Non-unitary Isometric Quantum Mechanical Time Evolution in Cosmology

Abstract

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.