The Force Transformation
In classical Newtonian mechanics force is defined as rate of change of momentum:
Special relativity changes the definition of both momentum and time, so the definition of force must change.
If we have inertial frames O and O', with O' moving along the positive x axis of O with speed u,
In the coordinate frame O'and
Substitutinginto the first of these gives
From the definition of forceso
If all the work done by a force manifests as an increase in the kinetic energy, KE, of the particle thenDividing both sides bygives