Well, ideally it is a counting argument (a quote from further down in the AMA):
We calculate probabilities by weighting things by the wave functions squared. And if you can always subdivide branches into worlds, then that is literally counting the maximum number of worlds you can subdivide into. ’Cause that’s just the dimensionality of Hilbert space. And so, if you tell someone your probability calculation is literally just counting things, they’re more persuaded than if you say it’s a weighting of a Bayesian credence in a state of self locating uncertainty.
1:28:55.1 SC: I know this empirically, they’re more likely to be persuaded, but I’m not sure if it works. I do know there are people who take it very seriously. I believe that David Deutsch is someone who thinks and talks that way. And I haven’t thought about it very deeply ’cause I don’t care that much. I’ve always been of the opinion that worlds are convenient higher level human constructions. That are very convenient, but they’re very obvious when they happen, when the branching happens. And what happens in more subtle cases just doesn’t bother me that much. Different people are welcome to do different things, as far as I’m concerned.
Or you can think of it like Eliezer does, “thickness” of each world. Personally I do not find this intuition compelling, but Sean doesn’t seem to mind.
That quote seems nonsensical. What do the Born probabilities have to do with a counting argument, or with the dimension of Hilbert space? A qubit lives in a two-dimensional space, so a dimension argument would seem to suggest that the probabilities of the qubit being 0 or 1 must both be 50%, and yet in reality the Born probabilities say they can be anything from 0% to 100%. What am I missing?
I think what you are missing is the quantum->classical transition. In a simple example, there are no “particles” in the expression for quantum evolution of an unstable excited state, and yet in a classical world you observe different decay channels. with an assortment of particles, or at least of particle momenta. They are emergent from unitary quantum evolution, and in MWI they all happen. If one could identify equally probable “MWI microstates” that you can count, like you often can in statistical mechanics, then the number of microstates corresponding to a given macrostate would be proportional to the Born probability. That is the counting argument. Does this make sense?
It seems like “equally probable MWI microstates” is doing a lot of work here. If we have some way of determining how probable a microstate is, then we are already assuming the Born probabilities. So it doesn’t work as a method of deriving them.
Well, microstates come before probabilities. They are just there, while probabilities are in the model that describes macrostates (emergence). This is similar to how one calculates entropy with the Boltzmann equation, assigning microstates to (emergent) macrostates, S= k ln W. But yes, there is no known argument that would derive the Born rule from just counting microstates. Anything like that would be a major breakthrough.
Well, ideally it is a counting argument (a quote from further down in the AMA):
Or you can think of it like Eliezer does, “thickness” of each world. Personally I do not find this intuition compelling, but Sean doesn’t seem to mind.
That quote seems nonsensical. What do the Born probabilities have to do with a counting argument, or with the dimension of Hilbert space? A qubit lives in a two-dimensional space, so a dimension argument would seem to suggest that the probabilities of the qubit being 0 or 1 must both be 50%, and yet in reality the Born probabilities say they can be anything from 0% to 100%. What am I missing?
I think what you are missing is the quantum->classical transition. In a simple example, there are no “particles” in the expression for quantum evolution of an unstable excited state, and yet in a classical world you observe different decay channels. with an assortment of particles, or at least of particle momenta. They are emergent from unitary quantum evolution, and in MWI they all happen. If one could identify equally probable “MWI microstates” that you can count, like you often can in statistical mechanics, then the number of microstates corresponding to a given macrostate would be proportional to the Born probability. That is the counting argument. Does this make sense?
It seems like “equally probable MWI microstates” is doing a lot of work here. If we have some way of determining how probable a microstate is, then we are already assuming the Born probabilities. So it doesn’t work as a method of deriving them.
Well, microstates come before probabilities. They are just there, while probabilities are in the model that describes macrostates (emergence). This is similar to how one calculates entropy with the Boltzmann equation, assigning microstates to (emergent) macrostates, S= k ln W. But yes, there is no known argument that would derive the Born rule from just counting microstates. Anything like that would be a major breakthrough.