⧗ Time dilation
How much slower? At walking pace, immeasurably; on an airliner, billionths of a second a day; near light speed, years.
The size of it
| Speed | γ (how many times slower) |
|---|---|
| 10% of light speed | 1.005 |
| 50% | 1.15 |
| 87% | 2.0 |
| 99% | 7.1 |
| 99.9% | 22 |
A car at 100 km/h loses about a tenth of a microsecond a year. On an airliner, speed slows a clock by about 30 billionths of a second a day, while the height — 10 km up, in weaker gravity — speeds it up by about 90 billionths: height wins. An astronaut on the ISS ends up about 25 millionths of a second a day behind. Established
Proper time: the length of your path
A clock measures the length of its own path through spacetime — its proper time. Between two meetings, the path that keeps to steady motion is the longest; any path with detours and turnarounds is shorter. That's the whole twin paradox: the travelling twin's path through spacetime is shorter, so less time passes for them. The turnaround is what breaks the symmetry. Established
Gravity's version
Deeper in gravity, clocks run slower: near Earth, a clock one metre lower loses about one part in 10¹⁶. Near a black hole the effect grows without limit: seen from far away, a clock held still just outside the horizon barely ticks. Established
Not an illusion — but relative
Two observers moving past each other each see the other's clock running slow; neither is wrong. When clocks are brought back together, though, the difference is real and permanent — measured with muons, flown atomic clocks and GPS. Established For the evidence, see Clocks disagree.
See it in the labs
Further exploring
- Ben Lansdell — Special relativity simulator ↗Steer a spaceship with one thrust slider and watch its worldline, proper time and γ.
- Terence Tao — Spacetime diagram applet ↗Build events, worldlines and lines of simultaneity in two frames; worked twin-paradox and pole-and-barn scenes.
Sources: Einstein (1905); Hafele & Keating (1972); Bailey et al. (1977); Chou et al. (2010); Ashby (2003).