The Universe as a Quantum Encoder

Abstract

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.

Hyperbolic Lattice for Scalar Field Theory in AdS$_3$

“…Recently in Ref. [48], similar finite element methods (FEM) were introduced in Minkowski space to address the interesting problem of unitarity in an expanding universe. However, to enter the realm of gravity in our context requires dynamical metric fluctuations for bulk gravity dual to a boundary CFT with a conserved energy momentum tensor.…”

Unitarity Problems for an Effective Field Theory Description of Early Universe Cosmology

“…It appears that the Hilbert space is time-dependent. As recently discussed in [7], this implies that the time evolution cannot be unitary and is at most isometric.…”

“…The unitarity problem for an effective field theory analysis comes from the fact that, in order to maintain the ultraviolet cutoff at a fixed physical scales, we must continuously add modes to the Hilbert space [6,7]. Thus, if k i denotes the comoving mode whose physical wavenumber equals the cutoff scale at some initial time t i and which hence determines the initial Hilbert space H i , then at a later time t the Hilbert space H(t) is larger than the initial Hilbert space:…”

“…The unitarity problem [6,7] for an effective field theory description of an expanding universe is closely related both to the Trans-Planckian Problem (TPP) and the Trans-Planckian Censorship Conjecture (TCC). If we demand that the factor of the state corresponding to all modes which crossed the Hubble radius during the primodial phase is unaffected by the non-unitarity of the time evolution 3 , our criterion becomes identical to the TCC, while if we only demand that modes which are currently of Hubble length and larger do not suffer from the unitarity problem, then we obtain the conclusions of the TPP [9].…”

Do Atoms Age?

“…Non-linear effects tied to QCD can shift the mass of the nucleus and these can change the properties of decaying nuclear states, thus showing that the concept of atom aging can also be extended to nuclear physics. Beyond the specific setup of [5], it is interesting to ask if the concept of atom aging manifests itself in other frameworks that have attempted to modify quantum mechanics such as the more general Lindlad evolution suggested in [2] or in other approaches [16][17][18].…”