Hi Tom,

Your essay contains fascinating information. Although many statements exist to the effect that experiments prove non-locality, the fact is that the experiments prove [or come very close to proving] that the experimentally found correlations agree with the correlations predicted by quantum mechanics. It is not physical experiment, but mathematics, that proves...

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Hi Tom,

Your essay contains fascinating information. Although many statements exist to the effect that experiments prove non-locality, the fact is that the experiments prove [or come very close to proving] that the experimentally found correlations agree with the correlations predicted by quantum mechanics. It is not physical experiment, but mathematics, that proves that Bell's models, as formulated, are incompatible with local realism. If Bell's model is correct, this seems to have physical implications for local causality, a.k.a. local realism.

Bell assumes as the basis of his model that the precession occurs in a constant field, which leads to a null result for Stern-Gerlach apparatus, and therefore an implicit contradiction, since 0 is not equal to +/-1; [zero being the result of the assumed constant field and +/-1 the result of the actual SG non-constant field employed in the experiment.]

In an attempt to avoid this inherent contradiction of Bell's constant-field model, I have analyzed the physics of the inhomogeneous field and constructed a local model that does produce the quantum correlation, -a.b, unless it is subjected to Bell's constraints.

This leads to the question, why does Bell impose these constraints, and I have attempted to answer this; Bell not being available to answer for himself. You are welcome to read my essay to see what I'm talking about.

It is for these reasons that I find your following statements fascinating [and find I must buy Solow's book, which I believe you have recommended before.]

You say:

"…Bell's Inequality – the formal mathematical statement of Bell's theorem – is only locally real. The issue of non-locality arises in the proof of the theorem and that proof is only by way of double negation."

"What double negation means is that the proposition A is proved by assuming it's negation (~A), and then proving A by contradiction without ever explicitly constructing A…"

As you remark "It's a perfectly legitimate proof technique; mathematicians use it all the time. However, in order to apply such a mathematical proof to physics, it would have to be explicitly shown that the physics is independent of the mathematics, which is impossible in the case of Bell's inequality … the result being derived by inductive inference."

Although you state quantum theorists know this, if so, they keep it well hidden. I have never seen it so clearly stated. Thank you for stating it so clearly. As soon as I finish this comment I will go buy Solow's book, How to Read and Do Proofs. Thanks for that, too.

Finally, congratulations on your contribution to the Springer book.

Good luck in the contest, and best wishes,

Edwin Eugene Klingman

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Hi Edwin,

Thanks for the kind comments. In fact, I had read your essay previously, and was impressed -- it's your clearest and most direct, in my opinion, of all your entries over these years. I am finally convinced that we're talking about the same thing.

Key to our agreement in principle is the value of a continuous function. Just as Einstein originally formulated mass-energy...

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Hi Edwin,

Thanks for the kind comments. In fact, I had read your essay previously, and was impressed -- it's your clearest and most direct, in my opinion, of all your entries over these years. I am finally convinced that we're talking about the same thing.

Key to our agreement in principle is the value of a continuous function. Just as Einstein originally formulated mass-energy equivalence in terms of the Lagrangian, I think your energy exchange theorem in terms of the Hamiltonian underscores the scale independence of analytical continuity in a physical system.

Quantum theorists are not bothered by the double negation foundation of conventional quantum theory, because they consider it irrelevant. The Bell model is what topologists call multiply connected -- i.e., local pathwise connections are independent of global structure; the assumption of nonlocality is an unavoidable assumption of a multiply connected space.

