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

Edwin,

You used to steer clear of BT as though it were in fact a hornets' net but now you've sort of gone at it with a bat (baseball or cricket depending on the reader's culture).

I'm not sure Korzybski would've would've considered math the map and physics the territory so much as holding that both math and physics are maps and the territory is the actual physical world. He was suspicious of all symbolic representation and physics is that as much as math is. A better icon might have been Eugene Wigner who wrote the classic essay alluded to without attribution in this contest's set-up: "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Maybe the FQXi honchos didn't speak his name because they were afraid contestants would go back and crib stuff. So don't do teasy b.s. like throwing out scare-quote hints, guys.

Speaking of Wigner, he also published the first paper by a major establishment scientist (which Bell certainly wasn't at that time) about BT. Back in 1970. Bell cites it in "Bertlmann's Socks and the Nature of Reality" and also incorporates him into what he named "the Wigner-d'Espagnat Inequality". That inequality is a particularly sweet formulation of Bell because it's simple Venn-diagrammable set algebra which anybody can get her or his head around and employ to conduct experiments on classical objects here in the macroworld. When you do that you get no violation. It's a description of a definitive feature of macroscopic ontology. It's pure distillate of local realism. (It has also been used in quantum experiments in which it's violated but for a number of reasons lost out to CHSH.)

Anyway ... isn't it conceivable that the only meaningful objections to Bell experimental outcomes are technical ones ... the need to close the experimental loopholes? Isn't the rest mainly intellectually reactionary metaphysical nitpicking?

Hi Nick,

Your first point is easy to address. Yes, math and physics are both Korzybski maps if "physics" is defined as the model(s) of physical reality. I was using "physics" to stand for physical reality, but technically you are perfectly correct.

And yes I did steer clear of JC's "topological" treatment of Bell. My essay, while complex, is pretty straightforward. An often repeated and almost universally believed statement is that "no local model can reproduce QM correlations, -a.b." I show that this is not the case. As 'entanglement' is the shaded space in the figure at the bottom of page 6, it disappears if the local model yields the cosine curve rather than the straight line. It only exists to bridge the gap between Bell's local models and reality. If the local model agrees with reality, as mine does, there is no need for a mystical 'entanglement'. The question is then why did Bell always get the straight line, and I argue that he unnecessarily and incorrectly imposes constraints on his models, based on his oversimplified assumptions. Recent scores indicate that this is not a popular argument. Quelle surprise!

I don't know how much effort you put into following my reasoning (backed up by references 2 and 4) but the problem has nothing to do with loopholes. Experimental results, quantum mechanical predictions, and my local model all agree with -a.b. It is Bell's models that don't agree, because he erases the physics that yields the correlations by imposing his constraints. My results imply that quantum mechanics is incomplete, which appears to be as popular as the skunk at the picnic. I've been accused of being "against" QM, and of saying that QM is "wrong". Not wrong, incomplete. Big difference. But there are probably no physicists alive who have not been sold that reality is quantum mechanical, and we only have to show how the classical world derives from it.

As is obvious from comments on this thread, the problem is extremely complex. That's also obvious from the fact that 50 years of Bell has left physicists confused about spin, entanglement, non-locality, etc. I think physicists are pretty bright guys, and would not remain in confusion over a simple problem. It's not a simple problem. I hope you find time to understand my essay, but I know how short time is. Anyway thanks for your comment and it's good to see you again.

Best,

Edwin Eugene Klingman

Hi Edwin,

I think a lot of the negative reaction to calling QM "incomplete" stems from the pejorative attitude that emanated all along from EPR, particularly E, in connection with the word. It was not meant in an objective way. They were singling QM out as historically anomalous, singularly unworthy of scientific status, a leper among theories. The attitude was hostile. Not as dreadful as JJC's, but then he does hold a unique position in the annals.

At best EPR were suggesting that not only was QM incomplete but that as a result it was fundamentally wrong.

I'm fairly laid back about incompleteness. I've studied stats and worked with statisticians. On one level statistics is not a complete theory, because it offers no physical explanation for a vast number of the correlations it presents to the world. Take as an example the Nielsen ratings. What is the causal relationship, if any, between the viewing patterns of a sample population numbering in the low four figures and the viewing habits of the hundreds of millions in the general population which the sample population is purported to reflect on an ongoing basis? Nobody can say or even make a good guess. But empirically we know the correlations are genuine, because you can double-check by setting up auxiliary sample populations and when you do you find those entirely separate groups in agreement. Statistical measurement is valid. It works. You just can't explain why and how except to say it probably has something to do with randomness. QM writ large.

