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Relativity

The faster you move, the slower your clock ticks compared to mine. Speed up to near light-speed and the universe gets weird.

Light-clock on a fast ship

ShipEarth

Earth time

0.00s

Ship time

0.00s

Ship speed50% c

Time-dilation γ

1.15×

For each second on the ship, 1.15 seconds pass on Earth.

γ = 1 / √(1 − v²/c²)

Two simple postulates

  1. The laws of physics are the same in every steadily-moving frame.
  2. The speed of light is the same — c — for everyone, no matter how fast they're moving.

Einstein took those two and showed that something has to give — and what gives is space and time themselves.

Time dilation

Δt' = γ · Δt, where γ = 1 / √(1 − v²/c²). At 87% the speed of light, γ = 2 — clocks on the ship tick at half the Earth-rate.

Length contraction

A spaceship moving past you isn't just slower in time — its length shrinks in the direction of motion. The same factor γ.

E = mc²

Mass is concentrated energy. A tiny bit of mass holds an enormous amount of energy because is huge. That's why fusion in the Sun and fission in a reactor release so much.

This isn't science fiction

GPS satellites must correct for time dilation every day or your location would drift by kilometres. Particle accelerators couldn't work without it. Cosmic-ray muons reach the ground only because their clocks slow down on the way through the atmosphere.