Crate deep_causality_metric 

deep_causality_metric

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

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

Key Features

• Single Source of Truth: Consolidates all metric signature logic
• Zero Dependencies: Serves as a foundational leaf crate
• Type-Safe Conventions: Compile-time enforcement of physics sign conventions
• Cross-Crate Integration: Enables consistent metric handling

Core Types

• Metric: The core enum representing Clifford algebra signatures
• MetricError: Error type for metric operations
• LorentzianMetric: Trait for convention-specific wrappers
• EastCoastMetric: Wrapper for (-+++) convention (GR)
• WestCoastMetric: Wrapper for (+—) convention (Particle Physics)

Sign Conventions

Convention	Signature	g_{μν}	Used By
East Coast	(-+++)	diag(-1,1,1,1)	MTW, GR textbooks
West Coast	(+—)	diag(1,-1,-1,-1)	Weinberg, Particle physics

Example

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

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

// Use type-safe wrappers for convention enforcement
let east = EastCoastMetric::minkowski_4d();
assert_eq!(east.time_sign(), -1);
assert_eq!(east.space_sign(), 1);

let west = WestCoastMetric::minkowski_4d();
assert_eq!(west.time_sign(), 1);
assert_eq!(west.space_sign(), -1);

Structs

EastCoastMetric

A Lorentzian metric in East Coast (-+++) convention.

WestCoastMetric

A Lorentzian metric in West Coast (+—) convention.

Enums

Metric

Defines the metric signature of the Clifford Algebra Cl(p, q, r).

MetricError

Errors that can occur during metric operations.

Constants

MINKOWSKI_4D

Default 4D Minkowski spacetime (East Coast convention).

PARTICLE_MINKOWSKI_4D

Standard 4D Minkowski spacetime for Particle Physics.

RELATIVITY_MINKOWSKI_4D

Standard 4D Minkowski spacetime for General Relativity.

Traits

LorentzianMetric

Trait for convention-specific Lorentzian metric wrappers.

Functions

detect_convention

Attempt to detect the sign convention of a Lorentzian metric.

east_to_west

Convert an East Coast (-+++) metric to West Coast (+—).

is_lorentzian

Check if a metric is a valid Lorentzian metric (has one time dimension).

west_to_east

Convert a West Coast (+—) metric to East Coast (-+++).

Type Aliases

ParticleMetric

For Particle Physics modules: West Coast (+—)

PhysicsMetric

Default physics metric (configurable): East Coast.

RelativityMetric

For General Relativity modules: East Coast (-+++)