I thought David Deutsch had already worked out a proof that the Born rule using decision theory? I guess it does not explain objective probability but as far as I know the question of what probability even means is very vague.
I know that the branching is just a metaphor for the human brain to understand MWI better, but the main question I wanted to ask is whether or not you can know the amplitude of different timelines that have “diverged” a long time ago. E.g. it is possible to know where an electron “is” once we measure it, and then the wave function of the electron evolves according to the Schrodinger equation. The measure of existence of a future timeline where electron is measured at X is equal to the amplitude of the wave function at X after being evolved forward using the Schrodinger equation. But I am guessing that it is impossible to go backwards, in the sense of deducing the state of the wave function before a measurement is made using the measurement result (what was the amplitude of the wave function at X before we measured the electron at X)? Does that make sense?
You are right, (apparent) collapse is not reversible, and there is no known way to figure out the pre-collapsed quantum state, and so there is no state to apply the Born rule to. This statement makes sense when discussing the evolution of quantum systems, not classical systems though.
I thought David Deutsch had already worked out a proof that the Born rule using decision theory? I guess it does not explain objective probability but as far as I know the question of what probability even means is very vague.
I know that the branching is just a metaphor for the human brain to understand MWI better, but the main question I wanted to ask is whether or not you can know the amplitude of different timelines that have “diverged” a long time ago. E.g. it is possible to know where an electron “is” once we measure it, and then the wave function of the electron evolves according to the Schrodinger equation. The measure of existence of a future timeline where electron is measured at X is equal to the amplitude of the wave function at X after being evolved forward using the Schrodinger equation. But I am guessing that it is impossible to go backwards, in the sense of deducing the state of the wave function before a measurement is made using the measurement result (what was the amplitude of the wave function at X before we measured the electron at X)? Does that make sense?
You are right, (apparent) collapse is not reversible, and there is no known way to figure out the pre-collapsed quantum state, and so there is no state to apply the Born rule to. This statement makes sense when discussing the evolution of quantum systems, not classical systems though.