The result of the Michelson experiment, the impossibility of proving any velocity of the earth in relation to the medium in which light is propagated, amounts to this: we have no means whatever of detecting a speed higher than that of light. This consequence of the Michelson experiment will be better understood, perhaps, if we put it in a tangible form. Here is an illustration that will serve our purpose.
In some astronomical novel an imaginary observer is supposed to recede from the earth at a speed greater than that of light—at 300,000 miles a second, let us say—yet to keep his eyes (armed with prodigious glasses) steadily fixed on this little globe of ours.
What will happen? Evidently, our observer will see the train of earthly events in inverse order, because in the course of his voyage he will catch up in succession the luminous waves which left the earth before him. The farther away they are, the longer it must be since they left the earth. After a time our man, or our superman, will witness the Battle of the Marne. He will first see the field strewn with the dead. Gradually the dead men will rise and join their regiments, and presently they will be seen in groups in Gallieni’s taxis, which will travel backwards at full speed to Paris, arriving in the midst of a population that is extremely anxious about the issue of the struggle, and the soldiers will, naturally, be unable to give them any news. In a word, our observer will, if he recedes from the earth at a speed greater than that of light, see terrestrial events happening as if he were ascending the stream of time.
It would be very different if the observer remained stationary, and the earth receded from him at a speed of 300,000 miles a second. What would happen then? It is clear that in this case our observer will see terrestrial events, not in inverse order, but as they are: except that they would seem to him to take place with majestic slowness, because the rays of light which leave the earth at the end of some particular event will take a much longer time to reach him than the rays which left the earth at the beginning of the event.
In sum, the phenomena observed by him being essentially different in the two cases, our imaginary observer would be able to say whether it is he who is receding from the earth or the earth that is receding from him; to detect the real movement of the event through space. This means, of course, movement relatively to the medium of the propagation of light, not necessarily, as we saw, movement in relation to absolute space.
The experiment we have imagined could not very well be carried out with the actual resources of our laboratories. We cannot attain these fantastic speeds, and even if we could the observer would not distinguish much. But we have chosen a colossal instance, and the results of it would be colossal, as there would be question of nothing less than a reversal of the order of time.
If we were to use more modest means, the results will be more modest, but according to the older theories they ought to be recorded in our instruments. But the Michelson experiment—a miniature version of what we have just described—shows that the differences we should expect are not observed. Therefore the premise we laid down—that there can be velocities greater than that of light in empty space—does not harmonise with reality. Hence this velocity of light is a wall, a limit that cannot be passed.
Now let us see what follows. There is at the base of classical mechanics, as it was founded by Galileo, Huyghens, and Newton, and as it is taught everywhere, a principle which is in the long run, like all the principles of mechanics, grounded upon experience. It is the principle of the composition of velocities. If a boat, which makes ten miles an hour in smooth water, sails down a river which flows at five miles an hour, the speed of the boat in relation to the bank will be, as we may find by actual measuring, equal to the sum of the two speeds, or fifteen miles an hour. This is the rule of the addition of velocities.
In a more general way, if a body starts from a state of rest, and under the action of some force takes on in a second the velocity V, what will it do if the action of the force is prolonged for another second? According to classical mechanics it will take on the velocity 2V.[7] Let us imagine an observer who is travelling at the velocity V, yet thinks he is at rest. It will seem to him, at the end of the first second, that the body is at rest (because it has the same velocity as the observer). In virtue of the Classical Principle of Relativity, the apparent movement of the body must be the same for our observer as if the rest were real. This means that at the end of the second second the relative velocity of the body in reference to the observer will be V, and, as the observer already has the velocity V, the absolute velocity of the body will be 2V. In the same way it will be 3V at the end of three seconds, 4V at the end of four seconds, and so on. Could it increase indefinitely if the force continues to act long enough? Classical mechanics says “yes.” Einstein says “no,” because there cannot be a greater velocity than that of light.