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