The preceding examples teach us two things: First of all, it is not sufficient to state that a concept is a relative; we must complete our statement by stipulating with respect to what surrounding conditions this concept happens to be relative: whether it be, e.g., to the distance of the observer, to his motion, or to the distribution of matter. Secondly, we see that the only experimental means we have of distinguishing a relative quantity from an absolute is by varying surrounding conditions and by modifying the nature of the motion and the position of the observer. Were the value of the quantity to vary under these conditions, we should be assured that it was a relative. But obviously it may be impossible for us to vary all surrounding conditions; we cannot vary, for instance, the star distribution. Inasmuch as in this universe the whole influences the part and the part influences the whole, it would appear that our differentiations between absolutes and relatives might reduce to a mere expression of our limitations.
This view is undoubtedly correct in theory, but it must be remembered that physics can proceed only by successive approximations. For example, experiment proves that the action of a certain phenomenon on another decreases with the distance. The physicist is therefore perfectly entitled to assume that if the disturbing cause is far enough removed its influence can be neglected. In this way, by a process of progressive elimination, he is enabled to conceive phenomena to proceed in complete isolation from all foreign disturbing influences. Henceforth it will be these ideally isolated phenomena which he will subject to the tests of relativity by submitting them in succession to those foreign influences over which he can exercise some control. Under these conditions the question of the absoluteness or the relativity of a given concept or magnitude acquires a definite physical meaning.
In classical science it was always assumed that a distance in space, a duration in time and a simultaneity between distant events were absolute concepts. Regardless of the relative motion or position of the observer, regardless of the distribution of matter, these concepts remained unchanged. Einstein succeeded in proving that these opinions must be erroneous, since they were incompatible with certain refined optical experiments. He showed that the relative motion of the observer could not help but exert a modifying influence. Henceforth, distance, duration and simultaneity become relatives expressing relationships between the magnitudes measured and the relative motion of the observer. Just as the visual angle under which an object appeared to an observer was in no wise immanent in the object itself, since it varied with the observer’s position, so now length, duration and simultaneity are in no wise immanent in the real world, since they vary with the observer’s motion.
Once more we must draw attention to the fact that the relativity we are discussing is essentially physical; it is posterior to our definitions of practical congruence. It follows that this relativity of distance and duration must correspond to variations which would be seen and felt. These variations are not due to mere arbitrary changes which we may introduce into our mathematical systems of measurement. They are not merely conceptual; they are perceptual.
The fact is that the systems of measurement are imposed upon us by nature, and by that we mean that they translate what we actually see and feel and not that which we might see and feel if the world happened to be such as some nebulous mathematician might posit it to be. In a similar way, Einstein in the special theory proved that mass, which classical science had considered absolute, was in reality relative, since it depended on the relative motion of the observer. The general theory of relativity went still farther, proving that mass was relative in yet another sense. It established that not only the relative motion of the observer, but also the distribution of surrounding matter, would influence the mass of a given body. In this way Mach’s premonitions were vindicated. Following the relativity of mass, a number of other concepts, such as temperature, pressure, electric and magnetic forces, and gravitational force, were in turn proved to be relative, depending on the motion of the observer.
Now, although the epithet relative in its widest sense implies relative to surrounding conditions, we shall find that in Einstein’s theory it is employed most generally with reference to the observer’s motion. A magnitude which is relative will, therefore, mean one whose value depends on the relative motion of the observer; a magnitude which is absolute will imply one whose value remains unaffected by this motion. The major aim of the theory will be to separate those magnitudes which are relative from those which are absolute. The absolute magnitudes will then be representative of the absolute, common world of which the various observers will obtain but private perspectives. This absolute world will be the world of space-time standing in contrast to the relative world of space and time.
Among the absolutes which the theory has discovered, we may mention electric charge, entropy, the velocity of light in vacuo (in the special theory, at least) and the length of what is known as the Einsteinian interval between any two points in four-dimensional space-time; this latter type of absolute holding throughout the entire theory, both special and general.
CHAPTER IX
THE PRINCIPLES OF RELATIVITY
MUCH of the difficulty which philosophers and laymen experience in understanding Einstein’s theory arises from a confusion between the different meanings that may be attributed to the concepts “relativity of space and motion.” For the student who already possesses some knowledge of classical science, confusions of this type, of course, are not to be feared. But in view of the general misconceptions on the subject we will mention briefly the various principles, elucidating them further as we come across them in the course of this book. We must name here:
1. The primordial mathematical relativity of space and time.