Newton did not regard it as such, not as a more or less precise approximation, but as a strict truth. That is why, when he saw that the planets do not travel in straight lines but in curved orbits, he concluded—which is a petitio principii—that they were subject to a central force, gravitation. That is why heavy bodies did not seem to him amenable to the mechanical laws which he had formulated for bodies left freely to themselves. That is why, in a word, Newton’s law of gravitation and his laws of dynamics are two distinct and separate things.
The great genius, the mind which had no equal, was nevertheless human. The immortal Descartes put forward strange statements and very occult hypotheses (about the pineal gland and animal spirits), after he had expressly resolved to affirm nothing that he did not perceive clearly and distinctly. In the same way Newton, after laying down as his principle Hypotheses non fingo, put the hypotheses of absolute time and space at the very basis of his mechanics. At the basis of his masterly theory of gravitation he put the hypothesis—which is a priori easier to admit—that there is a special force of gravitation.
These are weaknesses which the greatest of men do not escape. They ought to make us admire all the more the finer aspects of their work. So deep is the furrow ploughed by these great students of the unknown that, even when it is not straight, it takes two centuries and a half before men dream of inquiring afresh whether Newton’s distinction between purely mechanical and gravitational phenomena was just.
It is the signal distinction of Einstein that he successfully accomplished this: that, after erasing many things which were supposed to be finally settled, he blended mechanics and gravitation in a superb synthesis, and enabled us to see more clearly the sublime unity of the world.
To tell the truth—let us premise this before we go further into the profound and marvellous truths of General Relativity—it is a priori evident that Newton’s law of universal attraction can no longer be considered satisfactory.
It says: Bodies attract each other in direct proportion to their masses and in inverse proportion to the square of their distances. What does that mean? We saw that the mass of a body varies with its velocity. When, for instance, we introduce the mass of our planet into calculations which involve Newton’s law, what precisely do we mean? Do we mean the mass which the earth would have if it did not revolve round the sun? Or do we mean the larger mass which it has in virtue of its motion? This motion, however, is not always of the same speed, because the earth travels in an ellipse, not a circle. What value shall we give to this variable mass in the calculation? That which corresponds to perihelion or aphelion, the period when the earth travels most rapidly or most slowly? Moreover, ought we not also to take into account the velocity of translation of the solar system, which in turn increases or diminishes according to the season?
Again, under Newton’s law what shall we make the distance from the earth to the sun? Is it to be the distance relatively to an observer on the earth or on the sun, or to a stationary observer in the middle of the Milky Way who does not share the motion of our system across it? Here again we shall have different values in each case, because spatial distances vary, as we saw with Einstein, according to the relative velocity of the observer.
Hence Newton’s law is, in spite of its simple and artistic form, ambiguous and far from clear. I am aware that the differences I have just noted are not very important, but our calculations show that they are by no means negligible. Einsteinians therefore regard it as indisputable, apart from the considerations which we shall see presently, that Newton’s law, in its classical form, is obscure, and must be modified and completed.
These preliminary remarks will serve to at least put us in the frame of mind that is required of iconoclasts; and in science the iconoclasts are often the makers of progress. The particular idols at which we are preparing to deal a few audacious blows are the conception of the Newtonian law and gravitation.