lfm-physics 0.2.1

Lattice Field Medium physics simulation library

lfm-physics

Simulate a universe from two equations.

The Lattice Field Medium (LFM) framework runs two coupled wave equations on a discrete 3D lattice — and gravity, electromagnetism, dark matter, and cosmic structure all emerge from the dynamics. No forces injected. No constants assumed. Just a grid, two update rules, and initial noise.

Install

pip install lfm-physics

GPU acceleration (NVIDIA):

pip install lfm-physics[gpu]

Quick Start

import lfm

# 1. Create a 64³ lattice — empty space has χ = 19 everywhere
sim = lfm.Simulation(lfm.SimulationConfig(grid_size=64))

# 2. Drop a soliton (energy blob) onto the grid
sim.place_soliton((32, 32, 32), amplitude=6.0)

# 3. Let the substrate settle into equilibrium
sim.equilibrate()

# 4. Run the two equations for 5 000 steps
sim.run(steps=5000)

# 5. Measure what emerged
m = sim.metrics()
print(f"χ_min = {m['chi_min']:.2f}")   # χ dropped — a gravity well!
print(f"Wells = {m['well_fraction']*100:.1f}%")

# 6. Look at the shape of gravity
profile = lfm.radial_profile(sim.chi, center=(32,32,32), max_radius=20)
# profile['r'] and profile['profile'] — does it fall like 1/r?

Examples — Build a Universe in 14 Steps

Each example builds on the one before, from empty space to a simulated cosmos. Run them in order:

#	Example	What you'll see
1	01_empty_space.py	A grid with χ=19 everywhere — nothing happens (that's the point)
2	02_first_particle.py	Add energy → χ drops → a gravity well appears
3	03_measuring_gravity.py	Measure χ(r) and check for 1/r falloff
4	04_two_bodies.py	Two solitons attract — gravitational interaction emerges
5	05_electric_charge.py	Phase = charge: same phase repels, opposite attracts
6	06_dark_matter.py	Remove matter — the χ-well persists (substrate memory)
7	07_matter_creation.py	Oscillate χ at 2χ₀ — matter appears from nothing
8	08_universe.py	Random noise on 64³ → wells + voids → cosmic structure
9	09_hydrogen_atom.py	Proton χ-well traps an electron — energy-level ladder emerges
10	10_hydrogen_molecule.py	Two H atoms bond — bonding vs anti-bonding orbitals
11	11_oxygen.py	Heavier nucleus (8 electrons) — deeper well, richer structure
12	12_fluid_dynamics.py	40-soliton gas → Euler equation from the stress-energy tensor
13	13_weak_force.py	Turn epsilon_w on/off and measure parity asymmetry from chi + j
14	14_strong_force.py	Run color fields and measure confinement proxy via chi line integrals

cd examples
python 01_empty_space.py    # 30 seconds
# ... work through each one ...
python 08_universe.py       # the payoff
python 12_fluid_dynamics.py # fluid velocity from wave mechanics

Interactive tutorials with visualisations: https://emergentphysicslab.com/tutorials

What is LFM?

Two coupled wave equations on a cubic lattice:

GOV-01 — what matter does:

∂²Ψ/∂t² = c²∇²Ψ − χ²Ψ

GOV-02 — what the substrate does:

∂²χ/∂t² = c²∇²χ − κ(|Ψ|² − E₀²)

The substrate field χ starts at 19 everywhere (derived from 3D lattice geometry: 1 center + 6 face + 12 edge modes = 19). Energy (|Ψ|²) pushes χ down, creating wells. Waves curve toward low χ. That's gravity.

Complex phase differences in Ψ create interference — constructive (repulsion) or destructive (attraction). That's electromagnetism.

When matter leaves a region, χ doesn't snap back instantly — the well persists. That's dark matter.

No forces are coded in. Everything emerges from the two update rules.

Measurement Tools

The library includes tools to extract physics from your simulation:

# Radial χ profile around a soliton
profile = lfm.radial_profile(sim.chi, center=(32,32,32), max_radius=20)

# Find the N brightest energy peaks
peaks = lfm.find_peaks(sim.energy_density, n=5)

# Track separation between two bodies over time
sep = lfm.measure_separation(sim.energy_density)

# Map lattice ticks to physical units (Gyr, Mpc)
scale = lfm.CosmicScale(box_mpc=100.0, grid_size=64)
print(scale.format_cosmic_time(50_000))  # "1.28 Gyr"

Documentation

• Interactive Tutorials — step-by-step guides with live visualisations
• LFM Physics Papers
• Constants — χ₀ = 19, κ = 1/63, and the rest
• Contributing

License

MIT