File:MovingRodContraction.png

English: This is an x-ct plot of length-contraction for a rod moving rightward at ½[ly/ty] proper-speed with a proper-length of 10 (arbitrarily-sized) tick-marks, illustrated using radar-time simultaneity^[1] with only a single map-frame of yardsticks and synchronized clocks (measuring x and t), plus a timepiece carried by the traveler measuring elapsed proper-time τ. Since distances are measured using only times-elapsed on one clock associated with each world line, this radar-time approach allows measurement of apparent-length differences in curved-spacetimes with no extended-arrays of either yardsticks or synchronized-clocks!

Here the measurement of both rods is recorded when the left side of the rod is located at the shared traveler-time (τ) and map-time (t) coordinate-origin. Times of last-influence (-) and first-detection (+) are recorded for both right-side measurement events, which of course require right-side location values concurrent with the left-side location values in each frame. From these, differing length values follow from the radar-time analysis in the discussion section below.

Note that three separate events are needed to fully illustrate the length-contraction process. By comparison only two events are needed to illustrate time-dilation, even though these two effects are given complementary status in most introductory treatments.