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

Richard Gill

Tom said "Suppose you are an anti-crackpot who believes in a flat Earth among a whole lot of anti-crackpots who believe in a flat Earth".

Yes it is important to do these thought experiments. They show us that we should stop arguing back and forth, and instead go and get some data, do some observations. For instance: actually check Christian's maths. Or: stop all talking altogether, till someone has written the computer programs to prove they are right ...

Thomas Ray

". For instance: actually check Christian's maths. Or: stop all talking altogether, till someone has written the computer programs to prove they are right ... "

I resent your continued accusation that I have not "checked Christian's math." As Joy himself has repeatedly pointed out, all those learned individuals including you, who predicted that the math would only produce results of - 1 in a computer simulation were wrong; the program demonstrating otherwise has been replicated independently at least 5 times now. What's wrong with you?

Thomas Ray

From Gill on SPF:

"I am still waiting for Michel to contribute to the experiment of the century by helping prepare the computer software which we'll use to evaluate the result. It's very important that this is done by different people with different opinions. People of strong independent mind, and people of intelligence. People with expertise in computing."

People who don't know the difference between programming and computability. In other words, the mathematically naive.

Jonathan Dickau

A little diversion perhaps...

A question was raised that bears repeating and answering. On Apr. 15, 2014 @ 12:08 GMT; Thomas Howard Ray replied.. "If Richard and Florin think that the space of all practical purposes is identical to the space of all possible measurement results, let them prove it."

In fact; it is fairly easy to demonstrate that the reverse is true. In the case of FAPP, the smoothness constraint is adequate, since all we need is a well-defined function, with no gross discontinuities. But as I've noted in previous posts; Connes makes a particular point that the categories Smooth, Topological, and Measurable, forms and spaces comprise a hierarchy, where:

S > T > M

So to be specific; the category of Topological forms and spaces is a subset of Smooth, and Measurable is a subset of Topological forms and spaces. This means one cannot have measurability without topology entering the picture. Now topology only enters the picture at dimension 2, where it is possible to construct a continuous form - the circle - that has an interior and an exterior.

But in this discussion, it is the topological shift (from S^2 to S^3 topology) between dimensions 3 and 4 that deserves attention, because it forces us to regard certain relations as non-commutative. Understanding this is essential to grasping Dr. Christian's work.

Regards,

Jonathan

Jonathan Dickau

I guess it is meaningful to mention..

The case of the 0-sphere is worthy of note, because it is a degenerate case. The unit sphere S^0 is comprised of two isolated points on a line -1 and +1. Though it forms a bracket, which could be said to contain the point at 0 midway between the bracket points, it lacks a continuous surface - so on the geometric level it fails to be topological. So in going from S^0 to S^1, a binary choice becomes a continuous range of choices. This is a tremendous difference!

An either-or vs. a continuous range of possibilities; huh?

So what does S^3 get us? A continuous range in a 3-dimensional space, over a continuous range of inward-facing and outward facing vectors. And this turns out to be a choice that conveniently explains the Bell type experiments. So then the question should become; why can't the space we inhabit be described as being like S^3, and what would other observable consequences be?

One place the torsional effects Joy describes CAN already be observed, is in the slow-motion footage of atomic bomb blasts. So no colorful balls are needed; the experiment has already been done.

All the Best,

Jonathan

Jonathan Dickau

Sorry for over-using the word 'so' above.

All the Best,

Jonathan

Thomas Ray

" ... it is the topological shift (from S^2 to S^3 topology) between dimensions 3 and 4 that deserves attention, because it forces us to regard certain relations as non-commutative. Understanding this is essential to grasping Dr. Christian's work."

That is spot on, Jonathan. And because S^2 X S2 is identical to S^3, one cannot escape the continuous function mapping the whole S^3 manifold to its simply connected self. The loss of commutativity in parallelizable S^3 and the additional loss of associativity in parallelizable S^7 -- the limit of the division algebras -- maps the entire measure space of parallelized S^3 to the generalized Euclidean plane.

