DOI: 10.5281/zenodo.17731384
title: Negative Effective Mass as a Universal Consequence of the Kerr Bound Applied to Ordinary Collective Modes

description: NEW: Related work (interpretive consolidation):A8 — Kerr–de Broglie Universality: Mass Cancellation and Overlaid Rotational Participation from Particles to Galaxies (2025) https://zenodo.org/records/18006564This companion paper clarifies the geometric interpretation of the imaginary Kerr regime and proves the Mass Cancellation Theorem underlying the A7 results.

 

When the Kerr metric is applied without modification to any rotating or spinning collective excitation in ordinary matter, the spin length a = J/(Mc) exceeds the gravitational length R_g = GM/c² by many orders of magnitude in every realistic case. The Kerr outer horizon therefore becomes purely imaginary: r₊ ≈ i × J/(Mc).

An imaginary Kerr horizon is the geometric signature of negative effective inertial mass density in the resonant volume.

Equating the resulting scale |r₊| to the collective de Broglie wavelength λ_dB = h/(Mv) yields a unique mass M ≈ 10⁻⁴⁴ kg — identical to the vacuum-condensate grain mass estimated by Hawking (1978), Penrose, and loop quantum gravity since the 1970s.

The ubiquitous 0.5–5 Hz inertial/acoustic excess observed in all physical systems is proposed as the direct empirical signature of these spontaneous, metre-to-hundred-metre-scale, negative-mass vacuum resonance islands that arise naturally from standard physics.

The phenomenon is intrinsic to the vacuum and to ordinary matter. No exotic fields or laboratory apparatus are required
description: Full series of A1 - A7 articles: 

A5: Quantum-Gravitational Double-Resonance Propulsion Rings: Spacecraft-Scale Architecture and Physical Basis

A4: Imaginary Kerr Horizon in Every Rotating Body Below One Solar Mass - A Universal Quantum-Gravity Boundary

A3: De Broglie–Kerr Ergosphere Resonance in Rotating Coherent Systems  - Listening to the Horizon.

 A2: Soft-Matter Toroid for Quantum–Gravitational Resonance: Toward a Tabletop Realization of de Broglie–Schwarzschild Symmetry (DNA origami hydrgel self-symmetry resonance)

A1b:Toroid Models for Quantum–Gravitational Resonance via de Broglie–Schwarzschild Symmetry

 
description: Clarifying Note

Most treatments of quantum behavior implicitly tie the de Broglie wavelength to fully coherent particle ensembles. In practice, however, the wavelength is simply a kinematic phase-length associated with mass and momentum. Nothing in its definition requires microscopic coherence. What is normally neglected is that for mesoscopic or macroscopic masses, the wavelength is not zero—it is simply extremely short and therefore ignored. The present model does not introduce new physics; it only restores this kinematic phase as a variable even at scales where it is usually approximated away.

When the Kerr bound is exceeded, the formal horizon radius becomes a complex quantity. This does not mean that anything “ceases to exist”; it simply means that the classical notion of a horizon as a 4-dimensional surface is no longer applicable. The underlying mass–energy and angular momentum remain fully real, and the complex radius continues to appear in the gravitational invariants that govern the dynamics.

Physics provides many precedents: when new regimes are reached, old geometric interpretations break down while the underlying quantities persist. The Universe is not constrained by the limits of any particular theoretical framework; it continues to operate consistently even when our mathematical representations transition from real to complex values. The history of physics shows this repeatedly—from negative solutions discarded in early relativity to discarded roots in quantum theory that later proved essential.

Thus, a complex Kerr radius is not a signal of non-existence but of a shift in the regime where our classical interpretation fails. The invariant persists and can participate in resonance conditions even if it no longer corresponds to a spacetime surface in the classical sense.

All algebraic steps and physical interpretations were independently verified across multiple AI systems (Gemini, Claude, ChatGPT, Grok). Each confirmed the internal consistency of the de Broglie application and the Kerr condition. All AI systems agreed that matching the de Broglie wavelength and the Schwarzschild radius (in the early articles of A1-A7 series) is mathematically valid for any mass, coherent or not, and that exceeding the Kerr bound naturally leads to imaginary-radius regimes. While AI cannot serve as experimental proof, the cross-model convergence demonstrates internal logical consistency across unrelated reasoning frameworks. Every AI system started fresh without prior memory, with all A1–A7 uploads, has independently reached the same conclusions. This comes to tell us that physics, when read unbiased, surpass certain narrow interpretations. We offer that result for the readers to make their own conclusions. 
description: Author’s Clarifying Note (added December 2025)

When this work refers to “negative effective inertial mass density,” it does NOT mean that ordinary matter possesses negative rest mass. All material mass considered here is strictly positive and physical.

The terminology arises from applying the Kerr rotation condition to non-collapsed, rotation-dominated systems. For any realistic rotating body, the rotational length scale defined by angular momentum exceeds the gravitational length scale defined by mass. In this regime, the formal Kerr horizon radius becomes complex. This does not indicate non-existence or pathology; it indicates that the classical interpretation of a horizon as a real spacetime surface is no longer applicable.

What remains physically meaningful is the magnitude of the rotation-written length itself, which persists as a geometric invariant even when the horizon radius becomes complex. The “negative” contribution discussed in A7 refers to an effective geometric stress associated with rotation-dominated spacetime curvature, not to exotic matter or literal negative mass.

A companion paper (A8: Kerr–de Broglie Universality) proves a general Mass Cancellation Theorem showing that, for ordinary orbital motion and rigid-body rotation, this rotational length scale becomes independent of test mass and reflects properties of spacetime geometry rather than local inertial density. This result clarifies the interpretation of the imaginary Kerr regime used throughout A7 and shows that the phenomenon arises naturally from standard physics when rotation dominates over gravitation.