Spacetime interval

The Lorentz-invariant quantity combining the spatial and temporal separations between two events. Its sign classifies their separation as timelike, spacelike, or lightlike.

Minkowski metric: The metric that assigns spacetime intervals to pairs of events in special relativity. It defines the quadratic form whose value is the interval.
Spacetime: The four-dimensional setting in which events have spatial and temporal coordinates. The interval measures separation within this combined setting.
Euclidean distance: The ordinary straight-line distance between points in Euclidean space, derived from a positive-definite metric. Unlike Euclidean distance, the spacetime interval includes time with an opposing metric sign.
Causality (physics): The relation by which physical events can influence other events without faster-than-light signaling. Interval sign determines whether a causal signal can connect two events.
Lorentz transformation: A linear transformation between inertial coordinate systems that preserves the speed of light and the spacetime metric. It changes event coordinates while leaving their interval unchanged.
Event (relativity): A specified occurrence in spacetime, identified by a location and a time. An interval compares the coordinates of two such occurrences.
Coordinate time: The time coordinate assigned to an event in a chosen reference frame. Coordinate time between events can vary between frames, unlike their interval.
Twin paradox: A special-relativistic comparison in which twins following different paths through spacetime reunite at different ages. The elapsed ages follow different path lengths measured by proper time derived from the interval.
Timelike interval: A spacetime separation with positive squared interval under the sign convention where time contributes positively. This interval type permits a massive observer to travel between the events.
Inertial frame: A reference frame moving at constant velocity in which free bodies move uniformly. The interval connects coordinate descriptions made in different inertial frames.

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