Why Does E=mc2_ - Brian Cox [18]
Now, imagine putting the light clock on a train that is whizzing along past someone standing on a station platform. The million-dollar question is: How fast does the clock on the train tick according to the person on the platform? Until Einstein, everybody assumed that it ticks at the same rate—one tick every 6.67 nanoseconds.
Figure 2 shows how one tick of the clock on the train looks according to the person standing on the platform. Because the train is moving, the light must travel farther in one tick, as determined from the platform. Put another way, the starting point of the light beam’s journey is not in the same place as its end point according to the person on the platform, because the clock has moved during the tick. In order for the clock to tick at the same rate as it does when it stands still the light must travel a little bit faster. Otherwise it could not complete its longer journey in 6.67 nanoseconds. This is exactly what happens in Newton’s worldview, because the light is given a helping hand by the motion of the train. But—and this is the crucial step—applying Einstein’s logic means that the light cannot speed up because the speed of light must be the same to everyone. This has the disturbing consequence that the moving clock must genuinely take longer to tick, simply because the light has farther to travel, from the perspective of the person on the platform. This thought experiment teaches us that if we are to assert that the speed of light is a constant of nature, as Maxwell seems to be trying to tell us, then it follows that time ticks at different rates depending on how we are moving relative to someone else. In other words, absolute time is not consistent with the notion of a universal light speed.
FIGURE 2
It is very important to emphasize that this conclusion is not specific to light clocks. There is no important difference between a light clock and a pendulum clock, which works by “bouncing” the pendulum between two places once every second. Or for that matter an atomic clock, which counts the number of peaks and troughs of a light wave emitted from an atom to generate the ticks. Even the rate of decay of the cells in your body could be used as little clocks, and the conclusions would be the same because all these devices measure the passing of time. The light clock is in fact a bit of an old chestnut in the teaching of Einstein’s theory and provokes no end of confused discussion because it is such an unfamiliar clock. It can be tempting to attribute the weird conclusion we have just reached to this lack of familiarity, rather than to recognize it as an insight into the nature of time itself. To do so would be to make a bad mistake—our sole reason for picking a light clock rather than any other type of clock is that we can exploit Einstein’s bizarre demand that light should travel at the same speed for everyone to draw our conclusions. Any conclusion that we draw from thinking about the light clock must also apply to any other kind of clock, for the following reason. Imagine that we seal ourselves into a box with a light clock and a pendulum clock and set them ticking away in sync. If they are very accurate clocks, they will stay in sync and tell the same time forever. Now, let’s put the box onto the moving train. According to Einstein’s second axiom, we should not be able to tell whether we are moving. But if the light clock behaved differently than the pendulum clock, they would drift out of sync and we could say for certain from inside our sealed box that we were moving.3 So a pendulum clock and a light clock must count time in exactly the same way and that means that if the moving light clock is running slow as