In all fairness, both classicists and quants see the other side as arising from their own. In application, technocrats don't care which works, just that it does. jrc

Lawrence,

for no known reason, a couple of your posts are now missing. All disagreements are in some manner instructive as to what questions need be discovered. Relativity and Quantum diverged so rapidly from the outset that maybe something was missed. Hope FQXi can restore your comments. jrc

jrc,

I requested the administrator remove the last post, which made false accusations and included several gratuitous insults. I do not go on LC's thread and insult him. Most longtime FQXi'ers know that he and I have very different ideas of reality, and this is extremely unlikely to change.

I find quantum mechanics almost a miraculous machine for statistically predicting outcomes of situations which can be in one of N states. The cost of this is ignoring the physics of the process and merely calling it a 'jump' or a 'collapse of the wave function'. My suggestion that QM is incomplete may offend some, despite that it was Einstein's key question in EPR. Yet Zurek's "decoherence" program which attempts to derive classical physics from quantum mechanics, is, in my opinion, unconvincing. My classical model that yields quantum predictions may have struck a nerve. As I note, the question can be decided experimentally, which is the way physics works.

Technical arguments are welcome on my thread, but not gratuitous insults.

Edwin Eugene Klingman

Edwin,

If I may. Me thinks they doth protest too much. But in response to which I found in reading what looks like it might be a quantum corollary to your model in the 'quantum rotor model'. It has experimental confirmation in low energy electron dipole coupled systems such as quantum Hall effect devices. :-)jrc

jrc,

Thanks for your continued interest. You are correct that the "quantum rotor" is an apt analog. I have spent some time on the 'kicked rotor', which receives a cyclical kick and leads to chaos. If you look at my right hand figure on page 8 of my essay, you may be able to see how such a kick arises. I've done some work on this but it's not ready for prime time. Initial results seem to imply that chaos can account for the apparent quantum randomness in an otherwise deterministic model.

There is a ton of literature on kicked rotors, quantum and classical, with one of the latest being the 21 Nov 2014 Phys Rev Letters 113, 216802 treating the chaos of the kicked spin-1/2 rotor. Another PRL paper, 49,509 (23 Aug 1982) reports that

"The motion of nonlinear classical systems can display random characteristics... The solutions of the equations, although they may statistically be definite, are stochastic and behave as if they contain a random number generator... even though the equations themselves are deterministic and even simple."

They refer to

"The simplest example known, that of the kicked quantum rotator."

My basic model has proved to be exceedingly rich, and I see much low hanging fruit that I hope to harvest. One of the papers I just looked at online concludes that their kicked rotor model exhibits a quantum to classical transition. The kicked rotor treatment of my model may provide a classical to quantum transition.

Edwin Eugene Klingman

Maybe I will just leave this to Richard Feynman

https://www.youtube.com/watch?v=_sAfUpGmnm4

LC

Dear Edwin,

I'm afraid that this misses the point, both of Bell's proof and of the physics. The outcome of Alice's experiment just is reported as a +1 or -1, or "up" or "down", or however one wishes to code the response. The outcome reported out of the labs, and from which the correlations are calculated, simply are not anything else. That is the actual experimental situation in reality, and the sort of experimental situation Bell discusses (at least in the sort of experiment done by, e.g. Aspect). It also happens to be the sort of prediction made by quantum theory, but that is a side point. What a local theory cannot do is predict statistics of binary outcomes that violate Bel's inequality: that what the theorem shows. And such violations of the statistics of reported binary outcomes is what actually happens in the world.

You have misunderstood Bell's formula. It is a formula for experiments whose outcomes are reported as binary: one result or the other. That is what is actually done in the lab. So this formula applies to the actual lab results, produced in the real world. Bell nowhere asserts that the outcomes of all experiments must be binary, but the formula's a completely correct for experiments whose outcomes are, in fact, binary. So there is nothing wrong at all with how the problem has been set up.

I'm afraid that it is very hard to follow what you write above. Is there a single function F(a, lambda) whose range is (+1, -1) which encodes the local physics, i.e. which specifies, given the setting a and the additional parameters lambda (set at the source) which of the two outcomes gets recorded? If so, please state precisely what this function is. You mention of two functions, which you call +A and -A (or +B and -B) just confuses the situation since it should be impossible to get both the + and the - outcomes on any run. But, again, the plain physical fact in reality is that on every run the outcome on each side is either up or down, which may be called +1 and -1 by convention. If you claim that this is the problematic assumption of Bell, then you do not understand that this is actually what the experiments yield.

