Many-Worlds with no other choice

[tionis]

Are there certain events that must inevitably occur in all of the possible branches the wave function could split into? For example, if a black hole forms in our ''branch,'' what other possibility is there for that collapsing configuration of matter other than to turn into a black hole? Unless I'm missing something, my understanding is that in MWI, the laws of physics continue to be the same in all the possible branches, no? Is not like in another branch I can fly or something.

 

[Nugatory]

my understanding is that in MWI, the laws of physics continue to be the same in all the possible branches, no? Is not like in another branch I can fly or something.

That is correct.

 

[tionis]

Nugatory, thanks. But am I also correct in thinking that there are events that even the ''branching'' cannot avoid or change? What I'm trying to find out is if the branching is constrained from preventing a natural order of events from occurring, like the example I gave earlier about the formation of a black hole. My thinking is that if a BH forms here in our branch, then there is no way for the wave function to prevent that from happening in another decohered (?) branch.

 

[tionis]

Please, quantum mechanics experts. If the question is stupid, I would rather you tell me.

 

[naima]

Repeated measurements give the same outcomes with or without branchings.

 

[Nugatory]

Nugatory, thanks. But am I also correct in thinking that there are events that even the ''branching'' cannot avoid or change? What I'm trying to find out is if the branching is constrained from preventing a natural order of events from occurring, like the example I gave earlier about the formation of a black hole. My thinking is that if a BH forms here in our branch, then there is no way for the wave function to prevent that from happening in another decohered (?) branch.

You have to go back to the mathematical formalism. Suppose you have a quantum system whose state is:$$|\Psi\rangle=\alpha_1|\psi_1\rangle+\alpha_2|\psi_2\rangle+\alpha_3|\psi_3\rangle+\alpha_4|\psi_4\rangle+ ...$$where the $\psi_i$ are orthogonal (and the $\alpha_i$ are scaled to normalize the state). In a collapse interpretation, a measurement will cause the system state to collapse to one of the $\psi_i$ and yield the corresponding $\alpha_i$ as a result; in MWI we will get separate worlds, one for each of the $\psi_i$. Thus, the results in all worlds have to be consistent with the initial state - no world can end up in a state that is not reachable by forward evolution of the corresponding $\psi_i$.

(As an aside... This would be a good time for you to google for "MWI preferred basis problem")

 

[entropy1]

My thinking is that if a BH forms here in our branch, then there is no way for the wave function to prevent that from happening in another decohered (?) branch.

Perhaps you want to clarify that somewhat?

 

[tionis]

Repeated measurements give the same outcomes with or without branchings.

OK. Thanks.

You have to go back to the mathematical formalism. Suppose you have a quantum system whose state is:$$|\Psi\rangle=\alpha_1|\psi_1\rangle+\alpha_2|\psi_2\rangle+\alpha_3|\psi_3\rangle+\alpha_4|\psi_4\rangle+ ...$$where the $\psi_i$ are orthogonal (and the $\alpha_i$ are scaled to normalize the state). In a collapse interpretation, a measurement will cause the system state to collapse to one of the $\psi_i$ and yield the corresponding $\alpha_i$ as a result; in MWI we will get separate worlds, one for each of the $\psi_i$. Thus, the results in all worlds have to be consistent with the initial state - no world can end up in a state that is not reachable by forward evolution of the corresponding $\psi_i$.

(As an aside... This would be a good time for you to google for "MWI preferred basis problem")

Wow! Even tho your answer is way too advanced for me, you blew my mind with it. There is so much wealth of info in it. My whole thinking was based on a preferred ''world'' or branch which I now know is not correct. It never dawned on me that the wavefunction was relative? I also noticed the use of imaginary numbers after the wavefunction symbol which made me think that those branches weren't real, but after some search, it turned out that there is no difference between the use of imaginary and normal numbers in QM. Thanks, Nugatory. Your answer was AWESOME!

Perhaps you want to clarify that somewhat?

I don't know how else to explain it other than what I've posted, but Nugatory has explained it to my satisfaction, so thank you.

 

[Ilja]

Thus, the results in all worlds have to be consistent with the initial state - no world can end up in a state that is not reachable by forward evolution of the corresponding $\psi_i$.

Which, in general, excludes only a subspace $\langle \psi|\psi_0\rangle=0$. Or, in other words, essentially nothing, except in a few special cases like repeated identical measurements. Or not?