Matthew C: My criticisms of Kent’s criticisms of MWI (as formulated by Everett), in the paper you link to:
A Hilbert space has an inner product by definition, so mu is already an entity of the theory without needing any extra postulates.
In the example given, decoherence will result in the two terms of the RHS of (2) not being able to interfere with one another, which justifies considering them to be independent worlds, no intuition required.
Kent’s talk about bases seems confused, the dimensionality of a basis is fixed by the dimensionality of the state space. What he refers to as a 1-dimensional basis is in fact a 2-d basis (the two terms being added together are basis vectors).
In practice, one can chose a basis as follows: when a measurement is made, decoherence results in the system seperating into a noninterfering subsystem for each outcome. If there is a unique state for each measurement outcome, put together they are a basis; otherwise choose a basis for each outcome and put all the bases together to make the basis for the whole system, the ambiguity has no effect on the measurement outcome because different bases only mix together states with the same outcome. This doesn’t need to be made an axiom; any basis can be used in principle but some are a lot more useful in practice than others.
Of course, Everett didn’t know about decoherence, but we do now.
As for determining probabilities, I suggest you read the paper I linked earlier. It might be flawed, as I mentioned, but if so I think it can probably be amended to work.
Matthew C: My criticisms of Kent’s criticisms of MWI (as formulated by Everett), in the paper you link to:
A Hilbert space has an inner product by definition, so mu is already an entity of the theory without needing any extra postulates.
In the example given, decoherence will result in the two terms of the RHS of (2) not being able to interfere with one another, which justifies considering them to be independent worlds, no intuition required.
Kent’s talk about bases seems confused, the dimensionality of a basis is fixed by the dimensionality of the state space. What he refers to as a 1-dimensional basis is in fact a 2-d basis (the two terms being added together are basis vectors).
In practice, one can chose a basis as follows: when a measurement is made, decoherence results in the system seperating into a noninterfering subsystem for each outcome. If there is a unique state for each measurement outcome, put together they are a basis; otherwise choose a basis for each outcome and put all the bases together to make the basis for the whole system, the ambiguity has no effect on the measurement outcome because different bases only mix together states with the same outcome. This doesn’t need to be made an axiom; any basis can be used in principle but some are a lot more useful in practice than others.
Of course, Everett didn’t know about decoherence, but we do now.
As for determining probabilities, I suggest you read the paper I linked earlier. It might be flawed, as I mentioned, but if so I think it can probably be amended to work.