“Your Phone Finds You Using Clocks in Space” ended with a strange correction. Because of Einstein’s two theories of relativity, it said, the atomic clocks on GPS satellites run fast by about thirty-eight millionths of a second every day compared with clocks on the ground, and engineers deliberately set them to tick slightly slow before launch. It’s easy to read that as clever engineering covering for a quirk of the clocks. It isn’t. The clocks are perfect. It’s time itself that runs at different rates up there, and it runs at different rates down here too, even between your head and your feet.
Two separate effects are at work, and the piece mentioned both. The first comes from special relativity, Einstein’s theory from 1905: a moving clock runs slow compared with one at rest. You can see why with a thought experiment called a light clock. Imagine a clock that ticks by bouncing a pulse of light between two mirrors, one above the other. Each up-and-down trip is one tick. Now put that clock on a fast-moving train and watch it from the platform. From where you stand, the mirrors move sideways while the light is travelling, so the light has to follow a diagonal, zigzag path, which is longer than the straight up-and-down path. But one of the deepest facts in physics is that light always travels at exactly the same speed, for every observer. If the path is longer and the speed is the same, each tick must take longer. From the platform, the moving clock runs slow. This isn’t a trick of light clocks; it applies to every kind of clock, including atoms, hearts and ageing. GPS satellites move at nearly four kilometres a second, slow next to light, but fast enough that their clocks fall behind by about seven millionths of a second a day.
The second effect comes from general relativity, his theory of gravity from 1915, and it’s stranger. Clocks deeper in a gravitational field run slower than clocks higher up. One way to see this is to think about light climbing out of gravity. A beam of light sent upwards loses a little energy as it climbs, just as a thrown ball does, but light can’t slow down, so instead its frequency drops: it becomes slightly redder. Someone at the top, receiving light from a clock at the bottom, sees its ticks arriving slightly more slowly than their own clock’s ticks. The clock below is, genuinely, running slow. GPS satellites, twenty thousand kilometres up, sit much higher in the Earth’s gravity than we do, so their clocks run faster than ours, by about forty-five millionths of a second a day. Forty-five fast, minus seven slow: thirty-eight.
All of this has been tested directly, and the tests are wonderful. In 1959, at Harvard, two physicists sent gamma rays up and down a tower only twenty-two and a half metres tall, and measured the tiny shift in their frequency that gravity caused, matching Einstein’s prediction. In 1971, two scientists bought round-the-world tickets on ordinary passenger flights, strapped atomic clocks into the seats beside them, and flew once eastward and once westward, then compared the clocks with ones that had stayed in Washington. The flying clocks had gained or lost time by different amounts, depending on their speed relative to the Earth’s spinning surface and their height: the eastward clocks lost about fifty-nine billionths of a second, and the westward ones gained about two hundred and seventy-three. Relativity had predicted almost exactly that.
In 2010, the measurements came down to human scale. Physicists in the United States compared two optical atomic clocks, so precise they would lose less than a second in billions of years. When they raised one of them by just thirty-three centimetres, less than the height of a stair or two, they could see it run faster than the other. Time, measurably, goes faster upstairs.
Which brings us to your head. It is, on average, more than a metre and a half higher in the Earth’s gravity than your feet, so it ages slightly faster. Over a whole lifetime, the difference adds up to less than a millionth of a second. You’ll never notice. But it’s real, as real as the correction built into every satellite above you.
And that’s the point the GPS piece was making without quite saying it. Relativity isn’t an exotic theory about spaceships near the speed of light or black holes far away. It’s an everyday engineering fact. Every time the blue dot appears on your phone in the right place, a system built on the idea that time runs differently in different places has just worked, once again, exactly as Einstein said it would.