Special Relativity in 14 Easy (Hyper)steps

5. Two ways to measure the length of a moving object

Imagine that we'd like to measure the length of Sulaco as it coasts with speed v past Nostromo.

Here are two ways that come to mind:

Method 1:
Using a single clock, time how long it takes (call this interval Dt) for Sulaco to coast past the location of the clock. At the end of the time interval, disable the clock so that its reading is frozen at Dt.  Sulaco's length is vDt.



Method 2:
Using a large number of synchronized clocks (labeled 1 - 13 in the illustration), determine which clocks are closest to Sulaco's nose and tail at the instant at which each clock reads zero.  The length of Sulaco is the same as the separation between these two clocks.  Inscribe the result in Nostromo's ship's log.  In the drawing, Sulaco's length is the same as the separation between clocks 11 and 3.


Methods 1 and 2 will always yield the same answer.