Hi Edwin,
" ... you remark that we can use mathematical artifacts of extra dimensions to describe manifestly local results without rejecting scientific realism. Of course I have no objection to mathematical artifact. In my essay I explain how Hilbert space in an energy basis is appropriate, and how it correlates with probability. But you aren't implying that Joy's 7 (or 8) dimensions are only artifactual, are you?"
They are. It would be wrong, though, to say "only" so, as if to imply "mere." What I mean by "mathematical artifact" is a term that instantiates meaning without changing meaning. By the same token, Einstein's famous equation doesn't change meaning if the statement is truncated to E = m -- as an equation of state, though, E = mc^2 tells us that the rest state of matter contains more energy as kinetic potential (atomic binding energy) than is evident until we actually measure the excess, which of course, is the source of atomic power.
Joy's expectation (or correlation) value E(a,b) = -a.b is also an equation of state. That is, it prescribes a measurement limit, just as the constant c^2 in special relativity. And just as we expect a precise quantity of energy to be released from identical quantities of mass every time we "split" an atom, one should expect a precise correlation between an observer's potential result and her actual measure result at the limit, which turns out to be identical to quantum mechanical correlations.
When you speak of the Hilbert space and probability functions, you are out of the domain in which Joy's framework lives. One can't derive the orientability that obviates every probability function, from that basis. One gets it only in the limit of topology that Joy has described: " ... all possible quantum correlations is derived from the maximum of parallelizing torsions within all possible norm-composing parallelizable manifolds."
Just as binding energy is "hidden" in the potential kinetic energy of mass, the correlation function of quantum pairs is hidden in the topology of parallelizable spheres. Just as the measured potential of binding energy is realized at the kinetic limit as a local and real phenomenon, quantum correlations are realized at the topological limit as a local and real phenomenon. The self-limiting mathematical artifact in each case tells us that we have arrived at a closed logical judgment -- the result (value) will always be covariant with the (argument) limit; i.e., dependent on topological orientation and initial condition.
How we (you and I) arrive at a non-probabilistic wave function has nothing to do with Joy's framework. We use the term because we need a local artifact to describe a continuous function independent of discrete measurement results (a real continuous function is never probabilistic). Joy doesn't need it at all -- his topological framework obliterates the distinction between local and global. "All physics is local," as Einstein said.
You wrote, " We do agree about 'probability' in QM. But you seem to want to banish it, while I'm trying to explain why it works for a physical wave function."
It doesn't work for the wave function, and can't. The wave function is continuous; there is no continuous probability function.
Tom