vanesch said:
MWI is based upon taking unitarity seriously. And then you get locality for free, if the unitary interactions of the theory are local (which they are).
Most Everettians I've talked to say that the things with ontological status in their view (quantum states)
are nonlocal. (Sure, when doing a Bell experiment the Hamiltonians are local, but that doesn't make the whole description local - give me nonlocal Hamiltonians and I'll violate a Bell inequality for you with an unentangled "local" wavefunction!)
I think you have to go further than saying MWI is based upon taking Unitarity seriously. IMO it is based on taking one particular mathematical formulation of QM seriously, and in particular the tensor product structure is simply presumed (I'm far more worried about "preferred tensor product structures" than "preferred bases", since the former speaks to our notions of systems and locality far more deeply).
Let me elaborate on this "one particular math formalism point". I'm going to cut and paste from an email exchange, sorry!
>
> Imagine that we lived in a universe in which the Wigner distribution
> for every system was positive. That is, all of standard quantum
> mechanics is true (Born rule etc), but an additional restriction
> forces positivity of every Wigner distribution. The set of states with
> positive Wigner distribution is very large - it includes coherent
> states, and entangled states - such as squeezed states, in fact it
> includes all Gaussian states, but many other states as well. They form
> a convex set and thus a completely self contained subset of quantum
> mechanics (e.g. All Hamiltonians would be the same - implying the same
> hydrogen atom spectrum - and one can't evolve out of this set given
> only states within it). Interestingly, since the original EPR argument
> used only the
> (position-momentum) squeezed state and Gaussian type measurements,
> they could also have had an EPR paper and Bohrian answer!
>
> Now let's also imagine the people in this universe do not actually have
> the Wigner formalism - they only have the standard Hilbert space
> formalism. Thus they are writing down states in a Hilbert space,
> describing their measurements in the standard von-Neumann way as
> giving an entanglement between the system and apparatus and so on.
> They see an "intrinsically" probabilistic theory and nonseparability.
> They go through the same metaphysical convulsions we do about the
> collapse of the wavefunction.
>
> If these people adopt an Everettian approach to understanding the
> underlying reality implied by their physical theory, is it really
> justified? If one advocates that Everett follows from just accepting
> the math of QM, then it should be just as applicable to this universe
> - the math is identical. Only the original set of states is different.
>
> But in such a universe it is clear - the physicists have been tricked
> by their mathematics (inseparability of states with respect to a
> particular tensor product, a belief in "objective" probabilities and
> so on). In fact there is this perfectly good realist explanation (in
> terms of the Wiger probability densities as classical uncertainties
> over a phase
> space) lurking out there.
>
> Until I am convinced that this is not a good analogy for where we're
> at with quantum mechanics as it stands, I'm not prepared to take what
> I see as an extremist way out!
>
My point in that email is that the eye-glazing wonder an Everettian feels when they see
(|0>+|1>)|0>
evolve to
(|0>|0>+|1>|1>)
would be felt by inhabitants of "Gaussian World", since they have an identical Hilbert space structure. They may well adopt MWI. The only difference between that world and ours, IMO, is that we haven't found the equivalent probabilistic description over a suitable "ontic phase space".
I believe your other argument about not being able to "derive" the measurement observable of the device given its physical description as a particular justification for MWI is spurious. In Liouville mechanics, if I give you the Liouville distribution of one system (the apparatus) and the interaction Hamiltonian between it and some other system (which is described by another Liouville distribution), and you then evolve them both to the coupled (joint) Liouville distribution, you cannot "derive" what observable it corresponds to either. In this purely classical situation, just as in the quantum case, some other physical (generally empiricist) input is required.
I'm off to Pareee until monday afternoon, I look forward to reading your reply when I get back.
Tez