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

Richard Gill

I'm no longer interested in proofs, Tom, whether constructive or not. I'm interested in experiment. Let Nature determine whether or not Christian is right.

Richard Gill

The reason I insist on E(a, b) strictly within 0.7071... +/- 0.2 is that with the original "very round numbers" formulation, 0.7 +/- 0.2 includes 0.5 at its endpoints. But obviously, if all four correlations turned out to be +/- 0.5, Joy should clearly lose. So either we need more precision in specifiying "0.7" or we need to be clear about boundary cases or both.

Joy Christian

I am happy with the predictions

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

E(0, 135) = 0.7071...,

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

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

Nothing is known about the relationship between Alice's N u_k's and Bob's N u_k's until the experiment is done---apart from the fact that the index k in the kth run would be the same for both Alice and Bob (well, I do know a lot about the u_k's, but we are not talking about my theoretical model). In the experiment we will produce two independent files of N u_k's, one for Alice and one for Bob. We will then match the k's and compute the correlation in the usual manner [as described in eq.(16) of my experimental paper].

It is irrelevant to me which convention or coordinate system is used to record the two sets of u_k's on the two sides as long as just one, consistent coordinate system is used.

Thomas Ray

"I'm no longer interested in proofs, Tom, whether constructive or not. I'm interested in experiment. Let Nature determine whether or not Christian is right."

I don't think anyone is arguing otherwise, Richard. Consider, though, that nurse Lucia might still be in prison if you had let nature decide that murder(s) had been committed.

What I mean, is that causality is always determined by language proofs before being tested against physical results. There was nothing unnatural about Dutch prosecutors' belief that nature had already decided Lucia was a murderer.

Unless you had asked the question, "Is it a fact that any murder has been committed?" there would be no reason for you to look for correlations between infant deaths in the hospital and other nurses on duty at other times. Finding that regression to the mean shows no such correlation, one is compelled to conclude that either all the nurses were in a conspiracy to kill infants, or there were no murders.

It's the same with Joy's framework. So long as you believe that a set of results returns { 1, 0, - 1} there will be room for you to argue that there is a mystical correlation between 0 and any other result. That's your decision though (like the prosecutors'), and not nature's. There is no zero point in Joy's framework, such that one can claim that some correlation is nonlocal or unrealistic.

My main interest is that you have no wiggle room to reinforce your belief that there is a difference between quantum and classical domains, and their mechanics -- just as the prosecutors had no wiggle room to claim that a murder had been committed. Joy showed you the space of all possible correlated measurement results, just as you revealed the space of all possible correlated results in the hospital. There is no zero, no "murder." The quantum correlations survive at infinite distance.

This is why I offered my suggestion to overlay time-limited intervals of experimental results such that show the system's correlations are constant and continuous from the initial condition. That Joy's measurement framework is indeed complete.

Richard Gill

OK, let's call the directions of angular momentum in Bob's file v_k, k = 1, ..., N and the directions in Alice's file are u_k, k=1, ..., N. In theory one would have v_k = - u_k, but in practice that might not be exactly the case.

Then if I have picked measurement directions a and b, the outcomes left and right are A_k = sign(a . u_k) and B_k = sign(b . v_k), and the estimated (observed, sample, experimental ...) correlation is E(a, b) = 1/N sum_k A_k B_k

Here is a first attempt at a movie of the two theoretical (limiting, population, ensemble, ...) correlation surfaces rho(a, b), showing also the four points which interest me. The best way to "see" two interlocking 3-d objects is by a film of the things rotating.

http://www.math.leidenuniv.nl/~gill/Images/movie.gif

This could be useful in the PR campaigne to get funding for the experiment

http://www.math.leidenuniv.nl/~gill/Images/movie.gif

pjackson

Richard,

As "no" coin is different to "a" coin we can't do without the source entirely. The coin is a quanta of energy, whichever way up.

What 'arrives' is a set of 9 values between -1 and +1.

Picture planet Earth; The values represent momentum distribution over clockwise(+)and anticlockwise (-) hemispheres of a rotating sphere. For simplicity we can designate the 9 values as 22.5 degree increments between 0 to 180 degrees (or nine colours from the spectrum of green to red).

In modelling it we can't just say Heads=Red, Tails=Green. I could say one side just 90^o (green to sand), the other sand-red But I gave both sides the full spectrum but in reversed order, That does mean we can use just one side (and Bob's is symmetrically opposite).

So both have 9 values at 22.5 increments.

When you're happy with that I'll introduce you to Alice.

Best wishes

Peter

Richard Gill

Here's a new version of the movie. Now it's nearly 10 MB

http://www.math.leidenuniv.nl/~gill/Images/movie2.gif

I suggest you download it to your computer and then play it locally in a browser. It's a gif file, and browsers know how to display them

alpha and beta run from 0 to 180 degrees, corr from -1 to +1

One should imagine lots of copies of this cube, half of them upside down, tiling the whole alpha-beta plane, chess-board fashion.

