Relativity of simultaneity

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 $(c{t}^{\prime },x^{\prime })=(0,0)$ and $(-6\mathrm{m},10\mathrm{m})$. In contrast, simultaneous rod-frame measurements at $t^{\prime }=0$ 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 $t^{\prime }=0$ line in the figure is a set of simultaneous spacetime events, not a signal's trajectory. ^[ref].