Note that in this definition Dr. Whitehead has failed to identify
with either Maxwell’s constant or any other physical magnitude. Thus
is some unspecified magnitude; and we may express Dr. Whitehead’s definition in more familiar language as follows:
“The critical or maximum velocity is a velocity of undetermined value which may or may not be demanded by the world-structure. If, however, it should exist, it will be given by the same invariant in every Galilean frame, whatever the value of this invariant may be.”
In this definition no reference is made to any physical phenomena or laws, and this is the aspect which appears to constitute its superiority in Whitehead’s opinion. But the trouble is that if physical measurements or the existence of physical laws established empirically by the use of rod, clock, etc., are to be discarded, the definition turns out to be no definition at all. For what sort of definition is one which fails to apprise us of the magnitude of the velocity it proposes to define? The definition of the velocity of sound, for example, is that of a velocity of so many feet a second under specified conditions of observation. A definition which failed to give us this information would be no definition of the velocity of sound.
Now it might be contended that the precise magnitude of the invariant velocity is a matter of minor importance, and that its property of invariance (mentioned in the definition) is the fundamental point. We may safely say, however, that no physicist could ever subscribe to this view. Our entire outlook on nature depends essentially on the value of this invariant velocity.
If it is finite, and if, in addition, it is equal in value to Maxwell’s constant