For instance, restricting alpha and beta both to between 0 and 360 degrees, we have a 2x2 chessboard, with this cube twice, on the two diagonal squares, and this cube twice but upside down, on the two off diagonal squares.

Hard to picture!

Joy Christian

Cool!

Richard Gill

Tom said "So long as you believe that a set of results returns { 1, 0, - 1} there will be room for you to argue that there is a mystical correlation between 0 and any other result. That's your decision though (like the prosecutors'), and not nature's. "

This is not a question of belief, or *my* decision. It's a fact - both a fact with respect to the simuation program I wrote for Joy, and a fact with respect to real experiments such as those of Aspect and Weihs. A pair of photons is emitted at a source, two detectors are switched to chosen settings, and the detecion devices either register a "", or a "-", or "no detection".

I don't argue any mystical correlation between 0's and anything. I don't think there is anything mysterious going on here at all. What gave you that idea? I do think there is something non-classical going on. Something which appears magical to primitive persons, but not to sophisticated persons. Like iPhones for instance. Is the iPhone mystical? Depends whether you live today or back in the stone age. If beings from an advanced civilization arrive here on earth, will be think that their technology is some kind of magic? I expect so, initially.

Richard Gill

Peter says "As "no" coin is different to "a" coin we can't do without the source entirely. The coin is a quanta of energy, whichever way up. What 'arrives' is a set of 9 values between -1 and +1. "

OK so now you are telling me that in every round, the source sends to both Alice and to Bob a list of 9 numbers equally spaced between -1 and +1. If that is going to happen in every round, then there is no need for me to program it either. Alice and Bob know every time what they are going to receive. The source is superfluous.

We are not going anywhere, fast.

Thomas Ray

"What gave you that idea?"

You answered your own question:

"I do think there is something non-classical going on. Something which appears magical to primitive persons, but not to sophisticated persons."

If there's a magical black box, how sophisticated does one have to be to say that it's not magic, and how does one know?

John Cox

Tom,

Again thanks, for the Niles Johnson webpage link. That is just the sort of primer I've been looking for.

What I have been learning in the course of this discussion, to my utter horror, is that my perception of space has been wholly inadequate. It is much, much easier to simply assume space to be completely connected, than it is to show that all points in space are connected, simply. If one assumes space as somehow homogenous, it can then be disregarded and any preferred discrete point or particle or quanta of energy can go happily on it's way interacting with others, and the time-like quality then becomes the puzzle. Yet we really can't say there is anything different between time and space other than pi never comes full circle, and so the length of radii is never finitely proportional to circumference necessary to show that the change in size of a spherical volume is uniform. We find a continual spacetime that must somehow function in a simply connected manner which is subjectable to mathematical analysis.

My mind has been sufficiently blown. jrc

Thomas Ray

Richard,

To be a little clearer:

As Joy wrote earlier in this thread, "As I pointed out, the R code you had written was deeply flawed. It did not respect my condition of calculating each correlation separately, as demanded in the equation (16) of my paper. According to this equation, each correlation must be calculated on a separate set of particles. Where does it say in my paper that they must be calculated on the same set of particles? You can generate one list of vectors but you must sample without replacement so that no pair of vectors contributes to more than one correlation. Only then will it be equivalent to four separate sets, as both Michel and I have been insisting:"

The point is to eliminate entanglement from the possible explanations of quantum correlations. So long as there a hint of "something non-classical going on" entanglement is possible.

This is yet another reason I suggested time-limited-interval overlays of the data. It is impossible that correlations measured continuously from the initial condition can be mistaken for entangled particles; if they were correlated at t_0 and remain correlated at t_n, the map t --> T for orthogonally measured sets will show four perfectly correlated points of the 2-dimension circle at the same time interval no matter at which interval one observes. That is, the exploded circle shrunk in reverse will become a point, just as predicted by Perelman's proof of the Poincare conjecture, for the simply connected S^3 manifold. It's all classical, all the time.

Thomas Ray

"My mind has been sufficiently blown"

Great! If one never loses the capacity to be surprised, one never stops learning. Having referenced Barry Mazur previously, I am reminded that he wrote something to the effect that when he comes across a new mathematical result, his likely first reaction is, "I didn't know you could do that!"

[deleted]

Richard,

Remember Occam. 'Simple' progress trumps complexity. If it does the job - then it's correct; As you said. I did warn you it was unbelievably simple, but it'll be entirely unfamiliar at first so don't step back inside that mental 'box'!

Alice and Bob in fact know nothing, and remember the 1-9 sequence is 'non mirror symmetric' (NMS). (NMS is a fact of OAM, discerning clockwise from anticlockwise), so one approaches one way round; 1-9 (North pole leading) and the other half of THAT pair; 9-1 (South pole first).

