The Lorentz Transformation

Suppose two inertial frames

\[S, \: S'\]
coide at
, with moving at constant speed
along the
axis of

In the inertial frame

, an event
occurs at coordinates
\[(x, y, z, t)\]
according to an observer at the origin of
An observer at the origin of
will measure the coordinates of
to be
\[(x'.y',z',t')=(\frac{x-vt}{\sqrt{1-v^2/c^2}}), y, z, \frac{t-vx/c^2}{\sqrt{1-v^2/c^2}})\]
The transformation is symmetric, so
\[(x.y,z,t)=(\frac{x'+vt'}{\sqrt{1-v^2/c^2}}), y', z', \frac{t'+vx'/c^2}{\sqrt{1-v^2/c^2}})\]

The Lorentz Transformation supercedes the Galilean Transformation, which is only accurate in the limit of low speeds.