Reply To: Quantum causal models, faithfulness and retrocausality (onl. 7/16 @ 11pm UTC+10)

[Ken Wharton]

Hi Pete,

Thanks for this interesting and useful paper! I like the changes in 4.3 that I noticed from the original version, concerning how the final boundaries are implemented. And of course there’s a lot of connection between our papers here; the “internally cancelling paths” you refer to has got to be due to some *symmetry*, wouldn’t you think?

More thoughts…. I realize you’re throwing out a grab-bag of possible responses to Wood-Spekkens, but in 4.3 I kind of lost track of how all these various options relate to each other: which options were related and which were distinct approaches.

Concerning the analysis of Figure 4 that blends together A, B and \lambda into a “whole”, this sounds a little sketchy the way it’s described. The whole *point* of these retrocausal pictures is to get things back into spacetime, and this ‘holistic’ perspective backs off from that perhaps more than you need to. Why can’t they just be linked via “mutual causation”?

An explicit example might help here… and as you might guess, I have in mind the normal modes of a laser cavity, always my go-to-example for an “all at once” account. You could make the analogy where “A” is the position of the left cavity mirror, “B” the position of the right cavity mirror, and \lambda is the wavelength inbetween. The entanglement analog would then be a known probability distribution over possible wavelengths.

This example features what you’re going for, I think. Given a known distribution on lambda, you can treat A as causing a probability distribution for B, but you can also treat B as causing A. Furthermore, A and B together can “cause” particular values of lambda, etc. So all three of these parameters are *distinct*, but still maintain this mutual-causation relationship which I think is what you are going for with this Woodward-style account…?

I need to think a bit more about your treatment of amplitudes. My first instinct was that I didn’t like it, because I can’t imagine an “amplitude” is in any way ontological. But on another read I see that you’re just using mathematical cancellations, without much commitment as to what these amplitudes might mean. One warning I’ll give, though, is that the notion of “cancelling amplitudes” is not generally a spacetime-local concept, and only showed up that way in those papers of mine because we were using a discrete-path version of the path integral.

Best, Ken