Hi Alan,
I’m glad you found my perspective useful… any insight you can give us as to how you’ve been trying to implement the Lagrangian viewpoint?
It looks like you’re planning to be online right about now, but I haven’t had a chance to refresh my memory about your prior work… Still, you did raise this problem about how to extract a “prediction” from an all-at-once Lagrangian-style approach. I don’t know if you recall my low-level explanation of this from the ‘Universe is not a Computer’ essay, but here’s a higher-level account:
Suppose you have a time-symmetric, all-at-once theory that tells you the joint probability P(A,B) that a initial-preparation A will be associated with a final-outcome B. You also need a theory that tells you the allowed final outcomes B_i for any given measurement geometry G. But given these two pieces of the puzzle, I think predictions are fairly straightforward.
Essentially, what you do is use your knowledge of the actual initial preparation A and the actual future measurement settings/geometry G, to figure out the *possible* all-at-once solutions (A,B_i). Each of these all-at-once solutions has a joint probability P(A,B_i). You can then predict the conditional probability for any particular outcome B_j by the usual connection between conditional and joint probabilities:
P(B_j|A) = P(A,B_j) / [\sum_i P(A,B_i)]
Of course, this only works if you know the future measurement settings/geometry; if G is unknown, you’re forced to use a big configuration space of possibilities, a space that collapses to something more reasonable once you know what type of measurement is coming up.
Does this solution seem like it might mesh with your general approach? Any problems you see with this?
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