Suppose a body is moving with speed v in relation to a given reference. As the total energy AND of this body is given by:
And the amount of motion (linear momentum) can be obtained by:
It should be emphasized that:
A body with nonzero rest mass cannot reach the speed of light in a vacuum, since if we do v tend to ç, the mathematical expressions of energy and linear momentum will tend to infinity, which is absurd.
The expression that relates total energy to the amount of motion is given by:
Suppose that the resting mass of a particle is null, the expression above becomes:
So a particle with m0= 0 moves with velocity equal to ç. This is the case of photons, which have no resting mass. However, the linear momentum of the photons is not null and, therefore, can be obtained from the equation below: