right, I see how a lot of things can collapse to that approximately, classical dynamics even can collapse to this (e.g. noether's theorem)
here's what i'm thinking intuition wise. time evolution you do by multiplying the hamiltonian by the state vector. totally linear, but it presupposes you can project the state onto a Hilbert space described by the Hamiltonian? Is this the same Hamiltonian everywhere *actually*?
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metaphysical point almost, but it has "computational universe implications." it makes more sense for simulations to have one hamiltonian in one area around a singularity, as it may for nature, now, decide what to do on the edges and to synchronise!
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Any answer to this question will naturally depend on the formalism of QFT you choose to work in. In the geometry-centric pov I like, this sort of question has a natural answer. The first 15 pages of https://people.math.umass.edu/~gwilliam/vol1may8.pdf … may give you a sense
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Is the Hamiltonian's kinetic energy part nonlinear in the momentum, and thus not an inner product like a Hilbert space has? I'm trying to guess which argument the multiplication could be nonlinear in; you seem to be saying it's nonlinear bc H varies across spacetime?
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