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:

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

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:

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.

From GPE data to the metric (numerical pipeline)

For a concrete, line-by-line check: take the Madelung velocity $\mathbf{v}=(\hbar/m)\,\mathrm{Im}(\Psi^*\nabla\Psi)/|\Psi|^2$ and density $\rho=|\Psi|^2$ from the same 2D PG inflow wavefunction as sim_03, insert them into the Unruh line element above with $c_s^2 = (g/m)\rho$, and compare $g_{tt}$, $g_{tx}$ on the $y=0$ axis to the coefficients obtained by substituting the analytic $v_r=-c_s\sqrt{r_h/r}$ with that same $\rho(x)$ from the grid.

• Unruh / hydrodynamic metric built from |Ψ|² and v(Ψ)
• Radial null slopes $dr/dt$ from the quadratic constraint $g_{tt}+2g_{tr}u+g_{rr}u^2=0$
• Sonic horizon as $|v|/c_s=1$ with the same constant $c_s$ as sim_03

Implemented in Simulation 58 and stress-tested to 1024² in Simulation 80. Step-by-step derivation: acoustic_metric_derivation.md.

Weak-field limit (Einstein sector)

The Newtonian acoustic potential is extracted from $g_{tt}$ in the PG fit band; Simulation 79 shows the Madelung reconstruction matches the analytic PG reference within 10 % — the pen-and-paper step toward full Einstein equations.

Gauge structure and the Standard Model

The full $U(1)\times SU(2)\times SU(3)$ structure and three generations are not derived from the 2D single-component GPE alone. What the site documents today are partial bridges (braiding, knots, PMNS / CKM numerics in dedicated sims). Simulation 56 gives a numerical U(1) holonomy + SU(2) composition toy; Simulation 77 adds non-Abelian holonomy from adiabatic ψ transport. Anomaly-level SM closure is still open.

Cosmological constraints on variable $G(z)$

Background expansion and late-time structure data (BBN, CMB distances, growth, lensing) must be shown jointly compatible with any time-varying Newton constant. The shared module context/svt_cosmo.py implements μ(a) and μ(a,k) with ΛCDM H(z) fixed; Boltzmann closure is in sim_70– sim_72. IR protection: block-spin RG in sim_73 derives z_IR without hand-tuning to 0.30. See also Open issues and the minimal growth split in Simulation 57.

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:

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 major SVT claim on this site is backed by a runnable script in the repository: CPU GPE labs, native 3D GPU sims (sim_33–sim_37, sim_65, sim_78), literature-facing comparisons (sim_38 onward), and academic-hardening tracks sim_58–sim_80 (acoustic metric, Boltzmann closure, IR protection, Bell/Koide upgrades).