# Lorentz covariance

(Redirected from Lorentz invariant)

In physics, Lorentz covariance is a key property of spacetime that follows from special theory of relativity. Lorentz covariance requires that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. Quantities which remain the same under Lorentz transformations are said to be Lorentz invariant (i.e. they transform under the trivial representation).

According to the representation theory of the Lorentz group, Lorentz covariant quantities are built out of scalars, four-vectors, four-tensors, and spinors.

The space-time interval is a Lorentz-invariant quantity, as is the Minkowski norm of any four-vector.

Equations which are true in any inertial reference frame are also said to be Lorentz covariant (some use the term invariant here). Lorentz covariant equations can always be written in terms Lorentz covariant quantities. According to the principle of relativity all fundamental equations of physics must be Lorentz covariant.

Note: this usage of the term covariant should not be confused with the related concept of a covariant vector. On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Confusingly, both covariant and contravariant four-vectors can be Lorentz covariant quantities.

## Local Lorentz covariance

Local Lorentz covariance refers to Lorentz covariance applying only locally.