Part 1 — CHAPTER VIII THE MEANING OF THE WORD RELATIVITY

ALL our previous discussions and explanations have been made in order to prepare the ground for Einstein's theory of relativity. However, before we proceed to discuss Einstein’s theory proper, it may be useful to reach a more precise understanding of the scientific meaning of the words “relativity” and “absoluteness.”

In traditional philosophy an absolute reality is the primary, self-existing reality, the substance, the true being or the metaphysical reality, whereas a relative reality is a secondary, dependent reality owing its form of being to a relation of the genuinely real.[35]

Now, so far as scientific philosophy is concerned, absolute reality is a myth. All we can ever become cognisant of in nature reduces in the final analysis to structure, that is, to relationships. Hence, if we adopt this very general understanding of the word “relativity,” we may anticipate even at this stage that Einstein’s theory can add nothing to our belief in the fundamental relativity of all knowledge. Obviously, then, when physicists speak of absolutes and relatives, they are referring to categories of a nature differing from those of philosophers.

Consider, for instance, the length of an object, or again the comparison of two lengths situated in different parts of space. We have seen, when discussing mathematical space, that according to our measuring standards, which were conventional, these lengths might be equal or unequal; and it was this aspect of relativity which expressed the fundamental mathematical relativity of length. But we also saw that although in theory the definition of congruence was conventional, in practice, if we wished to define congruence so as not to enter into conflict with our sense perceptions, a definite type of congruence (practical congruence) was imposed upon us by nature. We saw further that bodies which were thereby defined as congruent constituted what are known as Euclidean solids, and that these were assumed to remain absolute in length, regardless of the observer’s motion.

Under these circumstances, when a physicist such as Einstein, in contradistinction to a mathematician, asserts that length is relative, he is referring to the actual length measured out by a so-called rigid body; and he wishes to imply that this length will turn out to be indeterminate and to depend essentially on our conditions of observation. We see, therefore, that the relativity of the physicist is not inevitable, as is that of the mathematician. It is not an a priori type of relativity expressing a trivial relativity to standard. It is essentially an empirical type of relativity, always subject to proof or disproof by precise empirical tests. The two following illustrations may be helpful:

Consider a telegraph pole rising vertically from the ground. The visual angle under which this pole will appear to us is essentially relative, since it varies in value with the distance of the observer from the pole. Of course, this visual angle is fundamentally relative, since its value depends on the system of geometry we may adopt, but we are no longer discussing this mathematical aspect of relativity. We are assuming that our system of measurements has been fixed according to the requirements of practical congruence, i.e., that our measurements are performed with ordinary rigid rods and hence are Euclidean. In this event the visual angle under which we perceive a given pole is perfectly determinate when our distance from the pole is specified. But, on the other hand, it is relative, inasmuch as it is not immanent in the pole; it varies with our relative distance and thereby reduces to a mere relationship between the pole and our distance therefrom.

In contradistinction to the relativity of the visual angle, classical science considered that the length of the pole itself was absolute, being irrelevant to our relative position as observers. Once again, if we argue as mathematicians, we may claim that this length in turn is relative, since it depends on our measuring conventions. But if we assume that our measuring conventions have been fixed by the requirements of practical congruence, this type of relativity is excluded. Such being the case, classical science believed that the length of the pole was an absolute, inasmuch as its numerical value was so many feet or so many metres regardless of our position and regardless of our motion. It is this last assumption that is contested by Einstein. The absolute magnitude is not the length of the pole; for this, analogously to visual angle, is relative. The absolute magnitude is rather a something which transcends space and time, and relates to the absolute world of space-time.

A second illustration may be given by the concepts of mass and weight. As a result of Newton’s discoveries, the weight of a body was realised to be relative, since its value varied with the proximity and distribution of matter. On the earth’s surface the value was so many tons, on the surface of the moon it was considerably reduced, and in interstellar space it vanished completely. A body of itself had no weight. Weight was not immanent in the body; it reduced to the mere expression of a physical relationship between the position of the body and that of surrounding matter.

In contradistinction to the relativity of weight, classical science assumed that mass was absolute. The mass of a body, wherever situated and in whatever circumstances observed, was supposed to be an invariant remaining always the same. For this reason, mass, in contrast to weight, was assumed to be immanent in matter. It was not the result of a physical relationship, but was a reflection of the very existence of matter.

True, when Bucherer’s experiments had shown that the mass of an electron appeared to increase with its velocity, mass unquestionably appeared to be relative. But it was assumed that this apparent increase in the mass of the electron was to be ascribed not to any variation in the mass of the electron itself, but to a deformation of its electromagnetic field brought about by motion through the ether. It was as though the ether was dragged along by the electron in its motion, just as a ship moving through the ocean carries along a more or less considerable volume of surrounding water according to the speed with which it is moving. In other words, there had been no real change in the mass of the electron itself, and this belief of classical science was expressed by the principle of the conservation of mass.

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.