📝 SummarXiv

Abstract

We propose that, for a sufficiently small spacelike region $B$, deviations of the metric field from flat space encode the information recorded by a quantum reference frame (RF) placed in $B$. This encoding underlies the metric's ability to specify infinitesimal proper times and proper distances that ideal observers would assign, without requiring their physical presence. For purely classical correlations between the RF and the quantum fields within $B$, our hypothesis reproduces the Einstein equation with an undetermined cosmological constant. In this regime, the metric encodes a classical description of the fields in $B$ as perceived by the RF. When local quantum correlations are included, the Einstein equation arises with a positive cosmological constant, proportional to the surface density of those correlations.