The Universe as a Quantum Encoder

TL;DR

The paper proposes that quantum time evolution in our expanding universe is inherently isometric rather than strictly unitary, arguing that expanding spatial volumes necessitate growing Hilbert spaces and new degrees of freedom. Using three 1+1D approaches—moving mirrors, Lorentzian FEM lattice discretization, and a dS$_2$ braneworld in AdS$_3$ tensor networks—it demonstrates that isometric maps can encode information and, in some cases, realize quantum error-correcting codes. Entanglement entropy calculations in 2D CFTs show net entropy production consistent with isometric evolution, while explicit lattice constructions reveal $K^{\dagger}K=I$ but $KK^{\dagger}$ as a projector, confirming non-unitary but isometric time evolution. The AdS$_3$/dS$_2$ tensor-network model further connects this to holography and dS/CFT, where time evolution corresponds to inverse RG flow and increases the boundary Hilbert space, with entanglement scaling $S_{ent} \sim \log R$. Collectively, the work suggests a fundamental encoding perspective on cosmological time evolution and highlights open questions about locality, contracting geometries, and the role of quantum error correction in cosmology.

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.

Figures (10)

• Figure 1: A mirror following the trajectory in Equation \ref{['pol']}.
• Figure 2: An FDM rectangular lattice regularization for a 1+1 spacetime with a moving left boundary. This was obtaining by tiling the entire upper half-plane with rectangles, and removing those rectangles which intersect with or fall to the left of the moving mirror boundary. To impose Dirichlet boundary conditions on the mirror, the field degrees of freedom on the left-most lattice sites of the remaining lattice are set to zero. A wave reflected off of the saw-tooth boundary can acquire an energy flux which becomes large in the $a\to 0$ continuum limit.
• Figure 3: Plot of a $\phi(t)$ in $\text{CPL}_a([0,T])$.
• Figure 4: Plots of $b(t)$, $b_L(t)$, and $b_L(t)$.
• Figure 5: A triangular FEM lattice regularization of a 1+1 scalar field in a spacetime with a moving boundary. The moving boundary is piecewise-linear-approximated by the lattice discretization, which is continuous for any cutoff scale; this is in contrast to the FEM saw-tooth approximation of Figure \ref{['fig:timedepbdy2']}. Note that the number of lattice sites on each Cauchy slice is increasing with time.