But suppose that for argument’s sake we wish to consider, even though it be in a purely conceptual way, a velocity greater than light—in particular, a velocity which would constitute infinite speed for any definite Galilean observer. How would a velocity of this sort manifest itself to some other Galilean observer in motion with respect to the first?—The sole point it will be necessary to stress is that this erstwhile infinite velocity could never be invariant without coming into conflict with the invariance of the velocity of 186,000 miles per second. This becomes obvious when we consider that, according to classical science, if we added any speed—say, the speed of light —to the infinite speed, we should obtain the infinite speed; whereas, in Einstein’s theory, we should obtain the speed of light. From this it follows that the premises of classical science and of relativity are incompatible. Inasmuch as it is Einstein’s theory that we propose to discuss, we shall abandon the classical belief in the invariance of the infinite velocity. Henceforth the invariant velocity of the universe is to be , or 186,000 miles per second. As for an infinite velocity, this will now become a relative, infinite for one observer, finite for another. Now it is obvious at first sight that if our space and time measurements were such as classical science believed them to be, it would be impossible for a ray of light to pass us with the same speed regardless of whether we were rushing towards it or fleeing away from it. A simple mathematical calculation shows us, however, that we can make our results of measurement compatible with the postulate of invariance provided we recognise that our space and time measurements are slightly different from what classical science had assumed. This is purely a mathematical problem and can be solved by mathematical means. It leads us, of course, to the Lorentz-Einstein transformations; and from these transformations it is easy to see that rods in relative motion must be shortened, durations of phenomena extended, and the simultaneity of spatially separated events disrupted. [Pg 163]