Time and Length

Moving Rod Measures Shorter

A five-meter rest rod measures four meters along the motion. 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 rest length

The rest length is 5 m and the same gamma is 5/4.

Lrest=5 mγ=54L_{\rm rest}=5\ \text{m}\quad \gamma=\frac{5}{4}
Length contractionGamma divides the rest length along motion.speedquiet leglimitbetagammarest lengthmoving length

The moving length is shorter

Dividing by gamma gives moving length 4 m.

5÷54=45\div\frac{5}{4}=4
Length contractionGamma divides the rest length along motion.speedquiet leglimitbetagammarest lengthmoving length