Suppose a particle has a velocity in
, then at time t its spacetime coordinates are
. In a frame
moving at
a speed v relative to
, its spacetime coordinates
will be:
The velocity in simply comes from dividing the space
parts by the time part i.e.
If and
then
This looks like the Galelian relative velocity if . If u=c,
, so we confirm the universality of the
the speed of light.