| _version_ | 1866901807824896000 |
|---|---|
| author | Miranda A., Luis M. |
| author_facet | Miranda A., Luis M. |
| contents | <p>We present a first-principles derivation of Newtonian gravity and Schwarzschild spacetime from the hydrodynamics of a compressible quantum vacuum. The vacuum is modeled as a macroscopic quantum fluid characterized by a density, velocity field, and an equation of state fixed by standard quantum statistical mechanics. Assuming only mass conservation, energy conservation, and thermodynamic consistency, we show that a unique radial stationary solution exists, leading unavoidably to an inverse-square force law and an effective spacetime geometry equivalent to that of General Relativity. This derivation relies strictly on the thermodynamic properties of an Ideal Quantum Gas with a polytropic index $\gamma=5/3$. We demonstrate that this specific value is not a tunable parameter but a requirement for the existence of stable, finite-energy stationary solutions. We further provide a dimensional analysis proving the absence of hidden fine-tuning, a linear stability analysis of the background flow, and a rigorous derivation of the acoustic metric in the Painlevé-Gullstrand form. The theory is explicitly falsifiable at experimental, observational, and numerical levels.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17943428 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | General Relativity as the Hydrodynamics of a Polytropic Quantum Vacuum Miranda A., Luis M. Emergent Gravity, Superfluid Vacuum, Analog Gravity, Schwarzschild Metric, Polytropic Gas, Quantum Hydrodynamics, General Relativity, Cosmology <p>We present a first-principles derivation of Newtonian gravity and Schwarzschild spacetime from the hydrodynamics of a compressible quantum vacuum. The vacuum is modeled as a macroscopic quantum fluid characterized by a density, velocity field, and an equation of state fixed by standard quantum statistical mechanics. Assuming only mass conservation, energy conservation, and thermodynamic consistency, we show that a unique radial stationary solution exists, leading unavoidably to an inverse-square force law and an effective spacetime geometry equivalent to that of General Relativity. This derivation relies strictly on the thermodynamic properties of an Ideal Quantum Gas with a polytropic index $\gamma=5/3$. We demonstrate that this specific value is not a tunable parameter but a requirement for the existence of stable, finite-energy stationary solutions. We further provide a dimensional analysis proving the absence of hidden fine-tuning, a linear stability analysis of the background flow, and a rigorous derivation of the acoustic metric in the Painlevé-Gullstrand form. The theory is explicitly falsifiable at experimental, observational, and numerical levels.</p> |
| title | General Relativity as the Hydrodynamics of a Polytropic Quantum Vacuum |
| topic | Emergent Gravity, Superfluid Vacuum, Analog Gravity, Schwarzschild Metric, Polytropic Gas, Quantum Hydrodynamics, General Relativity, Cosmology |
| url | https://doi.org/10.5281/zenodo.17943428 |