Special Relativity in Week One: 2) All Clocks Run Slow

In our initial article on teaching special relativity in the first week of an introductory physics course, we used the principle of relativity and Maxwell's theory of light to derive Einstein's second postulate (that the speed of light is the same to all observers).¹ In this paper we study thought experiments involving a light pulse clock moving past us with uniform motion at a speed v. Using Einstein's second postulate and the Pythagorean theorem, we see that the light pulse clock runs slow by a factor √1 − v²/c². We then show that it is a direct consequence of the principle of relativity that all clocks moving by us the same way run slow by precisely the same factor.