What does this research mean for the field?

Coulomb's law and the sign structure of electromagnetic interactions can be derived directly from the U(1) scalar phase component of the Relational Geometric Mechanics wave signature without requiring additional physical postulates. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

This paper aims to derive Coulomb's law using the U(1) scalar phase component of the RGM wave signature.

May 8, 2026Open Access

Relational Geometric Mechanics II: Electromagnetism — Coulomb's Law from U(1) Scalar Phase Interference

Key Points

This paper aims to derive Coulomb's law using the U(1) scalar phase component of the RGM wave signature.
Derived the electromagnetic coupling phase α_EM = π/2 based on charge interactions.
Utilized phase algebra to explain the sign structure of electromagnetic interactions without new assumptions.
Coulomb's law is successfully derived from the U(1) scalar phase without additional postulates.
The relationship between charges is explained solely through phase algebra.

Abstract

Paper II of the Relational Geometric Mechanics series. Derives Coulomb's law from the U (1) scalar phase component of the RGM wave signature. The electromagnetic coupling phase αEM = π/2 is derived — not assumed — from the requirement that opposite charges attract. The sign structure of electromagnetic interactions follows from the phase algebra with no additional postulates. No new physical assumptions are introduced beyond those established in Paper I.

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Timothy Gleason

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Relational Geometric Mechanics II: Electromagnetism — Coulomb's Law from U(1) Scalar Phase Interference

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Abstract

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