That's how we get the inductive inference, “If nonlocality exists in the present, it does not not-exist in the future.” One simply cannot discard nonlocality as an experimental assumption of Bell's theorem, because were the mathematical assumption correspondent to the experiment, the conclusion would have to be that nonlocality is an empty set. In Solow's chapter 11 ("Nots of Nots Lead to Knots") one finds that " ... to use the contrapositive method ... you must be able to write down the statement NOT B so that you can work forward from it. Similarly, you must know exactly what the statement NOT A is so that you can work backward from it." The statement A in Bell's theorem is never constructed; it is only found to be not not-A. Again, this assumption does not bother quantum theorists because counterfactual definiteness is exactly equivalent to, “If nonlocality exists in the present, it does not not-exist in the future.” There's a problem with causality here:

Think of it in terms of the Schrodinger's cat gedanken experiment. So long as the cat is in a state of superposition, neither dead nor alive, there's no problem with the counterfactual. Dead and alive are equally likely. Doing a measurement on the box "collapses" the state into a classical bit.

That creates the illusion of observer determinacy -- the free will to look or not, and find the locally real state. Schrodinger's wave equation, though, is fully deterministic, backward and forward in time. The experimenter's assumption in preparing the experiment is that the cat is in a state called "alive" as opposed to the other binary state called "dead." The contrapositives not-alive and not-dead, however, are never constructed -- the experimenter assumes when placing the cat in the box that it is not not-alive. Try and make the assumption that the cat is not not-dead, and I think there is little doubt about the state one will find the cat in, when the box is opened. The initial condition makes the difference between the states -- yet the experiment assumes that not not-alive = not not-dead. It begs its own conclusions.

I'll get around eventually to commenting in your forum. Good luck and all best,

Tom

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Tom,

I'll start a new thread to get back on topic. I detect a hidden variable in your essay approach, namely the original EPR wave equation which seems to be ignored in speculative arguments about the double slit experiment. EPR's argument was that it could be possible to discover a state of position or momentum of a particle following the correlating event of impact with another without...

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Tom,

I'll start a new thread to get back on topic. I detect a hidden variable in your essay approach, namely the original EPR wave equation which seems to be ignored in speculative arguments about the double slit experiment. EPR's argument was that it could be possible to discover a state of position or momentum of a particle following the correlating event of impact with another without disturbing the first mentioned particle ( let's use working class terms of solids and stripes referring to pool balls when betting prefers the faster game of 8-Ball, to Rotation ). Let's call the particle we'll subject to measurement 'solid' and the unmeasured object particle 'stripe'.

The EPR argument was that to deduce the position or momentum of the 'stripe' after impact with the 'solid', did not require measuring 'stripes' properties, but could be found from knowing one parameter such as position of 'solid' by it's passage through one of the double slits and by measuring the momentia change of the screen itself imparted by both particles. Consequently a measurement was not necessary of 'stripe' which would change its state. That was the argument, position and momentum can be determined from other properties without effecting or losing the intrinsic pair (q,p). And in your essay the prime criteria is that a closed logical argument can only be had if the probability has a binary outcome, q or p in the EPR scheme of things.

We can go on with other examples where your essay generalizes to math. Let's look at Schrodinger's Cat (anybody that would suggest doing that to a cat has some issues, anyway). Firstly, its only true of spherical cats and felines are predatiously linear, so is light. Illumination can be treated spherically, but to subject the detection of a 'photon' to a random probability on a spherical surface projection which relativistically increases eightfold with doubling of the time parameter, only means that the initial direction of emission is not known, or sought within the source.

In answer to the question posed by EPR, if QM is a complete theoretical description of reality, we really needn't resort to arguments on QM's terms. Max Planck, himself, fully expected that his self-avowed 'lucky guess' would eventually be rationalized. In the immediacy of events of that era, following two centuries of progressive Newtonian predeterminism intellectuals were starving for a ration of free will, and the new maths were simply more inviting than constructing a classical model of light that would reveal cause of the Quantum. The catch-22 of fundamental randominity is that it too results in not having means to determine choice. We have come full circle sociologically. Humanity does have free will to choose between two probable causal results, and none if the outcome is random anyway.

It is really time to let Schrodinger's cat out of the bag, and answer Planck's question. :-> jrc

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I find myself in the position of defending the views of both Alan Kadin and Michel Planat, who crossed swords in Alan's blog.

