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

John Cox

Judy,

I quite agree that all our science is ad hoc, we simply have to start somewhere. Peter and I have discussed at some length, his DFM construct, and I am in agreement with him that CHSH experiments can only be clues to the physical behavior of what we generically call energy. That is the classical model of experiment, and I personally would like an appropriate forum blog on the topic. That does not mean that if I were to develop a classical model that would mimic results of CHSH, that it would say anything about why QM obtains those results. I would have a LHV model which might discover what some variable might be, and thus make it a non-hidden parameter. My own prejudice is that we do not live in a perfect universe, sometimes, some thing, just doesn't happen. Like taking the divider grid out of a beer case and pulling a bottle, then we have random action among a set of discrete objects.

One of my feathers in a previous post was ambiguous, the expectation I was referring to was that of the averages of samples examined in the survey as opposed to the prior projected averaging. jrc

Joy Christian

Further false propaganda from Richard Gill.

Both Michel Fodje's simulation and Chantal Roth's simulation are intimately connected. I know this because I interacted with both of them for months to produce the two simulations, first with Chantal and then with Michel, with theoretical insights provided by me and the codes written by them. The links between the two simulations, as well as how they are based on (and reflect) various representations of the 3-sphere, have been extensively discussed in this paper: http://libertesphilosophica.info/blog/wp-content/uploads/2014/01/Book-Chapter.pdf

Richard Gill knows all this, but he still can't help perpetuating the false propaganda. I do not know what he intends to gain by such propaganda. This is not how science should be done.

Joy Christian

The link between the two simulations is eq.(A.9.33) on page 250 of this paper.

Thomas Ray

" ... This is S^2 version (aka 3D version: think of S^2 as a surface in R^3)

## This version has been adapted from Richard Gill's optimized version of

## Michel Fodje's original simulation of the model"

This is very clear. Richard, do you really not understand the difference between the manifold of a ball in 3 dimensions and a 3 manifold in 4 dimensions?

Your mistake is and always has been not grasping that Euclidean geometry extends smoothly to 2 and 3 dimensions, while the 3 manifold has one simple pole at infinity where R^3 is compactified.

Despite your opinion, I do know what is going on in the simulations. Also despite your opinion, programming does not produce new mathematics; it's quite the other way around.

Thomas Ray

"'Tom said in big black bold letters "There is no kind of sampling or probabilistic measure in Joy's framework.'"

True statement.

"Then Tom you should take a look at Joy's authorized simulation of Joy's model, written for Joy by Michel Fodje, Richard Gill and Chantal Roth."

Richard, until you understand that S^2 X S^2 is identical to S^3, such that the tangent space of the S^2 manifold is continuous over the S^3 manifold, you have no idea what you are talking about. A classical computer is physically limited to 3-space; the simulation by a finite state machine of a continuous function in 4-space cannot be represented without the topological twist (nonzero torsion) that compels a sign reversal in the dot product for the parallelized 3-sphere. That has to be programmed into the function, from the initial condition.

What you are trying to do is to truncate the space to a limit that nature does not impose. The finite state, as Joy explained, is determined only by the choice of initial condition; the continuous function does the rest.

"Joy tells us that he can't program and doesn't know any computer languages, so I suspect that he has no clue what is going on in those programs. Pretty clear you don't have a clue either."

Your motive to make programming the subject of this discourse is as transparent as your attempt at intimidation.

Thomas Ray

"I'll go a little further out the limb and suggest that this single 'cowlick' on S^2 is where the distinction is made of a single correlation of vectors to a point, so parity is then had by S^2 X S^2 = S^3 (?)."

Essentially, John, though there is a subtle distinction in this context between an equality and an idenity. S^2 X S^2 is identical to S^3; i.e., at every point of the simply connected manifold there is a smooth and continuous function from the 2-dimensional surface of the 3-dimension space to the 3-dimension surface of the 4-dimension space.

Thomas Ray

"Tom, what would you recommend?"

I already made my recommendation for time-interval overlays of correlated events.

John Cox

Tom,

The distinction between equality and identity is well taken, thank-you much. I'm not clear however if I follow the criteria offered by Joy's framework, which I recognize as being wholistic in constructing it's own reference system and as such needs-be accepted in all parts to be the whole.

