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

Richard Gill

... = r^2 < or = 1. Now define t = sqrt(1 - r^2). We now obtain two points (x, y, z, +/- t) on S^3 representing a qubit mixed state. It turns out that the geometry of S^3 is intimately related to quantum fidelity, a fundamental concept in quantum state reconstruction and other quantum informational tasks.

No idea if there are generalizations to higher spheres (higher spins, multipartite systems).

Thomas Ray

"Thus in their picture, pure states are represented by curves on S^3, not points; and there are no mixed states."

This is true in my picture, too. (3.3) When continuous curves are exchanged for discrete points, we get the Poincare Conjecture in physical terms.

"In fact, pure qubit states can be usefully represented by *points* on S^2: the Bloch sphere. Mixed states become geometrically points inside the sphere, ie in what one might call the Bloch ball. They have coordinates x, y, and z satisfying x^2 y^2 z^2"

And this local geometry lacks the extra degree of freedom required to satisfy the global topology.

Joy Christian

In the last paragraph of this paper I make the following observation:

"I hypothesize that the space we live in respects the symmetries and topologies of a parallelized 3-sphere, which is one of the infinitely many fibers of a parallelized 7-sphere. The EPR correlations are thus correlations among the points of a parallelized 3-sphere, whereas quantum correlations in general are correlations among the point of a parallelized 7-sphere."

This hypothesis is fully spelt out in this paper as well as this paper (see, especially, the main theorem and its proof on the pages 12 to 16 of the last paper).

Joy Christian

I messed up the first link. Here is the correct link.

Jonathan Dickau

I just wanted to mention..

The paper by Mosseri and Dandoloff cited by Richard on May 17 was introduced on this forum by Andrew Mendelsohn on March 10th, and discussed somewhat in relation to Joy's model at that time. It should be noted that at least one paper by Mosseri is also cited in Joy's book. I found about half a dozen papers of note myself, when I followed the thread from this paper to related works. So there has been some progress on this front by Mosseri and co-authors Richard, but I think Tom is also correct to assert that some more general results including Perelman's work allow several broad generalizations to be made in principle of the ideas in arXiv: quant-ph/0108137, and that Joy exploits this fact.

All the Best,

Jonathan

Joy Christian

Thank you, Jonathan.

Yes, I cite their paper in this paper of mine, which actually started this entire blog page (see Ref. 28).

Thomas Ray

Thanks, Jonathan. From the beginning, I have opposed Joy's detractors' claims that the work has no basis in previous results. Fact is, Joy's research is in principle a beautiful extension of general relativity to the microscale domain -- details need to be filled in; however, now the criticism has gone from denial to co-option, Says Richard, "The connection between the Bloch ball and S^3 was already known. They extended this connection between quantum states and classical spheres from one two-level system to two. However no-one has been able to take this correspondence further." If one understands that Einstein's program up to diffeomorphism extends by Joy's method to active diffeomorphism, one understands that this correspondence has been taken further, with one little topological twist that everyone missed.

Thomas Ray

Joy, I do like it! I think one of the hardest things to get across to Bell loyalists is "Clearly, a measurement event cannot occur if there does not exist a state which can bring about that event." It is clear to me that only an analytical measurement framework (yours) that is free of coordinate choice and scale dependence can identify that state for every measured event.

Thomas Ray

Oh come on! What legitimate offense could anyone have possibly taken to Joy's post to which my reply is directed? Let's stop these childish deletions.

Thomas Ray

I can at least repost the link to Joy's latest paper, so that my reply makes sense.

Thomas Ray

Thanks, moderators. I see Joy's original post has reappeared outside of this thread.

I think the point needs to be stressed, that Mosseri & Dandeloff's result regarding entanglement on Bloch spheres only fits Richard's (and Mosseri/Dandoloff's) a priori assumption of entangled states. No such assumption is necessary.

Progress in theoretical physics often depends on negative results that obviate superfluous assumptions. Discarding of phlogiston. Discarding of the luminiferous ether.

Add quantum entanglement to the list.

Judy Nabb

Brendan,

Two of my posts have been inappropriately removed from this string. I find that behaviour to be highly dishonest and unethical scientific censorship bordering on scandalous. I trust they'll be replaced as they don't breach the fqxi guidance.

Thank you.

Judy

pjackson

Judy,

A number of my posts falsifying the proposition Richard suggested have also vanished. It seems that when refutation is impossible the defence of censorship remains available. I'll none the less repeat my proof lest anybody can provide any falsification.

I replace the fundamental assumption 'Q', (singlet state) with the new assumption 'B')(both clockwise and anticlockwise spins, as ALL OAM, but only one 'hemisphere' at a time measurable). I then invoke science; i.e. spin flip, and 'measurement as 'transfer of OAM' to show that each finding, though remaining quantitatively 'random', is independent and liable to field direction (setting angle).

Bell's theorem is only logically valid if 'Q' is valid. Richard has suggested that Bells logic does NOT rely on 'Q'! but has not supported that claim. I hope somebody may offer some evidence for that claim so it can be examined. Otherwise it seems to remain clearly false.

Peter

pjackson

Richard,

I now understand the '!', so now; can you justify how the Bell/CHSH logic can stand without singlet states; i.e. If EM fields do what we know EM fields do to electron spin orientation, "rotate" it, which I show can simply and classically derive the "quantum correlations" then why does that no resolve the EPR paradox. It may no resolve it in the way most 'expected', but resolve it it does. Solutions are always, by definition, 'unexpected'.

I'm also bemused by your citing of the Mosseri paper which is consistent with my essay, which merely completes that Bloch sphere logic in a simpler more coherent way. Again I can't resolve the logic of your apparent position that by refusing to read my essay you find my mechanism and logic incorrect, yet cite Mosseri as correct when it's consistent with mine.

If you wish to maintain that position can you please justify it. I do feel your misunderstanding could have been avoided had you read my description (a universal truth).

Best wishes

Peter

Nick Mann

Get a room, you two!

Thomas Ray

Preferably, a laboratory.

Nick Mann

You guys must be capable of charm since you charm each other. Expand your circle and it ought to be a cinch to raise the scratch.

Thomas Ray

Charm comes with the confidence of knowing something worth knowing, Nick. After that, the scratch raises itself.

Nick Mann

Well, whatever. Anyway, from http://arxiv.org/pdf/1405.2355v1.pdf:

"Consequently, the detectors of Alice and Bob can receive the spin states [e-sub-o] only if the constraints (30) are satisfied. In other words, unlike Pearle's model, our model is not concerned about data rejection or detection loophole. ... Clearly, a measurement event cannot occur if there does not exist a state which can bring about that event. ..."

Would Tom and/or Joy relate the above to the contretemps concerning submission of the two thumb drives (or equivalent) containing separate data from Alice's and Bob's hypothetical detectors? Does Joy acknowledge that he agreed to such a submission? Did he, in his estimation, in fact submit the data in the format agreed to and Richard Gill is blowing smoke?

Thomas Ray

Joy is compelled to submit data in the format that his framework describes. We've all known all along that those who don't understand that framework would prefer that it were something it isn't.

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