Schmidhuber's paper explicitly assumes that only discrete universes exist,
so that theories of computation can be applied. But this assumption may
not be necessary. Consider a TM which implements an algorithm for
numerically solving a fixed system of partial differential equations
defining some continous universe. The TM would take as input a set of
arbitrary-precision coordinates defining a region in this universe and a
parameter specifying the precision of the output, and produce as output
the content of that region to the specified precision.
Under the interpretation I proposed earlier, the regions of this continous
universe would have physical existence as the output of the TM and
therefore the universe as a whole would have physical existence.
On a different note, I'm trying to learn enough quantum mechanics to
figure out what a program for our universe might look like. Does anyone
have suggestions for a good quantum mechanics text book?