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July 9, 20260 citationsOpen Access

A Lattice Quantum Field Theory Test of the Static Escrow Postulate: 1+1D and 3+1D Falsification with Modular-Hamiltonian Partial Survival

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GIGrant Lavell Whitmer III

Key Points

  • The aim is to evaluate the static gravitational entropy escrow postulate in different dimensional settings using lattice quantum field theory.
  • Conducted a 295-point scan of a free massless scalar in 1+1D with lattice sizes up to N = 3000.
  • Performed an N3-site scan in 3+1D, examining the area law and ratio R without a finite continuum limit.
  • Evaluated modular Hamiltonian content under the Bisognano–Wichmann conjecture.
  • In 1+1D, the ratio R spans 10.56 orders of magnitude, with mass-induced entanglement uniformly negative.
  • In 3+1D, R has no finite continuum limit, and mutual information decays as L−4, opposing linear growth.
  • In both dimensions, the literal interpretation of the static escrow postulate is ruled out.

Abstract

We test the static gravitational entropy escrow postulate Sesc = |Ugrav|/TU of Whitmer 1 using lattice quantum field theory. In 1+1D, a 295-point scan of a free massless scalar (lattice sizes up to N = 3000) finds the dimensionless ratio R = Sent/Sesc spanning 10.56 orders of magnitude; the mass-induced entanglement ΔS = Sent − Svac is uniformly negative and lattice-converged. In 3+1D, an N3-site scan confirms the Bombelli–Srednicki area law (Svac/N2 → 0.0228) and shows that R has no finite continuum limit, because the bipartition entropy is dominated by the area-law vacuum term while the mass-induced ratio RΔ is bounded by 10−3; two independent code paths agree to five decimals. Mutual information decays as L−4, opposite to the linear growth the postulate requires. The literal identification of Sesc with bipartition entanglement entropy is therefore ruled out in both dimensions. The modular Hamiltonian content ΔK, evaluated under the Bisognano–Wichmann conjecture, shows a positive, approximately linear-in-d1 window at m = 1 (an empirical non-perturbative feature, not a linear-response recovery of the BW asymptote—in the linear-response regime ΔK is negative and d1-flat), with prefactor ≈ 1/30 of the literal BW value (≈ 1/7 when energy-normalized). A companion paper 11 finds no BW recovery in 3+1D within the accessible d1 range. The framework's horizon-limit recoveries are independent of these flat-space tests.

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Cite This Study

Grant Lavell Whitmer III (2026) studied this question.

synapsesocial.com/papers/6a4f3b002b81a944af5750c2https://doi.org/10.5281/zenodo.21250629
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