It is confusion to argue from the continuity of the wave equation to the
continuity of the underlying physics—since there is no compelling reason to think that the wave equation is the final word on the issue—and discrete phenomena often look continuous if you observe them from a sufficiently great distance—e.g. see lattice gasses.
Re: “In reality, physics is continuous.”
That has yet to be established.
The universe could turn out to be finite and discrete—e.g. see my site:
http://finitenature.com/
It is confusion to argue from the continuity of the wave equation to the
continuity of the underlying physics—since there is no compelling reason to think that the wave equation is the final word on the issue—and discrete phenomena often look continuous if you observe them from a sufficiently great distance—e.g. see lattice gasses.
http://en.wikipedia.org/wiki/Loop_quantum_gravity is an example of a more modern discrete theory.