ABSTRACT
The main physical fact underlying the theory of special relativity is the invariance of the speed of light under a change of inertial reference frame; this fact, which is theoretically borne out of Maxwell’s equations, was first experimentally verified with precision by the well-known Michelson-Morley experiment. The reference frames used in special relativity are defined so that free particles, in the absence of external fields, move with constant velocities in such inertial or “Galilean,” to use Einstein’s terminology, reference frames. Near the end of the nineteenth century, whereas the laws of Newtonian mechanics were thought to obey Galilean transforms from one inertial frame to another, it became clear that Maxwell’s equations could not be written in invariant form under such transformations, which Barut writes in the following form:
(2.1)
Here,
O
represents an arbitrary orthogonal transformation of the spatial coordinates; that is, a transformation conserving both lengths and angles, while
v
is the relative velocity between the two frames.
