When two different Galilean observers measure the same object, or time the duration of the same phenomenon, their computations will differ according to the rules specified in the Lorentz-Einstein transformations. It follows that the observers may infer that they are discussing the same objects, not when their respective measurements agree according to the classical standards of absolute distance and duration, but when they agree with the new standards set by the Lorentz-Einstein transformations. Thus a definite criterion of objectivity is still possible, though its form differs from that of classical science. So in spite of the indefiniteness of the concepts on which classical science was founded (space, time, force, mass), Einstein’s theory does not deprive us of the possibility of conceiving of the existence of a common outside world.
Enough has been said even at this stage to show that Einstein’s theory cannot be considered a mere mathematical dream. The extraordinary difficulties with which classical science was confronted owing to the negative results of the experiments we have mentioned (and to numerous other problems) have disappeared. With them have vanished the miraculous compensations which Lorentz was compelled to invoke in order to explain these negative results. The complete relativity of Galilean motion explains all our troubles. Nature is no longer mischievous, but the ether or space is relative for Galilean motion. We had failed to recognise this relativity which was staring us in the face; in so doing we ourselves were the creators of our difficulties. Yet rather than abandon the classical concepts of space and time, physicists in general refused to follow Einstein. To-day criticisms have subsided (on the part of the great majority of scientists) as experiment after experiment has confirmed Einstein’s previsions. The majority of experiments, however, concerned the consequences of the theory and not its foundations. The experiments of de Sitter and Majorana have filled this gap by proving that a ray of light always passes the observer with the same invariant speed regardless of the relative velocity of observer and source.
Now one of the most important criticisms that has been directed against Einstein’s theory is that it deprives us of the possibility of conceiving of an objective ether. There is not the slightest doubt that Einstein’s theory compels us to abandon our conception of the stagnant ether of classical science, with reference to which motion could be measured. But this is not quite the same thing as holding that the theory banishes the ether entirely. Nevertheless, upon first inspection, the fact that whatever our Galilean motion may be, experiments conducted in our frame will always yield exactly the same results, would seem to relegate the ether to the realm of ghosts, making it a useless hypothesis. If this were the case we could no longer conceive of electromagnetic fields and light rays as expressing states of the ether, but should have to regard these fields as constituting independent realities of some new category, differing from matter but susceptible of existence in space without the support of a carrier, or without being the mere manifestations of its states. However, in the general theory which we shall discuss in the second part of this book we shall find that the ether is reinstated in the guise of the metrical field of space-time. But as this new ether has only its name in common with the stagnant Lorentzian ether, there does not appear to be much advantage in retaining the older appellation.
If, then, we wish to emphasise the great distinction between the classical view and the relativistic view, we must say: “According to classical science, the speed of light waves, and of electromagnetic waves generally, is constant in all directions with respect to the stagnant ether, hence also with respect to that particular observer who happens to be at rest in the stagnant ether. According to the relativistic point of view, the speed of light waves is constant throughout empty space when measured by any Galilean observer; that is, by any observer in any non-accelerated frame” (such frames being recognised by the absence of all centrifugal or inertial pushes and pulls).
For the present we are in no position to predict what would happen if the observer, instead of being posted in a Galilean frame, were situated in a non-Galilean, i.e., accelerated or rotating, frame. All the statements we have made up to this point concern only Galilean observers. Such are the restrictions which the special principle and the special theory of relativity impose upon us. It is most important to understand this fact, as many of the criticisms levelled at Einstein’s theory are due to a failure to grasp the point. As the theory now stands, acceleration and rotation remain absolute and are therefore excluded from the special principle of relativity, which refers solely to motions in space that are relative. These are Galilean motions.
Perhaps a definite illustration will make these points clearer. Consider, for example, Michelson’s latest experiment (not the celebrated one), or, again, consider Sagnac’s experiment. The essence of both these experiments is to show that a ray of light travelling round the earth in the direction of the earth’s rotation requires a longer time to return to its starting point than would be the case for a ray travelling in the opposite direction. Obviously the velocity of the light waves with reference to the earth is not the same in all directions, so that we are able to detect the rotation of the earth on which we stand. The critic then infers that Einstein’s principle of relativity is upset by experiment. But the critic fails to realise that the motion that has been detected is a rotation, hence an acceleration, and that Einstein’s special principle confines itself to denying any significance to absolute velocities, that is, to motions which are not accelerated. Had this not been the case, Einstein’s principle would have been untenable since it is a fact of common knowledge that a large number of experiments (Foucault’s pendulum, the gyroscope, etc.) are capable of revealing the earth’s rotation. It is absolute velocity and not acceleration that experiment has ever obstinately refused to reveal.
A very similar criticism consists in stating that inasmuch as the speed of light with reference to the earth’s surface is greater from east to west than from west to east, the postulate of the invariant velocity of light is refuted. But once again the same error is involved. The postulate states that the velocity of light is invariant through any Galilean frame when measured by the observer in the frame. The postulate ceases to be true in an accelerated frame, and the rotating earth does constitute an accelerated frame. True, in the negative experiments, the earth was treated as a Galilean frame; but it was always stated that this attitude was only approximately correct, and that experiments could be devised to detect the earth’s acceleration. However, the effects due to the earth’s absolute velocity (which was then assumed to exist) would have been so much more pronounced than those due to acceleration that as a first approximation we could afford to neglect these weaker effects of acceleration.
There is still another point on which we must insist, as it has given rise to a number of criticisms. The Newtonian principle of relativity stated that the velocity of matter through empty space was meaningless or relative. Einstein’s special theory of relativity, on the other hand, compels us to consider the velocity of light as an absolute. How, then, can Einstein’s special principle be a mere extension to electrodynamics or to the ether of the Newtonian principle?
To answer this question we must realise that although velocity was a relative in Newtonian science, yet there did exist one definite velocity which was assumed to be absolute. This was the infinite velocity. It was assumed that a velocity that was infinite or instantaneous for one observer would remain infinite or instantaneous for all other observers. So far, therefore, as velocity is concerned, the sole difference between Einstein and Newton is that with Einstein the absolute or invariant velocity is no longer infinite. Though very great (186,000 miles a second), it is now finite. It is this difference between the invariant velocities of Newton and Einstein which is responsible for all the major differences between classical and Einsteinian science, as will be explained more fully in a following chapter. In particular, it is this finiteness of the invariant velocity which precludes us from attaching any absolute value to shape and distance.
Viewing the question in another way, we should notice that as a matter of fact the Newtonian principle of relativity merely states that velocity of matter with respect to matter alone has physical significance. Velocity of matter through empty space is physically meaningless. It is the same in Einstein’s special principle. Einstein’s theory proves (see next chapter) that molar matter can never move with the absolute speed of light. We are therefore perfectly justified in saying that the velocity of matter remains essentially relative, since it can never attain that critical velocity (i.e. that of light) which is absolute.