Why is this interpretation of MWI wrong?

[entropy1]

If we take the wave function Ψ of a particle X that gets measured in a basis with a finite countable number of eigenvectors N, then according to MWI and myself, the interpretation suggests that we can write Ψ as the sum of projections of Ψ on the eigenvectors the following way:

Ψ= Σn |e(n)> ⊗ |E(n)>, where e(n) is the measurement outcome and E(n) the environment after measurement.

Some people take the N terms as different “worlds” because the factor |E(n)> represents the environment that is different in every term.

So why couldn't we just say that only one of those terms is real, like a reduction of the wave function?

I ask because I haven't seen it addressed anywhere. So it must be wrong but why?

I am an amateur, but because my question is so simple I thought I could ask it.

 

[PeterDonis]

Moderator's note: Thread moved to interpretations subforum.

 

[PeterDonis]

why couldn't we just say that only one of those terms is real, like a reduction of the wave function?

Um, because that's not what the MWI says?

The MWI is not a logical proof that all of the terms in the wave function are "real". It is just the assertion that they all are, as the basis of the interpretation. Other QM interpretations, that say only one of the terms is real ("wave function reduction") are collapse interpretations; they are perfectly good interpretations as far as intepretations go, they just aren't the MWI.

 

[entropy1]

The MWI is not a logical proof that all of the terms in the wave function are "real". It is just the assertion that they all are, as the basis of the interpretation.

If the Hilbert space is infinite, you can't have all of them real right? So then I see this as that a sort of collapse may not be avoided. Can you give your view on that?

 

[PeterDonis]

If the Hilbert space is infinite, you can't have all of them real right?

Why not?

 

[entropy1]

Why not?

Because if you have them all, you don't have them all?

 

[Vanadium 50]

Because if you have them all, you don't have them all.

Huh?

 

[entropy1]

Huh?

I am refering to possible outcomes. Like there's always one more.

 

[Vanadium 50]

You are still making no sense. "If you have them all, you don't have them all" is nonsense. Indeed, "according to MWI and myself" in the OP is a horrible start, as the MWI does not say what you say it does, and you are not an authority.

There may be a good question buried in there somewhere, but it hasn't been asked yet.

 

[PeterDonis]

I am refering to possible outcomes.

If the set of possible outcomes is infinite, then the MWI says you have an infinite number of branches, since that's what you get from unitary evolution. What's the problem?

 

[entropy1]

If the set of possible outcomes is infinite, then the MWI says you have an infinite number of branches, since that's what you get from unitary evolution. What's the problem?

I would say they can't all be realized and thus are not real. They are possible.

 

[Vanadium 50]

I would say they can't all be realized and thus are not real. They are possible.

You seem to be posting your own theory and calling it MWI.

 

[entropy1]

You seem to be posting your own theory and calling it MWI.

I have my own interpretation of an interpretation. Or rather of the math.

 

[PeterDonis]

I would say they can't all be realized and thus are not real. They are possible.

And you would be wrong, since nobody can make such a claim independent of any QM interpretation.

I have my own interpretation of an interpretation. Or rather of the math.

And that is personal theory and is off limits here. Thread closed.