Physics

Maxwell field derivation as a four-step monadic chain

A plane-wave configuration becomes a vector potential, then an EM field, then a gauge check, then a Poynting flux. Four bind calls.

Source: examples/physics_examples/maxwell/main.rs

This example lives at examples/physics_examples/maxwell/. It is the simplest demonstration of monadic composition over a physics chain: each step is a pure function from one physical state to the next, and bind glues them.

The chain reads top-to-bottom as the textbook derivation:

PlaneWaveConfig → Vector Potential (A) → EM Field (F = ∇A) → Gauge Check → Poynting Flux

The chain

use deep_causality::PropagatingEffect;
use model::{MaxwellState, PlaneWaveConfig};

let initial_state = MaxwellState::from_config(&config);

let result: PropagatingEffect<MaxwellState> =
    PropagatingEffect::pure(initial_state).bind(|state, _, _| {
        model::compute_potential(state.into_value().unwrap_or_default())
            .bind(|s, _, _| model::compute_em_field(s.into_value().unwrap_or_default()))
            .bind(|s, _, _| model::check_lorenz_gauge(s.into_value().unwrap_or_default()))
            .bind(|s, _, _| model::compute_poynting_flux(s.into_value().unwrap_or_default()))
    });

let final_state = result.value.into_value().unwrap_or_default();

Each bind receives the upstream MaxwellState and returns a new PropagatingEffect<MaxwellState> with a populated downstream field. The Lorenz-gauge check fails into the chain’s error slot if the divergence is non-zero; the Poynting-flux step still adds its log entry on top of whatever ran before it.

What to look at in the source

model.rs: MaxwellState, PlaneWaveConfig, and the four step functions. The implementation uses the deep_causality_multivector crate for geometric-algebra operations.
main.rs: the chain plus the result-extraction block that prints the field magnitudes, the gauge verdict, and the Poynting flux.

The crate ships sibling examples for GRMHD, quantum mechanics, thermodynamics, and fluid dynamics. They live alongside Maxwell under examples/physics_examples/.

Run it

git clone https://github.com/deepcausality-rs/deep_causality
cd deep_causality
cargo run --release -p physics_examples --example maxwell_example

The output prints the vector potential, the E and B fields, the Poynting flux, and the divergence test for the Lorenz gauge.

Why this is a good fit

A physics derivation is a sequence of well-defined transformations on a state. The monadic form preserves that sequence as a value: the chain can be tested, refactored, replayed against a different initial configuration, or extended with an extra step without rewriting the surrounding code.