, the velocity of light, is finite, as before, but is identical with the invariant velocity, which is therefore also finite. We also understand the deep-seated reason for the curious complicated form of the relativistic space and time transformations when we pass from one Galilean frame to another (the Lorentz-Einstein transformations) as contrasted with the classical transformations. We realise now that this more complicated form is due to the fact that the real world is one of space-time, and not of separate space and time, as was formerly believed.
Before closing this chapter, there is a point which we feel it advisable to discuss more fully. It deals with purely formal definitions in physics, and in particular with that of the critical velocity. We have mentioned that definitions which profess to dispense with the use of the rod, clock and physical measurements in general, are recognised as impossible. Einstein has repeatedly stressed this fact.
Possibly these points will be best understood if we discuss an illustration of a purely formal definition given by Dr. Whitehead. Thus, he writes:
“Experiment shows that this critical maximum velocity is a near approximation to the velocity of light in vacuo, but its definition in no way depends upon any reference to light.”[67]
Now any physicist would readily agree with this statement were it Dr. Whitehead’s desire merely to obviate an appeal to light propagation in the definition of the critical velocity of relativity. For, as we have seen, the critical or maximum velocity can be defined and has been defined by other physical means. Indeed, so far as we know, the existence of the critical velocity is not contingent on that of light. But Whitehead’s idea, it would seem from his writings, is to eliminate physical measurements entirely from the basic definitions of physics; whence his definition, or at least the nearest approach to a definition we have been able to find in his writings:
“The physical meaning of
is also well known; namely, any velocity which in any time-system is of magnitude
is of the same magnitude in every other time-system. No assumption of the existence of a velocity with this property or of the electromagnetic invariance has entered into the deduction of the kinematical equations of the hyperbolic type.”