Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Jonathan Dickau

P.S. -

The short videos illustrating the concept make it easy to understand.

All the Best,

Jonathan

Florin Moldoveanu

Tom, the link is broken.

In the original Michel's output he plots several graphs in one window. The visual evidence is in one of those graphs.

Thomas Ray

"Luckily; Joy's model is tractable both ways."

Nice point, Jonathan. The framework is coordinate free.

Thomas Ray

Sorry, Florin. Here is where I got the link info.

Joy Christian

Earlier Richard Gill wrote: "One issue is not yet covered in this morning's exchanges: namely the fact that Michel and my simulations do *not* exactly reproduce the (negative) cosine. They are both off by about 0.001 (depends on the angles). Mine (S^2) is closer than his (S^1). They are both definitely different, since a point in S^2 projected orthogonally onto the equatorial plane generates a point *inside* not *on* the unit circle, hence has a shorter inner-product with vectors a and b on the unit circle, hence is slightly more often rejected (fails the test of comparison of those inner-products with 1/2 sin^2 theta)."

Well, first of all, contrary to what the flatlanders keep claiming, no state has been "rejected", either in my analytical model, or in any of its increasing number of simulations. The analytical model is described by eight elementary equations in a self-contained manner, with further details available on my blog. No simulation is needed to confirm its validity. Simulations are interesting only for psychological reasons. They by themselves are not the actual model. The actual model is based on S^3, whereas all simulations to date are based on R^3. Moreover, the initial state in both the analytical model and the simulations is (e, t), not just e. Failing to understand this is the fundamental error from which all flatland resistance stems. There is one-to-one correspondence between the initial or complete state (e, t) and the measurement outcomes (A, B). Thus all states are being counted. No loophole, conspiracy, or voodoo is being exploited in the model. All it takes is checking eight elementary equations to verify the analytical model.

As for the "off by about 0.001" issue, I now have an improved version of Richard Gill's simulation in which no such issue arises. The slight discrepancy was there in his simulation because Alice and Bob were not careful enough to make sure that they are not detecting each other's particles in addition to their own. This has been rectified in the improved version. I will report on the improved version shortly. Suffice is to say that the match between the (negative) cosine curve and the event-by-event simulation of my analytical model is now exact. The psychological and sociological problems stemming from the flatland, however, are not so easy to rectify, especially if one does not know the physical significance of a "parallelized 3-sphere."

Joy Christian

My analytical model, just like quantum mechanics, predicts perfect anti-correlation at equal setting:

(8).

In the flatland (R^3) based simulations of my analytical model, or in any such simulation for that matter, an additional practical issue arises. For example, Richard Gill's version of Michel Fodje's simulation is off by some 0.001. This is because Alice and Bob are not careful enough in his simulation to not end up detecting each other's particles in addition to their own. I have now been able to correct this deficiency of his simulation. The corrected version now matches with the (negative) cosine curve exactly. I will report on this latest version as soon as it is ready to be published. Imperfections in simulations like these have no baring on the perfection of my analytical model.

Richard Gill

Joy, we look forward eagerly to your new version. The simulators are ready to put it through its paces.

Here is the most accurate simulation done to date of Christian's model, following his very own, very precise, and completely unambiguous instructions:

http://rpubs.com/gill1109/JCS2opt

The formulas for Cab, Na, Nb are taken from the publication http://arxiv.org/abs/1301.1653 C_ab is given in (A27), N_a and N_b are given by the expressions just after (A28) and (A29). The "phases" phi_o^p etc. also come from this paper. The procedure generating an outcome +/-1 for the product of Alice and Bob's measurement, or 0 for "no state", with the help of an auxiliary randomization, is also taken from this paper. The whole procedure is identical to that programmed in Java by Chantal Roth under your instructions.

Joy Christian

Please read my post just before yours carefully. All you have shown is that in your R version (pun intended) you need to adjust the two phase shifts so that Alice and Bob do not end up detecting each other's particles in addition to their own. That is all there is to it. There is no need for "much ado about nothing."

Richard Gill

I need to adjust my phases? Sorry, Joy, *you* need to adjust *your* phases. I am sure you can do it.

