Recurrent Nightmares?: Measurement Theory in de Sitter Space

TL;DR

This paper discusses how the finite Hilbert space in de Sitter space leads to measurement limitations, preventing verification of Poincare recurrences and implying non-uniqueness in the quantum description of de Sitter space.

Contribution

It introduces a measurement-theoretic perspective on de Sitter space, highlighting fundamental limitations and non-uniqueness in its quantum description due to finite Hilbert space constraints.

Findings

Measurement inaccuracies prevent verification of Poincare recurrences.

Multiple Hamiltonians can produce indistinguishable measurement outcomes.

Quantum theory of de Sitter space is inherently non-unique.

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.