## Galilean and Lorentz transformation

Suppose two inertial reference frames S and S’ are moving with velocity v with respect to each other. Also suppose that an observer at reference frame S measures an event as $(x, y, z, t)$ and another observer at frame S’ measures the same event as $(x', y', z', t')$. Now if we want to relate the measurements of S frame with S’ frame we have to use transformation equations.

If we take Newtonian mechanics granted then we use the Galilean transformation. Galilean or Classical transformation equations are:

$x'=x-vt$

$y'=y$

$z'=z$

$t'=t$

Notice that the time co-ordinates are measured the same by both observer—that is $t'=t$.

But if we take Special Relativity instead of Newtonian Mechanics than we use Lorentz transformation. Lorentz transformation equations are:

$x'=\frac {x-vt} {\sqrt{1-v^2/c^2}}$

$y'=y$

$z'=z$

$t'=\frac {t-vx/c^2}{\sqrt {1-v^2/c^2}}$

The fraction $\frac {1}{\sqrt {1-v^2/c^2}}$ is also called relativistic gamma $(\gamma)$.