Dear Doctor Crowell,
"Very little of human action really involves reason."
Probability learning, I would say-- for every possibility X sub i (i = 1 to n), regret at having chosen X sub i when the payoff occurs elsewhere; and in other situations, regret at having NOT chosen X sub i, when the payoff does occur there.
This is the signature of a learning algorithm, evident in the Born rule when Bohm and Hiley (in The Undivided Universe) are taken to heart-- that the two sides of the simplest possible equation for the Born rule represent two different concepts.
I just adopt/adapt this and instead say that the two sides of the equation are two different ALGORITHMS.
So of course, I have to resort to game theory. Hence the probability learning game.
The quantum particle doesn't KNOW the laws of physics, so it has to LEARN them.
(Who is doing the teaching?)
David Tong, in his notes for QFT which he teaches at Oxford, says there is a limit close to the Schwarzchild radius where some physicists believe that QFT will break down. And then there must be a different theory.
If I understand this correctly, it can't be QFT because that depends on nice results for Lorentz transformations, which would be expected to have exceptions, I guess, in the neighborhood of the Schwarzchild radius.
Then what would the new theory be, and how would QFT "emerge" from it, to use the popular term?
More generally, it seems to me there must therefore be an "infomorphism" from this other kind of theory to field(s), or field, if we respect string theory.
I have been thinking of this in terms of proper time.
And instead of another kind of field theory at that scale, I've been imagining a different kind of "particle" theory.
But instead of being an "object," I've been thinking of the particle as a "process" as in formally specifiable computer process. (algorithm)
Then to get an infomorphism, the proper time of such a process must map to a SET of all possible (string theoretic) fields, as represented by their coordinate times.
Hence there should be a game-theoretic selection of fields, and since the non-flat ones give indeterminate readings for number of particles created, we should expect that the field selected will be flat. Otherwise, any number of particles could be created. But we are looking for a deeper theory from which such fields will emerge, and therefore it is the "particles" (processes) that determine how many of themselves there are, not the fields, which are selected, and which do not in this idea determine the number of particles.
Here's the start of another discussion about this in the contest.
Do you agree with David Tong, as I interpret him, that the usefulness of QFT breaks down in the neighborhood of the Schwarzchild radius?
If so how would you see the particle-- not as an object-- but as a (computer) process?