Perhaps you could explain this sentence: "Now you ask where in his theorem do Bell's constraints appear. They appear in his first equation (1) where he states that +A(a, lambda) must equal +1, and -A(a, lambda) must be constrained to -1. There is no valid reason for these constraints.." I have Bell's paper before me, and cannot imagine why you have written this, as it is inaccurate. Bell nowhere mentions two functions, which you call +A(a,lambda) and -A(a lambda). He mentions one single function, A(a lambda), whose range is given as +1 and -1. All that means is that the outcome of the experiment is reported as one of two types. in the case of a Stern-Gerlach situation, the two types would be called "spin-up" and "spin-down". In the case of photons, the two types will depend on which of two output channels the photon is detected in. Bell is simply describing a certain sort of experiment, which is one where the outcomes are reported in this way.

If you look at the actual outcome of the Stern-Gerlach experiment, it is clear that for electrons that go down the center of the device there are indeed sorted into two distinct classes of results, which can be called "up" and "down" or "+1" and -1", or whatever one likes.

You seem to grant that Bell's theorem is indeed a theorem for experiments of this character. Since the actual experiments are of this character, Bell has made no error. What exactly you claim to have calculated for your model I cannot say, since you seem to be denying that in your model the outcomes are binary.

Regards,

Tim

John Cox,

Just like Edwin, you have missed what Bell is doing. He uses no "spin operator" of any sort, and the issue is not "excluded middle" in the logical sense of that term. He is simply proving a theorem about certain sorts of experiments, whose outcomes are reported as being of either one or another sort. It turns out that spin experiments, and certain polarization experiments are just, factually, like that. In a spin experiment using a Stern-Gerlach device (this is not, of course, what Aspect used in any case) one says: if the particle is detected on or above the midline, the result is "spin up" and if it is below the midline it is "spin down". (Since none ever hit at the midline that case is actually irrelevant.) For polarization using a birefringent crystal, there are two output channels with photomultiplier tubes. If one tube fires it is one result, if the other fires it is the other result. That is a correct description of the experimental situation. So there is no contentious assumption or error there. Your talk of "Bell's choice of operator" suggests that you have not read his theorem, which mentions no operators at all, and provides no attempt to physically model anything. He is talking about the possibility of any local theory at all, constructed in any way, being able to produce predictions for certain correlations among outcomes of experiments with binary outcomes (as described above). Exactly zero quantum mechanics or quantum-mechanical formalism is employed in the proof.

If an experiment is reported as having one of two outcomes--"spin up" vs. "spin down", or "photomultiplier 1 fired" vs. "photomultiplier 2 fired" or "the red light went on" vs. "the green light went on"--those can obviously be coded as "+1" vs. "-1". That is all Bell does in framing the theorem. I suppose that is what Edwin is trying to call "Bell's hidden constraint", but it is not at all hidden and is a perfectly accurate characterization of the experiments Aspect did and also how the result of "spin measurements" would come out. So in the relevant sense it is no constraint at all.

Insofar as Edwin is treating experiments that do not have outcomes described in this binary way he is making no contact with Bell's theorem, and therefore cannot possibly have shown that there is any error in it. I still can't tell what he thinks he has calculated or how.

As to your comments about Bell being naive, I can't make sense of them. As for whether one can generalize Bell's result to cover other sorts of experiments, whose outcomes are not reported with a binary outcome space...why should that even be of any concern? We have actual, concrete, performed experiments with a binary outcome space, covered by the theorem, that prove non-locality. There is nothing more to do.

Regards,

Tim Maudlin

John,

I'm not sure I understand your comment. There are actually ways to generalize Bell's result to cover more cases. One was the discovery of Werner states that violate no Bell inequality but predict statistics that cannot be recovered by any local theory. But it is no criticism of Bell, since his results are perfectly fine as they stand for the sorts of experiments he had in mind, and the sorts of experiments actually done. And, again, the 1964 result employs no quantum-mechanical mathematical apparatus (operators, for example) at all.

