Lorentz scalar

In a relativistic theory of physics, a Lorentz scalar is a scalar which is invariant under a Lorentz transformation. A Lorentz scalar may be generated from multiplication of vectors or tensors. While the components of vectors and tensors are in general altered by Lorentz transformations, scalars remain unchanged.

A Lorentz scalar is not a scalar in the mathematical sense, that is, invariant under any basis transformation. For example, the determinant of the matrix of basis vectors is a number that is invariant under Lorentz transformations, but it is not invariant under any basis transformation.

In special relativity the location of a particle in 4-dimensional spacetime is given by

where ${\displaystyle \mathbf {x} =\mathbf {v} t}$ is the position in 3-dimensional space of the particle, ${\displaystyle \mathbf {v} }$ is the velocity in 3-dimensional space and ${\displaystyle c}$ is the speed of light.

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