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arXiv · 2601.13491

Finite-resolution measurement induces topological curvature defects in spacetime

Ewa Czuchry·Jean-Pierre Gazeau
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Abstract

We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect. The regularized metric replaces $r^2$ by $r^2+\sigma^2$ in the angular part, where $\sigma$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2\pi$, independently of $\sigma$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $\sigma\to0$ leads to distributional Dirac-delta curvature and to appearance of topological defect at the origin. These results show that finite spatial resolution measurement does not merely smooth singularities but can shape spacetime geometry.

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Ewa Czuchry, Jean-Pierre Gazeau. 2026-01-20. Finite-resolution measurement induces topological curvature defects in spacetime. https://arxiv.org/abs/2601.13491

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