Conventional quantum theory does not have that generality, because it prescribes no more than probabilistic measures. That may be 'FAPP,' yet the model is not independent of the measure, making the QM framework hopelessly incomplete. While one provably cannot derive all classical results from quantum mechanics; the converse is not true.

Joy Christian

Jonathan,

You are an absolute treasure. Excellent comments, as always. I am particularly intrigued by your observation that "One place the torsional effects Joy describes CAN already be observed, is in the slow-motion footage of atomic bomb blasts."

Why didn't I think of that? The raw data of the bomb experiment I have been urging for since 2008 may already exist! Of course, one has to analyze the data carefully to construct the 3D maps of spins I describe in my experimental papers. But you may have reduced the cost of my proposed experiment by 4 or 5 orders of magnitude!

Many thanks,

Joy

Georgina Woodward

Hi Johnathon,

you asked "why can't the space we inhabit be described as being like S^3, and what would other observable consequences be?"

Because it isn't space. I would say it is a model of what is happening over time with a particular perspective rather than a model of the space we inhabit. The series of 2 spheres in 3D space would IMHO better describe the distribution of events in space in for example the bomb blast as you suggest; as the older arrangement is replaced by the younger, they do not all exist together as a sequence. It does mean that at each time when a selection of data can be made there is only a sub set of choices available rather than being able to choose from the whole distribution over the 3 sphere.

Quaternion modelling is used flight simulation dynamic modeling and flight control systems. Advantages: avoids singularities, easier calculation than principle angle/Euler axis combination or Euler angle representations, also avoiding singularity. Quote" The most useful feature of the quaternion representation for a frames attitude[orientation] is the rather simple composition rule buy which successive rotations can be combined".

Disadvantage, Quote "...redundancy which causes an attitude to be represented by more than one quaternion and sometimes leads to practical problems when employed in a flight control system. In order to reduce redundancy, the quaternion is often replaced by a closely related 3 parameter set such as either the Rodrigues or the modified Rodrigues parameters" (but they have singularities) The quaternion sign ambiguity can be understood by considering that rotation in either direction about an axis can give the same outcome.Quote "There is no loss of generality by always choosing the same sign."

" Quote," ...flight dynamics can be separated into translational flight dynamics and rotational dynamics. Generally translational flight dynamics deals with the motion of the center of mass in a reference frame at the center of mass of a celestial body, and attitude dynamics refers to rotation about the center of mass of the vehicle. The attitude or orientation of the body-fixed frame is generally measured relative to a third coordinate frame." Quotes from "Automatic Control of Atmospheric and Space Flight Vehicles" By Ashish Tewari:Springer 2011

I may be thinking about this in the wrong way but it seems to me that the quaternion representation is a way of imposing a particular kind of reference frame on to space over passage of time rather than description of the topology of the space itself that is inhabited. I don't believe that we inhabit 3n+1 space time either but that is what we observe due to data transmission and processing times built into our output, emergent reality.

Jonathan Dickau

Thanks Georgina,

You seem to have a fair grasp of things, and one that illustrates why the description Joy presents is so tricky to talk about in ordinary terms. I will read your comment for detail in a moment, but I note first the synchronicity - because my comment below must have posted while you were working on your comment here - and we introduce similar subject matter from different points of view.

I like that.

All the Best,

Jonathan

Georgina Woodward

Forgive me please, I should have written Jonathan.

Jonathan Dickau

Forgiveness granted..

The thought is what counts, and yours are always appreciated.

Regards,

Jonathan

Georgina Woodward

(While 'on paper' the choice of sign does not matter because the outcomes of the rotations are equivalent it would make a very big difference to an aircraft, especially in a combat scenario.)

Richard Gill

Sure, S > T > M. However if we restrict attention to finite sets the picture changes ...

