Simon, the trouble is that bit with the “very reasonable outside assumptions”.
If you think in mangled worlds terms, and then ask, “What if the mangled worlds theory were correct, but the cutoff point were not near the median amplitude density?”, then we would observe probabilities different from the Born probabilities. And the “very reasonable outside assumptions” would be suddenly revealed as unreasonable.
In the case of the Wallace paper that Robin quoted in “Quantum Orthodoxy”: Wallace assumes, roughly, that branching that goes on while you’re not looking, couldn’t possibly be rational to take into consideration, because so much of it happens, that no decision theorist could be bothered to keep track of it. Which, because quantum physics is unitary, hands him the Born probabilities on a silver platter—specifically, the decision-theoretic principle that you should care equally about bets with equivalent payoff and equal measure (“measure” = integral over squared modulus).
But if the mangled worlds cutoff point were different, and the Born probabilities were (perhaps slightly but noticeably) different, then decision agents would indeed be wise to think about the branching that went on while they weren’t looking.
If you start pondering theories where the Born probabilities are physically derived and hence physically contingent; then the theories where the Born probabilities are derived as a priori rational considerations, begin to look really suspicious.
I mean, you just shouldn’t be able to get that sort of thing a priori.
Also I follow in the path of Jaynes in regarding probability theory as more fundamental than decision theory.
I admit that when Wallace talks about the number of observers being unmeasurable because decoherence gives you a continuous tube of amplitude rather than distinct blobs—so that I’m not so much twins, as smeared—he manages to unnerve me even more than I was already unnerved, with regards to my feeble attempts to count observer-moments. But, ultimately, you could construct the same situation with Ebborians, so...
I only have limited experience studying mathematics seriously, but from what I understand of continuity, I can’t help think but that there’s no reason to expect reality to actually be continuous. It’s too easy to get apparent continuity out of (even sorta) large numbers.
I think that particular continuity is an illusion, anyhow. One should count eigenstates. There are countably many eigenstates, none of which is classical. It is in trying to assert a definite position that this particular continuity issue comes up.
Simon, the trouble is that bit with the “very reasonable outside assumptions”.
If you think in mangled worlds terms, and then ask, “What if the mangled worlds theory were correct, but the cutoff point were not near the median amplitude density?”, then we would observe probabilities different from the Born probabilities. And the “very reasonable outside assumptions” would be suddenly revealed as unreasonable.
In the case of the Wallace paper that Robin quoted in “Quantum Orthodoxy”: Wallace assumes, roughly, that branching that goes on while you’re not looking, couldn’t possibly be rational to take into consideration, because so much of it happens, that no decision theorist could be bothered to keep track of it. Which, because quantum physics is unitary, hands him the Born probabilities on a silver platter—specifically, the decision-theoretic principle that you should care equally about bets with equivalent payoff and equal measure (“measure” = integral over squared modulus).
But if the mangled worlds cutoff point were different, and the Born probabilities were (perhaps slightly but noticeably) different, then decision agents would indeed be wise to think about the branching that went on while they weren’t looking.
If you start pondering theories where the Born probabilities are physically derived and hence physically contingent; then the theories where the Born probabilities are derived as a priori rational considerations, begin to look really suspicious.
I mean, you just shouldn’t be able to get that sort of thing a priori.
Also I follow in the path of Jaynes in regarding probability theory as more fundamental than decision theory.
I admit that when Wallace talks about the number of observers being unmeasurable because decoherence gives you a continuous tube of amplitude rather than distinct blobs—so that I’m not so much twins, as smeared—he manages to unnerve me even more than I was already unnerved, with regards to my feeble attempts to count observer-moments. But, ultimately, you could construct the same situation with Ebborians, so...
I only have limited experience studying mathematics seriously, but from what I understand of continuity, I can’t help think but that there’s no reason to expect reality to actually be continuous. It’s too easy to get apparent continuity out of (even sorta) large numbers.
I think that particular continuity is an illusion, anyhow. One should count eigenstates. There are countably many eigenstates, none of which is classical. It is in trying to assert a definite position that this particular continuity issue comes up.