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arXiv · 2506.00265

Einstein's equation as a geometric encoding of correlations with quantum reference frames

Eduardo O. Dias
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Abstract

Spacetime intervals between events in general relativity acquire an operational meaning relative to material reference frames, whereas in quantum mechanics events are naturally accompanied by correlations with the local degrees of freedom of the frame. Motivated by this complementarity, we propose a geometry-information equivalence hypothesis (GIEH), according to which the metric field geometrically encodes local correlations that would otherwise arise between the system of interest and a local reference frame (LRF). Imposing ideal-LRF conditions, the GIEH yields the full nonlinear Einstein equation, without assuming an AdS background or an underlying CFT. The framework further allows background correlations to provide an informational origin for the cosmological constant, relates their local mutual-information density to the Gibbons--Hawking entropy per unit thermodynamic volume of de Sitter space, and permits a Minkowski reference spacetime even for a nonzero cosmological constant.

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Eduardo O. Dias. 2025-05-30. Einstein's equation as a geometric encoding of correlations with quantum reference frames. https://arxiv.org/abs/2506.00265

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