This has largely turned into a semantic dispute about the “correct” meaning of the term “world” in the context of MWI.
You’re using it to mean “summand with respect to the position basis” whereas I’m using it to mean “summand with respect to a decomposition of the Hilbert space into subspaces large enough that elements of two distinct subspaces represent ‘distinct macrostates’”. (Where “macroscopic distinctness” is not and does not pretend to be precisely definable.)
Right after the photon in the Mach-Zehnder apparatus splits, you see two worlds corresponding to the two different positions of the photon, whereas I see only a single world because all macroscopic variables still have determinate values. (Or rather, their values are still as close to being determinate as they ever are.)
In my use of the term “worlds” it is correct to say that the notion of “other worlds” breaks down if you push it too far (ultimately this is because the boundary between the “micro” and “macro” domains cannot be rigorously defined.) In your use of the term “worlds” it is trivially true that, at any given time, the state vector is uniquely expressible as a superposition of “worlds”.
I don’t want to say too much in defense of my usage, except that I think mine is the standard one. You might like to read this by the way. (Not to resolve our dispute, but because it’s awesome.)
However, since the experiment can only end one way, it all takes place within one “branch”.
You can detect it, but it doesn’t happen? Isn’t that like saying that the universe doesn’t exist, but we experience things as if it did?
Sorry, I can’t see how your questions relate to my statement.
I don’t understand. It explains it.
The reason I say it doesn’t explain it is that the notion of “constructive and destructive interference” between different possibilities is deeply bizarre. Simply declaring that all possibilities exist doesn’t explain why two possibilities can cancel each other out. But again, I suspect this is partly just a dispute over the semantics of “explain”.
ETA: I have to acknowledge a bait-and-switch on my part. Whereas in my previous comment I was seeking to characterise worlds directly in terms of decoherence, now I’m characterizing them by way of a third concept, namely “macroscopic distinctness”, which “under normal circumstances (i.e. not doing a two-slit experiment with people)” guarantees decoherence.
Sorry, I can’t see how your questions relate to my statement.
It was a misunderstanding you cleared up by specifying what you meant by “world”.
The reason I say it doesn’t explain it is that the notion of “constructive and destructive interference” between different possibilities is deeply bizarre.
The interference isn’t between probabilities. They don’t contain sufficient information. It’s between the amplitudes. Going from amplitudes to probabilities is the weird part. It’s not explained by any interpretation.
This has largely turned into a semantic dispute about the “correct” meaning of the term “world” in the context of MWI.
You’re using it to mean “summand with respect to the position basis” whereas I’m using it to mean “summand with respect to a decomposition of the Hilbert space into subspaces large enough that elements of two distinct subspaces represent ‘distinct macrostates’”. (Where “macroscopic distinctness” is not and does not pretend to be precisely definable.)
Right after the photon in the Mach-Zehnder apparatus splits, you see two worlds corresponding to the two different positions of the photon, whereas I see only a single world because all macroscopic variables still have determinate values. (Or rather, their values are still as close to being determinate as they ever are.)
In my use of the term “worlds” it is correct to say that the notion of “other worlds” breaks down if you push it too far (ultimately this is because the boundary between the “micro” and “macro” domains cannot be rigorously defined.) In your use of the term “worlds” it is trivially true that, at any given time, the state vector is uniquely expressible as a superposition of “worlds”.
I don’t want to say too much in defense of my usage, except that I think mine is the standard one. You might like to read this by the way. (Not to resolve our dispute, but because it’s awesome.)
Sorry, I can’t see how your questions relate to my statement.
The reason I say it doesn’t explain it is that the notion of “constructive and destructive interference” between different possibilities is deeply bizarre. Simply declaring that all possibilities exist doesn’t explain why two possibilities can cancel each other out. But again, I suspect this is partly just a dispute over the semantics of “explain”.
ETA: I have to acknowledge a bait-and-switch on my part. Whereas in my previous comment I was seeking to characterise worlds directly in terms of decoherence, now I’m characterizing them by way of a third concept, namely “macroscopic distinctness”, which “under normal circumstances (i.e. not doing a two-slit experiment with people)” guarantees decoherence.
It was a misunderstanding you cleared up by specifying what you meant by “world”.
The interference isn’t between probabilities. They don’t contain sufficient information. It’s between the amplitudes. Going from amplitudes to probabilities is the weird part. It’s not explained by any interpretation.
Good thing I didn’t say that, then!
Above, I said of MWI “I don’t think that was ever its “purpose”.”