No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.

I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late...

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I find myself in the position of defending the views of both Alan Kadin and Michel Planat, who crossed swords in Alan's blog.

No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.

I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late Walter Philipp that introduction of a time parameter generates the Bell "impossible" result E (a,b) = - a . b

That's only half the story, though. The other half is that the assumption of fundamental particle reality obviates that dot-product result a priori, while the assumption of a fundamental field theory requires no a priori assumption of fundamental particle existence (Kadin's claim).

Though I don't mean to be self-promoting -- my own view, that the Hilbert space (and the linear superposition of particles to which Alan refers) is deficient, is based on my prior research that metric continuity in the Hilbert space depends on deriving a real valued well ordered sequence without invoking the axiom of choice.

This would be true, regardless of whether one assumes particle discreteness or wave continuity. It comes down to the perennial question of what is being measured. Alan is very clear that his program obviates a domain boundary between classical and quantum. Bell-Aspect and CHSH programs, on the other hand, actually create a domain boundary, by observer dependence, and therefore cannot survive without an assumption of particle nonlocality.

So how would one show what is being measured, unless 'what' is discrete? And Is it a sharp point particle, or a wave packet? A quantum of something only implies measurability; it does not imply a definition of something. A field of something presents the same problem.

I think we are left with the same question that Einstein identified so many years ago -- that if we don't improve the mathematical methods, we can't expect resolution of the gap between quantum and classical mechanics.

I think that Planat and Kadin are equally sincere, honest and competent in their mutual quest to improve the mathematical methods. That's how science progresses.

Tom

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Hi everyone

I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179

He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing...

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Hi everyone

I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179

He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing bivectorial terms cancel out of his "correlation" (the answer has to be scalar, right?).

Of course it is easy to "fix" that mistake locally, by an ad hoc subtraction of what you don't want to have. He shows what you have to subtract to Christian's (17) in order to make the left hand side equal to the right hand side.

What Albert Jan *didn't* do is simulate the whole model. His computer program verifies a patched version of formulas (17) and (19) of quant-ph/0703179. So on the one hand, he shows that Christian's original math was wrong. On the other hand, he still has not checked whether the patch which he introduces to fix the gap between LHS of (17) and RHS of (19) is consistent with the rest of the story. After all, if you change the very definition of geometric product locally in one formula in a complex story, that might have repercussions elsewehere, right?

In fact, Albert Jan hasn't addressed the challenge yet of actually generating the measurement outcomes A_n(mu) of Christian's equation (16). Most readers, on a superficial reading, would suppose that (16) was a definition of the two measurement functions A(a, mu) and B(b, mu). However if you read carefully it is not a definition at all: in order to make it a definition one still has to specify the mapping from bivectorial measurement outcomes to {-1, +1}. Many are possible. None, of course, can deliver the goods ... because of Bell's theorem.

It's at this point that one sees the other major error in Christian's attempts to refute Bell: he computes some kind of bivectorial correlation between the outcomes represented as points in S^2, instead of the correlation between the corresponding values +/- 1. Bell is about experiments with binary outcomes. His "correlation" is just the probability that Alice's outcome equals Bob's, minus the probability that it doesn't. Quantum mechanics predicts probabilities; experimentalists observe relative frequencies. The problem is how to explain the relative frequencies?

In Christian's one page paper, four years later, it is clear that he has seen that there was something missing. He does give a definition of the measurement outcomes and now comes up with his daring bivectorial Pearson correlation instead of the "straight" correlation between the binary outcomes. After all, the labelling of the outcomes +/-1 is just convention.

His definition of the measurement functions is A(a) = -B(b) = +/- 1 (with equal probabilities for the two possibilities). Thus his model predicts that the correlation is -1. Bob's outcome is always opposite to Alice's.

"Out of the frying pan into the fire".

