The Universe as a Quantum Encoder

Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the hypothesis that quantum mechanical time evolution is always isometric, in the sense of preserving inner products, but not necessarily unitary. As evidence for this hypothesis we show that in two spacetime dimensions (i) there is net entanglement entropy produced in free field theory by a moving mirror or expanding geometry, (ii) the Lorentzian path integral for a finite elements lattice discretization gives non-unitary isometric time evolution, and (iii) tensor network descriptions of AdS$_3$ induce a non-unitary but isometric time evolution on an embedded two-dimensional de Sitter braneworld. In the last example time evolution is a quantum error-correcting code.