Rick Padua

Why only nuclear blasts? Why not puffs of smoke (colored, if desired) in an enclosed area?

Joy Christian

"Why only nuclear blasts? Why not puffs of smoke (colored, if desired) in an enclosed area?"

Sure. As Fred Diether suggested elsewhere, even ordinary bomb explosions would do.

Puffs of smoke won't work, however, because the initial state of the "bomb" must be a singlet state. That is to say, the total spin angular momentum of the bomb must remain zero: S_1 S_2 = 0. Only then we could hope to see the strong correlation. I think that would be difficult to ensure with puffs of smoke.

Rick Padua

The molecules of a smoke bomb, like most molecules, exist in a singlet state, in this case at least prior to ignition. Is that good enough?

Thomas Ray

There may be something to the cloud thing. Mitchell Feigenbaum made his bones studying patterns in clouds and smoke. Deterministic chaos would be an interesting angle on the experimental problem.

Joy Christian

"The molecules of a smoke bomb, like most molecules, exist in a singlet state, in this case at least prior to ignition. Is that good enough?"

Perhaps. The idea is certainly worth investigating further. But whatever system is used, if there is sufficient control possible---either observational or experimental---then we should be able to see the strong correlation.

Richard Gill

Using video footage of historical bomb explosions instead of making our own is a smart idea.

If we can find suitable material, the "wet" part of Joy's experiment has already been done. The dry part consists of analysing the video footage in order to produce two computer files consisting of directions of angular momentum of N pairs of fragments.

Finally we run this computer code, already authorized by Joy, on the two files:

http://rpubs.com/gill1109/Bet

It computes, exactly according to Joy's instructions, four correlations, and congratulates the winner of our bet.

Anyone like to guess the outcome?

Joy Christian

The results of the bomb experiment have been established since 2007 and recently confirmed in several event-by-event numerical simulations: http://rpubs.com/jjc/13965. But an actual experiment is still needed to teach a lesson or two to those who are too slow to understand basic physics, basic algebra, basic topology, and basic analysis.

Thomas Ray

" ... produce two computer files consisting of directions of angular momentum of N pairs of fragments."

My two cents -- sample groups of N exploded fragment pairs at different time scales.

t_epsilon, t_m, t_n ...

"Anyone like to guess the outcome?"

Any arbitrarily chosen t_m is isomorphic to t_n. That is, average spin angular momentum will correlate across scales, such that correlations are totally preserved as self-similar in all time intervals, as a function of the time dependent system state determined by the spinorial properties of space. t_epsilon is a nonzero interval of arbitrary practical measure, where the correlation function may be fixed in order to determine the system's initial condition, i.e., directions of spin.

The time interval maps may be graphically laid one atop the other, as many maps as desired. The correlation function for a significant number of interval overlays will correspond to the computer simulation.

Richard Gill

Joy Christian wrote " been established since 2007 and recently confirmed in several event-by-event numerical simulations: http://rpubs.com/jjc/13965. But an actual experiment is still needed to teach a lesson or two to those who are too slow to understand basic physics, basic algebra, basic topology, and basic analysis. ".

If Joy is right, we don't need an actual experiment to teach a lesson to slow-witted people like me. All Joy needs to do is to ask whoever programmed http://rpubs.com/jjc/13965 for him ((I believe it was Chantal Roth, who used my decoding of Pearle's 1970 detection loophole model) to use the program to generate two files each of N directions of angular momentum. I suggest spherical coordinates, and I suggest N = 10 000. Then we run Joy's bet-evaluation-program http://rpubs.com/gill1109/Bet to calculate four correlations, and inevitably award the prize to Joy. I apologize publicly to Dr. Christian and transfer 5 000 Euro to a charity of his choice. The science journalists love it, the blogosphere is abuzz. Joy gets the Nobel prize and quantum theory has to be rewritten.

Why are we waiting?

