The scalar field φ is a compressible cosmic fluid with self-generated interlocking crystalline order (liquid-crystal / quasicrystal hybrid).
| Feature | Physical Analogue | SRC Implementation |
|---|---|---|
| Interlocking lattice | Tetrahedral/hexagonal grains that shear but stay locked | Topological term **β/2 |
| Force transfer | Compression waves → gravity-like pull Shear waves → EM-like currents |
Linearised equations give two sound speeds: cₗ (compression/gravity) and cₜ (shear/light). |
| Vortices = particles | Lattice defects/dislocations (stable due to topology) | Hopfion/vortex solutions are defects with winding W. |
| Damping γ | Viscous drag | Explicit γ ∂ₜφ term. |
| Axial flow (expansion) | Global shear → cosmic expansion | Uniform background flow drives Hubble-like term. |
Speed of light: Photons are transverse shear waves → c = cₜ = √β (in natural units where ρ=1). Gravity waves are longitudinal compression at cₗ.
Bottom line: Forces propagate as elastic waves through the interlocking crystal-fluid. Vortices (particles) are stable defects. No action at a distance, no separate dark components.
See notebooks in notebooks/ for quantitative extraction of cₜ, cₗ, vortex statistics, and expansion rate.
The scalar field φ is interpreted as a compressible cosmic fluid with self-generated interlocking crystalline order (liquid-crystal / quasicrystal hybrid).
| Feature | Physical analogue | SRC implementation |
|---|---|---|
| Interlocking lattice | Grains that shear but stay locked | Term **β/2 |
| Force transfer | Compression waves → gravity Shear waves → light |
Linearised equations yield cₗ (gravity-like) and cₜ = √β (light-like) |
| Particles | Topologically stable lattice defects | Hopfions / vortices with winding number W |
| Damping γ | Viscous drag | Explicit γ ∂ₜφ term |
| Cosmic expansion | Global shear flow | Uniform background ∇φ drives Hubble-like term |
| Speed of light | Transverse shear waves | c = cₜ = √β (exact in linear regime) |
Core idea – All forces propagate as elastic waves through the interlocking crystal-fluid. Particles are stable topological defects. No action-at-a-distance, no separate dark components.
Linearised perturbations show that transverse (shear) modes propagate with exact phase speed cₜ = √β.
- Method: Exact Fourier spectral propagation (no numerical dispersion).
- Result (65,384 steps): measured cₜ = 0.01095052 (relative error 0.036% vs theoretical √β = 0.01095445).
- Figure: See
figures/wave_speed_measure.pdf(clean long-time oscillation + ultra-sharp spectral peak). - Code: Fully reproducible in
scripts/wave_speed_measure.py.
This sub-0.04% agreement confirms that transverse shear waves propagate at precisely √β, identified as the emergent speed of light.
Further details in docs/wave_speed_explanation.md.
These scripts provide simple, standalone demonstrations of key SRC concepts using real-world analogs.
scripts/ice_flexo_analog.py
2D quasi-static simulation of flexoelectricity in a bent water ice slab.
Reproduces the large measured flexoelectric coefficient (~1.14 nC/m from Wen et al., Nature Physics 2025) using scaled SRC parameters (G_shear, χ-inspired coupling).
Features temperature-dependent surface enhancement near the 160 K ferroelectric transition.
Dependencies: numpy, matplotlib
Run:python scripts/ice_flexo_analog.py
Example output: outputs/ice_flexo_T200K.png (or similar)
See also: Technical Manual Section 15.5 for the theoretical context (piezoelectric emergence and ice analog).