Tim

Prof. Maudlin,

Tim, I found your descriptive comparison of Newtonian and Relativistic geometries to be very clearly stated, and your argument that time is the progenitor of real geometry quite compelling.

Having never suffered any sort of gambling addiction, numbers games have always disinterested me and so topics such as Bell require more attention to detail than I really care about. None the less, his Theorem is often called (by some) to be among the greatest discoveries in science. As a Professor of Philosophy in Mathematics, you quite naturally find it easy to take the physics out of math while leaving the math in physics. But Bell was a physicist in an age of reactionism that was made the most divisive in human history by the development of a capacity to cause complete extermination of life on earth. It was Quantum Mechanics that built that capacity, in a deliberate methodology of 'this or that :: cut the difference in half'. In that era it was politically suicidal to question the 'why' of this or that. 'Just shut-up and calculate!' was the order of the day.

Relativity establishes non-locality, QM prescribes it. So does Bell's Theorem prove non-locality, or simply employ it? Since Minkowski it has simply been assumed that because there is nothing we can look to in establishing an absolute scale of measure; that the scale of a unit length of span in the dimension of direction in space, is the same scale as a unit length of span in the dimension of duration in time.

Given that paradigm, the Speed of Time would be the same in each of any non-locality, and constitute an initial condition mathematically. If OTOH the scales of spacetime were locally variable, any experiment to verify probable 'this or that' outcomes would be in the same gravitational reference frame of operational scale covariance, in which a split beam of EM would have a homogeneous scale ratio as would electrons from a single source. Preparation of a singlet pair experimentally sets an initial condition. In a scale invariant paradigm, Bell can't loose, but is that truth? or trick?

I don't think mankind has yet scratched the surface of reality, I know I haven't. :-) jrc

Der John,

Did you mean this:

"Relativity establishes non-locality, QM prescribes it."

Most people would say just the opposite, that Relativity is incompatible with non-locality rather than establishing it. In any case, we do know that non-locality is in principle compatible with complete Lorentz invariance. So the relation between non-locality and Relativistic space-time structure is not straightforward.

I just can't see what this has to do with Bell's theorem. The theorem concerns certain experiments, done "far away from each other" (a notion that makes sense even non-Relativistically, but can be made precise as "at space-like separation" in a Relativistic setting) and have binary outcomes. Bell shows that if the physics on each side is, in a certain well-defined sense, independent on what happens on the other side, then certain correlations between the outcomes on the two sides cannot be produced. Bell's theorem certainly does not "employ" non-locality: it uses a criterion for locality and shows that no theory (quantum mechanical or not) that is local can make certain predictions. So if you accept that these correlations really are produced for experiments where the two sides are far apart (in Aspect's case, this even means at space-like separation) then Bell has ruled out all local theories. This establishes non-locality as a physical fact. Many Worldser's try to avoid this by saying that the outcomes are not one of a binary outcome space: in each experiment you get both outcomes, in some sense. That move requires discussion, but that does not seem to be the tack taken here.

If we agree that experiments done at space-like separation, such as those done by Aspect and Zeilnger, count as "far apart", and they they have unique outcomes, and that the statistics of those outcomes violates Bell's inequality (and conform to quantum predictions), then we are done. There is nothing more to debate: the physics of the world is not local. I'm not sure I see which part of this you are inclined to dispute.

Regards,

Tim

Dear Tim,

Thank you for your responses. You have mixed so many terms and claims that sorting them out will take a while. I find your arguments inconsistent. For example you state without reservation that Bell's is a formula for experiments whose outcomes are reported as binary: one result or the other. You say "that is what is done in the lab." As you are the author of the book on Bell, can you supply a reference for that? I do not believe it is a true statement for Stern-Gerlach.

You seem to realize that you are claiming more than is true, as you then respond to John Cox by speaking of

"...accurate characterization of the experiments Aspect did and also how the result of "spin measurements" would come out."

Which is it? Did "spin measurements" of EPR actually come out binary or are you just assuming that this is how they "would have come out" since that is how Bell is "framing the theorem"? Do you have a factual reference to backup your opinion?

Again, you close one comment by saying: "we have actual, concrete, performed experiments with a binary outcome space, covered by the theorem, that prove non-locality."

As has been noted, some claim Bell's is the most significant science of the 20th century, so it would seem to require you to backup such a specific, unequivocal statement. Please do so.