I have written up a postmortem which includes a tutorial section on geometric algebra, so that no one has any excuse any more not to be able to work through the math of these classics, line by line, and check everything for themselves.

http://www.math.leidenuniv.nl/~gill/GA.pdf

Amusing
ly, I was not allowed to post this on arXiv.org: it was seen as a personal attack. I must say that my earlier drafts had a title which was a little bit over the top. Now the paper is simply entitled "Does Geometric Algebra provide a loophole to Bell’s Theorem?". The answer is of course, "no".

Showing that geometric algebra provides an alternative and beautiful way to describe the maths of spin half, including several spin half particles, entanglement and all that, was one of David Hestenes' greatest achievements. Two whole chapters are devoted to this topic in the textbook of Doran and Lasenby. They are worth careful study.

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This essay appears indeed highly erudite but I wonder how much the author has understood of the authors he is citing. Let me illustrate this with the citations he gives to papers in an area I know well: Bell inequalities.

Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that...

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This essay appears indeed highly erudite but I wonder how much the author has understood of the authors he is citing. Let me illustrate this with the citations he gives to papers in an area I know well: Bell inequalities.

Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that Bell had forgotten about time. Actually, if you take the care the read Bell's famous Bertlmann's socks paper, you will see that Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time.

Apart from an erudite verbal discussion of the issue of time in these experiments, Hess and Philipp also professed to have constructed a local hidden variables model which reproduced the singlet correlations but unfortunately -- inevitably, of course, by Bell's theorem -- their elaborate construction concealed a little math error. They forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure. This was pointed out by myself and others, and the model died a natural death. The time issues they raised *are* interesting. The possibility of a memory loophole was already being studied by several researchers including myself. All this activity led to Jan-Ake Larsson and myself discovering a "new" loophole in Aspect type experiments due to the fact that experimenters do not use a framework of predetermined time intervals for measurements. Instead, the detection times of two photons being close to one another is used to post-select the pair i.e. to discard all detection events which seem not to be paired. Disaster! A very non-local selection of which outcomes to keep, which to throw away. Biased sampling ... It turns out to be a far *worse* loophole than the famous detection loophole.

Later Hess used the Larsson-Gill approach to build simulation models for past experiments with these defect, together with Hans de Raedt. In his recent book, Hess claims that Larsson and I had *stolen* the idea from him. Well we were certainly inspired by his work, and as he pointed out, other people had noticed that there was an issue, before him.

The hidden title of Hess' book (published as "Einstein was Right!") is "Karl Hess was always right, at least, in retrospect".

Then a second authority whom Ray quotes is my friend Han Geurdes from the Netherlands who recently got a paper published in the journal RIP (results in physics) which is Elseviers' answer to predatory journals where, I am sorry to say, the author gets to pay an exhorbitant fee to have just about anything published. Geurdes' amazing insight is that an experimentally observed correlation might differ by some amount, in either direction, from the "true" theoretical correlation, hence that a local realist simulation model of a loophole free Bell-CHSH type experiment can easily produce a result larger than 2. The paper is discussed on PubPeer: https://pubpeer.com/publications/DBFF182E87F04FB92102CAC7E33
046

Yes! The measured value of some physical quantity might be larger than the true value! Disaster? The end of experimental physics?

Smart people have already known that about half the time, the "observed" value of CHSH would be bigger than 2, half the time it would be smaller. That's why physicists who actually do experiments make sure that the sample size is rather larger and they compute a standard error and do a statistical significance test in order to show that the deviation they have observed above 2 could not be ascribed to merely chance variation around a "true" value equal to 2.

Regarding Bell, EPR and all that I note that Ray does *not* refer to Christian's work so I wonder if this means that he has now abandoned support of that direction?

Before spending just a few words on that, it should be mentioned that Doran and Lasenby's book on geometric algebra contains two whole chapters "doing" spin half, the singlet state, and all that, with geometric algebra. It is very elegant, and very interesting, and just the tip of the iceberg in this area. The only thing they don't do is provide a local realist model for the singlet correlations. (For obvious reasons ... Bell's theorem).