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    • Post #124

    Karma is a funny thing. While those folks who have obviously voted down Dr. Klingman's work may think they are making a statement, the measureable truth is a little different. The essay rules indicate that an essay must receive at least 10 ratings to become a finalist. Dr. Klingman's essay is therefore the first essay to be eligible for that status.

    Congratulations Edwin! You too haters:-)

    Regards,

    Gary Simpson

    Hello Edwin Klingman,

    My initial comment, as I intend to return to make more, is that your effort to demystify the unnecessary mystery introduced into physics at the quantum level is to be encouraged especially given the coherence of your argument. It however seems, you believe that there is a mystery to be solved since you use the same kind of reasoning Bell used only leaving out the hidden constraints. I am not expert on the EPR argument and I have serious reservations about the starting premise. For example, in the EPR experiment using light polarization, it is a doctrine that a photon is indivisible and it is on this premise that an attribute called "spin" was foisted on light. Whereas, light as a wave can be split and made to interfere being a transverse wave and cancel each other. Let me leave that for now.

    Given, a large box full of black balls and another full of white balls. If you select one ball from each box and give to an assistant to package one ball each in a parcel and DHL one parcel to Alice on Venus and another to Bob on Mars. On receipt, Alice is to write parcel 1 = Black or White as the case may be; parcel 2 = Black or White as the case may be, etc up to parcel 12. Bob on Mars is to do the same. After the expedition they report back to you on Earth with their findings. You, who carefully prepared the parcels in the so-called 'singlet state' or binary as Tim prefers. Are you saying the report of Alice and Bob will give us new physics or mathematics, or am I missing something?

    I hope you will not like others claim that because of one controversial experiment by Aspect et al, which the late Caroline Thompson has discredited in my opinion as I have stated elsewhere on a blog post on the FQXi website we should be made to undergo unnecessary head splitting as is currently the case?

    In my opinion, unless you think otherwise, any time Alice marks Black ball, Bob will mark White ball, and if no ball perishes in transit they will be correlated 100% of the time. This is an experiment that can be performed cheaply on the classical scale. Or is it not as simple as I suggest? Perhaps, there are things I am ignorant of that I need to be taught?

    Best regards and always willing to learn from you,

    Akinbo

      Dear Akinbo Ojo,

      I do appreciate your kind remarks, and thank you for reading my paper. I'm very happy you intend to return to make more comments.

      I'm sure you understand that I claim John Bell significantly oversimplified the problem, leading to an erroneous conclusion. But even his oversimplification is complex! To go a level deeper, as I have done, makes the issue even more complex. (Actually, I think it simplifies the physics, but in the context of his theorem it requires both the new level of physics plus Bell's model and requires bringing in the Dirac fundamental helicity eigenvalue equation plus the Pauli provisional precession eigenvalue equation plus new arguments and the new Energy-Exchange theorem and local conservation of energy. Thus Bell supporters can either validly miss the point or can obfuscate by ignoring the points.)

      As I have noted, Bell's models do not work. Bell could easily have simply stated that "my model fails to produce either the quantum mechanical or the experimental measurements" and it would not have been a big deal. Instead Bell claims that no one's local model can possibly work (a pretty big assumption, if you ask me) and then claims that local reality, one of our most basic intuitions of the universe, is wrong. That is a big deal.

      Because Bell formulates this as a simple mathematical model and because his mathematics is essentially correct (his physics is wrong) those who work through his mathematical model conclude that no local model could escape his logic. The fact is that Bell imposes unwarranted constraints as the first equation in his theorem and this guarantees that no local model can beat his theorem. The only question is, are his constraints justified? I argue that they are not.

      As I do not assume that you have read all of the above comments, I will repeat a few points. First, Bell (and/or his defenders) make (at least) two false equivalencies:

      1.) The assumption that the Dirac equation and the Pauli equation are essentially equivalent.

      2.) The assumption that the Stern-Gerlach and the Aspect experiments are essentially equivalent.

      The first I have dealt with in detail in my essay and in the ~20 page paper Spin: Newton, Maxwell, Einstein, Dirac, Bell, so I won't repeat the arguments here. The second I have not yet written up in detail, so I will mention it here.

