## 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

But

Hence

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

Hence

Alsoand