A geometric resolution limit from vacuum entanglement: Topological Structure and Particle-Wave Asymmetry
Abstract
We establish that vacuum entanglement entropy, regulated by weak spacetime curvature, imposes a fundamental lower bound on radial resolution for quantum excitations. From the area law, weak gravity introduces a natural UV regulator via the perturbative Green's function. Geometric projection yields a minimal radial scale Δrmin ∝ rs2/R, where rs is the Schwarzschild radius and R the boundary radius. Consistency with the Compton wavelength defines a global mass scale mgeo ≡ ℏ R/(c rs2). Particle masses satisfy m = αmgeo, where α encodes vacuum structure. For Earth, mgeo ≈ 2.84 × 10−32 kg. We determine α via spectral analysis of curvature-induced mode shifts, implemented in Python with N=3000 radial points and nmodes=1000. The calculation yields α(2) ≈ 33, matching the electron benchmark without adjustable parameters, ruling out exponential ansätze in favor of slow power-law growth α(l) ∝ l1.27. Crucially, this resolution limit endows the quantum vacuum with the properties of a granular refractive medium. This elegantly explains a fundamental particle-wave asymmetry: massive excitations with λC ≪ Δrmin propagate in the geometric optics limit, following macroscopic gradients as classical geodesics. Conversely, photons with λ≪ Δrmin interact directly with the medium's granularity, leading to phase decoherence and anomalous dispersion. This framework reframes mass as a probe of vacuum-imposed resolution limits, yielding distinct, falsifiable predictions for high-energy photon propagation.
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BibTeX
@misc{martin2026geometric,
title = {{A geometric resolution limit from vacuum entanglement: Topological Structure and Particle-Wave Asymmetry}},
author = {Isbelia Martin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.27640},
eprint = {2608.27640},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27640},
}
RIS
TY - UNPB
TI - A geometric resolution limit from vacuum entanglement: Topological Structure and Particle-Wave Asymmetry
AU - Isbelia Martin
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2608.27640
UR - https://arxiv.org/abs/2608.27640
AB - We establish that vacuum entanglement entropy, regulated by weak spacetime curvature, imposes a fundamental lower bound on radial resolution for quantum excitations. From the area law, weak gravity introduces a natural UV regulator via the perturbative Green's function. Geometric projection yields a minimal radial scale Δr_min ∝ r_s^2/R, where r_s is the Schwarzschild radius and R the boundary radius. Consistency with the Compton wavelength defines a global mass scale m_geo ≡ ℏ R/(c r_s^2). Particle masses satisfy m = αm_geo, where α encodes vacuum structure. For Earth, m_geo ≈ 2.84 × 10^−32 kg. We determine α via spectral analysis of curvature-induced mode shifts, implemented in Python with N=3000 radial points and n_modes=1000. The calculation yields α(2) ≈ 33, matching the electron benchmark without adjustable parameters, ruling out exponential ansätze in favor of slow power-law growth α(l) ∝ l^1.27. Crucially, this resolution limit endows the quantum vacuum with the properties of a granular refractive medium. This elegantly explains a fundamental particle-wave asymmetry: massive excitations with λ_C ≪ Δr_min propagate in the geometric optics limit, following macroscopic gradients as classical geodesics. Conversely, photons with λ≪ Δr_min interact directly with the medium's granularity, leading to phase decoherence and anomalous dispersion. This framework reframes mass as a probe of vacuum-imposed resolution limits, yielding distinct, falsifiable predictions for high-energy photon propagation.
ER -