The twin paradox

Two twins are 20 years old. One stays on Earth; the other flies to a distant star and back near the speed of light. Moving clocks run slow by the Lorentz factor γ = 1/√(1 − v²/c²), so the traveller ages less. Push the speed up and watch the difference grow.

Under 15Here's something amazing: time doesn't tick at the same speed for everyone! If you zoom around in a super-fast spaceship, close to the speed of light, your time runs slower than time back home. So if one twin travels and the other stays on Earth, the traveller comes back younger. Slide the speed up, press Launch, and watch the two faces age.
20+ · going deeperEach twin's age is the proper time along their worldline, τ = ∫√(1 − v²/c²) dt. The stay-at-home worldline is a straight (inertial) line, which in Minkowski spacetime maximises proper time between the two meetings; any other path, like the traveller's, has less. The traveller's change of inertial frame at turnaround shifts their simultaneity surface, which is where the "missing" Earth years go in their accounting. Acceleration itself isn't the cause: the effect depends only on the path's geometry.
🌍 Stays on Earth
Portraits not found: add age-20 … age-80 images to visualize/twin/
20years old
Earth clock
0.0 years passed
🚀 Travels
Portraits not found: add age-20 … age-80 images to visualize/twin/
20years old
Ship clock
0.0 years passed
Lorentz factor γ
1 year on the ship =
Age gap so far0.0 yr
Star distance (Earth frame)

Why isn't it symmetric?

From the ship, Earth seems to be the one moving, so why doesn't the Earth twin age less? Because the twins are not equivalent: the traveller has to turn around to come home. Only the Earth twin stays in one inertial frame the whole time; the turnaround switches the traveller's frame, and that switch is where the "missing" years of Earth time appear. Experiments agree: atomic clocks flown around the world, and fast muons from cosmic rays, age exactly as special relativity predicts. (Here the ship cruises at a steady speed; acceleration is treated as instant.)