Recurrent Nightmares?: Measurement Theory in de Sitter Space

TL;DR

The paper argues that asymptotically de Sitter space admits a finite-dimensional Hilbert space, which enforces intrinsic imprecision in any measurement and prevents operational verification of Poincaré recurrences. Through Wheeler-DeWitt quantization, it shows time evolution can be described by a family of noncommuting, clock-dependent Hamiltonians, casting doubt on a unique quantum dynamics for AsdS spacetimes. It analyzes measurement theory in a local, horizon-structured setting, concluding that local observers cannot access the full S-matrix observables and that macroscopic pointer states are inherently fragile in finite systems. Ultimately, the authors contend that many Hamiltonians can yield indistinguishable experimental predictions within fundamental measurement limits, implying no single quantum theory of AsdS space, except in the $\Lambda\to0$ limit where universal observables re-emerge.

Abstract

The idea that asymptotic de Sitter space can be described by a finite Hilbert Space implies that any quantum measurement has an irreducible innacuracy. We argue that this prevents any measurement from verifying the existence of the Poincare recurrences that occur in the mathematical formulation of quantum de Sitter (dS) space. It also implies that the mathematical quantum theory of dS space is not unique. There will be many different Hamiltonians, which give the same results, within the uncertainty in all possible measurements.