Non-unitary Isometric Quantum Mechanical Time Evolution in Cosmology
Summary
The past and the future are tightly linked in conventional quantum mechanics
by unitary evolution. Perhaps too tightly in an expanding spacetime. A tweak to
the theory could let quantum possibilities increase as space expands. The tweak
corresponds in replacing unitary quantum mechanical time evolution with a nonunitary
isometric one. Cosmological expansion points into this direction since new
degrees of freedom arise during the time evolution. We motivate this hypothesis
from two different approaches, all in 1 + 1 spacetime dimensions: (i) the net entanglement
entropy produced by toy and cosmological models is increasing in time,
(ii) the Lorentzian path integral for a finite elements latticization gives non-unitary
isometric time evolution for a scalar and possibly a fermionic field.