## The Lorentz Transformation

Suppose two inertial frames

\[S, \: S'\]

coide at \[t=0\]

, with moving at constant speed \[v\]

along the \[x\]

axis of \[S'\]

.

In the inertial frame

\[S\]

, an event \[E_1\]

occurs at coordinates \[(x, y, z, t)\]

according to an observer at the origin of \[S'\]

.An observer at the origin of

\[S'\]

will measure the coordinates of \[E_1\]

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.