The Twin Paradox
The twin paradox is perhaps the most famous thought experiment in special relativity. Imagine identical twins: one stays on Earth, the other boards a spacecraft traveling at near-light speed to a distant star, then returns. When they reunite, the traveling twin has aged less — perhaps dramatically less — than the stay-at-home twin.
Why It's Not Really a Paradox
The apparent paradox arises from a naive application of the relativity principle: if all motion is relative, shouldn't each twin see the other's clock running slow? The resolution is that the situation is not symmetric. The traveling twin must accelerate to leave, decelerate and turn around at the destination, and decelerate again upon return. These accelerations break the symmetry — the traveling twin changes inertial reference frames, while the Earth twin remains in a single inertial frame throughout.
The Spacetime Diagram
On a Minkowski spacetime diagram, the Earth twin's worldline is a straight vertical line (stationary in space, advancing in time). The ship twin's worldline is a bent path — a V-shape for a simple out-and-back trip. The key insight: the proper time along a worldline is maximized for a straight (inertial) path. Any deviation (acceleration) results in less elapsed proper time. This is the spacetime analogue of the triangle inequality: in Minkowski geometry, a straight line is the longest path between two events.
Realistic Journeys
This simulator includes acceleration phases. At a comfortable 1g acceleration, a ship could reach 90% c in about 10 months of ship time. For a round trip to Alpha Centauri (4.37 ly), the ship twin ages ~6 years while the Earth twin ages ~12 years. For more distant targets at higher velocities, the differences grow enormously.