The A B C of Relativity

accident: there might be beings who would remember the future and have to infer the past. The feelings of such beings in these matters would be the exact opposite of our own, but no more fallacious. The moral of this is that, if an electron is only known by its “effects,” there is no reason to suppose that anything exists except the “effects.” In so far as these “effects” consist of light waves [Pg 216] and other electromagnetic disturbances, we may say that what is called “empty space” consists of regions where these disturbances are propagated freely. Every such disturbance, we find, has a center, and when we get very near the center (though still at a finite distance from it) we find that the law of propagation of the disturbance ceases to be valid. This region within which the law does not hold is called “matter”; it will be an electron or proton according to circumstances. The region so defined is found to move relatively to other such regions, and its movements follow the known laws of dynamics. So far, this theory provides for electromagnetic phenomena and the motions of matter; and it does so without assuming that “matter” is anything but systems of electromagnetic phenomena. In order to carry out the theory fully, it would no doubt be necessary to introduce many complications. But it seems fairly clear that all the facts and laws of physics can be interpreted without assuming that “matter” is anything more than groups of events, each event being of the sort which we should naturally regard as “caused” by the matter in question. This does not [Pg 217] involve any change in the symbols or formulæ of physics: it is merely a question of interpretation of the symbols. 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 [Pg 218] 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.