Warped Passages - Lisa Randall [46]
Here’s one argument why. Imagine two identical ships with identical masts. One ship is docked by the shore, while the other is moving away. Also imagine that the captains of the two ships synchronized their watches when the first ship sailed off.
Now suppose that the two captains do a rather odd thing: each decides to measure time on her ship by placing a mirror at the top of the mast and a second mirror at the bottom, shining a light from the bottom mirror to the top one, and measuring the number of times light hits the mirror and returns. As a practical matter, of course, this would be absurd, since light would cycle up and down far too frequently to count. But bear with me, and imagine that the captains can count extraordinarily fast; I’ll be using this somewhat contrived example to argue that time stretches out on the moving ship.
If each captain knows how long it takes for light to cycle once, she can calculate the passage of time by multiplying the light-cycle time by the number of times light cycles up and down between the mirrors. Now suppose, though, that instead of using her own stationary mirror clock, the captain on the docked ship measures time by the number of times the light on the moving ship hits the mast’s mirror and returns.
Now from the perspective of the captain on the moving ship, the light simply goes straight up and down. However, from the perspective of the captain on the docked ship, the light has to travel farther (in order to cover the distance traveled by the moving ship—see Figure 35). But—and this is the counterintuitive part—the speed of light is constant. It is the same for the light sent to the top of the mast on the docked ship as it is for the light sent to the top of the mast on the moving ship. Since speed measures distance traveled over time, and the speed of light for the moving ship is the same as the speed of light for the stationary one, the moving mirror clock has to “tick” at a slower rate to compensate for the longer distance the moving light has to travel. This very counterintuitive conclusion—that moving and stationary clocks must tick at different rates—follows from the fact that the speed of light in a moving reference frame is the same as the speed of light in a stationary one. And although this is a funny way to measure time, the same conclusion—that moving clocks run slower—would hold true independently of how time is measured. If the captains had watches on, they would observe the same thing (again, with the caveat that for normal speeds, the effect would be tiny).
Figure 35. The path of a light beam that bounces off the top of a mast of a stationary ship and of a moving one. The stationary observer (in a boat by the shore or in a lighthouse) would see a longer path in the second case.
While the above example is artificial, the phenomenon described produces genuinely measurable effects. For example, special relativity gives rise to the different time experienced by fast-moving objects—the phenomenon known as time dilation.
Physicists measure time dilation when they study elementary particles produced at colliders or in the atmosphere, which travel at relativistic speeds—speeds approaching that of light. For example, the elementary particle called a muon has the same charge as an electron, but is heavier and can decay (that is, it can turn into other, lighter particles). The muon’s lifetime, the time before it decays, is only 2 microseconds. If a moving muon had the same lifetime as a stationary one, it would be able to travel only about 600 meters before it disappeared. But muons manage to make it all the way through our atmosphere, and in colliders, to the edges of large detectors, because their near-light-speed velocity makes them appear to us much