This latitude in interpretation is a characteristic of mathematical physics. What we know is certain very abstract logical relations, which we express in mathematical formulæ; we know also that, at certain points, we arrive at results which are capable of being tested experimentally. Take, for example, the eclipse observations by which Einstein’s theory as to the bending of light was established. The actual observation consisted in the careful measurement of certain distances on certain photographic plates. The formulæ which were to be verified were concerned with the course of light in passing near the sun. Although the part of these formulæ which gives the observed result must always be interpreted in the same way, the other part of them may be capable of a great variety of interpretations. The formulæ giving the motions of the planets are almost exactly the same in Einstein’s theory as in Newton’s, but the meaning of the formulæ is quite different. It may be said generally that, in the mathematical treatment of nature, we can be far more certain that our formulæ are approximately correct than we can be as to the correctness of this or that interpretation of them. And so in the case with which this chapter is concerned: the question as to the nature of an electron or a proton is by no means answered when we know all that mathematical physics has to say as to the laws of its motion and the laws of its interaction with the environment. A definite and conclusive answer to our question is not possible just because a variety of answers are compatible with the truth of mathematical physics. Nevertheless some answers are preferable to others, because some have a greater probability in their favor. We have been seeking, in this chapter, to define matter so that there must be such a thing if the formulæ of physics are true. If we had made our definition such as to secure that a particle of matter should be what one thinks of as substantial, a hard, definite lump, we should not have been sure that any such thing exists. That is why our definition, though it may seem complicated, is preferable from the point of view of logical economy and scientific caution.
CHAPTER XV:
PHILOSOPHICAL CONSEQUENCES
The philosophical consequences of relativity are neither so great nor so startling as is sometimes thought. It throws very little light on time-honored controversies, such as that between realism and idealism. Some people think that it supports Kant’s view that space and time are “subjective” and are “forms of intuition.” I think such people have been misled by the way in which writers on relativity speak of “the observer.” It is natural to suppose that the observer is a human being, or at least a mind; but he is just as likely to be a photographic plate or a clock. That is to say, the odd results as to the difference between one “point of view” and another are concerned with “point of view” in a sense applicable to physical instruments just as much as to people with perceptions. The “subjectivity” concerned in the theory of relativity is a physical subjectivity, which would exist equally if there were no such things as minds or senses in the world.
Moreover, it is a strictly limited subjectivity. The theory does not say that everything is relative; on the contrary, it gives a technique for distinguishing what is relative from what belongs to a physical occurrence in its own right. If we are going to say that the theory supports Kant about space and time, we shall have to say that it refutes him about space-time. In my view, neither statement is correct. I see no reason why, on such issues, philosophers should not all stick to the views they previously held. There were no conclusive arguments on either side before, and there are none now; to hold either view shows a dogmatic rather than a scientific temper.
Nevertheless, when the ideas involved in Einstein’s work have become familiar, as they will when they are taught in schools, certain changes in our habits of thought are likely to result, and to have great importance in the long run.
One thing which emerges is that physics tells us much less about the physical world than we thought it did. Almost all the “great principles” of traditional physics turn out to be like the “great law” that there are always three feet to a yard; others turn out to be downright false. The conservation of mass may serve to illustrate both these misfortunes to which a “law” is liable. Mass used to be defined as “quantity of matter,” and as far as experiment showed it was never increased or diminished. But with the greater accuracy of modern measurements, curious things were found to happen. In the first place, the mass as measured was found to increase with the velocity; this kind of mass was found to be really the same thing as energy. This kind of mass is not constant for a given body, but the total amount of it in the universe is conserved, or at least obeys a law very closely analogous to conservation. This law itself, however, is to be regarded as a truism, of the nature of the “law” that there are three feet to a yard; it results from our methods of measurement, and does not express a genuine property of matter. The other kind of mass, which we may call “proper mass,” is that which is found to be the mass by an observer moving with the body. This is the ordinary terrestrial case, where the body we are weighing is not flying through the air. The “proper mass” of a body is very nearly constant, but not quite, and the total amount of “proper mass” in the world is not quite constant. One would suppose that if you have four one-pound weights, and you put them all together into the scales, they will together weigh four pounds. This is a fond delusion: they weigh rather less, though not enough less to be discovered by even the most careful measurements. In the case of four hydrogen atoms, however, when they are put together to make one helium atom, the defect is noticeable; the helium atom weighs measurably less than four separate hydrogen atoms.
Broadly speaking, traditional physics has collapsed into two portions, truisms and geography. There are, however, newer portions of physics, such as the theory of quanta, which do not come under this head, but appear to give genuine knowledge of laws reached by experiment.
The world which the theory of relativity presents to our imagination is not so much a world of “things” in “motion” as a world of events. It is true that there are still electrons and protons which persist, but these (as we saw in the preceding chapter) are really to be conceived as strings of connected events, like the successive notes of a song. It is events that are the stuff of relativity physics. Between two events which are not too remote from each other there is, in the general theory as in the special theory, a measurable relation called “interval,” which appears to be the physical reality of which lapse of time and distance in space are two more or less confused representations. Between two distant events, there is not any one definite interval. But there is one way of moving from one event to another which makes the sum of all the little intervals along the route greater than by any other route. This route is called a “geodesic,” and it is the route which a body will choose if left to itself.
The whole of relativity physics is a much more step-by-step matter than the physics and geometry of former days. Euclid’s straight lines have to be replaced by light rays, which do not quite come up to Euclid’s standard of straightness when they pass near the sun or any other very heavy body. The sum of the angles of a triangle is still thought to be two right angles in very remote regions of empty space, but not where there is matter in the neighborhood. We, who cannot leave the earth, are incapable of reaching a place where Euclid is true. Propositions which used to be proved by reasoning have now become either conventions, or merely approximate truths verified by observation.
It is a curious fact—of which relativity is not the only illustration—that, as reasoning improves, its claims to the power of proving facts grow less and less. Logic used to be thought to teach us how to draw inferences; now, it teaches us rather how not to draw inferences. Animals and children are terribly prone to inference: a horse is surprised beyond measure if you take an unusual turning. When men began to reason, they tried to justify the inferences that they had drawn unthinkingly in earlier days. A great deal of bad philosophy and bad science resulted from this propensity. “Great principles,” such as the “uniformity of nature,” the “law of universal causation,” and so on, are attempts to bolster up our belief that what has often happened before will happen again, which is no better founded than the horse’s belief that you will take the turning you usually take. It is not altogether easy to see what is to replace these pseudo-principles in the practice of science; but perhaps the theory of relativity gives us a glimpse of the kind of thing we may expect. Causation, in the old sense, no longer has a place in theoretical physics. There is, of course, something else which takes its place, but the substitute appears to have a better empirical foundation than the old principle which it has superseded.