Time Dilation — Two Clocks, One Trip

Both dials start together. The rest clock runs one full turn while the ship's clock, moving at β = v/c, only gets round part of the way — and the light pulse below shows why: at speed the pulse has a longer zigzag to cover before it can complete a single tick. Set the speed and the proper time, then read how far apart the two clocks end up.

Lorentz factor γ = 1 ÷ sqrt(1 − β²)

1.2500

The ship's clock ticks 1.2500 times slower than the rest clock.

Dilated time t = γ · t₀

12.500 s

proper time aboard t0 = 10.000 s

Clock drift Δt = t − t₀

Difference Δt2.500 s

Ship clock runs slow by20.00%

Speed

β = v / c0.600

v179,875.47 km/s

Speed β = v / c0.600

Proper time aboard t₀10 s

Fixed: c = 299,792,458 m/s · both clocks are compared over one trip · this lab shows elapsed time only, not length contraction

Tip: drag β down to 0.100 and watch γ barely leave 1 — a tenth of light speed still only costs half a percent. The readouts do not really move until β passes about 0.5.