for every base state composing a quantum superposition.
When you say such terms as “base state” and “superposition”, are you assuming a preferred basis?
the probability of an observer to find the system in that branch is the norm of the amplitude.
Isn’t it the squared norm?
This, very briefly, is the content of the Born rule (for pure states).
This seems a bit too brief to me. If we wish merely to assert that there is a number that corresponds to the probability of finding oneself in a branch, that is much too trivial an assertion to demand explanation.
As an example, consider a superposition of a quantum bit, and say that one branch has a higher measure with respect to the other by a factor of square root of 2. The environment needs in this case to have at least 8 different base states to be relabeled in such a way to make the indifference principle work.
When you say such terms as “base state” and “superposition”, are you assuming a preferred basis?
Well, yes and no. The paper itself doesn’t assume a preferred basis, but surely to have a completely coherent picture of MWI you need to solve the preferred basis problem. Decoherence supposedly does that with the concept of pointer basis.
Isn’t it the squared norm?
Yes, absolutely! Edited, thanks.
This seems a bit too brief to me. If we wish merely to assert that there is a number that corresponds to the probability of finding oneself in a branch, that is much too trivial an assertion to demand explanation.
Well, the probability of a branch is not just a number given from the theory, is a number derived from a complex amplitude, and this has a number of consequences that makes it non-trivial. Plus, the Born rule in the context of mixed states has a more complex formulation. In general though, since it’s usually (that is, outside of MWI) assumed as an axiom, I guess you could say that it’s trivial.
Can you explain the math on this?
I’m afraid not better than the original authors, so if you really want to get the math you’ll have to look at the article.
When you say such terms as “base state” and “superposition”, are you assuming a preferred basis?
Isn’t it the squared norm?
This seems a bit too brief to me. If we wish merely to assert that there is a number that corresponds to the probability of finding oneself in a branch, that is much too trivial an assertion to demand explanation.
Can you explain the math on this?
Well, yes and no. The paper itself doesn’t assume a preferred basis, but surely to have a completely coherent picture of MWI you need to solve the preferred basis problem.
Decoherence supposedly does that with the concept of pointer basis.
Yes, absolutely! Edited, thanks.
Well, the probability of a branch is not just a number given from the theory, is a number derived from a complex amplitude, and this has a number of consequences that makes it non-trivial. Plus, the Born rule in the context of mixed states has a more complex formulation.
In general though, since it’s usually (that is, outside of MWI) assumed as an axiom, I guess you could say that it’s trivial.
I’m afraid not better than the original authors, so if you really want to get the math you’ll have to look at the article.