rather difficult, we shall take a very simple kind of clock. The one we choose is rather a silly kind of clock, but it will work in principle: it is a rod(meter stick with a mirror at each end, and when we start a light signal between the mirrors the light keeps going up and down, making a click every time it comes down, like a standard ticking clock. We build two such clocks, with exactly the same lengths, and synchronize them by starting them together; then they agree always thereafter, because they are the same in length, and light always travels with speed c. We give one of these clocks to the man to take along in his space ship, and he mounts the rod perpendicular to the direction of motion of the ship; then the length of he rod will not change. How do we know that perpendicular lengths do not s system change? The men can agree to make marks on each other's y-meter stick as they pass each other. By symmetry, the two marks must come at the same y- and y-coordinates, since otherwise, when they get together to compare results, one mark will be above or below the other, and so we could tell who was really moving Now let us see what happens to the moving clock. Before the man took It aboard, he agreed that it was a nice, standard clock, and when he goes along in the space ship he will not see anything peculiar. If he did, he would know he was movingif anything at all changed because of the motion, he could tell he was oving. But the principle of relativity says this is impossible in a uniformly moving system, so nothing has changed. On the other hand, when the external observer looks at the clock going by, he sees that the light, in going from mirror to mirror, is"really"taking a zigzag path, since the rod is moving sidewise all the while dy analyzed such a zigzag motion in connection with the miche Glost Morley experiment. If in a given time the rod moves forward a distance propor- tional to c, and the vertical distance is therefore proportional to vc2-ye opor- tional to u in Fig. 15-3, the distance the light travels in the same time is propor- That is, it takes a longer time for light to go from end to end clock than in the stationary clock. Therefore the apparent time between clicks is longer for the moving clock, in the same proportion as shown in the hypotenuse of the triangle(that is the source of the square root expressions in our equations) From the figure it is also apparent that the greater u is, the more slowly the clock appears to run. Not only does this particular kind of clock run more but if the theory of relativity is correct, any other clock, operating on any principle whatsoever, would also appear to run slower, and in the same proportion-we can say this without further analysis. Why is this so? Fig. 15-3. la)A"light clock" To answer the above question, suppose we had two other clocks made exactly the S system. (b)The same clod alike with wheels and gears, or perhaps based on radioactive decay, or something moving through the S system. (c)Ilustra- else. Then we adjust these clocks so they both run in precise synchronism with ion of the diagonal path taken by the our first clocks. When light goes up and back in the first clocks and announces ht beam in a moving"light clock. its arrival with a click, the new models also complete some sort of cycle, which they simultaneously announce by some doubly coincident flash, or bong, or other signal. One of these clocks is taken into the space ship, along with the first kind. Perhaps this clock will not run slower, but will continue to keep the same time as its stationary counterpart, and thus disagree with the other moving clock. Ah no, if that should happen, the man in the ship could use this mismatch between his two clocks to determine the speed of his ship, which we have been supposing is impossible. We need not know anything about the machinery of the new clock that might cause the effect-we simply know that whatever the reason, it will appear to run slow, just like the first one Now if all moving clocks run slower, if no way of measuring time gives any thing but a slower rate we shall just hay elf appears to be slower in a space ship All the phenomena there-the man's pulse rate, his thought processes, the time he takes to light a cigar, how long it takes to grow up and get old-all these things must be slowed down in the same proportion, because he cannot tell he is moving. The biologists and medical men sometimes say it is not quite certain that the time it takes for a cancer to develop will be longer in a space ship, but from the viewpoint of a modern physicist it is nearly certain; otherwise one could use the rate of cancer development to determine the speed of the 15-6