Fred Diether

Why do you think quantum theory would have to be rewritten? NOT! You really don't understand Joy's classical local realistic model at all, do you?

Fred

Richard Gill

I meant, Fred, that quantum information theory, quantum computation, and all that would have to be thrown away. Qhantum entanglement would no longer be weird, no longer be quantum. The Aspect experiment and the Weihs experiment would have been superfluous. All based on grandiose misconceptions. Kept in place by a powerful elite who suppress the truth, that entanglement never existed.

Nobody understands Joy's theory except Joy. Nobody has been able to reproduce his theoretical calculations. Somehow, there's always a wong sign turning up somewhere, or the wrong universal quantifier, or the necessity to pick a point in an empty set. By now, nobody is trying any more.

Well: just a few people do understand the theory (Fred, Tom, Johnaton, ...). But they do not seem to be taking it anywhere. Where is a tutorial for undergraduate physics students? Youtube lectures? Why is the word not spreading? The young pick up new ideas, bide their time, and pull them out when the old generation's power is waning.

Richard Gill

If Joy is right, we don't need an actual experiment to teach a lesson to slow-witted people like me. All Joy needs to do is to ask the programmer of http://rpubs.com/jjc/, to use the program to generate two files each of N directions of angular momentum of N simulated pairs of spinning particles.

I suggest spherical coordinates, and I suggest N = 10 000.

Then we run Joy's bet-evaluation-program http://rpubs.com/gill1109/Bet to calculate four correlations and inevitably, since Joy is right, to award the prize to Joy.

I apologize publicly to Dr. Christian (and to Karl Hess, Bryan Sanctuary, Han Geurdes, Al Kraklauer, Luigi Accardi, Hans de Raedt, and several others), retract about 10 of my own favourite papers, and transfer 5 000 Euro to a charity of Joy's choice. A few years later Joy is granted the Nobel prize and all the text-books are rewritten.

What the hell are we waiting for?

Well one thing we are waiting for, is authorized and tested translations of http://rpubs.com/gill1109/Bet into Mathematica, Python, Java.

Joy Christian

The simulations have already been done. As I have noted, the results of the bomb experiment have been established (theoretically) since 2007. They have also been recently confirmed in several event-by-event numerical simulations, such as this one. But an actual experiment is still needed to teach a lesson or two to those who are too slow to understand basic physics, basic algebra, basic topology, and basic analysis.

[deleted]

" ... a powerful elite who suppress the truth, that entanglement never existed."

How long did it take to establish that the luminiferous ether doesn't exist as a physical phenomenon?

"Nobody understands Joy's theory except Joy. Nobody has been able to reproduce his theoretical calculations."

Who understood Einstein relativity in the beginning?

"Somehow, there's always a wong sign turning up somewhere, or the wrong universal quantifier, or the necessity to pick a point in an empty set. By now, nobody is trying any more."

They should try first to understand why they get different results. If one starts off assuming he can square the circle with compass and straightedge and discovers it's impossible, perhaps one should wake up to the possibility that he is using the wrong tools in the wrong space.

"Well: just a few people do understand the theory (Fred, Tom, Johnaton, ...). But they do not seem to be taking it anywhere. Where is a tutorial for undergraduate physics students? Youtube lectures? Why is the word not spreading? The young pick up new ideas, bide their time, and pull them out when the old generation's power is waning."

It's going to happen, Richard. You just have a fifty year head start. It takes time to untangle, before one can reweave.

Thomas Ray

Last was mine.

Richard Gill

Joy says the simulations are done. Good, then he can submit the two computer files of directions, and we can evaluate the winner, acording to the protocol agreed by Joy himself, today! What the hell are we waiting for?

