Classical v quantum correlations, and why none beyond

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Classical v quantum correlations, and why none beyond

Postby Joy Christian » Tue Oct 02, 2018 10:54 am

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In this thread, I want to discuss what in my view is the true difference between "classical" and "quantum" correlations and why "stronger-than-quantum" correlations are never observed in Nature. I have worked on this question for the past eleven years, starting with a short paper in 2007 and culminating in this latest: http://rsos.royalsocietypublishing.org/ ... 5/5/180526.

In my view, the difference between "classical" and "quantum" correlations has nothing much to do with how these words are traditionally understood in physics, especially in the literature inspired by Bell's so-called "theorem." Both "classical" and "quantum" correlations are simply correlations. But there is, of course, a difference between the two: "quantum" correlations are both stronger and more disciplined than "classical" correlations. Where does this difference originate from? We should be able to address this question without being prejudiced by the usual meanings of the words "classical" and "quantum." One might call this investigation a kind of "meta-investigation" into the question. I have carried out this "meta-investigation" in the paper I have linked above. It vindicates my initial hunch going back to my first paper on the subject in 2007. The difference arises from the difference between the first two and the last two of the only four possible normed division algebras, namely the real, the complex, the quaternionic and the octonionic division algebras, and their associated topological spheres S^0, S^1, S^3 and S^7. The first two of these algebras happen to be commutative, and the last two happen to be non-commutative. And that makes all the difference. How does this difference manifest itself in the correlations we observe in Nature? Well, that has to do with the algebraic, geometrical and topological properties of the 3D physical space in which we are confined to carry out all of our experiments. It turns out that these properties are deeply connected to the two non-commutative algebras. Further details can be found in my latest paper on the subject linked above.

Joy Christian

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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Tue Oct 09, 2018 12:18 am

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Joy Christian wrote:In this thread, I want to discuss what in my view is the true difference between "classical" and "quantum" correlations and why "stronger-than-quantum" correlations are never observed in Nature. I have worked on this question for the past eleven years, starting with a short paper in 2007 and culminating in this latest: http://rsos.royalsocietypublishing.org/ ... 5/5/180526.


So, then, what do the so-called Bell-test experiments test? Do they not distinguish the "quantum" correlations from "classical" correlations? Well, not quite. The results of the above paper suggest that when certain correlations in the Bell-test experiments are seen to exceed the absolute bound of 2 on the Bell-CHSH inequality, then those correlations stem from those aspects of spacetime geometry and topology that depend on the non-commutative quaternionic or octonionic numbers. If, instead, they depended on the commutative real or complex numbers, then for those correlations the absolute bound of 2 on the Bell-CHSH inequality would not be exceeded. That is all there is to it. It is both beautiful and non-mystical. There is no such thing as irreducible randomness, non-reality, "quantum" spooky-action-at-a-distance, non-signaling non-locality, or any other kind of silly voodoo in Nature. Nature is beautiful but not mystical.

Joy Christian

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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Tue Oct 09, 2018 7:43 pm

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Joy Christian wrote:In this thread, I want to discuss what in my view is the true difference between "classical" and "quantum" correlations and why "stronger-than-quantum" correlations are never observed in Nature. I have worked on this question for the past eleven years, starting with a short paper in 2007 and culminating in this latest: http://rsos.royalsocietypublishing.org/ ... 5/5/180526.

OK, so what I am saying is that the so-called "quantum" or strong correlations are "stronger-than-classical" correlations because of the algebraic, geometrical and topological properties of the 3D physical space in which we are confined to perform all our experiments. And these properties of the physical space are what they are because of the non-commutative quaternionic and octonionic algebras. So if I am right, then the strong correlations can be observed also in an appropriate classical experiment, such as a purely classical EPR-Bohm type experiment. In other words, what I am saying is not some idle theoretical speculation but can be verified in a very simple experiment, costing no more than a few hundred thousand dollars. In fact, I have proposed just such a simple experiment long ago in this published paper, and it is also summarized in this preprint for convenience: http://libertesphilosophica.info/blog/w ... opExp1.pdf.

Joy Christian

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Re: Classical v quantum correlations, and why none beyond

Postby ivica » Wed Oct 10, 2018 4:22 am

Joy I like your work and part of above have reposted at ASIF forum, here.
Off topic, forgive me :)
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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Wed Oct 10, 2018 4:29 am

ivica wrote:Joy I like your work and part of above have reposted at ASIF forum, here.
Off topic, forgive me :)

Thanks! :)

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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Thu Oct 11, 2018 5:29 am

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Joy Christian wrote:In this thread, I want to discuss what in my view is the true difference between "classical" and "quantum" correlations and why "stronger-than-quantum" correlations are never observed in Nature. I have worked on this question for the past eleven years, starting with a short paper in 2007 and culminating in this latest: http://rsos.royalsocietypublishing.org/ ... 5/5/180526.

So, to continue, what are usually called the "classical" correlations as opposed to "quantum" correlations should be renamed as "commutative" correlations as opposed to "non-commutative" correlations. That, in my view, is what separates the "classical" or "weak" correlations from the "quantum" or "stronger-than-classical" correlations. Bell inequalities (but not Bell's "theorem") thus have value after all, for they separate the commutative correlations form the non-commutative correlations. This will allow stripping away all mysticism associated with the quantum.

