= Length contraction
{title2=$L=L_0/\gamma$}
{wiki}
= Lorentz contraction
{c}
{synonym}
A rod of rest length $L_0$ moving parallel to its length has simultaneous laboratory length $L=L_0/\gamma$, where $\gamma$ is the <Lorentz factor>. Here $L_0$ is the rod's <proper length> measured in its <rest frame>. Transverse lengths are unchanged by the corresponding <Lorentz transformation>.
For a rod at rest in $S'$ with endpoints $x'=0$ and $x'=10\,\mathrm m$, let $S'$ move at $v=0.6c$ relative to the laboratory $S$. Record both endpoint <positions> at laboratory time $t=0$. The <Lorentz transformation> then gives $x'=1.25x$, so their recorded positions are $0$ and $8\,\mathrm m$: the laboratory length is $10/1.25=8\,\mathrm m$. This is an operational definition: synchronized laboratory detectors register the endpoints at the same laboratory time. A photograph collects light emitted at different times and need not show this length. https://fourmilab.ch/etexts/einstein/specrel/www/[Einstein (1905), sections 2 and 4: measuring moving rods]{ref}.
For those same two endpoint <spacetime events>, $\Delta t'=-1.25(0.6c)(8\,\mathrm m)/c^2=-6\,\mathrm m/c$. Thus the front-end measurement occurs earlier in $S'$ by about $20\,\mathrm{ns}$. <Length contraction> compares simultaneous endpoint measurements in each frame, which select different pairs of <spacetime events>; it does not mean that the rod has been compressed in its own <rest frame>.
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