John Cox pointed out that as a Professor of Philosophy in Mathematics you quite naturally "find it easy to take the physics out of math while leaving the math in physics." In this regard you seem to wish to convert physics experiments into logic exercises, because you believe Bell framed his theorem that way. I do not believe Bell was formulating a logic experiment; he was making assumptions about eigenvalues, as I discuss in detail in Spin: Newton, Maxwell, Einstein, Dirac, Bell

Yet you dismiss the idea that Bell's formulation was in any way based on quantum physics, and wish to convert his theory of physics into an exercise in logic. I do not accept this, and my hope is that a sufficient number of physicists will not accept this once they understand how and why Bell oversimplified.

Also, as a minor example, a philosopher easily states that "electrons that go down the center of the [Stern-Gerlach] device", while this grates on the ears of the physicist, who knows that the Stern-Gerlach simply does not work for electrons, requiring neutral particles with a magnetic moment to operate. Yes, it is traceable to an electron in the atom, but that illustrates the difference between a mathematician and physicist. You're a stickler for details that you think are important and dismiss those that physicists think are important.

The same lack of concern with physics causes you to lump "particle-spin-based" experiments and "photon-spin-based" experiments into one. They are significantly different, both in their physics and in their detection. Again, as you see these as 'logically equivalent' you believe them to be "physically equivalent". That is a mistake. For this reason I ask you to please stop arguing Aspect and photon experiments while we are engaged in a sufficiently complex discussion of Stern-Gerlach experiments. It is confusing enough for most people without your further confusing it by making a false equivalence.

You state, Bell states, and the literature states, that no local theory of physics can produce the -a.b correlation. It is not required nor logically necessary for one to provide both an atom-based and a photon-based theory to disprove this statement. My essay concerns the physics of Stern-Gerlach experiments. They are not equivalent to photon-based experiments and to consider them so only confuses the issue. So please forget Aspect for a while. Aspect did not perform a Stern-Gerlach test. You are mixing apples and oranges when you confuse the two types of experiments and lump them together.

To repeat, you claim that Bell test using Stern-Gerlach devices "done in the lab" report binary outcomes. I do not believe this. Please provide a reference to any such experiment, otherwise please stop insisting that this is the case.

I will return to some of the other points you make in a following comment.

Regards,

Edwin Eugene Klingman

Dear Edwin,

The fact the Bell's actual theorem is about experiments with a binary outcome space does not convert his mathematical theorem into a "logic problem". It is still a clean piece of mathematics. What it is not is a discussion of Stern-Gerlach magnets or any other concrete situation. Since you have the paper, you will note that the theorem is formulated in section 2 and proven in section 4. The intervening section 3, which is only part you seem to talk about, is titled "Illustration" because that is all it is, an illustrative example of a possible local theory. It just in no part of the theorem at all, and could be dropped from the paper without changing either the theorem or its proof.

I am happy to acknowledge that real Stern-Gerlach experiments are done on neutrons rather than electrons. I actually fail to see any bearing of that at all on these issues. The point is that the theorem covers experiments with binary outcomes spaces, which include the photon experiments of Aspect and Zeilnger and possible spin experiments on massive particles as well. For analytical purposes these are treated interchangeably because as far as the theorem goes they have exactly the same form. If one were using Stern-Gerlach magnets the outcomes would described as a binary outcome space as I mentioned above: call the appearance of the particle above or on the midline and "up" result and below a "down" result. Code these as +1 and -1. That is all there is to it. If there is some spread in the location, it makes no difference at all so long as the division into "above the midline" and "below the midline" is clear.

The point is that Bell has actually proven a theorem about such experiments. You have not disproven or shown any problem with his proof. The relevant correlations are correlations between the outcomes of experiments with binary outcome spaces, so if you are not using such a space you cannot possibly refute the theorem. What you call "Bell's hidden constraint" is neither hidden nor a constraint. It is a theorem about the statistics of certain sorts of experiments. If you choose to discuss some other sort of experiment, then whatever you have calculated it has no bearing on Bell's result. It is rather as if a mathematician had proven a theorem about bounded functions and someone objects that not all functions are bounded. That is true but not relevant. It is still a theorem.

