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, ringdown and remnants, energy, propagation, gravitons, backgrounds, lensing and cosmological distances
`gravitics`	Frontier gravity computed against general relativity and experiment, light in strong gravity, 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
Poisson's relation	a magnetised body's anomaly is its gravity gradient: `gravimetry`'s sphere and `magnetics`' sphere agree to 10⁻¹⁴, and a magnetic survey's pseudo-gravity from `geopotential::planar` is the gravity survey to 0.17%

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).

physica 0.3.3