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EHeller comments on Open thread, August 5-11, 2013 - Less Wrong Discussion
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But many of the more-general lagrangians of particle physics are non-linear, in general there should be higher order, non-linear corrections. So Schrödinger is a single-particle/linearized approximation. What does this do for your view of many worlds? When we try to extend many worlds naively to QFTs we run into all sorts of weird problems (much of the universal wavefunction's amplitude doesn't have well defined particle number,etc). Shouldn't we expect the 'proper' interpretation to generalize nicely to the full QFT framework?
Or rather, the proper interpretation should work in the full QFT framework, and may or may not work for ordinary QM.
What are you talking about? I've only taken one course in quantum field theory, but I've never heard of anything where quantum mechanics was not linear. Can you give me a citation? It seems to me that failure of linearity would either be irrelevant (superlinear case, low amplitudes) or so dominant that any linearity would be utterly irrelevant and the Born Probabilities wouldn't even be a good approximation.
Also, by 'the Schrodinger equation' I didn't mean the special form which is the fixed-particle Hamiltonian with pp/2m kinetic energy - I meant the general form -
i hbar (d/dt) Psi = Hamiltonian Psi
Note that the Dirac Equation is a special case of this general form of the Schrodinger Equation. MWI, 'naive' or not, has no trouble with variations in particle number.