Reply To: Thinking about QM as a variational principle (online 7/9 @ 9am UTC-6)

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Hi Ken,

I had originally been trying to devise a variational principle (VP) with the desired characteristics essentially as a mathematical exercise, deferring the question of how to justify it physically. The Lagrangian viewpoint tells me that I should use the extremization of the action as my VP, so my current approach is to start with a given Lagrangian and see if the resulting VP does what I want it to. I can find candidate Lagrangians in QFT, where interestingly enough the theory makes it natural to pursue the VP approach, but the conventional approach is to go in another direction altogether (interaction picture, path-integral methods and so on). So I’m trying to see what I can learn from that.
I agree with your use of the relationship between joint and conditional probabilities to understand what happens in a measurement. But I’ve been hopeful that an improved theory might allow one to calculate more than just a joint probability P(A,B). If the theory doesn’t take us any further than that, we still need a collapse model of some sort to explain how nature picks a particular outcome, and I’d like to see a theory that resolves that issue as well.
In the work I wrote up previously, I proposed that the phase of the wavefunction (or equivalently, the start time of a measurement) might serve as a hidden variable that controls the final choice among possible outcomes. (Of course, here I use “final” in a logical rather than temporal sense!) [It turns out that Pearle proposed the same idea in 1976 (Phys. Rev. D 13,857-868).] So my idea of prediction would ultimately include something like this, and my comment above alluded to the fact that I don’t understand this mechanism in detail yet. I’d like to find a promising VP first, and then return to this issue.

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