Given that there is a smooth continuous function from the 2 dimensional surface of 3 dimension space (without a timelike attribute) to the 3 dimensional surface of 4 dimension space, is it appropriate within the framework to envision numerous possible orientations of vector magnitudes being shown on the S^2 surface as culminating to that point at infinity, such that its location is the same as that of culminating vectors on another S^2 surface. Such an identity would then be an equality, where if the vectors on the second surface produced a point different than the first it would be an inequality yet the S^2 manifolds together would have the same identity as S^3. (?) jrc

Thomas Ray

John, quantum correlations in Joy's framemwork are correlated points of the Hopf fibration.

pjackson

Richard,

"What information..". OK, I can simplify it; A Dipole, which is the most basic form of two charges, and - orbiting each other as a binary system. They propagate along their axis so form clockwise or anti-clockwise quanta of Orbiting Angular Momentum (randomly). There's a distribution between the and -, with zero half way between.

I was trying to pre-empt any later objections by closely modelling the physics. On arrival the interaction will give an output distribution dependent on the detector field electron orientation, so bear in mind that each 'state' is accompanied by the opposite state, just as Earth clockwise spin is accompanied by it's anti-clockwise spin. Which way is 'found' then depends only on 1, which way was it spinning to start with on the x axis, and 2 which way it's heading. If we turn the axis 180 degrees the 'up' becomes 'down'. As with Earth, there is also a distribution which tends to zero at the equator. Bear that in mind, but for simplicity, for now the random 'superposition' will do.

The parallel classroom experiment analogy models the dipole as colours; Green = , Red = -. and is a disc (coin) either way up, non mirror symmetric as in reality - so red behind green. (That will prove not to matter).

So we have 'spin up' (distribution 0-1). Just one will do.

Can the programme do that ok?

Thanks

Peter

PS, I didn't read Judy's comment as referring to how many correlations. It's certainly no problem to me. Judy understands the analyser electrons, orientated by the setting, are what dictates the output "energy level" of the interaction. It's the recognition and acceptance of that fundamentally new possibility which requires 'thinking outside the box'. It's also letting go of the; 'artifact of human intellect' John described, to find new and better foundations.

Richard Gill

Peter, I can't program anything if you don't tell me what to do. The word "dipole" is not in my vocabulary. I do have some intuitive grasp of packs of cards or spinning disks.

You tell me what information goes from the source to Alice's measurement station. In plain (non-technical) English. House, town and garden words. Can you do that?

Richard Gill

OK Joy. You win.

You give me two files, one containing N directions of angular momentum u_k, k = 1, ... N, the other containing N directions - u _k.

I will then pick two measurement directions a and b, and show you that your correlation is more than 0.2 away from the quantum predicted correlation.

Is that a deal?

Richard Gill

Tom said

" " ... This is S^2 version (aka 3D version: think of S^2 as a surface in R^3)

## This version has been adapted from Richard Gill's optimized version of

## Michel Fodje's original simulation of the model"

This is very clear. Richard, do you really not understand the difference between the manifold of a ball in 3 dimensions and a 3 manifold in 4 dimensions?"

Yes I do. Very clear. I know what I'm talking about. I wrote the code of this simulation. I wrote the words "this is the S^2 version" which Joy let stand, when he got Chantal Roth to run the code for him and increase the sample size.

I called it an S^2 version because Michel Fodje's original simulation "epr-simple" picked random points lambda on S^1. I was the one who lifted Fodje's model to S^2, which immediatly made it a whole lot more accurate. At that point I realised the connections between Fodje's (lifted) model, Caroline Thompson's chaotic spinning ball model, the Gisin and Gisin model, and the Pearle model, all based on picking random points lambda on S^2 together with some rejection rules.

I then decoded Pearle's maths (I think I was the first person to do that, in 40 years, it turned out to be incredibly simple but no one had ever seen it, no-one had ever actually simulated it because it looked so complex. In fact some people describe his work as an "existence theorem", implying that it was non-constructive) . In other words, I deduced the good rejection rule so that it reproduced *exactly* the singlet correlations.

