Energy and Momentum at High Speeds

Abstract

The special theory of relativity shows that the Newtonian concepts of energy and momentum need to be modified if they are to correctly describe bodies moving at high speeds. The modifications lead to the best-known prediction of the theory of relativity: Energy has mass and vice versa,

$$E = mc^2 ,$$

and they also show that the relationship between kinetic energy and momen-tum that you have frequently used, $K = \frac{{p^2 }} {{2m}} = \frac{1} {2}mv^2$, is only an approximation of the equations that are exact at all speeds. You now need to become familiar with the relativistically correct relationships and how they are used to extract information about atoms and the particles they are made of.