Finite-resolution measurement induces topological curvature defects in spacetime
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914470443352064 |
|---|---|
| author | Czuchry, Ewa Gazeau, Jean-Pierre |
| author_facet | Czuchry, Ewa Gazeau, Jean-Pierre |
| contents | 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 $r^2+σ^2$ in the angular part, where $σ$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2π$, independently of $σ$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $σ\to0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13491 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-resolution measurement induces topological curvature defects in spacetime Czuchry, Ewa Gazeau, Jean-Pierre General Relativity and Quantum Cosmology High Energy Physics - Theory 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 $r^2+σ^2$ in the angular part, where $σ$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2π$, independently of $σ$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $σ\to0$ 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. |
| title | Finite-resolution measurement induces topological curvature defects in spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.13491 |