David - thank you for your comments. I would not describe subtime as a second time axis. If anything, it is a "no time axis" solution: setting aside Minkowski's global background of time with a purely local "element of physical reality" between emitter and absorber. Unlike Minkowski space, time doesn't exist beyond both ends of each photon path.
I have thought about how to describe subtime mathematically. it seems obvious that Hilbert spaces have very little to say regarding time in their inner-products/conservation/unitary evolution. Its just a set of rules that gives us the right answer for statistical experiments. I think this is what David Mermin (Boojums all the way through) was getting at when he said that explicit "denial" is built into the mathematical formalisms of QT.
At the basic level, subtime doesn't seem to need any more than Euler's equation and the triangle identity (see attached summary) to describe it. As Feynman discovered, half the exp(-iwt) wave plus half the exp(+wt) advanced wave gets the right answer. 聽However, I think Feynman missed it because he built QED on top of Minkowski space, giving rise to statements like "electrons going back in time".
In my view, nothing goes back in time. From the perspective of the emitter, it is time itself that is going backwards in the retarded wave along the photon path. To the absorber, time is going forwards as it receives what it sees as an advanced wave. The sign of "time" in this context specifies the direction of information transfer, it has nothing at all to do with what we call forwards or backwards, past or future; we need's Born's modulus applied to subtime to yield observable evolution in classical time (Tc). This is nothing more than the triangle identity.
You are right, the mathematics is there. But it's so simple it seems hardly necessary. I do plan to publish the paper, but I need to follow the rules of the fqxi contest first.
I would enjoy an extended conversation with you on this, and will take up your offer to contact you directly by email. However, we can also continue to interact on this web site; only the community voting was shut down the day you left your comment.
Kind regards, PaulAttachment #1: 1_TimeOneSummaryV1.1a.pdf
