Time dilation

Intermediate

Moving clocks run slow.

Key relationΔt = γΔt₀

A moving clock runs slow by γ: Δt = γΔt₀, where Δt₀ is the proper time on the clock itself. Observed with muons and atomic clocks on jets.

Worked example

At 0.8c, γ = 1.67: 3 s on the clock is 5 s for you.

Common mistake

Symmetric between frames; each sees the other's clock run slow.

In more detail

Moving clocks run slower than clocks at rest, as seen by a stationary observer. The time dilation factor is gamma, the Lorentz factor, so Δt = γΔt0.

Muons created in the atmosphere live longer when moving at high speed.
GPS satellites correct clocks for time dilation.
Muons created high in the atmosphere reach the ground in larger numbers than expected, because their clocks run slow at high speed.

Does a moving clock really tick slower?

Yes, in the frame where it is moving, and the effect is measured in experiments.

Is time dilation symmetric?

Yes, each observer sees the other's clock running slow.

Does time dilation affect everyday life?

Only slightly at everyday speeds, but GPS and particle accelerators must include it to work accurately.