Florin Moldoveanu

Tom, the image looks like this (look at the circled graph):

I uploaded my own file, but you need the Michel's original picture.

Joy Christian

Contrary to what the flatlanders keep claiming, no state has been "rejected", either in my analytical model, or in any of its increasing number of simulations. The analytical model is described by eight elementary equations in a self-contained manner, with further details available on my blog. No simulation is needed to confirm its validity. Simulations are interesting only for psychological reasons. They by themselves are not the actual model. The actual model is based on S^3, whereas all simulations to date are based on R^3. Moreover, the initial state in both the analytical model and the simulations is (e, t), not just e. Failing to understand this is the fundamental error from which all flatland resistance stems. There is one-to-one correspondence between the initial or complete state (e, t) and the measurement outcomes (A, B). Thus all states are being counted. No loophole, conspiracy, or voodoo is being exploited in the model. All it takes is checking eight elementary equations to verify the analytical model.

Jonathan Dickau

It is intriguing how some elementary points can be so elusive.

I see large areas of agreement, but differences in the definition of terms and criteria of evaluation, or the interpretation of observed results, highlight the areas of disagreement instead. And I wish I could explain the important distinctions better.

Regards,

Jonathan

Thomas Ray

I do recall seeing that image, Florin, but your point escapes me. As Joy explained, "There is one-to-one correspondence between the initial or complete state (e, t) and the measurement outcomes (A, B). Thus all states are being counted."

This should be crystal clear -- dependence on the initial condition, and not on the measurement settings, determines the outcome for any range and experimental run of randomly selected initial conditions. The domain -- parallelized S^3 which is characterized by nonzero torsion -- accounts for the phenomenological and locally real outcome - a.b (a Bell's theorem impossibility) at any scale of measure.

I think the problem with the way that you and Richard have recast the issue, is that you allow, by simple fiat, no correlation of random values from random initial conditions. You assume that probabilistic measures apply to every initial condition independent of domain and range, such that every initial condition is assumed to be observer-created. That's the whole reason that conventional quantum theory is mathematically incomplete, and arguably not foundational.

Robert McEachern

Jonathan and Tom,

It is indeed "intriguing how some elementary points can be so elusive."

But the problem is much worse than seeing "large areas of agreement." As I have pointed out repeatedly, even a SINGLE theory (hence NO area of disagreement) can, and usually will, be the victim of wildly different "interpretations of observed results". The problems stem from attempting to find any one-to-one correspondence between the theory's intermediate results and reality, as opposed to merely noting the correspondence between the theory's final result and an observation. A(B+C) and AB+AC may produce the same final result, but they imply different physical manifestations (one vs. two multipliers). If all you can ever observe is the final result, then it will never be possible to deduce which of the various "intermediate manifestations" corresponds to reality. This is the problem with using the principle of superposition to produce a final, theoretical result, that can be compared to an observation, but then insisting that the individual terms, in the superposition, must also exist, in spite of the fact that they obviously do not have any unique manifestation.

"you allow, by simple fiat, no correlation of random values from random initial conditions." Given the same initial conditions, correlations between purely classical objects, like pairs of gloves and pairs of coins, behave differently, precisely because of the point noted above. Unlike gloves, coins should not be "interpreted" as having any "components" to find correlations between. Hence such objects behave rather oddly, when you have assumed that they do, in fact (as opposed to merely existing as intermediate theoretical computations), have components that can be measured.

Rob McEachern

Thomas Ray

Your point is well taken, Rob. However, it is not a fact in evidence that " ... Given the same initial conditions, correlations between purely classical objects, like pairs of gloves and pairs of coins, behave differently ..." If they behave differently, they are not correlated.

The topological constraints of Joy's framework, which are identical to the constraints of physical space, guarantee that correlations of the initial condition remain continuous for the outcome of any time interval. This is in fact what Einstein said in his 1921 "Geometry and Experience" paper. It is what we observe in nature.

Richard Gill

Joy writes "the detractors, who by and large claim to be scientists, are not intrigued in the slightest why I have been able to produce such concrete results. One would think that any good scientist would be intrigued by the evidence I have presented. "

I am very intrigued. I study the evidence carefully. I discover that it is not what it seems, it is not what it is "sold" as being. I report my scientific findings.

