The twin paradox

What you are looking at

Two twins, both 30. One stays on Earth. The other boards a ship, flies to a star 4 light years away and comes straight back.

Press Launch. At 80% of the speed of light the trip takes 10 years by Earth’s clocks. The twin at home is 40 when the ship lands. The twin who steps out of it is 36.

Move the slider and fly again. The faster the ship, the bigger the gap: at 99% of light speed the traveller ages little more than a year while eight pass on Earth.

Why time slows down

Light travels at the same speed for everyone, however they are moving. That one fact, tested over and over, forces everything else. If two people moving past each other must both measure the same speed for the same beam of light, they cannot also agree on distances and durations. What gives way is time: a moving clock ticks slowly, by a factor that is almost nothing at everyday speeds and grows without limit near the speed of light.

This is not a trick of mechanical clocks. Heartbeats, thoughts and the decay of atoms all slow together. The traveller notices nothing odd on board. They simply live through fewer years.

So where is the paradox

Motion is relative. From the ship, it is Earth that rushes away and comes back. So the traveller should see the home twin’s clock running slow, and expect to find them younger. Each twin younger than the other is impossible. They meet, and compare, and only one answer can be true.

The way out is that the two journeys are not alike. The twin on Earth sits in one steady frame of reference the whole time. The traveller uses two: one going out, another coming back. At the star they have to turn round, and they feel it, pressed into the seat. Nothing like that happens on Earth. The symmetry was never there.

The diagram

The chart beside the clocks draws the trip with distance across and time upwards. The twin at home goes straight up. The traveller goes out and back, a bent line.

On ordinary paper a bent line is longer than a straight one. In spacetime the rule is reversed: the straight path between two events is the one that holds the most time, and every detour holds less. Count the marks on the two lines. That count is the whole paradox.

Is it real

Yes. In 1971 Joseph Hafele and Richard Keating flew atomic clocks around the world on commercial airliners and compared them with clocks left on the ground. They disagreed by the predicted billionths of a second. The satellites of GPS correct for the same effect every day; without it your position would drift by kilometres.

Einstein pointed out the effect on clocks in 1905. Paul Langevin turned it into a story about a traveller in 1911.