Operational Geometry on de Sitter Spacetime

TL;DR

This paper explores how realistic quantum probes, such as composite objects with internal energy and spin, affect the effective geometry of de Sitter spacetime, revealing dependencies beyond classical notions.

Contribution

It introduces a method to define effective spacetime geometry using quantum probes' centroids, highlighting how internal properties influence perceived curvature.

Findings

Effective sectional curvature depends on probe's internal energy, size, and spin.

Quantum probes modify classical geometric notions in de Sitter spacetime.

Results have implications for quantum gravity research.

Abstract

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity.