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

This repository presents a theoretical framework for achieving quantum–gravitational resonance through engineered symmetry between the de Broglie wavelength and the Schwarzschild radius:

$\lambda = R_s$

While this relationship naturally arises only at the Planck scale — and in a single object under extreme relativistic conditions — we propose a two-subsystem approach to realize it in laboratory-accessible systems.

---

Core Idea

The resonance condition is constructed between two physical subsystems:

• Mass subsystem (tungsten): provides most of the gravitational mass

$R_s = \frac{2GM}{c^2}$

• Wave subsystem (graphene electrons): provides mobile quantum waves

$\lambda = \frac{h}{mv}$

By tuning electron velocities or using relativistic drift, one can match the effective wave to the mass’s Schwarzschild radius.

---

Investigated Configurations

Main experimentally relevant configuration

1. Graphene-coated tungsten toroid
   Electrons in the graphene layer form a tunable wave-like subsystem, while the tungsten core supplies mass. This configuration is shown to approach [ \lambda = R_s \approx 10^{-25},\mathrm{m} ] under realistic laboratory conditions, requiring no exotic particles or modifications to known physics.

Conceptual exploratory pathways

These configurations are retained as speculative ideas for future research (see Appendix B in the Zenodo document):

• Nanoparticles of tungsten and graphene-coated tungsten
• A massive tungsten core toroid surrounded by graphene nanoparticles
• Other combinations in which the total conduction electrons could exceed those in the original graphene sheet

Such setups could, in principle, allow $\lambda$ to match even smaller $R_s$ more easily. These ideas are not experimentally validated but illustrate potential avenues for further study.

---

Visual Illustrations

Fig. 1 — Graphene-coated tungsten toroid achieving λ = Rₛ symmetry.

Fig. 2 — Conceptual nanoparticle cloud to illustrate potential future pathways.

Fig. 3 — Possible toroidal assembly of nanoparticles (speculative).

---

Motivation

• Explore possible access to quantum–gravitational interaction without exotic particles or speculative physics
• Inspire new experimental directions using structured mass–wave systems
• Open avenues for speculative applications in resonant energy systems, propulsion concepts, and black hole analogs

---

Companion Resources

• Zenodo Record, all versions
• Zenodo Version 2
• OSF Archive (linked in Zenodo description)

---

📄 Citation & Licensing

• Author: Gravity Resonance (pseudonym)
• License: CC-BY-NC 4.0

This project is published under the pseudonym Gravity Resonance to preserve privacy. Collaboration may be requested via Zenodo private messaging or GitHub Discussions with verified scientific partners.

---

BibTeX (for citation managers)

@misc{gravity_resonance_2025,
  author       = {Gravity Resonance},
  title        = {Toroid Models for Quantum–Gravitational Resonance via de Broglie–Schwarzschild Symmetry},
  year         = {2025},
  doi          = {10.5281/zenodo.16371537},
  publisher    = {Zenodo},
  url          = {https://doi.org/10.5281/zenodo.16371537}
}