Dear FQXi'ers,
An interesting situation has arisen where Joy's use of the topological spheres S0, S1, S3, S7 has 'collided with' Michael James Goodband's use of the same topologies. Joy, of course, claims that S7 is the *ONLY* solution to Bell's quantum correlation problem, while Michael Goodband employs S7 as 'particle space'. Although I am NOT an expert in these issues, they seem to be (or Joy claims them to be) relevant to my approach, so I have a natural interest here. After an initial period of familiarization with each others use of these topologies, Christian and Goodband are now comparing and contrasting...
What I find most interesting is that Joy appears to be working in quantum mechanics (QM), where particle number is fixed, while Goodband is working at the deeper level of quantum field theory (QFT) where the number of particles varies. From this perspective Goodband has just (Aug 9, 2012 @15:53) noted the following [with notation as e^|e_ for electron spin up e^ and electron spin down e_ ]:
"My point is that this is just quantum mechanics, think quantum field theory. Just as the emission of a photon converts e^ to e_ the emission of a W-boson converts an electron into an neutrino, an up quark into a down quark etc. and there are also inter-family conversion reactions. Such interactions mean that the most general EPR 2 particle scenario in QFT is *not* of the form A^|A_ but A^|B_ where particles A and B can be of any type; A=B is just a special case in QFT.
The observables to consider in the correlation analysis are both the spin eigenvalues of the rotation group SU(2) - group space S3 - and the particle types which are eigenvalues of some 'particle space'. I use this term in place of particle symmetry group, because grand unified theories assumed that it was going to be a group - a hidden assumption I could have raised in my essay - whereas my work says that it is the quotient group SU(4)/SU(3) isomorphic to S7. So there are 2 sets of observables with quantum correlations {^,_} and {A,B,...} where the values of the first set are the eigenvalues of the rotation group with space S3. In my case the second set contains eigenvalues of SU(4)/SU(3) ~ S7 (after the symmetry has been broken) and the S3 is clearly distinct from this S7.
Your analysis should also apply to the quantum correlations between the observables in each of the 2 sets {^,_} and {A,B,...} for the most general EPR 2 particle scenario A^|B_ in the Standard Model QFT. Ultimately my question is whether there is a way to use your analysis in reverse to place a constraint on the origin of these observables?
I.e. some argument of the form
Parallelised S3 => group space S3 for the observables {^, _}
Parallelised S7 => 'group space' S7 for the observables {A,B,...}
A straightforward argument doesn't seem to work, which is why I am asking :-)
Michael"
For those who have been following the "Disproof" blogs for a year or so, this is a fascinating new development..This is getting curiouser and curiouser.
Edwin Eugene Klingman
