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pengvado comments on Bayesian Flame - Less Wrong
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I had another thought on the subject. Consider flipping a coin; a Bayesian says that the 50% estimate of getting tails is just your own inability to predict with sufficient accuracy; a frequentist says that the 50% is a property of the coin - or to be less straw-making about it, a property of large sets of indistinguishable coin-flips. So, ok, in principle you could build a coin-predictor and remove the uncertainty. But now consider an electron passing through a beam splitter. Here there is no method even in principle of predicting which Everett branch you find yourself in. (Given some reasonable assumptions about locality and such.) The coin has hidden variables like the precise location of your thumb and the exact force your muscles apply to it; if you were smart enough, you could tease a prediction out of them. But an electron has no such hidden properties. Is it not reasonable, then, to say that the 50% chance really is a property of the electron, and not the predictor?
The relevant property of the electron+beamsplitter(+everything else) system is that its wavefunction will be evenly split between the two Everett branches. No chance involved. 50% is how much I care about each branch.
And after performing the experiment but before looking at the result, I can continue using the same reasoning: "I have already decohered, but whatever deterministic decision algorithm I apply now will return the same answer in both branches, so I can and should optimize both outcomes at once." Or I can switch to indexical uncertainty: "I am uncertain about which instance I am, even though I know the state of the universe with certainty." These two methods should be equivalent.
If we ever do find some nondeterministic physical law, then you can have your probability as a fundamental property of particles. Maybe. I'm not sure how one would experimentally distinguish "one stochastic world" from "branch both ways" or from "secure pseudo-random number generator" in the absence of any interference pattern to have a precise theory of; but I'm not going to speculate here about what physicists can or can't learn.