Time and Length

Moving Clock Takes More Lab Time

A four-second moving-clock interval becomes five seconds in the lab. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start with the moving clock reading

The moving clock reads 4 s and uses gamma 5/4.

Δtproper=4 sγ=54\Delta t_{\rm proper}=4\ \text{s}\quad \gamma=\frac{5}{4}
Time dilationGamma scales a moving clock interval in the lab.speedquiet leglimitbetagammaproper timelab time

The lab interval is longer

Multiplying by gamma gives lab time 5 s.

4⋅54=54\cdot\frac{5}{4}=5
Time dilationGamma scales a moving clock interval in the lab.speedquiet leglimitbetagammaproper timelab time