This need not surprise us either, if we will but reflect that the second velocity effects a second revision of length and time measurements between the systems involved. And now, if we let either v, or u, or even both of them, take the value C, the resultant still is C. In another way we have found C to behave like the mathematician’s infinity, to which, in the words of the blind poet, if we add untold thousands, we effect no real increment.
Assumption and Consequence
A good many correspondents who have given the subject sufficient thought to realize that the limiting character of the velocity C is really read into Einstein’s system by assumption have written, in more or less perturbed inquiry, to know whether this does not invalidate the whole structure. The answer, of course, is yes—provided you can show this assumption to be invalid. The same answer may be made of any scientific doctrine whatever, and in reference to any one of the multitudinous assumptions underlying it. If we were to discover, tomorrow, a way of sending signals absolutely instantaneously, Einstein’s whole structure would collapse as soon as we had agreed to use this new method. If we were to discover a signalling agent with finite velocity greater than that of light, relativity would persist with this velocity written in its formulae in the place of C.
It is a mistake to quote Einstein’s theory in support of the statement that such a velocity can never be. An assumption proves its consequences, but never can prove itself; it must remain always an assumption. But in the presence of long human experience supporting Einstein’s assumption that no velocity in excess of C can be found, it is fair to demand that it be disputed not with argument but with demonstration. The one line of argument that would hold out a priori hope of reducing the assumption to an absurdity would be one based on the familiar idea of adding velocities; but Einstein has spiked this argument before it is started by replacing the direct addition of velocities with another method of combining them that fits in with his assumption and as well with the observed facts. The burden of proof is then on the prosecution; anyone who would contradict our assertion that C is the greatest velocity attainable may do so only by showing us a greater one. Until this has been done, the admission that it may properly be attempted can in no way be construed as a confession of weakness on the part of Einstein.
It may be well to point out that in no event may analogy be drawn with sound, as many have tried to do. In the first place sound requires a material medium and its velocity with regard to this rather than relative to the observer we know to be fixed; in the second place, requiring a material medium, sound is not a universal signalling agent; in the third place, we know definitely that its velocity can be exceeded, and are therefore barred from making the assumption necessary to establish the analogy. The very extraordinary behavior of light in presenting a velocity that is the same for all observers, and in refusing to betray the least material evidence of any medium for its transmission, rather fortifies us in believing that Einstein’s assumption regarding the ultimate character of this velocity is in accord with the nature of things.
Relativity and the Layman
A great deal can be said in the direction of general comment making the Special Theory and its surprising accompaniments easier of acceptance, and we shall conclude the present discussion by saying some of these things.]* [It has been objected that the various effects catalogued above are only apparent, due to the finite velocity of light—that the real shape and size of a body or the real time of an event cannot be affected by the point of view or the motion of an observer. This argument would be perfectly valid, if there were real times and distances; but there are not. These are earth-bound notions, due to our experience on an apparently motionless platform, with slow-moving bodies. Under these circumstances different observations of the same thing or of the same event agree. But when we no longer have the solid earth to stand on, and are dealing with velocities so high that the relativity effects become appreciable, there is no standard by which to resolve the disagreements. No one of the observations can claim to be nearer reality than any other. To demand the real size of a thing is to demand a stationary observer or an instantaneous means of information. Both are impossible.