical, except for the fact that if you observe one member of the pair along the correct viewing axis (which must always be perpendicular to the coins surface), then you will correctly decode the intended message - either heads or tails) And if you view the other person's coin from the exact opposite direction, you will always get the exact same bit value - the same, redundant message.

Now you might object, that the interrogator has no way of knowing, a priori, what the one and only correct viewing axis is, for each pair of coins, particularly since the people present each entangled pair at a different, random angle. Bingo! If the interrogator ignorantly assumes that he can simply measure the coins state from any old angle and subsequently deduce the correct message, he is sadly mistaken. But that is exactly what Bell's theorem has done. Bell has unwittingly assumed he can correctly make sense, out of a conversation encoded with an unknown one-time-pad. But that is known to be logically impossible. The correlation statistics of the resulting bit-errors, are exactly those observed in the quantum correlations produced by Bell experiments.

Rob McEachern

For some reason, the link in the reference to page 166 disappeared when it was posted. Here is the link:

https://www.scientificamerican.com/media/pdf/197911_0158.pdf

Anthony

The dialog is interesting and good. I like that you are interested in the hidden variable ideas. I regard them as very important.

I think that you should take more interest in anomalies in physics, like:

destructive superposition

gravitational anomalies during solar eclipses

Pioneer anomaly and flyby anomaly

With best regards from __________________ John-Erik Persson

No such assumption is being made: It is a logical impossibility to interrogate two independent (uncorrelated) entities, when only one exists. Bell assumed that there must always be more than one - which is why you have talked about "two persons". Bell assumed he is hearing two responses, from an entity that can only give one. He hears what he hears, but he has completely misinterpreted why he is hearing it. He is not listening to two persons in adjacent rooms: in effect, there is only one person in a peculiar echo chamber. It is peculiar, because the "echo" (AKA entangled entity) is produced simultaneously with its pair.

You seem to be ignoring the additional claim, made by Bell, that no classical system can reproduce the observed correlations. That claim has been falsified by direct construction of a peculiar, classical system that exhibits the same correlations. How is that possible, when Bell's theorem claims it is impossible? - by exploiting this bad assumption upon which Bell's theorem is based.

All you have to do, to see the problem, is to ask yourself the question "How on earth is it possible to make uncorrelated measurements of an object that only EVER exhibits a single bit of information?" You can make all the measurements you want. And you can analyze them any way you want. But when you conclude that they all seem to exhibit weird correlations, you have made an error - because such correlations are inevitable - because it is impossible to make two uncorrelated measurements of a single bit of information.

Rob McEachern

No. What is the interrogator supposed to conclude, if they always both answer by simply holding up a coin, in a random direction? What would he conclude, even if their coins were always somehow anti-parallel, even though they faced in a different random direction, relative to the interrogator's line-of-sight, after each question?

Rob McEachern

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

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