Joy likes repeating himself, so I will follow his example:

"If Joy is right, we don't need an actual experiment to teach a lesson to slow-witted people like me. All Joy needs to do is to ask the programmer of http://rpubs.com/jjc/, to use the program to generate two files each of N = 10 000 directions of angular momentum of N simulated pairs of spinning particles. Then we run Joy's own approved bet-evaluation-program http://rpubs.com/gill1109/Bet to calculate four correlations and inevitably, since Joy is right, to declare Joy the winner. I then moreover apologize publicly to Dr. Christian (and several others), retract about 10 of my own favourite papers, and transfer 5 000 Euro to a charity of Joy's choice. I oredict that a few years later Joy is granted the Nobel prize and all the text-books are rewritten. What the hell are we waiting for?"

Joy Christian

The simulations have already been done. As I have noted, the results of the bomb experiment have been established (analytically) since 2007. They have also been recently confirmed in several event-by-event numerical simulations, such as this one. But an actual experiment is still needed to teach a lesson or two to those who are too slow to understand basic physics, basic algebra, basic topology, and basic analysis. Therefore, what we are waiting for is actual data, either observational or experimental.

Richard Gill

pjackson

Richard,

I'm happy to meet your challenge, but no more fame please, I'm already a legend in my own lunchtime. But I'm no programmer so I must ask you to translate the thought experiment into numbers. You should only need the cosine law, Pi.r^2, and Malus' Law to classically produce E(a,b) = a.b. I hope the 5,000 Euro's retained will be an adequate fee?

Just one point on your description. A pure singlet state is not generated at source, two 'superposed' states (spin directions) are generated, which are reduced ('collapsed') to single states when measured. I show how these states are reduced and what actually physically produces the cosine distribution.

To get closer to the real thing I've evolved the disc into a sphere, little more than a simple Bloch sphere. The 3D geometry seems nothing like as complex as Joys 'parelellelised 3/7-spheres' and maths, which (though I invoked Hopf fibration in a recent essay) I can't get my head round at all. Then Joy can't see mine either so perhaps they're quite different.

If you're happy with that I'll pass you the diagrams and logical description of exactly what happens in the box. I've also re-run the experiment using your angles and it works perfectly. I have a table and a plot of the findings.

By the way, seeing what the Max Planck Institute have been doing I think they're right. They look very close behind. They just seem to have missed one tiny quantum leap in fundamental analysis.

Is that fair?

Best wishes

Peter

Jonathan Dickau

A further comment..

Above I ask "So what does S^3 get us?" and I answer "A continuous range in a 3-dimensional space, over a continuous range of inward-facing and outward facing vectors." This is my description of what S^3 corresponds to in the realm of R3 space plus time - i.e. the Classical or Euclidean approximation of 4-d spacetime. My query is whether this description corresponds to or is isomorphic with the Hopf fibration of S^2 to yield parallelized S^3. So I guess equivalently we have to answer "does this description yield the properties of the quaternions?"

It is known that quaternion algebra compactly describes the dynamics of flight. So we can ask "Is there, in the dynamics of aircraft or spacecraft navigation 'a continuous range of inward-facing and outward-facing vectors'?" This correspondence is true if we are reckoning with respect to the planet's center, when speaking about inward and outward. There is decidedly a continuous range of vectors toward or away from the ground or open sky. But this continuous range of flight vectors is only available if you have enough elevation above the surface to start with.

So does my layman's description of how S^3 differs, or is derived, from S^2 help people to understand what Joy's model is about? I think having an intuitive grasp of the difference between the two figures is of key importance. For what it is worth, I have not seen a moving target - as Joy's description of the target system remains consistent - but I have seen Joy adopt one metaphor after another, to find a way to describe his work in a way others can relate to - largely without success.

Regards,

Jonathan

Joy Christian

Thanks again, Jonathan.

You wrote: "For what it is worth, I have not seen a moving target - as Joy's description of the target system remains consistent - but I have seen Joy adopt one metaphor after another, to find a way to describe his work in a way others can relate to - largely without success."

