Elementary derivation of the expressions of momentum and energy in special relativity

Dedução elementar das expressões do momento e da energia na relatividade restrita

Abstract

The derivation of the expressions of momentum and energy of a particle in special relativity is often less than satisfactory in elementary texts. In some, it is obtained by resorting to quantum or electrodynamic considerations, in others by introducing non-elementary concepts, like that of a four-vector, or even misleading ones, like “relativistic mass”. Nevertheless it is possible, following ideas described by Einstein in 1935, to obtain a fully elementary derivation of these expressions based only on the Lorentz transformations, on the conservation laws, and on the Newtonian limit. The resulting argument allows for a clearer and logically consistent introduction to the basic concepts of relativistic dynamics.

Keywords:
Special relativity; Lorentz transformations; energy; momentum; conservation laws