This great philosophic principle was derived of course from the study of natural science; i.e., from observations and experiments conducted upon the earth. Their comprehensiveness is therefore limited by the fact that the observer is always in a state of rest, or nearly so, as compared with the earth. All observers upon the earth are moving through space at the same velocity; and it was possible to argue that the uniformity of law might only hold good, when experiments were conducted at this velocity. An observer moving at very different velocity might discover that the laws of nature under these new conditions were somewhat different.
Such a view could indeed never be very plausible, for motion is only a relative conception. Imagine a universe consisting of infinite “empty” space, in which there is poised a single material body. How shall we determine whether this body is at rest, or whether it is moving at high or low velocity through space? It is never getting nearer to anything or farther from anything, since there is no other body for it to get nearer to or farther from. If we say it is moving at a uniform velocity of a thousand miles a second, our statement really has no significance. We have no more reason for affirming that it is in motion than we have for affirming that it is at rest. In short, there is no such thing as absolute motion; the conception of motion only arises when there are two or more bodies changing their position relatively to one another. This is what is meant by the relativity of motion. It seemed therefore improbable that the laws of nature would be different if the observer were moving at high velocity; for the movement of the observer is not an absolute quantity, but merely a statement of his relation to other bodies, and if there were no other bodies, the statement itself would be meaningless.
The Behavior of Light
Now among the established laws of nature is that which specifies the velocity of light moving through a vacuum. If the laws of nature are invariable, this velocity will always be the same. But consider what would happen under the following circumstances: Suppose that we are at rest, and that an observer on another body flies past us at 150,000 miles a second. Suppose that at the moment he passes, a piece of flint projecting from him grazes a piece of steel projecting from us, giving rise to a spark; and that we both thereupon set about to measure the velocity of the light so produced. After one second, we should find that the light had traveled about 186,000 miles away, and since during this second the other observer had traveled 150,000 miles, we should infer that the light traveling in his direction was only about 36,000 miles ahead of him. We should also infer that he would find this out by his experiment, and that he would estimate the velocity of light as only 36,000 miles a second in his own direction, and 336,000 miles a second in the opposite direction. But if this is so, then that law of nature which specifies the velocity of light is quite different for him and for us: the laws of nature must be dependent upon the observer’s motion—a conclusion which appears incompatible with the idea of the relativity of motion.
And it so happens that it is also contradictory to experimental conclusions. Experiments undertaken to settle the point show that each observer finds the same velocity for the light of the spark; and after one second, each observer finds that the light has traveled 186,000 miles from himself. But how is it possible that when it has traveled 186,000 miles in the same direction as the other observer who himself has moved 150,000 miles meanwhile, he should still think it 186,000 miles ahead of him? That is the initial paradox; and since there has been no room for error in the experiments, we are forced to conclude that there was something wrong in the assumptions and preconceptions with which we started.
Space and Time
There can in fact be only one interpretation. If we each find that the light has moved the same number of miles in the same number of seconds, then we must be meaning something different when we speak of miles and seconds. We are speaking in different languages. Some subsidence has occurred in the foundations of our systems of measurement. We are each referring to one and the same objective fact; but since we describe it quite differently, and at first sight incompatibly, some profound alteration must have occurred in our perceptions—all unsuspected by ourselves. It has been shown precisely what this alteration is. A body moving at high velocity must become flattened in the direction of its motion; all its measuring apparatus, when turned in that direction, is shortened, so that no hint of the flattening can be obtained from it. Furthermore, the standards of time are lengthened out, and clocks go slower. The extent of this alteration in standards of space and time is stated in the equations of the so-called Lorentz transformation.
Objection might be urged to the above paragraph on the ground that the connection of the observer with the variability of measured lengths and times is not sufficiently indicated, and that this variability therefore might be taken as an intrinsic property of the observed body—which of course it is not.—Editor.