Unitary SU(2) Operators and Quantum Correlations

[Yablon]

This is my first post ever on this forum about anything related to Bell's Theorem. As you know I stayed away from the Bell discussions for years, until the Retraction Watch (RW) discussion about Joy's paper being retracted by Annals of Physics heated up and Joy Christian and Richard Gill agreed to me trying to be a "mediator" which required me to take what has now been a full-semester course on Bell under the tutelage of folks like Joy and Richard and several others who have studied this material extensively and who come to the subject with some degree of mastery and authority. So I am sharing below, I post that is also going up simultaneously on RW:

It has been rather quiet here for the past several days.

I would like to break the silence with a nine-page document I prepared and posted at https://jayryablon.files.wordpress.com/ ... ations.pdf.

As I have stated before, one of the thing I find incredibly frustrating about the EPR-Bell discussion is that there are too many words and too many different uses of language and definitions, all of which causes a great deal of confusion and miscommunication and makes it even more difficult to resolve issues on which there is true disagreement.

I prefer sticking as closely as possible to the mathematics, and that is what I have done in this document. Basically: the EPR-Bell experiments and the quantum correlations all center around five (normalized to magnitude 1 unit) vectors which point in various directions in three-dimensional space: the four a, a’, b, b’, detector vectors for Alice and Bob which are given are fixed orientation in a single plane, and a fifth set of vectors s_n in which a succession of n=1…N randomly-distributed “arrows” or “pointers” or “spins” are thrown toward Alice and Bob to be detected.

It seems that we should at least engage in the basic geometric exercise of carefully mapping out these vectors in physical space using the unitary matrices of SU(2) which conveniently allow us to represent angle and angle differences in space whether we are looking at a classical problem or at a quantum mechanics problem. And it does not hurt as I shown in (1.10) of this document, that these same matrices are organically-embedded in the correlations predicted by quantum mechanics. So that is what I have done here. I do not think that anything in this document should generate any disagreement from any Bell faction, and would like to know whether I am correct in this belief.

Happy holidays and new year to everyone, whether that means Chag Sameach for Hanukkah or Merry Christmas or anything else!

Jay

[FrediFizzx]

Hi Jay,

Nice. Your math looks OK after a quick read-thru. I would argue that the vectors a, a', b, and b' should also be indexed with "n" as far as using a CHSH-like analysis goes. It is actually difficult for any experiment to do many different "a's" and "b's" to completely prove the QM prediction of -a.b.

Looks like all the Bell fans have bailed out on the RW discussion. A possible explanation is that they can't respond to our challenges without admitting that Bell was wrong. Usually if pushed for an answer, they will claim fatigue and/or lost interest.

The bottom line is that they can't prove with rigorous math that QM or the experiments actually "violate" Bell-CHSH. It is really easy to disprove that QM violates Bell-CHSH because it is impossible for a and a' or b and b' to happen at the same time.

Happy Holidays to all.

[Yablon]

Nice. Your math looks OK after a quick read-thru. I would argue that the vectors a, a', b, and b' should also be indexed with "n" as far as using a CHSH-like analysis goes. It is actually difficult for any experiment to do many different "a's" and "b's" to completely prove the QM prediction of -a.b.

Hi Fred, I first wrote it with the "n" index in those vectors also, but to avoid clutter, because etc. for all I decided to keep that index out and have it be understood that the detector settings need to stay fixed if you are going to "average" results over multiple trials. Jay

[minkwe]

Jay,
Your math looks ok to me too.

[lkcl]

hmmm... two things that cause me to question the validity of the entanglement of particles experiments. the first is: i *really* feel that it would be a *really* good idea to actually have a *really* good understanding of particles... *before* using them to draw conclusions such as the ones being made involving bell's theorem.

the second is: i am reminded of professor c d yang's work on "complex mechanics" - he derives quantum mechanics equations from their classical equivalents by moving them into the complex numberplane. it's an amazing ingenious life's work, which he uses to good effect to teach engineers about quantum mechanics.

BUT...

there is an accompanying paper in which he explains the consequences of complex numbers being part of the way our universe operates, that involve instantaneous communication... it's complicated, and worth reading, and bearing in mind in the context of bell's theorem.

[Dirkman]

You're talking about this paper right ? https://www.researchgate.net/profile/Ci ... ion_detail

[lkcl]

hiya jay: i don't believe i was specifically referring to that one, so i'm glad it led to something in which he specifically deals with bell's theorem. given the nature of professor yang's work it does not surprise me at all that he has though about it