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.
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.