Struct TangentSpacetime 

pub struct TangentSpacetime { /* private fields */ }

A 4D+4D spacetime model combining position and motion, with support for curved geometry.

TangentBundleSpacetime represents an event in spacetime along with its tangent vector (velocity or proper motion). It also carries an embedded metric tensor gᵤᵥ that defines the local geometry of spacetime, allowing for proper interval calculations in curved manifolds.

This model generalizes both flat Minkowski spacetime and dynamic curved spacetime (e.g., Schwarzschild or cosmological spacetimes) by exposing its metric via the MetricTensor4D trait, and supporting runtime updates via update_metric_tensor().

Fields

• id: Unique numeric identifier
• x: X-coordinate in meters
• y: Y-coordinate in meters
• z: Z-coordinate in meters
• t: time (e.g., seconds)
• dt: Proper time velocity (usually 1.0)
• dx, dy, dz: Spatial velocity components (in meters/second)
• metric: Local 4×4 metric tensor defining the geometry

Coordinate Index Mapping

When used with the Coordinate trait, the following index mapping applies:

• 0 => x
• 1 => y
• 2 => z
• 3 => t

Curvature Support

The default metric is flat Minkowski (− + + +), but this can be replaced at runtime:

use deep_causality::*;

let mut s = TangentSpacetime::new(1, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0);

// Replace with a custom curved spacetime metric (e.g., anisotropic)
let warped = [
    [-8.98755179e16, 0.0, 0.0, 0.0],
    [0.0, 1.05, 0.0, 0.0],
    [0.0, 0.0, 0.95, 0.0],
    [0.0, 0.0, 0.0, 0.90],
];

s.update_metric_tensor(warped);
let s2 = TangentSpacetime::new(2, 2.0, 3.0, 4.0, 0.0, 1.0, 0.0, 0.0, 0.0);

let interval = s.interval_squared(&s2);
println!("Curved spacetime interval²: {interval}");

References

• J.M. Lee, Introduction to Smooth Manifolds, Springer, 2012 — Chapter 8: Tangent Bundles
• R.M. Wald, General Relativity, University of Chicago Press, 1984 — Ch. 3: Curved Spacetime Geometry

See also

• SpacetimeInterval — for causal separation calculations
• MetricTensor4D — for curvature configuration

Implementations

impl TangentSpacetime

pub fn x(&self) -> f64

pub fn y(&self) -> f64

pub fn z(&self) -> f64

pub fn position(&self) -> [f64; 3]

Returns position as [x, y, z]

pub fn velocity(&self) -> [f64; 4]

Returns velocity as [dt, dx, dy, dz]

pub fn time_velocity(&self) -> f64

Returns the coordinate-time velocity (∂t/∂τ)

pub fn spatial_velocity(&self) -> f64

Computes spatial velocity magnitude (ignoring dt)

pub fn velocity_vector(&self) -> [f64; 3]

Returns 3D velocity vector

pub fn euclidean_distance(&self, other: &Self) -> f64

Computes Euclidean spatial distance to another point

impl TangentSpacetime

pub fn new( id: u64, x: f64, y: f64, z: f64, t: f64, dt: f64, dx: f64, dy: f64, dz: f64, ) -> Self

Create a new tangent bundle point with a default Minkowski metric.

Trait Implementations

impl Adjustable<f64> for TangentSpacetime

Updates the position of the TangentSpacetime node. The metric tensor is updated via the ‘update_metric_tensor’ method.

fn adjust<const W: usize, const H: usize, const D: usize, const C: usize>( &mut self, array_grid: &ArrayGrid<f64, W, H, D, C>, ) -> Result<(), AdjustmentError>

Adjust the position of the TangentSpacetime node. The metric tensor is updated via the ‘update_metric_tensor’ method.

fn update<const W: usize, const H: usize, const D: usize, const C: usize>( &mut self, array_grid: &ArrayGrid<f64, W, H, D, C>, ) -> Result<(), UpdateError>

The default implementation does nothing to keep update optional. Override this method to implement a node update when needed. For a sample implementation, see src/types/context_types/node_types_adjustable

impl Clone for TangentSpacetime

fn clone(&self) -> TangentSpacetime

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Coordinate<f64> for TangentSpacetime

fn dimension(&self) -> usize

Returns the number of dimensions in the coordinate system (always 4).

fn coordinate(&self, index: usize) -> Result<&f64, IndexError>

Returns a reference to the coordinate value at the specified index.

Index Mapping

• 0 => x
• 1 => y
• 2 => z
• 3 => t

Errors

Returns IndexError if the index is out of bounds.

impl Debug for TangentSpacetime

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for TangentSpacetime

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Identifiable for TangentSpacetime

fn id(&self) -> u64

impl MetricTensor4D for TangentSpacetime

fn metric_tensor(&self) -> [[f64; 4]; 4]

Returns the current local metric tensor gᵤᵥ.

fn update_metric_tensor(&mut self, new_metric: [[f64; 4]; 4])

Updates the internal metric tensor to a new 4×4 matrix.

impl PartialEq for TangentSpacetime

fn eq(&self, other: &TangentSpacetime) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl SpaceTemporal<f64, f64> for TangentSpacetime

fn t(&self) -> &f64

Returns the value associated with the temporal (4th) dimension.

impl SpaceTemporalInterval for TangentSpacetime

fn time(&self) -> f64

Returns the time coordinate in seconds.

fn position(&self) -> [f64; 3]

Returns the spatial coordinates [x, y, z] in meters.

fn interval_squared(&self, other: &Self) -> f64

Computes the squared Minkowski interval between self and other.

impl Temporal<f64> for TangentSpacetime

fn time_scale(&self) -> TimeScale

Returns the unit scale of time (e.g. TimeScale::Milliseconds).

fn time_unit(&self) -> f64

Returns a reference to the numeric time unit (e.g. 0, 100, 32768).

impl Copy for TangentSpacetime

impl Spatial<f64> for TangentSpacetime

impl StructuralPartialEq for TangentSpacetime