Hi Ken,
I’ll try to respond to your comments in the paragraph order you list them.
1. Agreed. In the source of the internal cancelling paths idea, a paper by Paul Näger, it is a quirk of the causal relationships that provides the cancelling. The model that I present, originating from Gerard Milburn, employs no such quirk, and the internal cancelling paths arises from restricting the possible amplitudes that contribute to the final joint probability. Insofar as you say, “imposing symmetries is itself a sort of fine tuning, in that a large parameter space is restricted to a special (symmetrical) subset”, I think that these are catching on to the very same idea (though obviously with different detail).
(In fact, putting it this way could provide a more general statement of the conditions under which an internal cancelling paths mechanism could work retrocausally.)
2. I think “grab-bag” is the right sort of phrase to describe the mess I left at the end of the paper! The main thrust of that section is that the analyses of Hausman and Woodward are essentially the same, and the view therein is amenable to being interpreted along perspectival lines. I’m hoping that this can be an illuminating exercise for understanding how to tell some sort of dynamical story about the dependence relations (a different story for each perspective)—this is related to the point I was making in reply to Mark above—and to illustrate that the right dynamical story may not be representable in an orthodox causal model.
3/4/5. Yes, sketchy it is. This issue also relates a little to the appropriateness of the instrument of causal modelling. Causal modelling requires distinct variables with distinct causal mechanisms relating them. Of course, it’s partly up to us as modellers to choose the most suitable variables, etc, and explicate the relations between them. I take your question to be, why can’t we describe the relation as mutual causation rather than some more “holistic” story? Well, I would like to think that that is the way I’m describing it. But my “grab-bag” obviously isn’t doing that job very well! Point taken.
I think your laser example is great—in fact, as I re-read it a couple of times it really does capture a lot of what I want to say about the EPRB case. This might provide a robust analogy… let me consider it some more.
6. In what sense do you mean spacetime-local? Am I right in assuming you mean Lorentz invariant or, equivalently, action-by-contact? Hmmm… perhaps you could say a bit more please about this problem?
Cheers,
Pete
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