As a simple example, consider two particles with rest masses 
and
, moving with speeds 
and 
, which collide and
coalesce [ see Figure 2.2 ]. What is the mass M and speed U of
the resulting particle.
Figure 2.2: The colliding particles in Example 2.1.
The initial four- momenta are
where 
and
The final four- momentum is
Conservation of four- momentum gives
and squaring this relation gives
Now
and
This gives
For 
and 
, 
which is the usual
Newtonian result.
From the x and t components of the four- momentum equation we have
Dividing we get
For and we obtain
