Page "Relativistic mechanics" Paragraph 15

There are a couple of ( equivalent ) ways to define momentum and energy in SR. One method uses conservation laws.

If these laws are to remain valid in SR they must be true in every possible reference frame.

However, if one does some simple thought experiments using the Newtonian definitions of momentum and energy, one sees that these quantities are not conserved in SR. One can rescue the idea of conservation by making some small modifications to the definitions to account for relativistic velocities.

It is these new definitions which are taken as the correct ones for momentum and energy in SR.