For instance, the resultant of two velocities, each equal to a hundred kilometres a second (which is far higher than any velocities obtainable by Galileo and Newton), amounts to, not 200 kilometres, but 199·999978 kilometres. The difference is scarcely twenty-two millimetres in 200 kilometres! We can quite understand that the earlier experimenters could not detect differences even less minute than that.
Amongst the verifications of the new law of composition of velocities we may quote one, the outcome of an early experiment of the great Fizeau, which is very striking.
Imagine a pipe full of some liquid, such as water, and a ray of light travelling along it. We know the speed of light in water: it is much lower than in air or in empty space. Suppose, further, that the water is not stationary, but flows through the pipe at a certain speed. What will be the velocity of the ray of light when it leaves the pipe after traversing the moving liquid? That was what Fizeau, with many variations of the conditions of the experiment, tried to ascertain.
The velocity of light in water is about 220,000 kilometres a second. There is question here of so rapid a propagation that there is a great difference between the law of addition of the old classical mechanics and of Einsteinian mechanics. Now the results of Fizeau’s experiment are in complete harmony with Einstein’s formula, and are not in harmony with that of the older mechanics. Many observers, including, recently, the Dutch physicist Zeeman, have repeated Fizeau’s experiment with the greatest care, but the result was the same.
When Fizeau made the experiment in the last century, attempts were made to interpret his results in the light of the older theories. This, however, led to very improbable hypotheses. Fresnel, for instance, trying to explain Fizeau’s results, had been compelled to admit that the ether is partially borne along by the water as it flows, and that this partial displacement varies with the length of the luminous waves sent through, or that it is not the same for the blue as for the red waves! A very startling deduction, and one very difficult to admit.
The new law of composition of velocities given to us by Einstein, on the other hand, immediately and with perfect accuracy explains Fizeau’s results. They are opposed to the classical law.
The facts, the sovereign judges and criteria, show in this case that the new mechanics corresponds to reality; the earlier mechanics does not, at least in its traditional form. Here is something, therefore, which enables us to see at once the profound truth (scientific truth being what is verifiable), the beauty, of the doctrine of Einstein: something which shows us, superbly, how a scientific, a physical, theory differs from an arbitrary and more or less consistent philosophical system.
Experience, the supreme judge, decides in favour of the Einsteinian mechanics against the older mechanics. We shall see further examples; and we shall not find a single case in which the verdict is the other way.