That is the explanation proposed by Fitzgerald. At first it seemed to be very strange and arbitrary, yet there was, apparently, no other way of explaining the result of Michelson’s experiment.
Moreover, when you reflect on it this contraction is found to be less extraordinary, less startling, than one’s common sense at first pronounces it. If we throw some non-rigid object, such as one of those little balls with which children play, quickly against an obstacle, we see that it is slightly pushed in at the surface by the obstacle, precisely in the same sense as the Fitzgerald-Lorentz contraction. The ball is no longer round. It is a little flattened, so that its diameter is shortened in the direction of the obstacle. We have much the same phenomenon, though in a more violent form, when a bullet is flattened against a target. Therefore, if solid bodies are thus capable of deformation—as they are, for cold is sufficient of itself to concentrate their molecules more closely—there is nothing absurd or impossible in supposing that a violent wind of ether may press them out of shape.
But it is far less easy to admit that this alteration may be exactly the same, in the given conditions, for all bodies, whatever be the material of which they are composed. The little ball we referred to would by no means be flattened so much if it were made of steel instead of rubber.
Moreover, there is in this explanation something quite improbable, something that shocks both our good sense and that caricature of it which we call common sense. Is it possible to admit that the contraction of bodies always exactly compensates for the optic effect which we seek, whatever be the conditions of the experiment (and they have been greatly varied)? Is it possible to admit that nature acts as if it were playing hide-and-seek with us? By what mysterious chance can there be a special circumstance, providentially and exactly compensating for every phenomenon?
Clearly there must be some affinity, some hidden connection, between this mysterious material contraction of Fitzgerald and the lengthening of the light path for which it compensates. We shall see presently how Einstein has illumined the mystery, revealed the mechanism which connects the two phenomena, and thrown a broad and brilliant light upon the whole subject. But we must not anticipate.
The contraction of the apparatus in Michelson’s experiment is extremely slight. It is so slight that if the length of the instrument were equal to the diameter of the earth—that is to say, 8,000 miles—it would be shortened in the direction of the earth’s motion by only six and a half centimetres! In other words, the contraction would be far too small to be in any way measurable in the laboratory.
There is a further reason for this. Even if Michelson’s apparatus were shortened by several inches—that is to say, if the earth travelled thousands of times as rapidly as it does round the sun—we could not detect and measure it. The measuring rods which we would use for the purpose would contract in the same proportion. The deformation of any object by a Fitzgerald-Lorentz contraction could not be established by any observer on the earth. It could be discovered only by an observer who did not share the movement of the earth: an observer on the sun, for instance, or on a slow-moving planet like Jupiter or Saturn.
Micromegas would, before he left his planet to visit us, have been able to discover, by optical means, that our globe is shortened by several inches in the direction of its orbital movement; supposing that Voltaire’s genial hero were provided with trigonometrical apparatus infinitely more delicate than that used by our surveyors and astronomers. But when he reached the earth, Micromegas, with all his precise apparatus, would have found it impossible to detect the contraction. He would have been greatly surprised—until he met Einstein and heard, as we shall hear, the explanation of the mystery.
I have, unfortunately, neither the time nor the space—it is here, especially, that space is relative, and is constantly shortened by the flow of the pen—to give the dialogue which would have taken place between Micromegas and Einstein. Perhaps, indeed, if we are to be faithful to the Voltairean original, the dialogue would have been very superficial, for—to speak confidentially—I believe that Voltaire never quite understood Newton, though he wrote much about him, and Newton was less difficult to understand than Einstein is. Neither did Mme. du Châtelet, for all the praise that has been lavished upon her translation of the immortal Principia. It swarms with meaningless passages which show that, whether she knew Latin or no, she did not understand Newton. But all this is another story, as Kipling would say.
The movement of the apparatus in the ether varies in speed according to the hour and the month in which the Michelson and similar experiments are made. As the compensation is always precise, we may try to calculate the exact law which governs the contraction as a function of velocities, and makes it, as we find, a precise compensation for the latter. Lorentz has done this. Taking V as the velocity of light and v as the velocity of the body moving in ether, Lorentz found that, in order to have compensation in all cases, the length of the moving body must be shortened, in the plane of its progress, in the proportion of