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Vladimir_Nesov comments on The Born Probabilities - Less Wrong
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My guess is that the Born's Rule is related to the Solomonoff Prior. Consider a program P that takes 4 inputs:
What P does is take the boundary conditions, use Schrödinger's equation to compute the wavefunction at time T, then sample the wavefunction using the Born probabilities and the random input string, and finally output the particles in the region R and their relative positions.
Suppose this program, along with the inputs that cause it to output the description of a given human brain, is what makes the largest contribution to the probability mass of the bitstring representing that brain in the Solomonoff Prior. This seems like a plausible conjecture (putting aside the fact that quantum mechanics isn't actually the TOE of this universe).
(Does anyone think this is not true, or if it is true, has nothing to do with the answer to the mystery of "why squared amplitudes"?)
This idea seems fairly obvious, but I don't recall seeing it proposed by anyone yet. One possible direction to explore is to try to prove that any modification to Born's rule would cause a drastic decrease in the probability that P, given random inputs, would output the description of a sentient being. But I have no idea how to go about doing this. I'm also not sure how to develop this observation/conjecture into a full answer of the mystery.
More specifically, to replace my previous summary comment: the above statement sounds kind-a redeemable, but it's so vague and common-sensually absurd that I think it makes a negative contribution. Things like this need to be said clearly, or not at all. It invites all sorts of kookery, not just with the format of presentation, but in own mind as well.
Huh, that's a surprising response. I thought that at least the intended meaning would be obvious for someone familiar with the Solomonoff Prior. I guess "vague" I can address by making my claim mathematically precise, but why "common-sensually absurd"?
Re absurd: It's not clear why you would say something like the quote.
I was hoping that it would trigger an insight in someone who might solve this mystery for me. As I said, I'm not sure how to develop it into a full answer myself (but it might be related to this other vague/possibly-absurd idea).
Perhaps I'm abusing this community by presenting ideas that are half-formed and "epistemically unhygienic", but I expect that's not a serious danger. It seems like a promising direction to explore, that I don't see anyone else exploring (kind of like UDT until recently). I have too many questions I'd like to see answered, and not enough time and ability to answer them all myself.