However it seems that geometric algebra is not so popular in this area any more. I suppose it did a good job at describing all the facts - all the facts which are also described in the conventional Hilbert space approach. It links them nicely to geometry. But it didn't take us any further. And just like the conventional Hilbert space approach, it does not tell us what is going on "under the hood" event by event. It is "just" another (mathematically isomorphic) way to derive the probabilities of what happens.

My recent analysis of Christian's early works including a tutorial on geometric algebra is on viXra: http://vixra.org/abs/1504.0102 "Does Geometric Algebra Provide a Loophole to Bell's Theorem?"

and Ray has given a link to a pdf discussing my paper here: http://fqxi.org/data/forum-attachments/Continuing_misguided_
attacks_by.pdf

The point I want to make is that time and time again in this essay, I am sorry to say, the essayist does show that he does not know what he is talking about. IMHO. Sorry.

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John Cox has an elegant way of bringing the issues in line with everyday experience.

Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .

Because initial condition changes with time, moment-to-moment action (event...

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John Cox has an elegant way of bringing the issues in line with everyday experience.

Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .

Because initial condition changes with time, moment-to-moment action (event by event in QM simulation terms) avoids action at a distance " ... by letting the probability measure be a superposition of setting-dependent subspace product measures with two important properties: (i) the factors of the product measure depend only on parameters of the station that they describe, and (ii) the joint density of the pairs of setting-dependent parameters in the two stations is uniform."

The multiple time scales of a pool game range from the interval of contact of hand with cue, cue with cue ball, cue ball with object ball, ball with rail, etc. These are well understood causal events whose outcomes are all dependent on initial condition and energy content in the specified interval.

Gill, et al, criticism of Hess-Philipp completely avoids the causal framework -- they claim, " ... "(Hess-Philipp) forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure" -- which is completely irrelevant to the point made by H-P above (and well supported by the mathematics of the paper). Normalization of probability density in a time dependent causal relation is independent of energy density and initial condition. Hess-Philipp show that initial energy condition determines joint probability -- while Gill et al avow that (" ... because of Bell's theorem" as Gill claims) probability is prior to measurement. The measurement protocol of Bell-Aspect merely demonstrates its own prior conclusion.

While Gill et al are completely off the mark in convincing themselves that they have refuted Hess-Philipp -- the science of complex systems, in line with Bar-Yam's theory of multi-scale variety, supports timelike correlated parameters at multiple scales: http://home.comcast.net/~thomasray1209/ICCS2007PP.ppt

Tom

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More should be said about why the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.

Criticisms of Hess-Philipp have failed...

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More should be said about why the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.

Criticisms of Hess-Philipp have failed to even address the key issues of Einstein separability and special relativity that drive the paper's conclusions. The critics know that these issues cannot be confronted head-on, because they are well-understood physical principles that cannot be refuted.

Let's return to a point I made in my essay (p.6), that Einstein's original quest for E = mc^2 substituted the Lagrangian (a system's energy content) for the E term, where E was then generalized to rest energy, so we get that famous equation. The continuous values of the Lagrangian, however -- vary with mass -- local measured. In reply to critics, Philipp-Hess simplified their explanation of the model (attached), such that " ... Imagine the time axis wrapped around a circle of circumference that corresponds to a time interval related to a simple measurement and normalized to 1. We suppose that for a fixed N each interval [(m − 1)/N, m/N ], m = 1, 2, . . . , N of arc length 1/N on the circle gets about its proper share of time measurement points over the measurement period." The authors go on to show time correlations that the critics ignore, and reproduce quantum correlations in a complete framework of distributed time-dependent energy/information. These results satisfy Einstein separability and special relativity in a way that the critics do not and cannot:

Because a continuous range of time-dependent energy values attends every classical measure, normalization of the time interval locally does not imply a global normalization (as Gill claims) -- because of the special relativity limit. Each measure carries its own time stamp, and it is always local.

Tom

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