ItemArticle

Relational Time as a Stochastic Variable in ADM Gravity

Title
Relational Time as a Stochastic Variable in ADM Gravity
Creator
Pradosh Keshav, M.V.
Description
The absence of a fundamental time parameter in canonical quantum gravity is motivating the search for internal clocks by which evolution is defined relationally. While formal solutions are provided classical deparametrization schemes they often rely on semiclassical limits or fixed foliations that break general covariance. In this work, a canonical framework is constructed where time emerges dynamically as a stochastic degree of freedom, identified with a massless scalar field whose conserved momentum current defines a relational foliation. Unlike semiclassical stochastic gravity approaches where noise is introduced externally, here the stochasticity arises from coarse-graining of unresolved transverse-traceless graviton modes, leading to an intrinsic, dynamically coupled stochastic clock field. This leads to a diffusion-like broadening of the wavefunctional across neighboring clock slices, offering a novel stochastic phenomenology of the WheelerDeWitt equation. The resulting evolution remains consistent with hypersurface-deformation algebra in an ensemble sense, while introducing an intrinsic probabilistic nature to relational time. This work thus establishes the theoretical foundation for future applications in quantum cosmology and the emergence of classicality from quantum gravitational systems. 2025 Wiley-VCH GmbH.
Source
Fortschritte der Physik;Volume;73;Issue;2026-10-09 00:00:00;Article No.;e70024;
Date
01-01-2025
Publisher
John Wiley and Sons Inc
Subject
relational time; scalar clocks; stochastic clocks; wheeler-dewitt equation
Coverage
Pradosh Keshav M.V., Department of Physics and Electronics, Christ University, Bangalore, 560029, India
Rights
Restricted Access; Hardcopy may be available in the library
Relation
ISSN: 158208;
Format
online
Language
English
Type
Article

Citation

Pradosh Keshav, M.V., “Relational Time as a Stochastic Variable in ADM Gravity,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 18, 2026, https://archives.christuniversity.in/items/show/21806.

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