Crate physica 

physica

The whole physica family in one dependency, plus the equations its domains share.

Seven crates cover Earth’s gravity field, satellite gravimetry, gravitational waves, frontier gravity proposals, fusion plasma, magnetism and the constants behind them. They are published separately so a project can take only what it needs; this crate re-exports all of them and adds the one thing none of them can hold alone — the identities that join them, each written as a test.

Install

cargo add physica

Every crate is re-exported under its own name, so physica::magnetics::main_field::wmm2025() and magnetics::main_field::wmm2025() are the same function.

Example: three fields of the Earth through one interface

Gravity, the main magnetic field and the gravitomagnetic field of Earth’s spin are all potential fields, so one trait evaluates all three.

use physica::geopotential::{Coefficients, Field};
use physica::gravitics::gem::GravitomagneticDipole;
use physica::magnetics::main_field::wmm2025;

let mut gravity = Coefficients::zeros(3.986_004_415e14, 6_378_136.3, 2);
gravity.set(0, 0, 1.0, 0.0);
gravity.set(2, 0, -4.841_694_95e-4, 0.0);
let magnetism = wmm2025().at(2025.0);
let spin = GravitomagneticDipole { j: 5.86e33 };

let fields: [&dyn Field; 3] = [&gravity, &magnetism, &spin];
let r = 6_371_200.0 + 450e3;
let values: Vec<f64> = fields.iter().map(|f| f.magnitude(r, 0.5, 1.0)).collect();
assert!((8.0..8.8).contains(&values[0]));        // m/s²
assert!((20_000.0..60_000.0).contains(&values[1])); // nT
assert!(values[2] < 1e-5);                        // m/s², and far smaller

Example: the same equation in two domains

use physica::metrology::{C, G, MU_0};
use physica::plasmoid::fusion::spinning_shell_field;

// Inside a spinning charged shell the magnetic field is (2/3)(μ₀/4π)Qω/R; inside a spinning
// massive shell, frames are dragged at 4GMω/(3c²R). Swap μ₀/4π for G/c² and charge for mass, and
// gravity is exactly twice as strong — because the graviton has spin 2.
let (m, r, omega) = (1e4, 1.0, 300.0);
let analogue = spinning_shell_field(m, r, omega) * (G / (C * C)) / (MU_0 / (4.0 * core::f64::consts::PI));
let frame_dragging = 4.0 * G * m * omega / (3.0 * C * C * r);
assert!((frame_dragging / analogue - 2.0).abs() < 1e-12);

What is inside

Re-export	What it covers
metrology	The physical constants every crate shares
geopotential	Earth’s gravity field from spherical harmonics, the .gfc reader, the shared Field trait
gravimetry	Gravity missions and quantum sensors, GRACE processing, earthquake gravity, local forward models, atmospheric waves
gravitational	Gravitational waves from nanohertz to terahertz: detectors, inspirals, energy, propagation, gravitons, backgrounds
gravitics	Frontier gravity computed against general relativity and experiment, the Schwinger limit, gravity’s anomalies, gravitoelectromagnetism
magnetics	Earth’s magnetic field, magnetohydrodynamics, magnets, space weather
plasmoid	Fusion reactivities and Lawson, pinches, plasmoids, aneutronic power, tokamak limits
analogies	The cross-domain identities, as doc tests

The analogies

Each is an exact identity a test asserts, not a loose resemblance.

Analogy	The shared equation
One spherical-harmonic engine	gravity V with GM, R, C̄ ↔ the magnetic field with a², a, g/√(2n+1)
Spinning dipoles	both are twice as strong at the pole as at the equator
The spin-2 factor	frame dragging inside a spinning shell is exactly 2× its electromagnetic analogue
One charge-to-mass constant	√(4πε₀G) behind the extremal black hole, the weak-gravity scale, and the drift at which two protons’ magnetism matches their gravity — whose product with the proton ratio is exactly c
Pinch and filament	Bennett’s μ₀I²/4π ↔ Ostriker’s Gλ²
Schwinger and Unruh	pair-creation suppression e^(−πE_S/E) is a Boltzmann factor at the Unruh temperature
Gravity’s vacuum constants	1/(4πG) and 4πG/c² give 1/√(εμ) = c
One plasma, three crates	the plasma frequency and Alfvén speed written in gravitational, magnetics and plasmoid agree: exactly, and to the 2.7×10⁻⁴ the electrons’ mass makes

Applications

Taking the whole family at once suits work that crosses domains: evaluating Earth’s gravity and magnetic fields along one orbit, checking a frontier proposal against both the relativity and the plasma physics it invokes, or teaching where one equation reappears under another name. For a single domain, depend on that crate alone.

How it is checked

Every analogy above is a doc test, so cargo test asserts each identity to 10⁻¹² or its stated tolerance. The examples/ directory evaluates three fields of the Earth through one trait and reproduces NOAA’s published WMM2025 value at 100 km altitude. gravity_patent rebuilds the rig of US 12,417,870 (a ball on a thread between high-voltage coils, claimed to move by a gravitational field) and simulates it: the field of its coils and leads, every force and torque on the ball from five crates (charge, polarisation, gas, magnetism, the field’s own gravity, and the claim’s own model with its constants), integrated at 1 ms. It is a calibration case for the physics, so it lives in the examples, not the library. A 3D model of the same rig, computed with the same equations, is in the repository’s web/ directory.

One of eight crates in physica: physica (all of them, plus cross-domain analogies) · metrology (constants) · geopotential (the gravity field) · gravimetry (missions and GRACE) · gravitational (waves) · gravitics (frontier gravity) · magnetics (magnetism and MHD) · plasmoid (fusion plasma).

Re-exports

pub use geopotential;

pub use gravimetry;

pub use gravitational;

pub use gravitics;

pub use magnetics;

pub use metrology;

pub use plasmoid;

Modules

analogies

The same equations across gravity, electromagnetism and plasma, each stated as a test that calls the crates on both sides.