Time dilation

A clock moving relative to an observer ticks more slowly than an identical clock at rest in the observer's own frame — the closer the relative speed is to the speed of light, the larger the effect.

Practise this concept

If the speed of light is the same for everyone, clocks cannot be. Picture a clock that works by bouncing a light pulse between two mirrors, one tick per round trip. Watch that clock fly past you and the pulse no longer travels straight up and down — from your position it traces a zigzag, a longer path. Since it covers that longer path at the same speed c, each tick takes longer. The moving clock runs slow.

Nothing has gone wrong with the clock. The mechanism is untouched, and the result does not depend on the clock being made of mirrors — a mechanical watch, a decaying particle and a human heartbeat all slow by the same factor, because it is the time between the events that has changed, not the machinery marking it. Nor is it an artefact of signal delay: the effect survives after you correct for how long the light took to reach you.

The effect is also symmetric, which is the part most worth sitting with. Each observer measures the other's clock as the slow one, and neither is mistaken, because "at the same time" means something different in each frame. Cosmic-ray muons are the standard demonstration: they reach the ground in numbers that their at-rest lifetime forbids, because in our frame their internal clocks are stretched — while in their own frame it is the atmosphere that is thin, not their lifetime that is long.

Key ideas

Requires: Postulates of special relativity

Unlocks: Length contraction, Lorentz transformations, Relativity of simultaneity

Formulas

\Delta t = \frac{\Delta t_0}{\sqrt{1 - v^2/c^2}}

Symbol	Name	Unit
$t$	time	s (second)
$t0$	time	s (second)
$v$	velocity	m/s (metre per second)

Common misconceptions

A moving clock runs slow because the motion physically damages or disturbs its mechanism.
Time dilation is an illusion — the moving clock only looks slow because the light from it takes time to arrive.
Only one of two observers in relative motion sees the other's clock run slow; the situation is not symmetric.

Resources

Articles

Part of these UT courses

This concept is mapped as covering part of the following course(s) in the University of Tartu curriculum.

Special relativityLOFY.04.003