One may also wonder about non-associativity in this context. But I sympathize with Dirac's view in this regard, for although octonions are non-associative in general, their role in physics is not as clear as that of the associative quaternions (e.g., ask any aviation engineer). In any event, non-associativity does not play any role in the results presented in my paper linked above.

Joy Christian

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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Thu Oct 11, 2018 4:54 pm

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Joy Christian wrote:In this thread, I want to discuss what in my view is the true difference between "classical" and "quantum" correlations and why "stronger-than-quantum" correlations are never observed in Nature. I have worked on this question for the past eleven years, starting with a short paper in 2007 and culminating in this latest: http://rsos.royalsocietypublishing.org/ ... 5/5/180526.


S^0 and/or S^1 = R and/or C = classical or comutative numbers ==>> |CHSH| < 2

S^3 and/or S^7 = H and/or O = non-commutative numbers ==>> 2 < |CHSH| < 2\/2

No irreducible randomness, no non-reality, no spooky-action-at-a-distance, no non-signaling non-locality, no voodoo in Nature.

Joy Christian

***
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Re: Classical v quantum correlations, and why none beyond

Postby FrediFizzx » Thu Oct 11, 2018 11:22 pm

Joy Christian wrote:***

Joy Christian wrote:In this thread, I want to discuss what in my view is the true difference between "classical" and "quantum" correlations and why "stronger-than-quantum" correlations are never observed in Nature. I have worked on this question for the past eleven years, starting with a short paper in 2007 and culminating in this latest: http://rsos.royalsocietypublishing.org/ ... 5/5/180526.


S^0 and/or S^1 = R and/or C = classical or comutative numbers ==>> |CHSH| < 2

S^3 and/or S^7 = H and/or O = non-commutative numbers ==>> 2 < |CHSH| < 2\/2

No irreducible randomness, no non-reality, no spooky-action-at-a-distance, no non-signaling non-locality, no voodoo in Nature.

Joy Christian

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That's good. Now, how does or how can S^3 and/or S^7 explain the double-slit experiment? The interference pattern is sort of a correlation.
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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Fri Oct 12, 2018 7:08 am

FrediFizzx wrote:That's good. Now, how does or how can S^3 and/or S^7 explain the double-slit experiment? The interference pattern is sort of a correlation.

Good question, Fred. There is no issue of non-signaling non-locality of the EPR-Bohm kind in the double-slit experiment because what is involved in that experiment is just superposition, not entanglement. Nevertheless, one can certainly view the double-slit experiment as a correlation experiment. In fact, all quantum phenomena are simply manifestations of the strong or quantum correlations of one kind or another. In other words, the strong correlations we observe in our experiments are the essence of *all* quantum phenomena. It was established by von Neumann long ago that --- regardless of the model of physics one is concerned with --- whether it is the quantum mechanical model or a hidden variable model --- it is sufficient to consider the expectation values of the observables measured in possible states of the physical systems. In other words, it is sufficient to study strong correlations. And since all quantum correlations are reproducible within the S^7 model considered in my paper, it should be possible to reproduce the results of the double-slit experiment within the S^7 model. The question then is: How?

The first step would be to rewrite the standard narrative of the double-slit experiment in terms of the expectation value of some quantum mechanical operator [cf. eq. (3.25) of my paper]. While I have not been able to find that done anywhere in the literature, here is a good description of the experiment in terms of a quantum mechanical formalism. Once expectation value of the corresponding quantum mechanical operator is found, translation of the experiment within the S^7 model would be straightforward.

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Re: Classical v quantum correlations, and why none beyond

Postby FrediFizzx » Fri Oct 12, 2018 10:18 am

It looks like the slit arrangement is dependent on the de Broglie wavelength of the particles being measured after reading that paper. I suspect some other ingredient would be required to translate to wave mechanics.
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Re: Classical v quantum correlations, and why none beyond

Postby Joy Christian » Fri Oct 12, 2018 10:30 am

FrediFizzx wrote:It looks like the slit arrangement is dependent on the de Broglie wavelength of the particles being measured after reading that paper. I suspect some other ingredient would be required to translate to wave mechanics.

How can that be? I am not sure I understand this. It is up to the experimenters to arrange the slits as they please. The slit arrangement shouldn't depend on the particles being measured.

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Re: Classical v quantum correlations, and why none beyond

Postby FrediFizzx » Fri Oct 12, 2018 10:37 am

Joy Christian wrote:
FrediFizzx wrote:It looks like the slit arrangement is dependent on the de Broglie wavelength of the particles being measured after reading that paper. I suspect some other ingredient would be required to translate to wave mechanics.

How can that be? I am not sure I understand this. It is up to the experimenters to arrange the slits as they please. The slit arrangement shouldn't depend on the particles being measured.

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Well, you couldn't have slits with openings of one inch and one inch apart as an extreme example. You have to be "in the ballpark" of the wavelengths of the particles in order to get the interference pattern.
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