Gravitational length stretching: Curvature-induced modulation of quantum probability densities
Year: 2025
Type: article
Abstract: We introduce gravitational length stretching (GLS) as a novel quantum-gravitational phenomenon that distorts the spatial probability distribution of quantum particles in curved spacetime. Through quantum field theory in curved spacetime (QFT-CS), we demonstrate that GLS originates from the amplitude modulation function B k ( t , x → ) {B}_{k}\left(t,\overrightarrow{x}) in WKB solutions, governed by the covariant continuity equation ∇ μ ( B k 2 k μ ) = 0 {\nabla }_{\mu }\left({B}_{k}^{2}{k}^{\mu })=0 . This effect causes quantum objects to stretch in regions of stronger curvature, increasing their proper spatial extent by ∼ 20 % \sim 20 \% over millimeter scales for ultracold neutrons (UCNs) in Earth’s gravity. Our derivation of the Schrödinger equation in weak gravitational fields from the Klein–Gordon equation in Cartesian Schwarzschild coordinates reveals curvature-induced corrections absent in semi-classical approaches. Crucially, QFT-CS yields a covariant quantization condition ∫ k μ d x μ = n π \int {k}_{\mu }{\rm{d}}{x}^{\mu }=n\pi , resolving ambiguities in the noncovariant semi-classical formalism. We predict observable energy level shifts ( Δ E n ∕ E n ∼ 1 % \Delta {E}_{n}/{E}_{n}\hspace{0.33em} \sim \hspace{0.33em}1 \% ) and probability density gradients ( ∂ z B k 2 ≈ 202 m − 1 {\partial
Source: Open Physics
Author: Benliang Li
Institutions: University of South China, University of Bologna
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,356
Funder: China Scholarship Council
OpenAlex ID: W4415759528