= Relativity of simultaneity
{title2=$\Delta t'=-\gamma v\Delta x/c^2\quad(\Delta t=0)$}
{wiki}
Spatially separated simultaneous events in one <inertial frame> are generally not simultaneous in a relatively moving frame. The <Lorentz transformation> explicitly mixes position into time. This is essential when comparing distances between moving light pulses: one must compare their positions at the same time in the measuring frame.
At $v=0.6c$, the rod's simultaneous laboratory endpoint measurements in <length contraction> have $(ct,x)=(0,0)$ and $(0,8\,\mathrm m)$. They become $(ct',x')=(0,0)$ and $(-6\,\mathrm m,10\,\mathrm m)$. In contrast, simultaneous rod-frame measurements at $t'=0$ use $(ct,x)=(0,0)$ and $(7.5\,\mathrm m,12.5\,\mathrm m)$. The latter front-end event occurs later in the laboratory, after the front has moved. The sloping $t'=0$ line in the figure is a set of simultaneous <spacetime events>, not a signal's trajectory. https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_Lorentz_transforms.htm[Joe Wolfe, UNSW: Lorentz transformations and spacetime]{ref}.
\Image[/lorentz-simultaneity.png]
{title=The same moving rod measured on laboratory and rod-frame simultaneity slices; length measurements use different endpoint events}
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