That was an exciting and rewarding adventure, and it made be happy to make Joy happy, for a change.

Richard Gill

We have a deal.

Joy will give me two files, one containing N directions of angular momentum u_k, k = 1, ... N, the other containing N directions - u _k.

I will then pick two measurement directions a and b, and show him that his correlation is more than 0.2 away from the quantum predicted correlation.

My choice will be one of my four favourite pairs of directions ... in other words E(0, 45), or E(0, 135), or E(90, 45), or E(90, 135).

Joy predicts the values - 0.7, 0.7, - 0.7 and - 0.7.

I predict that at least one will be off by 0.2 or more.

The experiment is the experiment of Joy's 2008 paper, http://arxiv.org/abs/0806.3078

Richard Gill

Are you telling me (in the classroom analogy) that the message sent from the source to Alice's classroom is a coin placed in a box, heads up (heads coloured red, tails green)? And is that going to be the "message" in every round? In other words, we can do without the source altogether?

Amazing.

My program for that part is easy. It is empty.

If I'm on track I will now ask you what is the message sent to Bob's classroom but I guess it will be equally trivial, i.e. superfluous.

Thomas Ray

"In fact some people describe his work as an "existence theorem", implying that it was non-constructive)"

Absolutely right. I think I already pointed out that all Bell-Aspect type proofs -- including yours -- are nonconstructive.

Florin Moldoveanu

Because I was the first one to announce publicly the mathematical mistakes in "Bell's theorem disproof" (although I was not the first or the only one to discover them - 4 people discovered them independently at various times), I want to state my position before the results of this experiment are announced.

- If Bell's theorem is upheld, this will not magically erase the acrimony of the dispute.

- If Bell's theorem is proven wrong, while I will respect and study Nature's choice, I will never accept that +1=-1. The mathematical invalidity of "Bell's theorem disproof" is here to stay regardless of Nature's verdict on Bell's theorem.

Joy Christian

It should be noted that I have systematically debunked all of the bogus and misguided claims made against my local realistic framework by certain uninformed, unqualified, and unpublished individuals. What these individuals do is replace my model X with its grossly distorted misrepresentation Y, and then pretend---by refuting their own distortion Y (by resorting to deliberate dishonesty or out of sheer incompetence)---that they have undermined my actual model X. Such a dishonest strategy is an insult to scientific process.

Richard Gill

It is great that we have left Bell and CHSH and all that behind us, and are focussed on a simple experiment, whose observed correlations E(a, b) will either match to Joy's predictions rho(a, b) = - cos(a . b), or they won't. And everything will be decided by just one correlation.

I would like to add a little bit of precision, for the benefit of the adjudicators and with the aim of total transparency

Recall that cos(45 degrees) = sqrt(2) / 2 = 0.7071...

So to be more precise, Joy Christian's four targets are

E(0, 45) = - 0.7071..., E(0, 135) = 0.7071..., E(90, 45) = - 0.7071..., E(90, 135) = - 0.7071....

I bet that at least one will be missed by an amount 0.2 (= 1/5) or more.

I don't mind how large N will be.

As a matter of interest, will the two files contain exactly equal and opposite directions u_k and - u_k or only approximately equal and opposite directions? In the former case, just one file of N directions is enough. The second file contains the set of exactly opposite directions. Add 180 degrees to the longitude (azimuthal angle) theta, change the sign of the co-latitude (zenith angle, polar angle) phi.

I use mathematician's notation. I read on wikipedia that physicists tend to use theta for the zenith angle, phi for the azimuthal angle. We have to be agreed on what is in the files (azimuth and zenith, or zenith and azimuth).

It's important that everything is completely clear and agreed by the two bettors and the three adjudicators, and that everything is also totally clear to all interested observers.

Richard Gill

Sorry, to map a measurement direction (theta, phi) [azimuthal angle, zenith or polar angle] to its opposite one adds 180 degrees to theta and subtracts phi from 180 degrees. Not reverse its sign. I was confused with latitude.

My measurement directions are all in the equatorial plane and the angles alpha = 0, 90 degrees and beta = 45, 135 degrees which I mention are their azimuthal angles theta (mathematicians' notation).

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