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

arXiv:2506.00265v5 Announce Type: replace-cross 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.

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.

arXiv:2506.00265 [gr-qc]

(or arXiv:2506.00265v5 [gr-qc] for this version)

From: Eduardo Dias DSc. [view email] [v1] Fri, 30 May 2025 21:56:45 UTC (11 KB) [v2] Sat, 13 Sep 2025 18:23:28 UTC (12 KB) [v3] Thu, 2 Oct 2025 02:08:53 UTC (12 KB) [v4] Fri, 3 Apr 2026 21:09:18 UTC (12 KB) [v5] Sat, 29 Aug 2026 17:09:30 UTC (15 KB)

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

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