This is a comment by someone who has actually tried to read what I have written, with great deal of knowledge as well as willingness to understand the subject matter.

On the other hand, if one's goal is to criticise and reject without any knowledge or understanding (or even intellectual capacity to understand in some cases), then it is entirely different matter. It is especially difficult for someone to understand something if they are desperately trying not to understand it---because of their own weaknesses such as deep-seated prior prejudices, and because they know that they will not be able to stand the conclusion they would have to accept if they did understand what I have written.

Jonathan Dickau

Thank You Joy,

I think it is perhaps hasty to conclude that people lack the mental capacity, as it is more likely a well-worn groove that catches the wheels of the mind when traversing a certain stretch. People value certainty, and they are fiercely compelled by society to maintain an air of certainty - if they hope to assume or maintain a role as an expert. While true understanding requires one to uplevel or question beliefs in supposed facts, the vast majority do not seek knowledge for its own sake, but rather to establish a position of strength from which their expertise will be seen as valuable to others.

Someone like myself does not need to maintain an appearance of knowing all the answers cold, and I can therefore approach certain things with an open eyed and childlike sense of wonder. I have no entrenched position to defend, you see, and only a healthy curiosity to learn more and understand things better. I am the eternal beginner, because I never will assume I understand things well, but rather I'm always trying to see past the common misconceptions and learn what the universe and nature are actually telling us.

All the Best,

Jonathan

Thomas Ray

" ... the vast majority do not seek knowledge for its own sake, but rather to establish a position of strength from which their expertise will be seen as valuable to others."

A quotable truism that rates with the best. Well said, Jonathan.

Richard Gill

PS the peacock in a cage metaphor is beautiful.

I think there is no cage implied by the experimental constraints. You might say "look the bird is blue, therefore it's a peacock". But budgerigars can be blue too. Peter's model needs to be tested fairly and stringently. It's not just the four numbers. It's also the situation in which those four numbers emerge.

Richard Gill

PS accidentally posted in wrong thread. Peacocks are for Judy and Peter.

Richard Gill

Peter: my description does not say what physics goes on in those three boxes. You generate whatever you like at the source.

I am not going to program your physics. Get someone to do it for you. You can promise them 5 000 Euro.

Tom: give your advice on the advisability of character assassination in scientific debate to Joy.

I criticise Joy's maths, he assassinates my character. This gives everyone iindirect information as to his reliability as a mathematian.

Karl Hess and Walter Philip were very upset when we found a forgotten index in their Bell counterexample, which sank it. Instead of withdrawing their PNAS paper they spread the rumour that the great Joe Doob had said that I was a third-rate statistician. Later, Karl teamed up with Hans de Raedt, who had perceptively noticed that the "bug" could be converted into a feature of a detection-loophole based computer simulation.

But I never got a word of thanks or apology.

Richard Gill

When we evaluate the outcome of an experiment, we process experimental data in a computer. If the experiment is contentious, this has to be done transparently. It has to be reproducible.

Tom does not believe in experiment. We are talking about Joy's experiment, which is meant to prove to the world that Joy is right. We are talking about Joy's instructions to Joy's own lab IT specialists. About the supplementary materials to be published by "Nature". But Tom doesn't need experiment.

Richard Gill

What counts is E(a, b) = - a . b

If Joy is right then Joy or one of his supporters can easily win my challenges - both the programming challenge I described here, or the bet on the experiment with colourful exploding balls (which should be easy to program - classical mechanics. Geometric algebra is a wonderful tool here). I don't understand why Michel Fodje has not done it yet. He is wonderful at Python and he has a better grasp of CHSH than anyone.

We really need his Python code for the bet-evaluation-stage. When we have it, we can submit it to the adjudicators. Till then, the preparations for the experiment are on hold. I planned to talk about it at Vaxjo in June, but time is running out for that.

Instead everyone is more busy with making derogatory personal remarks. We need Judy back on the forum to add a touch of civilization.

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