DOI: 10.5281/zenodo.16371538
title: Toroid and Nanoparticle Models for Quantum-Gravitational Resonance via de Broglie–Schwarzschild Symmetry

description: ⚠️ NOTICE – SUPERCEDED VERSION

This is Version 1 (July 23, 2025, DOI 10.5281/zenodo.16371538): please note that this version has been superseded by Version 2 (August 25, 2025) with updates and conceptual extensions:  https://doi.org/10.5281/zenodo.16449277 All Versions: https://doi.org/10.5281/zenodo.16371537  

This update retains the main toroidal graphene–tungsten model as the primary experimentally relevant design.

 

Toroid Models for Quantum–Gravitational Resonance via De Broglie–Schwarzschild (DBS) Resonance/Symmetry

Description:We propose a conceptual framework for De Broglie–Schwarzschild (DBS) Resonance/Symmetry, in which the quantum de Broglie wavelength of a system matches the Schwarzschild radius of its gravitational mass:

λ = Rₛ

A crucial aspect of this approach is the separation into two interacting subsystems:





A mass subsystem generating the gravitational scale Rₛ via total mass.




A wave subsystem defining λ  via particle motion or collective quantum effects.



This dual-subsystem design makes the DBS resonance potentially accessible at mesoscopic scales in the laboratory, without invoking exotic particles or new physical laws.

The framework is conceptual first, highlighting the symmetry principle. Experimental implementations may include toroidal currents, graphene-coated nanoparticle ensembles, superconducting circuits, Cooper pairs, Bose–Einstein condensates, or other collective quantum systems. The collective de Broglie wavelength of the subsystem can significantly differ from single-particle wavelengths, allowing resonance even when individual particle λ would be too large.

The Schwarzschild radius is used as a gravitational scale, not as a physical boundary; no singularities are implied. Such applications of Rₛ at small scales are consistent with theoretical treatments in quantum gravity, and Hawking’s proposals for quantum wormholes.

This work lays the conceptual foundation for controllable quantum–gravitational interactions and is open to further research across quantum physics, nanotechnology, and materials science.

👉 [Zenodo DOI 10.5281/zenodo.16371537]

The author uses the pseudonym Gravity Resonance to preserve anonymity and avoid personal indexing, while welcoming collaboration via Zenodo private messages.
description: Note 1:

This framework introduces the resonance principle λ = Rₛ, potentially applicable across a range of quantum–gravitational, energy, and propulsion systems. While the present formulation uses tungsten and graphene, any future implementations—including those using alternative materials—should acknowledge the original model. This work is protected under a CC-BY-NC 4.0 license and may not be used commercially without prior agreement. Recognition is requested in both scientific and technological applications.

Note 2:

 For background material and development history, see the companion OSF archive (author pseudonym maintained): OSF Project: Toroid Resonance Model for Quantum–Gravitational Interaction of Schwarzschild radius and de Broglie wavelength. The core idea was independently developed between 1997–2005 and publicly documented on OSF prior to Zenodo submission.

Note 3 (Disclaimer, Nanoparticle Model):

The nanoparticle cloud model described in Appendix B is a conceptual extension rather than a practical experimental design. Its purpose is to illustrate a possible pathway for applying the de Broglie–Schwarzschild resonance condition in mesoscopic systems. Physical feasibility and stability remain open questions for future research.