As you have explained things so far, Schroedinger's equation is local in configuration space, not necessarily physical space. You seem to be claiming locality in physical space as well.
You can compute the rate of change of amplitude in a configuration from derivatives of amplitude over similar configurations. Are you claiming you can also compute that rate of change from a much lower-dimensional neighborhood of configurations that only have changes in a local patch of space?
Even more, I don't see how to slice the wavefunction locally. You could fix the sta... (read more)
As you have explained things so far, Schroedinger's equation is local in configuration space, not necessarily physical space. You seem to be claiming locality in physical space as well.
You can compute the rate of change of amplitude in a configuration from derivatives of amplitude over similar configurations. Are you claiming you can also compute that rate of change from a much lower-dimensional neighborhood of configurations that only have changes in a local patch of space?
Even more, I don't see how to slice the wavefunction locally. You could fix the sta... (read more)