> the structure of the wavefunction is that it divides cleanly into those two branches, and that's true in any basis.
It's not. It only has this Schmidt decomposition in one basis. In other bases there will be cross terms among the basis elements. What you're doing is privileging Schmidt bases as ones that give experiences. In another basis with states w,z say the state will be: |w>|w> + |z>|z> + |w>|z> + |z>|w>
So you won't be able to give this clean "experience" reading unless you posit we can't experience in things like the w,z basis here and only in Schmidt bases, but then you run into the problem that for real macroscopic systems they won't admit a Schmidt basis.
This seems like the kind of a "vague" Many Worlds where one doesn't look any deeper than pretending a macro-device is a qubit (e.g. no thermal states etc) and looking at one basis. There's a reason properly developed MWI is nothing like this such as the Spacetime State realism of Wallace and Timpson.
Why one would believe in quantum state realism at all is a separate question.
>Of course you can
No you can't, it's a direct consequence of the Kochen-Specker theorem. If the device is treated quantum mechanically and it enters an entangled state of the form you gave then you cannot perform conditioning as the Kochen-Specker theorem, via the non-uniqueness of Hilbert space orthogonal decompositions, prevents an unambiguous formulation of Bayes's law. I can link to papers proving this if you wish.
The fact that we do experiments where we can condition is, in light of this theorem, a demonstration that our measurement devices do not enter into the kind of CHSH states you're giving.
The state's evolution will be completely equivalent to (a linear superposition of) the evolution of |x>|x> and |y>|y>. That's a physically observable fact that's independent of your choice of basis (it's less obvious in the |z>/|w> basis, but it's still true).
Any physically valid concept of "experience" would have to behave the same way. If your state is equivalent to a linear superposition of "experiencing x" and "experiencing y" then it can be characterised completely in terms of "experiencing x" and "experiencing y", and that's not dependent on your choice of basis (though it may be easier to see in one basis or another).
> No you can't, it's a direct consequence of the Kochen-Specker theorem. If the device is treated quantum mechanically and it enters an entangled state of the form you gave then you cannot perform conditioning as the Kochen-Specker theorem, via the non-uniqueness of Hilbert space orthogonal decompositions, prevents an unambiguous formulation of Bayes's law. I can link to papers proving this if you wish.
> The fact that we do experiments where we can condition is, in light of this theorem, a demonstration that our measurement devices do not enter into the kind of CHSH states you're giving.
I don't know what you're trying to claim here. All the available evidence is that measurement devices, being ordinary physical objects, follow the laws of quantum mechanics, and that includes conditioning behaving as entanglement; if you've got evidence that that's not the case then a Nobel prize awaits. Non-uniqueness is a red herring, because choice of basis does not and cannot change experimental predictions; the basis exists only in the map, not the territory.
The point is that there is no reason to select out any particular basis over another. You can't just retreat into "well this is the only basis I can experience" because the human sensory apparatus would be able to select out a range of bases in a full unitary account and also the ambiguity of basis decomposition means you can't perform conditioning which we do all the time in experiments.
I mean that if you decompose along a different basis than experiencing x/experiencing y, you just get an ensemble of states each of which is a superposition of experiencing x and experiencing y. So you end up with the same thing.
It's like looking at an entangled state (because that's exactly what it is) - if we have a two-particle state like 1/sqrt(2)(|x>|x> + |y>|y>), that behaves like the first particle being in |x> and experiencing the other particle being in |x>, or being in |y> and experiencing the other particle being in |y>, and it might look like that's an artifact of this particular basis decomposition, but it actually isn't - the structure of the wavefunction is that it divides cleanly into those two branches, and that's true in any basis.
> You can't just retreat into "well this is the only basis I can experience" because the human sensory apparatus would be able to select out a range of bases in a full unitary account
A system that's freely interacting will become entangled; whatever we consider ourself is constantly interacting with the rest of ourself, almost by definition.
> also the ambiguity of basis decomposition means you can't perform conditioning which we do all the time in experiments.
Of course you can, and it works exactly the way you'd expect - we already do experiments where some isolated apparatus inside the experiment does something if it detects one thing and something else if it detects something else. Choice of basis is a tool for understanding the wavefunction, not a physically real thing.
