deep_causality_metric

Metric signature types and sign conventions for Clifford algebras and physics.

Overview

This crate provides a foundational set of types for working with metric signatures in Clifford algebras Cl(p, q, r), Riemannian geometry, and physics applications.

Key Features

• Single Source of Truth: Consolidates all metric signature logic into one crate
• Zero Dependencies: Serves as a foundational leaf crate in the dependency graph
• Type-Safe Conventions: Compile-time enforcement of physics sign conventions
• Cross-Crate Integration: Enables consistent metric handling across multivector, tensor, topology, and physics crates

Core Types

Sign Conventions

Type Aliases

For domain-specific clarity:

Usage

Basic Metric Operations

use deep_causality_metric::Metric;

// Create a standard 4D Minkowski metric (West Coast convention)
let minkowski = Metric::Minkowski(4);
assert_eq!(minkowski.dimension(), 4);
assert_eq!(minkowski.sign_of_sq(0), 1);   // time is +1
assert_eq!(minkowski.sign_of_sq(1), -1);  // space is -1

// Get signature tuple (p, q, r)
assert_eq!(minkowski.signature(), (1, 3, 0));

// Create from signature
let euclidean = Metric::from_signature(3, 0, 0);
assert_eq!(euclidean, Metric::Euclidean(3));

Type-Safe Convention Wrappers

use deep_causality_metric::{EastCoastMetric, WestCoastMetric, LorentzianMetric};

// East Coast convention (-+++) for General Relativity
let east = EastCoastMetric::minkowski_4d();
assert_eq!(east.time_sign(), -1);
assert_eq!(east.space_sign(), 1);
assert!(east.is_east_coast());

// West Coast convention (+---) for Particle Physics
let west = WestCoastMetric::minkowski_4d();
assert_eq!(west.time_sign(), 1);
assert_eq!(west.space_sign(), -1);
assert!(west.is_west_coast());

Convention Conversion

use deep_causality_metric::{Metric, EastCoastMetric, WestCoastMetric};

// Convert from West Coast to East Coast
let west = Metric::Minkowski(4);
let east = EastCoastMetric::from_west_coast(west).unwrap();

// Convert back
let west_again = WestCoastMetric::from_east_coast(east.into_metric()).unwrap();

Using Type Aliases

use deep_causality_metric::{RelativityMetric, ParticleMetric, MINKOWSKI_4D};

// For GR code
fn relativistic_calculation(metric: RelativityMetric) {
    // Uses East Coast convention internally
    assert!(metric.is_east_coast());
}

// For particle physics code
fn particle_calculation(metric: ParticleMetric) {
    // Uses West Coast convention internally
    assert!(metric.is_west_coast());
}

Mathematical Background

Clifford Algebra Signature

A Clifford algebra Cl(p, q, r) over ℝⁿ where n = p + q + r is defined by:

$$e_i \cdot e_j + e_j \cdot e_i = 2g_{ij}$$

where the metric tensor g has:

• p eigenvalues of +1
• q eigenvalues of -1
• r eigenvalues of 0 (degenerate)

Metric Variants

Feature Flags

For no_std environments, disable default features:

[dependencies]
deep_causality_metric = { version = "0.1", default-features = false, features = ["alloc"] }

License

MIT License - see LICENSE for details.