To me it wasn't completely clear. + A discrete, infinite Hilbert space, with (wave) functions defined at each point. Why discrete? + An operator across this H

To me it wasn't completely clear. + A discrete, infinite Hilbert space, with (wave) functions defined at each point. Why discrete? + An operator across this Hilbert space that describes the evoltion of the universe. + A non-recurring property of the overall system that depends on the infinity of the system. - Question. If the system is really big, can we see if it is recurrent or not? - Question. Deviations from equilibrium should be "minor". However, minor deviations on a very fundamental level (of quantumgravity) might perhaps result in genesis/destruction of complete universes. If there is some kind of process that goes to low entropy can it be self-inforcing till it big bangs? - Question. If time is a parameter for the universe's walk in Hilbert space, why is it real?