File:XctauRodContraction.png

English: An x-cτ plot of length contraction for a rod (in blue) traveling rightward with a proper-speed of w ≡ dx/dτ = γv = (4/3)c ≈ 1.33c i.e. just over the 1.23c proper-speed of 300 keV electrons in our Center for NanoScience HR-TEM. This corresponds to a Lorentz-factor γ ≡ dt/dτ of 5/3, and a coordinate velocity v ≡ dx/dt of (4/5)c. The figure was inspired by Figure 5-19 in Epstein^[1].

The dashed-lines represent length-measurements in the map-frame, while the solid lines represent length-measurements in the rod-frame. In the map-frame the rod appears to have a length of L/γ = 12 map-feet, while in the rod-frame the L = 20 foot-long rod appears to have a length in map-distance units of γL ≈ 33.33 feet because map-yardsticks have contracted instead!

A similar proper-time interval for a stationary rod is illustrated in red. As mentioned above, on x-cτ plots Cartesian-distances between event-points on a single trajectory correspond to map-time differences cΔt between those points. We cannot however say this for distances between event-points on different trajectories, which may instead to first order be meaningless.