De Broglie–Kerr Ergosphere Resonance in Rotating Coherent Systems

Kerr solution for de Broglie wave yields imaginary-valued spatial horizon—a theoretical signature of quantum-gravitational coupling at laboratory scale . We explore a Kerr ergosphere analogue in rotating, resonant coherent systems—DNA-origami hydrogels, graphene toroids, or beyond. Resonance occurs when λ = h/M v = re = 2GM/c2 , linking de Broglie wave to ergosphere radius. When Kerr spin a ≫ Mgeo, the outer horizon turns imaginary-valued—proof of quantum-gravity coupling at lab scale. Detection: entangled photons, optical, acoustic, phase scattering. _________________________________________________________________________________ A note on coherence and the scope of the A-series: Early papers (A1–A6) propose engineered systems — toroids, hydrogel rings, nanoparticle arrays — designed to bring a macroscopic body into a resonance condition. The coherence properties of these systems, particularly the DNA-origami hydrogel toroid in A2, are not fully characterized. Whether such a system exhibits quantum coherence in the strict sense, mechanical coherence, or some intermediate biological quantum coherence of the kind observed in photosynthetic complexes remains an open experimental question. What A2 proposes is precisely to test this — the experiment itself would shed light on the coherence question. De Broglie's original formulation applied the wave relation to the center of mass of any system, not only to coherent quantum beams — empirically supported by Sagnac interferometry and SQUID measurements of macroscopic rotating bodies. Papers A7, A8, and A9 operate on entirely different ground. They do not propose any engineered body or coherence condition. Instead, they derive the mass and geometric scale of vacuum granules already present in the universe — from the observed 1–5 Hz noise floor common to all precision instruments, from the Kerr metric applied to any rotating body, and from Compton wavelength reasoning. The question of coherence does not arise in A7–A9: we are not creating a resonance condition, we are detecting one that already exists, at scales of 22 metres to 22+ kilometres — within the reach of LIGO, Virgo, the Einstein Telescope, and tabletop rotating systems. The A-series as a whole move from engineering proposals toward geometric discovery. The later papers stand independently of any coherence assumption. ____________________________________________________________________________________ Companion and foundational work: Gravity Resonance (M.P.) A1b — Toroid Models for Quantum-Gravitational Resonance via de Broglie–Schwarzschild Symmetry DOI: https://doi.org/10.5281/zenodo.16449277 A2 — Soft-Matter Toroid for Quantum–Gravitational Resonance: Toward a Tabletop Realization of de Broglie–Schwarzschild Symmetry DOI: https://doi.org/10.5281/zenodo.17541112 A3 — De Broglie–Kerr Ergosphere Resonance in Rotating Coherent Systems: Listening to the Horizon DOI: https://doi.org/10.5281/zenodo.17594467 A4 — Imaginary Kerr Horizon in Every Rotating Body Below One Solar Mass: A Universal Quantum-Gravity Boundary DOI: https://doi.org/10.5281/zenodo.17619734 A5 — Quantum-Gravitational Double-Resonance Propulsion Rings: Spacecraft-Scale Architecture and Physical Basis DOI: https://doi.org/10.5281/zenodo.17634226 A6 — Hybrid van der Waals Graphene–Hydrogel–Mass-Seed Resonator for Asymmetric Mechanical Response and Electromechanical Output DOI: https://doi.org/10.5281/zenodo.17684823 A7 (Version 2)— Imaginary Kerr Horizons in Ordinary Rotating Matter: A New Geometric Property and Its Possible Connection to the Universal 1–5 Hz Signal DOI: https://doi.org/10.5281/zenodo.19320019 A8 (Version 2) — Kerr Geometry and the Angular-Duality Wavelength: Mass Cancellation and Borderline Resonance from Nanoparticle to Galaxy DOI: 10.5281/zenodo.19275058 A9: The Quantum Vacuum Granule: Three Complementary Mass Scales from the 1--5 Hz Universal Hum https://doi.org/10.5281/zenodo.18888582