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Emergent Time from Phase Dynamics: A Noether-Based Scalar Field Framework for Gravity and Dark Matter

Author:

Gersiyor, Ferhat

Category:

Research Papers

Sub-Category:

Relativity Theory

Language:

English

Date Published:

March 24, 2026

File:

/Research Papers-Relativity Theory/Download/10494

Downloads:

Keywords:

N/A

Abstract:

We propose a theoretical framework in which time is not a fundamental background parameter, but instead emerges dynamically from the phase structure of a complex scalar field. By decomposing the field as Φ(x) = A(x)eiθ(x), we interpret the gradient of the phase field as defining a local temporal direction. A global phase symmetry leads, via Noether’s theorem, to a conserved current jμ = A2∂μθ, which we identify as a physical temporal flow. This current contributes directly to the energymomentum tensor and provides a dynamical source for spacetime curvature when coupled to gravity. In a cosmological context, the phase dynamics naturally reproduces ultra-light dark matter behavior. In particular, coherent oscillations of the scalar field yield an effective pressureless fluid at large scales, consistent with standard cold dark matter phenomenology. We further analyze linear perturbations and demonstrate that phase excitations propagate relativistically, ensuring stability under appropriate conditions. Within this framework, particle mass arises dynamically from the curvature of the scalar potential around its vacuum configuration, rather than being introduced as a fundamental parameter. This approach establishes a unified connection between time, symmetry, gravity, and dark matter within a single scalar field model, suggesting that temporal structure itself is an emergent feature of underlying field dynamics.

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