DOI: 10.5281/zenodo.18006565
title: Kerr–de Broglie Universality: Mass Cancellation and Overlaid Rotational Participation from Particles to Galaxies

description: This paper (A8) introduces a unifying perspective on two foundational length scales in physics: the de Broglie wavelength associated with linear motion, and the Kerr spin length associated with rotation. While traditionally treated as belonging to separate domains—quantum mechanics and general relativity—the two expressions share an identical dimensional structure: action divided by momentum yields a length.

We define an angular-duality wavelength, λ_ad = J/(Mc), and show via a Mass Cancellation Theorem that for ordinary orbital motion and rigid-body rotation this length becomes independent of the test mass. Instead, it depends only on geometry and kinematics (v, R, ω). As a result, all bodies participating in the same rotation—particles, planets, laboratory systems—share the same rotational wavelength, with multiple such wavelengths overlaid due to nested motions (atomic, planetary, galactic).

Order-of-magnitude estimates are given from intrinsic particle spin to galactic rotation. Applying the Kerr horizon formula outside the collapsed-object regime shows that ordinary rotating matter generically enters a complex-root regime, where no classical horizon exists but a real, rotation-defined length scale remains. This scale coincides with the angular-duality wavelength.

The paper also notes that naive Casimir scaling at very small separations implies vacuum stresses that exceed rest-mass energy, indicating a regime where effective field descriptions break down and vacuum structure becomes dynamically significant.

No new forces or exotic matter are introduced. The work follows standard formulas applied beyond their usual interpretive boundaries. A cautious motivation is offered: mass-independent rotational length scales may contribute to effective stresses in large-scale dynamics, in the same phenomenological category where “dark” components are currently invoked.

This paper is theoretical and conceptual. It proposes no devices.

Companion and foundational work:Gravity Resonance, Toroid Models for Quantum-Gravitational Resonance via de Broglie–Schwarzschild Symmetry (A1-A7), Zenodo (2025), DOI: 10.5281/zenodo.16449277

Soft-Matter Toroid for Quantum–Gravitational Resonance: Toward a Tabletop Realization of de Broglie–Schwarzschild Symmetry (A2) DOI: DOI: 10.5281/zenodo.17541112

De Broglie–Kerr Ergosphere Resonance in Rotating Coherent Systems - Listening to the Horizon (A3) DOI: 10.5281/zenodo.17594467 

Imaginary Kerr Horizon in Every Rotating Body Below One Solar Mass - A Universal Quantum-Gravity Boundary (A4) DOI: 10.5281/zenodo.17619734 

Quantum-Gravitational Double-Resonance Propulsion Rings: Spacecraft-Scale Architecture and Physical Basis (A5) DOI: 10.5281/zenodo.17634226

Hybrid van der Waals Graphene–Hydrogel–Mass-Seed Resonator for Asymmetric Mechanical Response and Electromechanical Output — Provisional-Style Disclosure Document (A6) DOI: 10.5281/zenodo.17684823  

Negative Effective Mass as a Universal Consequence of the Kerr Bound Applied to Ordinary Collective Modes (A7)  DOI: 10.5281/zenodo.17731385