Why Does E=mc2_ - Brian Cox [93]
Ingenious and arcane as the double pulsar measurements are, general relativity makes its presence felt here on Earth too in a much more commonplace phenomenon. The GPS satellite system is ubiquitous throughout the world, and its successful functioning depends upon the accuracy of Einstein’s theories. A twenty-four-strong network of satellites circle the earth at an altitude of 20,000 kilometers, each performing two complete circuits every day. The satellites are used to “triangulate” locations on Earth using precise onboard clocks. In their high-altitude orbits the clocks experience a weaker gravitational field, which means that spacetime is warped differently for them compared to similar clocks on Earth. The effect is that the clocks speed up at a rate of 45 microseconds each day. Apart from the gravitational effect, the satellites are also whizzing around at pretty high speeds (around 14,000 kilometers per hour) and the time dilation predicted by Einstein’s special theory amounts to a slowing down of the clocks by 7 microseconds each day. Taken together, the two effects amount to a net speeding up of 38 microseconds per day. That doesn’t sound like much but ignoring it would lead to a complete failure of the GPS system within a few hours. Light travels around 30 centimeters in 1 nanosecond, which is 1,000-millionth of a second. Thirty-eight microseconds is therefore equivalent to over 10 kilometers in position per day, which wouldn’t make for accurate navigation. The solution is simple enough: The satellite clocks are made to run slow by 38 microseconds per day, which allows the system to work to accuracies of meters rather than kilometers.
The faster running of the GPS satellite clocks relative to the clocks on the ground can be quite easily understood using what we’ve learned in this chapter. In fact, the speeding up of clocks is really a direct consequence of the principle of equivalence. To understand how it comes about, let us travel back in time to 1959 to a laboratory at Harvard University. Robert Pound and Glen Rebka have set about designing an experiment to “drop” light from the top of their laboratory to the basement, 22.5 meters below. If the light falls in strict accord with the principle of equivalence, then, as it falls, its energy should increase by exactly the same fraction that it increases for any other thing we could imagine dropping.14 We need to know what happens to the light as it gains energy. In other words, what can Pound and Rebka expect to see at the bottom of their laboratory when the dropped light arrives? There is only one way for the light to increase its energy. We know that it cannot speed up, because it is already traveling at the universal speed limit, but it can increase its frequency. Remember, light can be thought of as a wave motion; a series of peaks and troughs rather like the water waves emanating outward when a stone is thrown into a still pond. The frequency of the waves is simply the number of peaks (or troughs) that pass a particular point every second, and these peaks and troughs can be used as the ticks of a clock. In particular, in the Pound-Rebka experiment you might imagine that Pound is sitting beside the light source at the top of the tower. He can count how many peaks of light are emitted for every beat of his heart. Now suppose that down in the basement Rebka is sitting beside an identical light source. He too can count how many peaks correspond to each beat of his heart and he should get the same answer as his colleague because they are identical light-source clocks and identical hearts. Okay, they will get exactly the same number only if they really have identical hearts, and that isn’t going to be the case, but we can imagine for the sake of this argument that their hearts do beat as one. Now, let’s think about how Rebka, sitting in the basement, sees the light that is arriving from Pound’s light source at the top. Because the