The conservation of energy and momentum

Abstract

We have now arrived at the point where we need to take stock. In the last chapter we derived the Lorentz transformation, which we claimed was the correct transformation of the coordinates of an event from one inertial frame to another. The results were quite different from the corresponding ones for the Galilean transformation. On the other hand, the Galilean transformation did leave Newton’s equations form invariant. The question then remains, how do these equations transform under the Lorentz transformation? Are they form invariant? If they are not, we seem to be in the same difficulty that led us to derive the new transformation, namely that half of nineteenth-century physics does not satisfy the principle of relativity.