One twin stays on Earth. The other flies to a nearby star and back at close to the speed of light. When they meet again, the traveller is younger. Not by a trick of signals: they really have lived fewer years.
At 0.866 c, every second on the ship takes 2 seconds on Earth.
A light clock ticks each time a pulse of light goes up to a mirror and back. On the moving ship, Earth sees the light travel a longer, slanted path. Light moves at the same speed for everyone, so each tick takes longer. That stretch factor is γ = 1 / √(1 − v²/c²).
Below, both twins start aged 30. The dials and bars show how much time each one lives through. On the spacetime diagram, each dot marks the same amount of a twin's own time, and the traveller's dots are spaced further apart.
Motion is relative, so from the ship it's Earth's clocks that run slow. Then why is the traveller the younger one? Because only the traveller turns around. To get home they switch from one moving frame to another, and the two twins take different paths through spacetime. The straight path, staying home, is the one with the most time on it.
The traveller also sees the distance shrink by γ, which is how, fast enough, they cover 4.24 light-years in under 4.24 years of their own time without ever outrunning light.
Nobody has flown to a star, but time dilation is measured every day. Engineers correct for it, and particle physicists depend on it.
GPS satellites move at about 3.9 km/s, which slows their clocks by about 7 microseconds a day. Weaker gravity in orbit speeds them up by about 45. The net 38 microseconds a day is corrected by building the clocks to tick slightly slow. Left alone, position errors would grow by roughly 10 km a day.
In the demo: the speed part is the slow light clock, at a tiny γ.Cosmic rays make muons about 15 km up. A muon lives 2.2 microseconds on average, enough to travel only about 660 m. They reach the ground because their clocks run slow. Muon imaging found a large hidden void in the Great Pyramid of Giza in 2017 and is used to look inside volcanoes.
In the demo: the muon is the traveller, living a short life over a long trip.At CERN in 1977, muons circling a ring at γ ≈ 29.3 lived about 29 times longer than muons at rest, matching Einstein to about 0.1%. Fermilab's Muon g-2 experiment uses the same speed, so its muons survive long enough to be measured.
In the demo: push the speed slider to 0.9994c for a γ of about 29.A B meson lasts about 1.5 trillionths of a second, enough to move less than half a millimetre at light speed. In the LHCb detector, time dilation stretches that to about a centimetre, long enough to see where it decays and measure its lifetime.
In the demo: the ship covers far more ground than its own clock seems to allow.In 1971 Hafele and Keating flew caesium clocks around the world on airliners. Eastbound they lost about 59 nanoseconds and westbound gained about 273, close to relativity's predictions. In 2010 NIST's aluminium-ion clocks detected the slowing at speeds below 10 m/s.
In the demo: any speed above zero gives a γ above 1.Orbiting at about 7.7 km/s, an astronaut's clock loses roughly 25 microseconds a day compared with Earth, after allowing for gravity. Cosmonaut Sergei Krikalev's 803 days in orbit left him about 1/50 of a second younger than if he had stayed home.
In the demo: a real-life twin paradox, at a γ of 1.0000000003.