Laplace wrote, in his Exposition du Système du Monde: “It is impossible to deny that nothing is more fully proved in natural philosophy than the principle of universal gravitation in virtue of mass and in inverse proportion to the square of the distance.” Nothing can better show us than this sentence of the great mathematician the importance of the step taken by Einstein when he, as we shall see, improved what had been regarded as the very type, the most perfect example, of scientific truth: the famous Newtonian law.
Gravitation, or weight, has this in common with inertia, that it is a quite general phenomenon. All material objects, whatever may be their physical and chemical condition, are both inert (that is to say, according to their mass they resist forces which tend to displace them) and heavy (they fall when they are left to themselves). But it is a strange thing, noted by Newton, though he did not realise the significance of it—he regarded it merely as an extraordinary coincidence—that the same figure which defines the inertia of a body also defines its weight. This figure is the mass of the body.
Let us return to the illustration which I used in a [previous chapter] in dealing with Einstein’s mechanics. If two trains drawn by two similar locomotives start in the same conditions, and if the velocity communicated to the first train at the end of a second is double that communicated to the second, we conclude that the inertia, the inert mass, of the second train (leaving out of account the friction with the rails) is twice as great as that of the first. If we afterwards weigh our two trains, we find that the weight of the second is similarly twice as great as that of the first.
This experiment, though crude enough in our illustration, has been made with great precision by physicists, who used delicate methods which we need not describe here. The result was the same. The inert mass and the weight of bodies are exactly expressed by the same figures. Newton saw in this a mere coincidence. Einstein found in it the key to the hermetically sealed and inviolate dungeon in which gravitation was isolated from the rest of nature. Let us see how.
There is one remarkable feature of weight or gravitation: whatever be the nature of the objects, they always fall at the same speed (apart from atmospheric resistance). This is easily proved by causing a number of different objects to fall, in the same period of time, down a long tube in which a vacuum has been created. They all reach the bottom of the tube at the same time. A ton of lead and a sheet of paper will, if they are launched into the void simultaneously from the summit of a tower, reach the ground simultaneously, with a velocity the acceleration of which is, near the ground, 981 centimetres a second. This fact was known to Lucretius. Two thousand years ago that profound and immortal poet wrote:
Nulli, de nulla parte, neque ullo
Tempore, inane potest vacuum subsistere rei,
Quin sua quod natura petit concedere pergat.
Omnia quapropter debent per inane quietum