An Etymological Dictionary of Astronomy and Astrophysics

A set of linear equations that expresses the time and space coordinates of one → reference frame in terms of those of another one when one frame moves at a constant velocity with respect to the other. In general, the Lorentz transformation allows a change of the origin of a coordinate system, a rotation around the origin, a reversal of
spatial or temporal direction, and a uniform movement along a spatial axis. If the system S’(x’,y’,z’,t’) moves at the velocity v with respect to S(x,y,z,t) in the positive direction of the x-axis, the Lorentz transformations will be:

x’ = γ(x - vt), y’ = y, z’ = z, t’ = γ [t - (vx/c²)], where c is the → velocity of light and γ = [1 - (v/c)²]^-1/2. For the special case of velocities much less than c, the Lorentz transformation reduces to → Galilean transformation.

See also: → Lorentz; → transformation.