| _version_ | 1866901883456585728 |
|---|---|
| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <div> <h4>Abstract</h4> <p>We present the quantum gravity theory that emerges from the topological soliton framework. Gravity is not a fundamental interaction to be quantized but an emergent phenomenon arising from the collective dynamics of the Faddeev-Niemi field $\mathbf{n}: \mathbb{R}^{3,1} \to S^2$. The graviton is an $S^3$ Goldstone mode of the Hopf medium, arising from spontaneous breaking $SO(4) \times \text{Diff}(M_4) \to SO(3) \times \text{Diff}(M_3)$. The Einstein-Hilbert action is the leading term in a derivative expansion of the effective action obtained by integrating out soliton fluctuations (Sakharov's induced gravity). UV-finiteness is automatic: the soliton form factor $F(k^2/\Lambda^2)$ suppresses graviton modes above $k \sim 1/l_P$, cutting off all loop divergences without regularization. The graviton propagator is modified at Planck energies: $D(k) \to D(k) \times F(k^2)$ with $F(0) = 1$ (GR recovered at low energies) and $F(\infty) = 0$ (UV-finite). We derive Newton's constant from soliton parameters: $G = \hbar c^3/(8\pi \kappa_2 m_e^2)$ where $\kappa_2$ is the Faddeev-Niemi coupling. Black hole singularities are resolved: the soliton repulsion at short distances bounds the curvature at $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma} < l_P^{-4}$, replacing the singularity with a Planck-density soliton core. The Big Bang singularity is similarly resolved as a maximally compressed soliton state that bounces. We compare with string theory, loop quantum gravity, and asymptotic safety, noting that the emergent nature of gravity provides qualitatively different physics — especially for singularity resolution and the cosmological constant. <b>This is the most speculative paper in the series and is clearly labeled as such.</b> Key open problems are identified, including the need for explicit 2-loop graviton-graviton scattering calculations.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>topology</span> <span>soliton</span> <span>quantum gravity</span> <span>emergence</span> <span>graviton</span> <span>UV finiteness</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-26</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163351">10.5281/zenodo.19163351</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19349106 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quantum Gravity as Emergent Soliton Dynamics Novickis, Alexander physics topology soliton quantum-gravity emergence graviton UV-finiteness <div> <h4>Abstract</h4> <p>We present the quantum gravity theory that emerges from the topological soliton framework. Gravity is not a fundamental interaction to be quantized but an emergent phenomenon arising from the collective dynamics of the Faddeev-Niemi field $\mathbf{n}: \mathbb{R}^{3,1} \to S^2$. The graviton is an $S^3$ Goldstone mode of the Hopf medium, arising from spontaneous breaking $SO(4) \times \text{Diff}(M_4) \to SO(3) \times \text{Diff}(M_3)$. The Einstein-Hilbert action is the leading term in a derivative expansion of the effective action obtained by integrating out soliton fluctuations (Sakharov's induced gravity). UV-finiteness is automatic: the soliton form factor $F(k^2/\Lambda^2)$ suppresses graviton modes above $k \sim 1/l_P$, cutting off all loop divergences without regularization. The graviton propagator is modified at Planck energies: $D(k) \to D(k) \times F(k^2)$ with $F(0) = 1$ (GR recovered at low energies) and $F(\infty) = 0$ (UV-finite). We derive Newton's constant from soliton parameters: $G = \hbar c^3/(8\pi \kappa_2 m_e^2)$ where $\kappa_2$ is the Faddeev-Niemi coupling. Black hole singularities are resolved: the soliton repulsion at short distances bounds the curvature at $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma} < l_P^{-4}$, replacing the singularity with a Planck-density soliton core. The Big Bang singularity is similarly resolved as a maximally compressed soliton state that bounces. We compare with string theory, loop quantum gravity, and asymptotic safety, noting that the emergent nature of gravity provides qualitatively different physics — especially for singularity resolution and the cosmological constant. <b>This is the most speculative paper in the series and is clearly labeled as such.</b> Key open problems are identified, including the need for explicit 2-loop graviton-graviton scattering calculations.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>topology</span> <span>soliton</span> <span>quantum gravity</span> <span>emergence</span> <span>graviton</span> <span>UV finiteness</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-26</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163351">10.5281/zenodo.19163351</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| title | Quantum Gravity as Emergent Soliton Dynamics |
| topic | physics topology soliton quantum-gravity emergence graviton UV-finiteness |
| url | https://doi.org/10.5281/zenodo.19349106 |