The Relativistic Addition Of Velocity
The Relativistic Addition of Velocity: In classical physics, if we consider a case of a train moving with velocity with respect to ground and a passenger on the train moving with a velocity
with respect to train, Then the velocity of passanger with respect to the ground is,
....................... ( 1 )
This is simply Galilean or classical velocity addition theorem. Let us discuss how the velocities are added according to special theory of relativity.
Consider for a special case, all velocities are along x -direction of two inertial frames
and
is the laboratory frame and
- is moving frame with constant velocity
. A body moves in
frame with a velocity
and its position can be written as
. The speed of the body with respect to
frame can be calculated as follows,
where = x / t is the velocity of body with respect to
frame. This is the relativistic or Einstien velocity addition theorem.
If and
are small compared to
which is the classical result. On the other hand, if
would also be equal to
irrespective of the value of
.
Hence, when