Lorentz invariant

In physics, Lorentz symmetry, named for Hendrik Lorentz, is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space". In everyday language, it means that the laws of physics stay the same for all observers that are moving with respect to one another with a uniform velocity. Lorentz covariance, a related concept, is a key property of spacetime following from the special theory of relativity. Lorentz covariance has two distinct, but closely related meanings:

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, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance.

In general, the nature of a Lorentz tensor can be identified by its tensor order, which is the number of free indices it has. No indices implies it is a scalar, one implies that it is a vector, etc. Furthermore, any number of new scalars, vectors, etc. can be made by contracting or creating an outer product of any kinds of tensors together, but many of these may not have any real physical meaning. Some of those tensors that do have a physical interpretation are listed (by no means exhaustively) below.

Please note, the metric sign convention such that η = diag (1, −1, −1, −1) is used throughout the article.

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