Page:Popular Science Monthly Volume 84.djvu/440

436 points A, B, C (Fig. 2), are moving to the right with a uniform unknown velocity through still air, and if a sound wave were sent out from A, it would be exceedingly simple to determine the velocity of the point A by a comparison of the time necessary for sound to travel from A to B and from A to C. But now if the same three points move through stationary ether, and if the wave emanating from A is a light wave, there is absolutely no way in which an observer connected with these three points can determine whether he is moving or not. Thus we are, in consequence of the Michelson and Morley experiment, driven to the first fundamental postulate of relativity: The uniform velocity of a body can not be determined by experiments made by observers on the body.

Consider now one of the fundamental concepts of mechanics, time. Physicists have not attempted to define it, admitting the impossibility of a definition, but still insisting that this impossibility was not owing to our lack of knowledge, but was due to the fact that there are no simpler concepts in terms of which time can be defined. As Newton says:

Let us examine this statement, which embodies fairly our notion of time, in the light of the first fundamental principle of relativity just laid down. Suppose A and B (Fig. 3) are two observers, some distance apart, and they wish to set their clocks together. At a given instant agreed upon before hand, A sends out a signal, by wireless if you wish, and B sets his clock at this instant. But obviously the signal has taken some time to pass from A to B, so B's clock is slow. But this seems easy to correct; B sends a signal and A receives, and they take the mean of the correction. But says the first principle of relativity, both A and B are moving through the ether with a velocity which neither knows, and which neither can know, and therefore the time taken for the signal to pass from A to B is not the same as that taken to pass from B to A. Therefore the clocks are not together, and never can be, and when As clock indicates half-past two, Bs does not indicate this instant, and worse yet, there is absolutely no way of determining what time it does indicate. Time then is purely a local affair. The well-known phrase, "at the same instant" has no meaning for A and B, unless a definition be laid down giving it a meaning. The "now" of A may be the "past" or "future" of B. To state the case in still other words, two events can no more happen simultaneously at two different places, than can two bodies occupy the same position.

But doubtless the reader is anxious to say, this matter of adjusting the clocks together can still be settled. Let there be two clocks having the same rate at a point A, and let them be set together. Then let one