Your phone’s map would be useless without Einstein. GPS satellites carry atomic clocks, and relativity makes those clocks run about 38 microseconds a day faster than identical clocks on the ground. That sounds like nothing. But a receiver finds you by timing radio signals, and light covers about 30 centimetres in a billionth of a second. Leave 38 microseconds uncorrected and the position you see would be wrong within about two minutes, with the error growing by about 10 kilometres every day. So the system corrects the satellite clocks for relativity, and every blue dot on every map depends on it.
A position made of time
A GPS satellite is, at heart, a very good clock with a radio. The satellites orbit about 20,000 kilometres up, and each one keeps time with an atomic clock and broadcasts it. Your receiver listens to several of them at once. A signal that left a satellite a little earlier has travelled a little further, so the differences in arrival time become differences in distance, and the distances pin down where you are.
That is why the timing has to be so fine. Light, and radio, travels about 30 centimetres in a billionth of a second. A clock that is wrong by a millionth of a second puts you hundreds of metres out. Every tiny tick matters.
Moving clocks run slow
The first effect comes from special relativity. The satellites race along at about 14,000 kilometres an hour, and a moving clock, seen from the ground, runs slow. For GPS the loss adds up to about 7 microseconds a day.
If that were the whole story, the satellite clocks would fall behind. It is not the whole story.
Weaker gravity, faster clocks
The second effect comes from general relativity. Clocks run more slowly deep in gravity and faster where gravity is weaker. Twenty thousand kilometres up, the satellites sit much higher in Earth’s gravity than we do, and their clocks gain about 45 microseconds a day.
The two effects pull in opposite directions, and gravity wins:
What 38 microseconds would cost
Thirty-eight microseconds is far too short to notice. Multiply it by the speed of light, though, and it becomes a distance of kilometres. Ignore it, and the position your receiver works out would already be off after about two minutes, and the error would keep growing, by about 10 kilometres every day.
So the system does not ignore it. The satellite clocks are corrected for relativity, so that they keep step with clocks on the ground. Einstein’s two theories, written to answer questions about light and gravity, are built into a device most of us carry in a pocket.
Our Physics Shorts video shows it in under a minute: a map pin sliding away across a city, two clocks drifting apart, and a counter climbing to 38.
Every time your map finds you, Einstein is in the maths. And that’s how we found out.