Let's avoid being drawn into a discussion "who is the good scientist". For a good scientist, all that counts is the scientific evidence. Allegations of unscientific behaviour, improper motives ... have no place here. They will be reported.

Florin Moldoveanu

Tom,

I made no point yet. The graph I uploaded corresponds to my tinkering with the code and has no value for the discussion. What I wanted to do is point you to the type of graph I want to discuss in Michel's simulation. If you find HIS graph, please post the image and I'll make my point on it.

Fred Diether

Here is the graph for the John Reed Mathematica version of Michel's simulation. For 10 million trials. You can see some slight deviations from the curve but that is just due to limitations imposed in the code such as rounding to 1 degree increments, etc.

Fred Diether

The graph can also be found here along with much discussion.

Richard Gill

Fred, the deviation is not due to rounding. It is systematic. Joy can adjust phase shifts to get the curve closer to the cosine at some points, but then it will be off target at others.

Richard Gill

So far, the most accurate implementation of the Michel Fodje type simulation algorithm is http://rpubs.com/gill1109/EPRB3opt

Joy has agreed that phase shifts need to be introduced into the algorithm.

Richard Gill

Chantal programmed formula (A27) for Cab, with Na and Nb given by the epression just after (A28) and (A29), in arXiv 1301.1653 ("Whither...").

a and b are measurement settings.

Cab is somehow related in some way to the product of the measurement functions A and B. It depends on various constants and on e0. It's a number between -1 and 1.

Chantal picks e0 at random, and performs a Bernoulli trial with success probability |Cab|. If the trial resulted in "success", the sign of Cab is returned, otherwise a zero.

This result (-1, 0 or 1) is averaged over many runs (or the 0's are rejected and only the +/-1's averaged?).

Joy Christian

"Chantal programmed formula (A27) for Cab, with Na and Nb given by the epression just after (A28) and (A29), in arXiv 1301.1653 ("Whither...").

a and b are measurement settings.

Cab is somehow related in some way to the product of the measurement functions A and B. It depends on various constants and on e0. It's a number between -1 and 1."

Chantal did what I asked her to do. Brilliant as she is, she simulated my theoretical model brilliantly. There is no "somehow" or "some way" in my work. Everything follows from the well known physics and mathematics of the physical space, which is modelled as S^3 in my work. |Cab| provides a joint probability density function for observing simultaneously measurement results A and B. There is nothing mysterious about that.

"Chantal picks e0 at random, and performs a Bernoulli trial with success probability |Cab|. If the trial resulted in "success", the sign of Cab is returned, otherwise a zero."

Success indicates simultaneous occurrence of measurement events A and B. It is all explained very transparently using elementary mathematics in my paper.

"This result (-1, 0 or 1) is averaged over many runs (or the 0's are rejected and only the +/-1's averaged?)."

0 indicates 0 probability of simultaneous occurrence of measurements events. Again, there is nothing mysterious about any of these things, even for a flatlander.

Richard Gill

For a version of Chantal's algorithm written in R, see

http://rpubs.com/gill1109/13494

The plot shows the sum of the true outcomes (+/-1) over the runs, which I took equal to 100 thousand per setting pair. Curiously its maximum is at 25 thousand and its minimum is at - 5 thousand.

(Actually I reverse one sign: my curve is upside down relative to Chantal's)

Doing this exercise I noticed some strange features in the Java code at

http://libertesphilosophica.info/eprsim/eprsim.txt

(Javascript version of Chantal's code by Daniel Sabsay).

Some of them duplicate similar odd features of Chantal Roth's Java code at

https://github.com/chenopodium/JCS2

others seem to be original.

Common to both simulations:

In each run, two particle pairs are generated, not one. But the pair is only counted once when reporting the number of runs.

Alongside these two, another pair is generated with equal and opposite angle between them.

The generation of uniform random points on the sphere is done in an extremely primitive way by Sabsay. It is computationally ineffient and it is inaccurate. He uses the multivariate normal method and his normal variables are sums of 6 uniforms.