      It is an error to assume that Stern-Gerlach and Aspect experiments are equivalent due to two facts. The first and obvious fact is the quite different physical nature of the entities being tested. The fact that quantum mechanical kets look similar, or that simplistic models are plane waves obscures this but does not erase the essential difference between charged spinor fermions and uncharged bosons, and no one who is serious can claim that these physical entities are equivalent.

      But even more significant, from the Bell's theorem perspective, is the essentially different measurement techniques involved. Despite many comments above, Stern-Gerlach, whether measuring silver atoms or neutrons, produces a distribution of deflections. It is a scattering experiment, whose outputs are position measurements. Aspect-type experiments count photons, and the output is a count. In the deflection measurements, the initial spin (lambda) is indirectly exhibited, and clearly exists. In the counts, the photon-equivalent of the initial orientation is subsumed, and is not evident as it is in Stern-Gerlach. This is one reason I have focused on SG experiments.

      On page 84, in Bell's "Speakable..." Bell states "let A be a variable which takes the values +1 or -1 according to whether counter one does or does not register. [and same for B...]" This, whether it is currently realized by Bell defenders or not, is significantly different from his claim on page 15 that "the result A of measuring sigma_dot_a ... [is +1 or -1 ]." One is a deflection, the other is a count. One exhibits the 'hidden variable' in the value of a deflection, the other subsumes it in a count. To expand on this as it deserves would take another essay. The point is, it is overly simplistic to equate these two types of experiments as almost all Bell defenders do. Such a claim is based on either ignorance of the physics, ignorance of the nature of the measurements, or both.

      As Nick mentioned above, this battle has often been fought on the grounds of "loopholes", and Caroline Thompson, as I recall, focused on loopholes, forgive me if I'm wrong on this. That argument, I believe, is essentially that the measurements are wrong, and loophole free measurements would agree with local models. That is significantly different from my argument which is that Bell imposed erroneous constraints on local models and that is the reason his local models do not work. I have presented a local model, the physics underlying the local model, a computer experiment based on the local model, and the results of the local model, which agree with experiments and with quantum mechanics. Loopholes play no part in my argument and are simply a distraction. Bell's oversimplified physics is the essence of my argument and I present physics that, as Einstein demanded is "as simple as possible, but not simpler."

      Akinbo, yours is a very relevant comment, and to address all your points in one response would require a longer comment, so I'll stop here, and address your other points in another comment(s).

      I hope to address two types of readers in this forum - one type is the Perimeter-type, like Pusey and Leifer, "the big boys" in the field who have entered FQXi contests in the past and who contribute to FQXi. I hope for the sake of the FQXi community they respond. You represent the other type - informed, brilliant, interested non-physicists - so I hope you will return with more comments. The effort to move me down in the rankings is, I believe, to decrease the visibility of my essay and my arguments and I consider that a good sign.

      My very best regards,

      Edwin Eugene Klingman

      Dear Akinbo,

      You are correct that I am against mysticism in science. If mysticism is real, it belongs in religion. The mystical has no place in science. In my opinion entanglement is mysticism. Technically, it is represented by the shaded area shown at bottom right of page 6 in my essay. Both quantum mechanics and experiment yield the cosine curve shown, while Bell's constrained local models yield straight lines. 'Entanglement' is the non-local bridge designed to get one from Bell's "local" model to reality. As such, it is a mystical figment that cannot be explained, accurately described, or measured, despite hundreds or thousands of papers that work in the shaded realm. That statement does not make friends in the Bell community, but that does not affect its truth value.

      I am not certain what other mysticism you refer to. As noted in my first comment to you, photon-based experiments are essentially different from Stern-Gerlach scattering of magnetic dipoles in an inhomogeneous field. It only complicates things further to deal with the difference, and it is not necessary to do so to "disprove" Bell, who clearly was thinking of Stern-Gerlach as he addressed EPR issues.

      Bell's formulation adds a "hidden variable", lambda, that Bell essentially allows to be "anything". The designer of a local theory can choose whatever physical attribute he wishes for lambda. The goal of the game is to compute the physics of the local model, based on a distribution of lambdas input to Alice and Bob's measurements, such that the outputs of Alice and Bob's measurements will be correlated as predicted by quantum mechanics, and as found by (photon-based) experiments.

