In physics, the invariant interval is the measure of separation between two arbitrarily close events

Event (relativity)

In physics, and in particular relativity, an event indicates a physical situation or occurrence, located at a specific point in space and time. For example, a glass breaking on the floor is an event; it occurs at a unique place and a unique time, in a given frame of reference.Strictly speaking, the...

 in the spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

 of general

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 or special

Special relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

 theory of relativity. It is invariant under the coordinate transformations from the covariance group

Covariance group

In physics, covariance group is a group of coordinate transformations between admissible frames of reference . The frames are assumed to provide equivalent description of physical phenomena...

 of the theory. That is, in special relativity it is invariant under Lorentz transformation

Lorentz transformation

In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...

s; in general relativity it is invariant under arbitrary invertible differentiable coordinate transformations.

The invariant interval is usually denoted as and is given in terms of the metric tensor

Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...

as
where is the coordinate differential between the two events.