# Special Case of Equal Mass Particles

For incoming electrons moving only in the z-direction, we can write

We can perform a Lorentz transformation to the Center of Mass frame, with zero total momentum

Without knowing the values for gamma or beta, we can utalize the fact that lengths of the two 4-momenta are invariant

This gives,

Using the fact that

since the rest mass energy of the electrons remains the same in inertial frames.

Substituting, we find

This confirms that the mass remains constant between the frames of reference.