**Momentum and energy**

Perhaps the most famous equation in physics is

** E = m c^{2}**
.

It expresses the fact that an object at rest
has a large amount of energy as a result of its mass ** m **. This energy is
significant in situations where the mass changes, for example in nuclear physics interactions where
nuclei are created or destroyed.

The energy of a moving object is of course still larger -- in Newtonian physics by an
amount given by the well-known kinetic energy formula *(1/2) m v ^{2}*.
The correct expression according to relativity is

*E = ***g**
*m c ^{2}*

*E = ***(g**
* - 1) m c ^{2}*

for the kinetic energy,
where **g** is the
same relativity factor used previously:

The momentum, which in Newtonian physics is given by *m v*, is given by

*p = ***g**
*m v*

If the velocity * v* is small compared to

If the velocity * v* approaches

The energy and momentum formulas can also be used to understand the case
of particles like the photon that have zero mass.
For the energy and momentum to remain finite in the limit m --> 0,
it must be that
g
--> *infinity*, and hence v --> c. Thus ** particles with
zero mass always travel with velocity c**. The energy and momentum
formulas imply *p/E = v/c ^{2}*, and hence