The A B C of Relativity

are not an electron, you cannot move at these terrific speeds, no man of science has ever made the observations which would prove the truth of your assertion. Nevertheless, as we shall see [Pg 24] in the sequel, there is good ground for the assertion—ground, first of all, in experiment, and—what is remarkable—ground in reasonings which could have been made at any time, but were not made until experiments had shown that the old reasonings must be wrong. There is a general principle to which the theory of relativity appeals, which turns out to be more powerful than anybody would suppose. If you know that one man is twice as rich as another, this fact must appear equally whether you estimate the wealth of both in pounds or dollars or francs or any other currency. The numbers representing their fortunes will be changed, but one number will always be double the other. The same sort of thing, in more complicated forms, reappears in physics. Since all motion is relative, you may take any body you like as your standard body of reference, and estimate all other motions with reference to that one. If you are in a train and walking to the dining-car, you naturally, for the moment, treat the train as fixed and estimate your motion by relation to it. But when you think of the journey you are making, you think of the earth as fixed, and say you [Pg 25] are moving at the rate of sixty miles an hour. An astronomer who is concerned with the solar system takes the sun as fixed, and regards you as rotating and revolving; in comparison with this motion, that of the train is so slow that it hardly counts. An astronomer who is interested in the stellar universe may add the motion of the sun relatively to the average of the stars. You cannot say that one of these ways of estimating your motion is more correct than another; each is perfectly correct as soon as the reference body is assigned. Now just as you can estimate a man’s fortune in different currencies without altering its relations to the fortunes of other men, so you can estimate a body’s motion by means of different reference bodies without altering its relations to other motions. And as physics is entirely concerned with relations, it must be possible to express all the laws of physics by referring all motions to any given body as the standard. We may put the matter in another way. Physics is intended to give information about what really occurs in the physical world, and not only about the private perceptions of separate observers. Physics must, therefore, be concerned with those features which a physical [Pg 26] process has in common for all observers, since such features alone can be regarded as belonging to the physical occurrence itself. This requires that the laws of phenomena should be the same whether the phenomena are described as they appear to one observer or as they appear to another. This single principle is the generating motive of the whole theory of relativity. Now what we have hitherto regarded as the spatial and temporal properties of physical occurrences are found to be in large part dependent upon the observer; only a residue can be attributed to the occurrences in themselves, and only this residue can be involved in the formulation of any physical law which is to have an à priori chance of being true. Einstein found ready to his hand an instrument of pure mathematics, called the theory of tensors, which enabled him to discover laws expressed in terms of the objective residue and agreeing approximately with the old laws. Where Einstein’s laws differed from the old ones, they have hitherto proved more in accord with observation. If there were no reality in the physical world, but only a number of dreams dreamed by different people, we should not expect to find any [Pg 27] laws connecting the dreams of one man with the dreams of another. It is the close connection between the perceptions of one man and the (roughly) simultaneous perceptions of another that makes us believe in a common external origin of the different related perceptions. Physics accounts both for the likenesses and for the differences between different people’s perceptions of what we call the “same” occurrence. But in order to do this it is first necessary for the physicist to find out just what are the likenesses. They are not quite those traditionally assumed, because neither space nor time separately can be taken as strictly objective. What is objective is a kind of mixture of the two called “space-time.” To explain this is not easy, but the attempt must be made; it will be begun in the next chapter.