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.
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.