Hi again, Ken,
Regarding the “extra” time, it was there in the original Stochastic Quantization paper and subsequent works, but it is also possible (as they occasionally note) to simply stipulate an “equilirium distribution” to begin with, and then there’s no need for the “equilibration” to “occur” as this “extra” time tends to infinity (of course, the “equilibration” here is distinct from that of Bohmian mechnics). So if you don’t like the “extra” time, you can simply do without it. I myself would also prefer it that way (of course, that begs the question how the different parts of space time “know” about each other, but I don’t think we should allow ourselves to be bothered by that; think of Newton, who disliked the long-range instantaneous character of gravitational forces, but developed his theory anyway).
Regarding the model, I was trying to stay as close as possible to Bell’s analysis, so I initially used $\lambda$ to denote all of the relevant hidden variables. I then focused on the one which represents the photons’ polarization as they leave the source (or, if you like, the direction of the angular momentum of the intermediate state of the emission cascade, assuming a source of doubly-excited Ca-40 atoms). The remaining variables are then essentially redundant. Thus, I would look at your model as a more detailed version, where you describe the whole sequence of angles. You could have, say, a distinct angle for every picosecond of photon flight, but in the gamma-to-0 limit there’s only one dominant rotation, so they’re mostly redundant. My lambda is then the angle corresponding to the moment the photons leave the source. It was just not necessary to give a more detailed description.
I like the details of your model which you stressed – the fact that it’s not “collapsey,” and the fact that it’s clearly determined by the boundaries at the time of measurement. I did mention in my work that there’s something special about irreversible measurements that must be a determining factor, because if you think of Alice just letting her photon go through a polarizing cube, then she may later recombine (with another cube) the two partial beams to recreate the original photon polarization (i.e., she may construct an interferometer and regain the original photon state, or a rotated one), and then she can measure with a different orientation by using yet another cube. In order for the toy-model to work, only the irreversible measurement counts, with the proper rotations taken into account.
Best, Nathan.
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