      Your box of black and white balls does not have anything corresponding to lambda, therefore it is not analogous to a Bell experiment. I have spent a short while considering adding colors to your balls and letting Alice and Bob look through a third color filter, but it gets too complicated for a comment. I hope you get the idea however.

      In my local model, lambda is the initial orientation of the spin, which can be any vector in 3-D space. If this spin vector is sent to Alice, the opposite will be sent to Bob. As outlined in detail in my essay and references, whatever the initial value of spin vector is sent to Alice, it will align with the field direction (that she chooses) or it will anti-align with the field. But this process of alignment is a dynamic process, that involves energy exchange between the "precessional" energy and the "deflectional" energy modes, in such a way that (since both energy modes depend on the angle between Alice's field and the initial spin direction) the deflection contains information, recorded as position, about the initial value of lambda. That information is absent from quantum mechanics, hence quantum mechanics is incomplete. Not wrong, incomplete.

      The question is whether, given the value of this (hidden) variable lambda, a local theory can determine the deflection such that the actual values, calculated locally by Alice (and Bob does the same for the field angle he chooses), when correlated (on a pairwise basis) agree with the statistical quantum mechanical predictions, or not. My local model does agree with quantum mechanics, whereas Bell says this is impossible.

      But Bell does not measure deflection - the information is there but he throws it away and says, in effect, "I care only about whether it was deflected "up" or "down", not how far up or down. Thus he allows you to put additional information (the initial direction, lambda) into the problem, and even to calculate the physics with a local theory, but then he erases all of the physical information content in the "how far up or down" by using only simply "up" or "down". (+1 or -1).

      Why does he do this? To understand this you need some concept of eigenvalues and eigenvalue equations, and this involves the Dirac and the Pauli equations which Bell apparently considers equivalent (they are not!) In essence, a simplistic idea from 1925, Goudsmit and Uhlenbeck's idea that "the projection of spin on any axis is +1 or -1" has added a mystical aspect to spin that no one can understand, and makes spin 'look like' one bit of information instead of a physical spin that simply aligns with a complex local apparatus. It is absolutely not an essential concept of quantum mechanics. If it were it would be an axiom. It is simply more confusion that came about historically and is treasured by those who worship quantum mechanical mysticism. It's got nothing to do with the statistical results of the quantum mechanical formalism.

      I hope that the above helps you understand why the black and white ball example is not a good analogy for Bell's theorem.

      Best regards,

      Edwin Eugene Klingman

      Akimbo, - I should probably add one more brief comment. The experiment with balls that you describe corresponds to Alice and Bob always choosing the same direction of magnetic field in their respective instruments. In that case, yes, the (anti-)correlation is perfect. The problem of Bell and EPR is when Alice and Bob can freely choose any direction, uncorrelated with each other, and unknown to each other. That aspect of the problem does not show up in your B&W analogy. - Edwin Eugene Klingman

      Edwin,

      Personally, I agree with your premise that the 'timing device' of spin is not the determinant of deflection in SG positional plots. But as an editorial comment, in the interest of 'sales presentation', spin should and must be given its due in quantum mechanical methodology. The eventual abandonment of the electron as a classical particle in an atomic volume was in part due to the Goudsmit-Uhlenbeck hypothesis, but the utility of +1 or -1 symmetry extends to establishing a benchmark for an otherwise chaotic atomic structure. I have not found anything in reading that suggests that the constant rate of spin was for the specific purpose of the classical particle of the GU model always presenting the same designated point on an equatorial plane towards the nucleus (spin is like the dark side of moon) against which the rotational speed could be metered, but it works that way. Actually at the time numerous notables contributed to the spin orthodoxy and the 1:1 rotation to orbit may simply have mathematically become evident, and casually accepted as axiomatic.

      So while the definition of inertia provides sufficient reference from trajectory to protract axial deviation from the normal line in a particle-like form exhibiting a magnetic dipole, and macroscopically deflection dependent on the a continuous measure of that deviation, spin is simply subsumed not necessarily absent.

      Give a little thought to putting some friendly spin on your sales pitch. :-) jrc

      Dear John,

      "Give a little thought to putting some friendly spin on your sales pitch. :-) jrc"

      Thanks,

      It's so easy to get caught up in the logic and the politics, and forget what is being communicated to whom. I thank you for this reminder, and hope to respond accordingly.

