To finish with Einstein’s mechanics, let me reproduce a very suggestive application of these ideas about the identity of energy and mass.
There is in chemistry a well-known elementary law which is called “Prout’s Law.” It states that the atomic masses of all the elements must be whole multiples of the mass of hydrogen. Since hydrogen has the lightest atoms amongst all known bodies Prout’s Law started from the hypothesis that all the atoms are built up of a fundamental element, the atom of hydrogen. This supposed unity of matter seems to be more and more confirmed by the facts. On the one hand, it is proved that the electrons which come from different chemical elements are identical. On the other hand, in the transformation of radio-active bodies we find heavy atoms simplifying themselves by successively emitting atoms of helium gas. Lastly, the great British physicist Sir Ernest Rutherford showed in 1919 that by bombarding the atoms of nitrogen gas, in certain circumstances, by means of radium emanation, we can detach hydrogen atoms from them. This experiment, the importance of which has not been fully realised—it is the first instance of transmutation really effected by man—also tends to prove the soundness of Prout’s hypothesis.
Yet, when we accurately measure and compare the atomic masses of the various chemical elements, we find that they do not strictly conform to Prout’s Law. For instance, while the atomic mass of hydrogen is 1, that of chlorium is 35·46, which is not a whole multiple of 1.
But we can calculate that, if the formation of complex atoms from hydrogen upwards is accompanied, as is probable, by variations of internal energy, as a consequence of the radiation of a certain amount of energy during the combination, it necessarily follows (since the lost energy has weight) that there will be variations in the mass of the body composed, and these will explain the known departures from Prout’s Law.
In our somewhat hurried and informal excursion into the bush of the new facts which confirm the mechanics outlined by Lorentz and completed by Einstein our progress has been rather difficult. It is because, since we could not use terminology and technical formulæ which would be unsuitable in this work, we have had to be content with bold and rapid moves into the districts we wished to reconnoitre. Perhaps they have sufficed to enable the reader to understand what a revolution in the very bases of science, what an explosion amidst its age-old foundations, the brilliant synthesis of Einstein has caused. New light now streams upon all who slowly climb the slopes of knowledge: upon all who, wisely renouncing the desire to know “why,” would at least learn the “how” in many things.
A little before his death, foreseeing, with the intuition of genius, that a new era opened in mechanics, Poincaré advised professors not to teach the new truths to the young until they were steeped to the very marrow of their bones in the older mechanics.
“It is,” he added, “with ordinary mechanics that their life is concerned: it is that alone that they will ever have to apply. Whatever speed our motor-cars may attain, they will never reach a speed at which the old mechanics ceases to be true. The new is a luxury, and we must think of luxuries only when it can be done without injury to necessaries.”
I would appeal from Poincaré’s text to the man himself. For him this luxury, the truth, was a necessary. On the day in question, it is true, he thought of the young. But do men ever cease to be children? To that the master, too early taken from us, would have replied, in his grave, smiling manner: “Yes—at all events, it is better to suppose so.”