Ok yes, it is named that, but what the theory postulates is really just that "when Schrodinger opens the box to check on his cat, he himself is in a superposition just like the cat was -- and what it feels like to be in a superposition is that you don't notice you're in a superposition, because your superposed states each only observe one cat."
Again, I have to ask: what do you think "many worlds" means? Because what you've just described is exactly what the advocates of the MWI describe when they talk about "many worlds", which they absolutely do. The MWI literature is festooned with references to "copies" or "versions" of yourself, and "the branching structure of the multiverse".
Many MWI advocates will describe that physical wavefunction in those terms, but that's a metaphor/model/aid to understanding, not a "point of metaphysical fact". The only thing that MWI demands we take as metaphysically real is the wavefunction. Given a wavefunction like 1/sqrt2(|experimenter who observed a live cat> + |experimenter who observed a dead cat>) many people find it convenient to think of this as "two Everett branches with ...", in the same way that people who hear a particular pattern of sound might find it convenient to think of it as a chord of two or three notes. But if you prefer to think of it as simply a unitary (in the everyday sense) wavefunction that's fine, you'll make exactly the same experimental predictions.
"When I introduced tangible and shadow photons I apparently distinguished them by saying that we can see the former, but not the latter. But who are ‘we’? While I was writing that, hosts of shadow Davids were writing it too. They too drew a distinction between tangible and shadow photons; but the photons they called ‘shadow’ include the ones I called ‘tangible’, and the photons they called ‘tangible’ are among those I called ‘shadow’.
Not only do none of the copies of an object have any privileged position in the explanation of shadows that I have just outlined, neither do they have a privileged position in the full mathematical explanation provided by quantum theory. I may feel subjectively that I am distinguished among the copies as the ‘tangible’ one, because I can directly perceive myself and not the others, but I must come to terms with the fact that all the others feel the same about themselves.
Many of those Davids are at this moment writing these very words. Some are putting it better. Others have gone for a cup of tea."
And his summary:
"the whole of physical reality, the multiverse, contains vast numbers of parallel universes"
So no, Deutsch, who is arguably the leading advocate of MWI, does not consider parallel universes to be a "metaphor/model/aid to understanding". He insists that they are real. He even defends this position at extraordinary length in chapter 10 of TFOR.
Either the other versions of reality are tangible, or they're not. If they're just abstractions, you have't solved the problem - you've taken a long way around a circular argument that starts with the wavefunction and ends with it doing something that results in a measurement, maybe.
Unfortunately explaining how that happens is the problem you're trying to solve. It's not an answer to the problem.
If they are real, there are all kinds of other issues, the Born Rule being the most obvious.
The wavefunction is physically real. Whatever you interpret it as is your business. We've solved a real problem: we can explain the evolution of the wavefunction and the results of experiments without needing some weird collapse/decoherence concept that breaks all the usual rules. The Born Rule is still something that remains to be explained, agreed, but it's a much smaller something than the full Copenhagen style collapse.
But you still have to peel back the words to think about what kind of mechanism they are describing, which Deutsch is trying to communicate. You can't just complain that he says "reality contains parallel universes" without accepting that he's taken the time to map "parallel universes" to a well-defined concept.
“To those who still cling to a single-universe world-view, I issue this challenge: explain how Shor’s algorithm works. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor’s algorithm has factorized a number, using 10^500 or so times the computational resources than can be seen to be present, where was the number factorized? There are only about 10^80 atoms in the entire visible universe, an utterly minuscule number compared with 10^500. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed?”
[1] https://www.newyorker.com/magazine/2011/05/02/dream-machine/...
- Peter Shor (https://www.scottaaronson.com/blog/?p=218#comment-5753)
An analogous question: when three objects are orbiting each other in space, where is the computation being performed that provides the solution to the three-body problem that represents their motions?
Well, obviously, the computation in the latter case is being "performed" by the three bodies themselves, and the Shor computation is being performed inside a quantum computer that exists in our universe. It's just that the stuff that is performing the computation isn't atoms, it's entangled qbits. There's no need to bring entire parallel universes into it.
You seem annoyed by the terminology of words like "worlds" or "multiverse", but are you also thinking about what a MWI advocate is referring to by the usage of those words? They are shorthand for "the observable wave function" and "the global wave function".
There being "copies" of Schrodinger observing his cat is the most intuitive and expressive way to summarize Schrodinger being in a linear superposition of two states in a (cat alive, cat dead) basis. It's not any different from how a Copenhagenist would treat a photon passing through a polarizating beamsplitter as being in a superposition of having passed through and having been reflected; if the photon then goes and interacts with other things, they would keep track of what would have happened in each "branch" of the superposition.
If you have an issue with those, why don't you have an issue with the idea of superposition itself? It's exactly the same concept.
(UPDATE)
In particular, when MWI people say "multiverse", it's not a sleight of hand where we are being deceptive when we actually mean "observable and unobservable components of the wave function". The term "multiverse" had no prior meaning in physics; MWI is defining it to mean the global wave function, using that word to draw attention to the fact that it has unobservable components.
These words are being given rigorous definitions that align with their intuitive meaning. You seem to be arguing against that practice?
Should I complain that when a Copenhagenist says "collapse", nothing is actually falling down and so it's misleading?
You may consider this a distinction without a difference, but the fact of the matter is that people do argue about this. A lot.
Also "metaphysical fact" is a questionable term.
So detecting the first, definitely 'collapsed the wave function'. This is not an unknown result in physics.
As for collapse, Copenhagenists can't seem to explain why an interaction between a photon and electrons in a polarizing filter does not collapse the wave function, but an interaction between a photon and electrons in my retina does. They're made of the same stuff and should be following the same quantum rules; why does one of them perform a unitary transformation and the other a lossy projection?