Lorentz transformation

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A visualisation of the Lorentz transformation (full animation). Only one space coordinate is considered. The thin solid lines crossing at right angles depict the time and distance coordinates of an observer at rest; the skewed solid straight lines depict the coordinate grid of a moving observer.

In physics, the Lorentz transformation, named after the Dutch physicist Hendrik Lorentz, 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 reflects the surprising fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.

The Lorentz transformation was originally the result of attempts by Lorentz and others to explain observed properties of light propagating in what was presumed to be the luminiferous aether; Albert Einstein later reinterpreted the transformation to be a statement about the nature of both space and time, and he independently re-derived the transformation from his postulates of special relativity. The Lorentz transformation supersedes the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). According to special relativity, this is only a good approximation at relative speeds much smaller than the speed of light.

If space is homogeneous, then the Lorentz transformation must be a linear transformation. Also, since relativity postulates that the speed of light is the same for all observers, it must preserve the spacetime interval between any two events in Minkowski space. The Lorentz transformation describes only the transformations in which the spacetime event at the origin is left fixed, so they can be considered as a rotation of Minkowski space. The more general set of transformations that also includes translations is known as the Poincaré group.