How it works

How much slower. The amount depends only on how fast the clock is moving compared with you. These figures were worked out here from Einstein’s formula, which is one divided by the square root of (1 minus the speed squared, with the speed given as a fraction of the speed of light).

Speed, as a share of the speed of light	For every second on the moving clock, your clock ticks
A tenth	1.005 seconds
Half	1.15 seconds
87 per cent	2 seconds
99 per cent	7.1 seconds
99.9 per cent	22 seconds

It works both ways. Somebody riding with the moving clock sees nothing odd about it. To them it is your clock that is moving and running slow. Neither view is the wrong one. That is what the word relativity means here: how much time passes between two events depends on how you are moving, and no one way of moving has the true answer.

Measured with two clocks in one room. In 2010 physicists at NIST in the United States compared two atomic clocks so steady that each would stray by less than a second in more than three billion years. When they set the atom in one of them moving at only a few metres a second, about the speed of a car in town, that clock ticked measurably slower than the other.

Measured with particles from space. Particles called muons are made high in the air when cosmic rays strike it. A muon at rest lasts about two millionths of a second, which is not long enough to get down to the ground even at nearly the speed of light. Yet they arrive in great numbers. They are moving so fast that their own clocks run about nine times slow, so they last long enough to make the trip. This was first checked in the 1940s by counting them at different heights.

The satellites. The clocks on navigation satellites are changed by two things. Their speed makes them run slow by about 7 millionths of a second a day. Being higher up, where the Earth’s gravity is weaker, makes them run fast by about 45 millionths of a second a day, which is the subject of the lesson on gravity as bent space and time. The net effect is 38 millionths of a second a day fast, and the system is built to allow for it.

The speed limit, tested. The Large Hadron Collider at CERN sends protons round a ring nearly 27 kilometres long. At full power they make 11,245 laps every second. They are already so close to the speed of light that adding still more energy makes them hardly any faster.

What E = mc² says. E is energy, m is mass, and c is the speed of light. Because c is so large, and it is multiplied by itself, a very little mass is a great deal of energy. In the Sun’s core about four million tonnes of matter are turned into light every second, and the Sun is big enough to go on doing that for billions of years.