The argument I made there was that we should consider observer-moments to be ‘real’ according to their Hilbert measure, since that is what we use to predict our own sense-experiences. This does imply that observer-weight will be preserved over time, since unitary evolution preserves the measure(as you say, this also proves it is conserved by splitting into branches, since you can consider that to be projecting onto different subspaces)
Even without unitarity, you shouldn’t expect the total amount of observer-weight to increase exponentially in time, since that would cause the total amount of observer-weight to diverge, giving undefined predictions.
Our sense-experiences are “unitary” (in some sense which I hope we can agree on without defining rigorously), so of course we use unitary measure to predict them. Branching worlds are not unitary in that sense, so carrying over unitarity from the former to the latter seems an entirely arbitrary assumption.
A finite number (say, the number of particles in the known universe), raised to a finite number (say, the number of Planck time intervals before dark energy tears the universe apart), gives a finite number. No need for divergence. (I think both of those are severe overestimates for the actual possible branching, but they are reasonable as handwavy demonstrations of the existence of finite upper bounds)
Ah, by ‘unitary’ I mean a unitary operator, that is an operator which preserves the Hilbert measure. It’s an axiom of quantum mechanics that time evolution is represented by a unitary operator.
Fair point about the probable finitude of time(but wouldn’t it be better if our theory could handle the possibility of infinite time as well?)
The argument I made there was that we should consider observer-moments to be ‘real’ according to their Hilbert measure, since that is what we use to predict our own sense-experiences. This does imply that observer-weight will be preserved over time, since unitary evolution preserves the measure(as you say, this also proves it is conserved by splitting into branches, since you can consider that to be projecting onto different subspaces)
Even without unitarity, you shouldn’t expect the total amount of observer-weight to increase exponentially in time, since that would cause the total amount of observer-weight to diverge, giving undefined predictions.
Our sense-experiences are “unitary” (in some sense which I hope we can agree on without defining rigorously), so of course we use unitary measure to predict them. Branching worlds are not unitary in that sense, so carrying over unitarity from the former to the latter seems an entirely arbitrary assumption.
A finite number (say, the number of particles in the known universe), raised to a finite number (say, the number of Planck time intervals before dark energy tears the universe apart), gives a finite number. No need for divergence. (I think both of those are severe overestimates for the actual possible branching, but they are reasonable as handwavy demonstrations of the existence of finite upper bounds)
Ah, by ‘unitary’ I mean a unitary operator, that is an operator which preserves the Hilbert measure. It’s an axiom of quantum mechanics that time evolution is represented by a unitary operator.
Fair point about the probable finitude of time(but wouldn’t it be better if our theory could handle the possibility of infinite time as well?)