Relativity and Cosmology

A Phase-Dynamics-Based Derivation of the Tully-Fisher Relation

Authors: Enno Matthiesen

This paper presents a derivation of the Tully-Fisher relation based on a phase-dynamics-driven description of galactic rotation. Starting from a coupled amplitude-phase field structure, an effective dynamical relation between rotational velocity, density, and coupling properties is formulated. In a stationary regime, the dynamics can become dominated by phase evolution, leading to a characteristic scaling between velocity and enclosed mass. Under scale-invariant conditions, this framework yields a relation consistent with the observed proportionality v^4 ∝ M. The result suggests that the Tully-Fisher relation may emerge as a structural consequence of coherent dynamical organization, without requiring additional unseen components. The derivation is presented in a self-contained form and is compatible with a broader relational field framework.

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[v1] 2026-04-10 13:17:26

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