ABSTRACT
Before tackling Einstein’s law, it is as well to convince ourselves, on logical grounds, that Newton’s law of gravitation cannot be quite right.
Newton said that between any two particles of matter there is a force which is proportional to the product of their masses and inversely proportional to the square of their distance. That is to say, ignoring for the present the question of mass, if there is a certain attraction when the particles are a mile apart, there will be a quarter as much attraction when they are two miles apart, a ninth as much when they are three miles apart, and so on: the attraction diminishes much faster than the distance increases. Now, of course, Newton, when he spoke of the distance, meant the distance at a given time: he thought there could be no ambiguity about time. But we have seen that this was a mistake. What one observer judges to be the same moment on the earth and the sun, another will judge to be two different moments. ‘Distance at a given moment’ is therefore a subjective
conception, which can hardly enter into a cosmic law. Of course, we could make our law unambiguous by saying that we are going to estimate times as they are estimated by Greenwich Observatory. But we can hardly believe that the accidental circumstances of the earth deserve to be taken so seriously. And the estimate of distance, also, will vary for different observers. We cannot therefore allow that Newton’s form of the law of gravitation can be quite correct, since it will give different results according to which of many equally legitimate conventions we adopt. This is as absurd as it would be if the question whether one person had murdered another were to depend upon whether they were described by their first names or their surnames. It is obvious that physical laws must be the same whether distances are measured in miles or in kilometres, and we are concerned with what is essentially only an extension of the same principle.
