The Consistent Classical Theory of Entanglement-Sourced Gravity: A No-Go Theorem, Classification, and Completion
Abstract
Several recent sketches have proposed that quantum entanglement, treated as a local density, sources spacetime curvature through hand-written modifications of Einstein's equations. We systematize these proposals. Our central result is a no-go theorem: under diffeomorphism invariance, the Noether identity requires the divergence of any scalar-sector metric contribution to be parallel to the scalar gradient; the second-derivative structures appearing in the sketches violate this condition via an explicit Ricci obstruction, and therefore cannot arise from any local diffeomorphism-invariant action. The obstruction is constructive: we prove a covariant Hessian completion theorem showing that the Ricci term forbidding the isolated scalar Hessian dictates the curvature coupling F(S)R that completes it. We classify the completion: under five stated assumptions the four structures admit a common Bianchi-consistent scalar-tensor completion, unique up to free functions F, K, V (two after field redefinition). We give the completion explicitly, derive observational constraints (Cassini, varying G), and state what remains open.
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BibTeX
@misc{godin2026consistent,
title = {{The Consistent Classical Theory of Entanglement-Sourced Gravity: A No-Go Theorem, Classification, and Completion}},
author = {Yan Godin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23431714},
url = {https://zenodo.org/records/23431714},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Consistent Classical Theory of Entanglement-Sourced Gravity: A No-Go Theorem, Classification, and Completion
AU - Yan Godin
PY - 2026
DA - 2026/10/17
PB - Zenodo
DO - 10.5281/zenodo.23431714
UR - https://zenodo.org/records/23431714
AB - Several recent sketches have proposed that quantum entanglement, treated as a local density, sources spacetime curvature through hand-written modifications of Einstein's equations. We systematize these proposals. Our central result is a no-go theorem: under diffeomorphism invariance, the Noether identity requires the divergence of any scalar-sector metric contribution to be parallel to the scalar gradient; the second-derivative structures appearing in the sketches violate this condition via an explicit Ricci obstruction, and therefore cannot arise from any local diffeomorphism-invariant action. The obstruction is constructive: we prove a covariant Hessian completion theorem showing that the Ricci term forbidding the isolated scalar Hessian dictates the curvature coupling F(S)R that completes it. We classify the completion: under five stated assumptions the four structures admit a common Bianchi-consistent scalar-tensor completion, unique up to free functions F, K, V (two after field redefinition). We give the completion explicitly, derive observational constraints (Cassini, varying G), and state what remains open.
ER -