My reference to the Aspect experiments is obviously relevant if one wants to know whether, in fact, physics is non-local. If you are only presenting some analysis of possible experiments that have never been done, that's fine. But if the physics is local, the predicted statistics will not violate Bell's inequality. I asked you to point out the assumption Bell makes, and you did not mention an assumption but rather the very subject matter of the proof. I have also asked what function you are using to calculate the outcomes of your hypothetical experiment and how the graph you generate was generated. These are central questions. Since you say that imposing Bell's constraint in your model makes the violations of the inequality go away, that seems to suggest that the model shows no violation of the theorem. What it does show cannot be determined without more detail.

Regards,

Tim

Dear Tim,

You have essentially confirmed my comment. You state that Bell is "still a clean piece of mathematics." I do not contest that statement. It is a flawed piece of physics; mathematics, unrelated to physics, has no real significance for the physical world, let alone major aspects of reality like "locality" versus "non-locality".

You have converted real physics into logic and math by erasing the physical output and replacing it with a logical output. As Howard Wiseman relates in "The Two Theorems of Bell", Bell's thinking evolved over the years, and he "proves" several things. Physicists, I believe, wish to understand Nature, and they do not do so by discarding the most significant aspects of an experiment, as Bell does by converting analog outputs, in the case of Stern-Gerlach, the binary outputs, based on misinterpretation of the relevant eigenvalue equation.

You seem to gloss over the lack of experimental backup for your statements by your statement that "real Stern-Gerlach experiments are done on neutrons rather than electrons." What you have not done is supply references to such experiments with "binary outcomes."

In a description of such a neutron experiment I find the statement:

6. "The following table is an actual experimental record of neutron impact positions on such a screen." [Followed by a table with neutron counts from positions -60 to +60 in steps of 10.]

This "actual experimental record" is not binary but has 13 outcomes. As far as I'm concerned that is proof that your continued statement that "real experiments have binary outcomes" is simply wrong. Perhaps you can find such an experiment, I doubt it. Until you do I consider your statement not only mistaken and contrary to the facts, but proof that you are simply trying to convert a physics experiment into logic exercise. And even if you manage to find an experiment conducted with only binary outputs, this does not erase the fact that the actual physics, which is the important thing, is analog.

If you have any actual experimental data to backup your statements, please show us, otherwise I believe the facts contradict you.

You can repeat statements that ignore physics until the cows come home, but they have no significance for the real world, only for the "mathematical world", and that is not the issue physicists care about.

You say "the point is that Bell has actually proven a theorem about such experiments." The physics data contradict this. Bell is proving a mathematical theorem, based on faulty physics assumptions, and has imposed constraints that have no meaning in the real world.

You still do not seem to be able to distinguish Stern-Gerlach experiments from Aspect type experiments.

Please address the fact that the 13 outcomes for actual experimental record of neutron impact positions on the screen is not binary.

Regards,

Edwin Eugene Klingman

Dear Edwin,

I cannot understand why you refuse to simply pay attention to what I have repeatedly written. Send a neutron through a Stern-Gerlach apparatus and report the outcome as either "spin up" meaning "neutron recorded above the midline" or "spin down" meaning "outcome recorded below the midline". The outcome space is now binary and Bell's result applies. This is what is meant everywhere by "doing a spin measurement on a neutron" and it is what is understood by saying "a spin measurement on a spin ½ particle is always either spin-up or spin-down". The actual results cluster in a small group well above the midline and a small group well below, and for the purposes of reporting the result the former count as "spin up" and the latter as "spin down".This describes the outcome of every such experiment ever done, including the very first ones whose data you have reproduced. This is, of course also physics. It is both the behavior predicted by standard quantum mechanics and, more importantly, the behavior observed in the lab. None of this is controversial, so I can't imagine why there should be any time spent on it.

Tim

Dear Tim,

When it suits you, you invoke quantum mechanics, and when it does not suit you, you say Bell's theorem has nothing to do with quantum mechanics.

Bell was asking whether any local theory could produce the statistical correlation that quantum mechanics predicts. I have presented a local theory that does so (see page 7).

You have insisted that Stern-Gerlach experiments "really" only measure two classes. I have produced experimental records of data in 13 "classes" or "positional domains", definitely indicative of real physics of spin. Because this destroys your argument you ignore the real data and go back to your "logical" data, having nothing to do with the experiment, but supporting a physically flawed, if mathematically "clean" theorem.