      Edwin Eugene Klingman

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      • Post #131

      Hi Nick,

      In re-reading your first comment above, you bring up Wigner's "Unreasonable effectiveness..." paper, answering which was a key motivation for my dissertation, [link:www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=Klingman+Automatic+]The Automatic Theory of Physics[/link]. The figure on the first page of my essay encapsulates the way in which physical counters, producing natural numbers, can make counter-based measurements (recall that the heart of quantum field theory is the number operator.) The measurement map is the plane at the far left, and the measurements are generated automatically, one way or another. The question is what to do with all these numbers. To answer that, I invoke a robot. This allows algorithmic computations but removes intuition. (Whatever one thinks of the eventual possibilities of robots gaining intuition, it was beyond doubt that when I wrote this, robots did not have intuition. But even in those dark ages we had neural net algorithms and other self-modifying-map architectures for learning.)

      My design of the robot anticipates Max Tegmark's concern with 'baggage' - I left the baggage out. The robot has access to resources, including random number generators, arithmetic-logic-language circuitry and systems, and sensors and activators to interface to the physical world, but no consciousness or intuition or beliefs - no baggage - just designed-in algorithms, including learning and self-modifying-map algorithms. This response to Wigner is a vehicle for testing "A theory of theories of physics", and some similar work by others in 2009 extended this idea.

      The relevance of this to your being laid back about the incompleteness of QM is that the measurement space on the left of the figure consists of nothing but numbers, all of which can be accessed by the robot who performs cluster mapping on involving intercept and interest set distances, grouping the data into n-dimensional cluster space. This is not necessarily the optimal dimensional representation of physical reality (i.e., the object/source of measurements) so I employ a Karhunen-Loeve transformation from n-space to lower dimensional m-space, from which the feature vectors are formed. The eigenvalues are the vector elements and the eigenvalue equations are the transforms that preserve them - quantum mechanics!

      In this view the quantum mechanical formulation arises from statistical clustering of measurement numbers, but what is being measured? What is at the left of the number space that is the real source of measurements? What is its nature? There is no obvious answer.

      If one believes all of physical reality is somehow quantized, and it is impossible to measure any other value, then one assumes

      A eigenstates exist, and

      B ideal measurements yield eigenvalues

      But the robot doesn't carry this baggage, the ingrained belief of almost a century of QM. There is no way for him to tell whether the numbers represent eigenstates or random digitized data derived from measurements on a continuum. Not being a robot, I do carry baggage, and my personal view is that reality is a continuum, with only action quantized, not time or length or even energy, except when boundaries are imposed on a subsystem. The magnitude of intrinsic spin is quantized, but its direction is 3-dimensional unless and until it is caused to align with the local field, as in Stern-Gerlach.

      This view has led to a local model that produces the same correlation as quantum mechanics, with implications for entanglement and it seems to imply that QM is incomplete. I repeat, not wrong, but incomplete. As you mention, there is EPR baggage that causes some resistance to this notion. Not sure how to handle it.

      Edwin Eugene Klingman

      John,

      Reading a book on Schrodinger, I just came across the following:

      "Arguably the most significant development in science in the 20th century - was the resolution of the EPR 'Paradox' and experimental confirmation that quantum entanglement ... is real."

      Sometimes I am at a loss as to how to put a happy spin on tackling this, as some are hostile to the idea that entanglement and 'non-locality' are not what they've been taught for 50 years. If you have any helpful suggestions (other than to drop all snarky references to "worship of quantum mysticism") please give them to me off-line at klingman@geneman.com. And again, thanks for your sage advice.

      Edwin Eugene Klingman

      Dear Doc,

      I'll be pleased to. Though the abundance of literature seems to be more about eliminating loopholes than demonstrating the dependence of both quantum and relativistic theory on firm classical grounds. Forgotten in the application of textbook inventory formulae, is the stated rationale at inception of many concepts. In particular to 'spin', the 1/2 value is prescribed quite simply by Maxwell's authoritative qualification of Faraday's 'right hand rule', even Heisenberg recognized that. 1/2pi, is (gee) 90 degrees. Which goes to Minkowski, which goes to spin being an intrinsic property of real measurement function. That no doubt might sound cranky to one without a dissertation on file, so if I run across a choicy item I'll email. Kind regards, jrc