SVT at a glance

Superfluid Vortex Theory (SVT) posits that the physical vacuum is a coherent quantum fluid described by a complex order parameter $\Psi(\mathbf{x},\,t)$ . Low-energy excitations come in two flavours: sound modes (linearised phonons) and topological defects (quantised vortex filaments). Together they reproduce the standard model, general relativity in the low-energy limit, and the observed cosmology.

The governing equation

The time-dependent Gross - Pitaevskii equation governs the order parameter:

i\hbar\,\partial_{t}\Psi \;=\; -\frac{\hbar^{2}}{2m}\,\nabla^{2}\Psi \;+\; V(\mathbf{x})\,\Psi \;+\; g\,|\Psi|^{2}\,\Psi

At long wavelengths ( $k\,\xi \ll 1$ ), linearised phonon excitations reproduce the Schrödinger equation for a point particle; at short wavelengths the Bogoliubov dispersion restores relativistic kinematics. Vortex cores have a natural size

\xi \;=\; \dfrac{\hbar}{\sqrt{\,2\,m\,g\,\rho_{0}\,}}

that sets the Planck scale in the effective theory.

Emergent acoustic metric

A moving background flow $\mathbf{v}(\mathbf{x},t)$ induces a Lorentzian metric for phonons — the analogue-gravity line element:

ds^{2} \;=\; \frac{\rho_{0}}{c}\Big[-\big(c^{2}-v^{2}\big)\,dt^{2} \;-\; 2\,\mathbf{v}\!\cdot\!d\mathbf{x}\,dt \;+\; d\mathbf{x}\cdot d\mathbf{x}\Big]

When $|\mathbf{v}|=c$ a sonic horizon forms; Hawking-like phonon radiation follows by the standard Unruh argument (sim_03, sim_36).

See Simulation #3 for the full sonic-horizon validation of this acoustic metric.

Variable Newton coupling

The RG flow of the condensate self-coupling produces a redshift-dependent Newton constant, fixed today by $\,G_{0}$ and normalised so that at the JWST benchmark $\,z=12\,$ we recover a factor-of-three enhancement:

\frac{G(z)}{G_{0}} \;=\; (1 + \lambda\,z)^{\gamma}, \qquad \gamma \;=\; \frac{\ln 3}{\ln(1 + 12\,\lambda)}

What emerges

Particles are stable knotted or linked vortex filaments. Their masses scale with topological rope-length and phase winding (sim_10, sim_27, sim_37, sim_42).
Quantum mechanics is the long-wavelength linear regime (sim_01, sim_17, sim_18).
Entanglement is phase braiding of paired vortices (sim_02).
Gravity is the acoustic metric induced by background flow (sim_03, sim_04, sim_36).
Dark matter is a large-scale vortex lattice (sim_06).
Dark energy is vortex-tangle tension (sim_24, sim_39).
Variable G(z) emerges from the RG flow of the vacuum superfluid (sim_05, sim_11, sim_19, sim_38, sim_43).

Why GPE?

The Gross - Pitaevskii equation is the canonical low-energy effective action of a dilute weakly-interacting Bose superfluid. It has been validated to ppm-level precision in ultra-cold atomic gases, helium-II, and polariton condensates. SVT treats the vacuum as one more realisation of the same class, with couplings set by Planck-scale data.

Numerical laboratory

Every SVT claim on this site corresponds to at least one finite-size GPE simulation that can be rerun locally. 32 sims run on CPU; 5 are native 3D and GPU-accelerated via CuPy (see sim_33 - sim_37). Seven additional sims (sim_38 - sim_44) compare the SVT predictions against pinned 2025 / 26 observational data.