Signature Failure and Minimum Spatial Quanta: Shear-Induced Quantum Boundaries for Gravitational Path Integrals
Abstract
We investigate whether quantum metric fluctuations can destroy the differentiable Lorentzian support required for spacetime. We conjecture that non-Lorentzian metric elements are absent from the physical manifold and restrict admissible histories to a single continuing, causally connected four-dimensional geometry. To explore this proposal, we extrapolate the Gaussian transverse-traceless graviton vacuum to an additive metric ensemble with physical Fourier cutoff kmax=1/q. A lattice model with local repair and selection of periodically winding differentiable-state components gives a minimum surviving scale qmin≃1.9 ℓP over the simulated duration. We then examine two complementary curvature-induced deformations. For the Schwarzschild electric Weyl field, the smallest boundary radius at the center of a black hole, occurring when q≃2.5 ℓP, is rqb≃2.62 CW1/3(rgℓP2)1/3 ≃1.91×10−22 CW1/3(M/M⊙)1/3m, where rg=GM/c2 and CW parameterizes the finite-q Weyl response. For homogeneous radiation, a supplementary Gaussian four-metric ensemble subject to linearized de Donder conditions gives ρqb/ρP≃1.31×10−2/CR at q=2.5 ℓP, where CR is the corresponding Ricci-response coefficient. The local homogeneous criterion is unchanged under reversal of the expansion rate. These model-dependent thresholds motivate a possible replacement of classical singular continuations by finite-curvature quantum boundaries.
Related
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BibTeX
@misc{shaya2026signature,
title = {{Signature Failure and Minimum Spatial Quanta: Shear-Induced Quantum Boundaries for Gravitational Path Integrals}},
author = {Edward J. Shaya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03732},
eprint = {2610.03732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03732},
}
RIS
TY - UNPB
TI - Signature Failure and Minimum Spatial Quanta: Shear-Induced Quantum Boundaries for Gravitational Path Integrals
AU - Edward J. Shaya
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03732
UR - https://arxiv.org/abs/2610.03732
AB - We investigate whether quantum metric fluctuations can destroy the differentiable Lorentzian support required for spacetime. We conjecture that non-Lorentzian metric elements are absent from the physical manifold and restrict admissible histories to a single continuing, causally connected four-dimensional geometry. To explore this proposal, we extrapolate the Gaussian transverse-traceless graviton vacuum to an additive metric ensemble with physical Fourier cutoff k_max=1/q. A lattice model with local repair and selection of periodically winding differentiable-state components gives a minimum surviving scale q_min≃1.9 ℓ_P over the simulated duration. We then examine two complementary curvature-induced deformations. For the Schwarzschild electric Weyl field, the smallest boundary radius at the center of a black hole, occurring when q≃2.5 ℓ_P, is r_qb≃2.62 C_W^1/3(r_gℓ_P^2)^1/3 ≃1.91×10^−22 C_W^1/3(M/M_⊙)^1/3m, where r_g=GM/c^2 and C_W parameterizes the finite-q Weyl response. For homogeneous radiation, a supplementary Gaussian four-metric ensemble subject to linearized de Donder conditions gives ρ_qb/ρ_P≃1.31×10^−2/C_R at q=2.5 ℓ_P, where C_R is the corresponding Ricci-response coefficient. The local homogeneous criterion is unchanged under reversal of the expansion rate. These model-dependent thresholds motivate a possible replacement of classical singular continuations by finite-curvature quantum boundaries.
ER -