Jules Verne described this state of things in the projectile which he imagined taking his heroes from the earth to the moon, at the moment when the romantic projectile reaches the “neutral point”: that is to say, the point where it leaves the earth’s sphere of gravitation, but has not yet entered that of the moon. We might add that Jules Verne perpetrated a few little scientific heresies in connection with his projectile. In particular, he forgot that, in compliance with what is most conspicuously evident in the principle of inertia, the unfortunate passengers ought to have been flattened like pancakes against the bottom of the projectile when the charge was fired. He also wrongly supposed that objects ceased to have weight in the projectile only at the point where it was exactly between the two spheres of attraction, that of the earth and that of the moon.
But let us overlook these trifles and return to the admirable illustration he has prophetically provided for our convenience in explaining Einstein’s system.
Let us take the projectile when it begins to fall freely toward the moon.[9] It is evident that from this point onward, until it lands on the moon, it will behave exactly like the lift which we have described.
During this fall upon the moon the passengers, if they have miraculously escaped being flattened at the start, will see the various objects about them suddenly deprived of their weight, floating in the air, and, at the slightest shake, adhering to the walls or the vaulted roof of the projectile. They will feel themselves extraordinarily light, and they will be able to make prodigious leaps without any effort. This is because they and all the objects about them fall toward the moon with the same velocity as the projectile. Hence the disappearance of weight or gravitation, which vanish as if spirited away by some magician. The magician is the properly accelerated movement, the unimpeded fall of the observers.
In a word, to get rid of the apparent effects of gravitation in any place whatever it is enough for the observer to acquire a properly accelerated velocity. That is what Einstein calls the “principle of equivalence”: equivalence of the effects of weight and of an accelerated movement. The one cannot be distinguished from the other.
Let us imagine Jules Verne’s projectile and its unfortunate passengers transported a long distance from the moon, the earth, and the sun, to some deserted and glacial region of the Milky Way where there is no matter, and so remote from the stars that there is no longer any weight or attraction. Let us suppose that our projectile is abandoned there, and motionless. It is clear that in these circumstances there will be no such thing as high or low—no such thing as weight—for the passengers. They will find themselves relieved of every inconvenience of weight. They may, if they choose, stand on the inner wall of the upper part of the projectile or on the floor, as it was when they were falling upon the moon.
Now let us suppose that the wizard Merlin quietly approaches and, fastening a cord to the ring on the top of the projectile, begins to drag it with a uniformly accelerated movement. What will happen to the passengers? They will notice that they have suddenly recovered their weight, and that they are riveted to the floor of the projectile, much as they were drawn to the surface of our planet before they left it. Indeed, if the motion of Merlin is accelerated 981 centimetres a second, they will have exactly the same sensations of weight as they had on the earth.
They will notice that if they throw a plate into the air at a given moment, it will fall upon the floor and be broken. “This is,” they will think, “because we are again subject to weight. The plate falls in virtue of its weight, its inert mass.” But Merlin will say: “The plate falls because, on account of its inertia, it has retained the increasing velocity which it had at the moment when it was thrown. Immediately afterwards, as I drew the projectile with an accelerated movement, the ascending velocity of the projectile was greater than that of the plate. That is why the bottom of the projectile, in its accelerated ascending course, knocked against the plate and broke it.”
This proves that the weight or gravitation of a body is indistinguishable from its inertia. Inert mass and heavy mass are not, as Newton supposed, two things which happen by some extraordinary coincidence to be equal; they are identical and inseparable. The two things are really one.