PART 2

Now I imagine we can move on?

So you can intuitively visualise what's going to happen I'll remind you of the famous 'third filter' case; Two polarising filters at 90^o cut out all light. insert another between the two at 45^o, some light is then released through the final one. This is because the filter 'rotates' the light, i.e. the filter field electrons absorb and re-emit it in line with the field electron orientation. Weihs reported exactly the same using electrons and his electro-optic analyser field.

However. Now we find that the orientation of the analyser field electrons has rotational freedom on ALL THREE AXES! i.e. There is NO 'UP' IN SPACE! so we can turn the analyser upside down or face any way we like. It has only ONE controllable axis, which is that of the magnetic field lines, (designated the x axis) which the setting angle dictates. That all bears some careful thinking about to avoid invalid 'objections' when we expose the simplicity of the output distribution.

Now all this is what the insides of the box looks like, BEFORE the arrival of the H/T state. There is more but it's all physicsystuff. Do ask any questions.

(In the classroom analogy. The dial pointer is a 'slot'. 'Alice and Bob simply turn the dial to some setting, then on 'arrival' some colour from the spectrum shows in the slot).

Best regards

Peter

Judith/John. Please do chirp in with anything you think I've missed. (The cones and non-linearity subject to distance from poles are saved for the next step).

Richard Gill

Peter, it certainly is getting simple. In every round, the source sends nothing to Alice or Bob.

OK. Now remember the buttons. Alice receives from me the instruction to press the button marked "90" on her perspex box. Remember, the box has two buttons and two lights.

What happens inside the box? (in terms of cards and disks)

Richard Gill

Tom wrote "As Joy wrote earlier in this thread, "As I pointed out, the R code you had written was deeply flawed. It did not respect my condition of calculating each correlation separately, as demanded in the equation (16) of my paper. According to this equation, each correlation must be calculated on a separate set of particles. Where does it say in my paper that they must be calculated on the same set of particles? You can generate one list of vectors but you must sample without replacement so that no pair of vectors contributes to more than one correlation. Only then will it be equivalent to four separate sets, as both Michel and I have been insisting:" "

You are a day or two behind, Tom. Things have been moving fast.

The situation now is that, exactly according to Joy's experimental paper, Joy and his experimenter will fim and explode N balls and do a lot of image processing in order to provide me with two computer files each containing N directions of angular momentum of paired halves of those balls. Say: u_k and v_k where v_k is probably close to, or equal to, - u_k.

I am then going to show to Joy that one of the four sample correlations E(0, 45), E(0, 135), E(90, 45), E(90, 135) differs by 0.2 or more from its target - 0.7071, - 0.7071, - 0.7071, - 0.7071.

There is one set of particles. As Joy's experimental paper makes perfectly clear.

I'll report the a, b and E(a, b) which does the job to the adjudicating committee and to Joy and everyone can check.

E(a, b) = sum sign(a. u_k) sign(b . v_k) /N

= ( N(++) + N(--) - N(+-) - N(-+) ) / ( N(++) + N(--) + N(+-) + N(-+) )

and this calculation can be done on the back of an envelope. (Though one will need a bit of trigonometry to calculate each sign(a. u_k) and sign(b . v_k)

The bet is decided by just one of four correlations.

I decide which of the four (or lose, of course, if I can't provide one).

The four correlations are calculated competely separately, after the experiment.

The outcome of each measurement of each particle is +/- 1

sign(a . u) and sign(b . v) are not continuous functions on S^2 x S^2 but we are here dealing with the discrete representations of numbers and functions in an ordinary computer. 64 bit "reals". IEEE and ACM standardized floating point arithmetic.

Richard Gill

An interactve graphic of the two correlation surfaces and the four points on each surface predicted by each theory:

http://www.math.leidenuniv.nl/~gill/surface/

Enjoy!

pjackson

Richard,

Good. You ain't seen nuffin yet, it gets simpler! Inside the box is the spectrum and a low tech spectroscope. Press button 90(^o) and the dial moves to half way between 1 and -1, exposing a colour there, which we've called 'Sand'.

The spectroscope has to decide if 'Sand' is closer to Red or Green. Of course it hasn't got a clue, so we get output 50:50 R/G.

The experiment itself used a short queue of people one at a time to 'look through the perspex' and tick a Red or Green Box. All settings were used - giving nine points on the full curve, but your limited sample can be extracted without problems.

(Nature uses angular momentum. AM varies in direction between 'sides' of the entity, changing mid way, so in that case we can simply have a spinning spheroid or toroid).

Have you ever discovered a new short-cut to achieve something horribly complex? Your first reaction will be; "but you can't do it that way"! Only then does it start to dawn that you can.

Thomas Ray

"Things have been moving fast."

I see that! It looks good to me now.

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