As far as I can see Chantal computes the final correlation properly, dividing the sum of -1 and +1 outcomes by the number of runs. However Sabsay simply normalizes the raw sum of outcomes by scaling it to the interval [-1, 1]

Richard Gill

Since posting my R port of Chantal Roth's Java, I discovered a couple of bugs. They are now ironed out. We get a nice reproduction of the hoped-for cosine curve. I think the R code is a good deal more transparent that the Java versions! It is certainly a lot shorter.

Everyone isof course welcome to run it (copy-paste into the R console window) and experiment with it. R is free ("free" both as in "free speech", and as in "free beer")

http://rpubs.com/gill1109/13494

I would like someone to explain where the specific values of the phases

phi(op) = 0.000

phi(oq) = 0.000

phi(or) = -1.517

phi(os) = 0.663

I take it that these are numerical approximations (our Good Lord did not create the world using a decimal system with only three decimal places). I am guessing that 0.000 and 0.000 are both exactly 0. What about the other two? Where do they come from? Have they been found by tuning simulation programs i.e. by empirically squeezing the model towards the desired result? Or is there a theory which predicts these particular numbers?

Richard Gill

PS, by the way, Joy writes "|Cab| provides a joint probability density function for observing simultaneously measurement results A and B."

It is not a density function. It is *the* conditional probability of observing simultaneously measurement results A and B, conditional on a particular realization of the hidden variable e_0.

The probability of observing measurement results, given the hidden state e_0, depends on the measurement settings a and b. The observed *product* of the two outcomes (+/- 1) is given by the sign of Cab, and also depends on the pair of settings.

Thomas Ray

"It is *the* conditional probability of observing simultaneously measurement results A and B, conditional on a particular realization of the hidden variable e_0."

Do you not understand that the pair (e,t) relation to outcomes (A,B) is dependent on a random choice of initial condition and not on a pair of measurement settings?

There is no probability measure in Joy's framework, which obviates any assumption of conditional probability.

Richard Gill

Tom, you wrote "Do you not understand that the pair (e,t) relation to outcomes (A,B) is dependent on a random choice of initial condition and not on a pair of measurement settings? There is no probability measure in Joy's framework, which obviates any assumption of conditional probability."

I am not "assuming conditional probability". It is there, in the code, and in Joy's papers.

Study Chantal Roth's code, Daniel Sabsay's, or mine. Or read Joy's papers, for that matter!

He talks about a loaded die but others would call it a biased coin (if it is a die, it is a two-sided die).

The bias of the coin is determined by the measurement settings and the hidden variables. The coin is tossed and the outcome is random. Christian's "probability density" in his paper "Whither..." is exactly a conditional probability of the outcome of the coin toss, given the value of the hidden variable e.

This is exactly how Chantal, Daniel and I have simulated the model in three different computer languages. Chantal's and Daniel's algorithms have the approval of Joy, and Chantal confirms that mine does exactly the same as hers.

Joy Christian

"The bias of the coin is determined by the measurement settings and the hidden variables."

This is misleading, if not entirely incorrect. The bias of the coin does depend on the hidden variables, as it should do. But it does not depend on the measurement settings, as it shouldn't do. The measurement settings are chosen completely freely. The bias, if one can call it by that name, is determined by the geometry and topology of the 3-sphere. That is the point of the whole demonstration. This will never be understood if you keep looking at it with your deep-seated preconceptions. The demonstration must be looked at from the perspective of the 3-sphere to understand its true significance.

Richard Gill

The now existing computer codings (three or four) are descriptions of the same, abstract, mathematical structure. The abstract mathematical structure is described in papers by J.C. It has been put out into the wild, it has escaped its creator, it now stands alone. An abstract construction of the mind, or an independently existing mathematical object - depending on your metaphysical ideas about the nature of mathematics (invented or discovered).

Anyone is free to interpret this mathematical structure, physically, how they like. When I use words like "conditional probability" I am describing abstract mathematical features of the abstract mathematical structure which J.C. has given us. Such a word is just a precise technical term in an established and powerful branch of modern mathematics. It is not a "value judgement". It is not an "interpretation".

Feel free to "see the model" in S^3 if you like.

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