You are wrong to state that it describes the "output" of every experiment ever done, because all Stern-Gerlach experiments, whether based on neutrons or silver atoms, or other atoms, yield analog distributions, not your binary outcomes. Only by throwing away the experimentally measured physical data and replacing it with your "logic" data can you make your argument.

Edwin Eugene Klingman

Dear Tim,

Can you tell me what physical data (not 'logical') is being measured in the Stern-Gerlach-based experiment?

Can you tell me what is being measured in an Aspect-experiment?

And can you tell me HOW these are being measured?

You say "for analytical purposes these are treated interchangeably ... because as far as the theorem goes they have exactly the same form." This is exactly the trap Bell falls into based on Dirac and Pauli's eigenvalue equations having "exactly the same form"! That is significant mathematically but meaningless physically. It is true only if you consider "logical equivalence" to imply "physical equivalence." But you would be wrong to imply this, as they are distinctly and significantly different physics and different detection methods. To gloss over these differences is once again to move from the world of physics into the world of mathematics. That may be interesting to a mathematician, but it has no consequences in the real world, and certainly says nothing about "local realism" versus "non-locality". It is simple logic based on oversimplified (incorrect) physics.

You say Bell has "actually proven a theorem about such experiments" and I have "not disproven or shown any problem with his proof." As you see his proof as "a clean piece of mathematics" this is all that counts for you. But while I do not find fault with his mathematics, I do show that his physical reasoning is faulty, and good logic based on faulty assumptions leads nowhere of any importance to physics. This is what you steadfastly refuse to recognize.

I see no value in a "clean piece of mathematics" based on false assumptions, and your assumption of 'binary outcomes' for Stern-Gerlach experiment is faulty and your assumption that Stern-Gerlach and Aspect experiments are "analytically equivalent" because they have the same "form" is faulty, as far as any physical significance is concerned. You wish to divorce all physics from Bell's theorem and then claim it has physical significance. It does not, and shouting "does too!" forever will not change that.

Nor will it prevent my local model from obtaining the results Bell "proves" cannot be obtained.

Again, you say Bell has "proven a theorem". I too have "proven a theorem". Experiments confirm that Bell's model fails to match reality. Thus any theory based on his faulty model is of no physical significance. If an experimental test of my Energy-Exchange theorem-based physics fails to match my model, then I too will be proved to have a faulty model/theory. If, on the other hand, an experimental test of my theory shows it to match reality, then my model, which supports local realism, will be shown to agree with reality.

Finally, you ask what 'function' I am using to calculate the outcomes of my hypothetical experiment. Like your use of 'toy model' this is an incorrect description. My model is a Monte Carlo type model of the energy exchange physics and is a real computer experiment, not a 'hypothetical' experiment. I have presented the key 'function' as the significant contribution to deflection on page 5 of my essay, and I have described the physics in the papers referenced therein. I have stated that I use the standard formula for calculating expectation value and I have diagrammed the model on page 6, and showed typical vector data used in the model, and showed the cosine correlation derived from the model on page 7. This should be sufficient information to allow you or anyone else to develop a model for yourself and prove to your own satisfaction that it reproduces the quantum mechanical correlation, -a.b. My model is implemented in the very high level language Mathematica, and is not as transparent as lower-level code. The function, the standard formula, the physics, the diagram, and the data are all straightforward and produce the results shown. Bell did not make a mistake in his math nor have I made a mistake in my math, so that is beside the point. The point is the physics of Bell's model versus the physics of my model. One of us has definitely made a mistake in his physics. You are not attacking my physics, you are erasing the physics from the problem and pretending that logic and mathematics divorced from physics have physical consequences. That is a radical proposition.

Regards,

Edwin Eugene Klingman

Dear Dr. Klingman,

Your essay has prompted more comments than any others, and it is evident that a hostility towards any non-quantum approach in general has eroded the community rating your brief synopsis of work initially deserved.

I would ask any community members who might yet evaluate your essay to revisit how the ad hoc category of 'spin' originated, before assuming that results of a classical experiment that clearly can be explained by orbital angular momentum, must be interpreted with the constraint of an 'adjustment' to OAM in an obsolete Newtonian atomic model. Members, ask yourselves; 'why doesn't spin change speed?' And why would that necessarily apply to a projected neutron's magnetic moment precession? Think. Thanks, :-) jrc