= Equal-frequency light between equal-speed inertial observers
{title2=$\mathbf n\cdot(\mathbf v_1-\mathbf v_2)=0$}
For two <inertial frames> with equal <speed> in a laboratory, a <photon> is measured at equal <angular frequency> by their comoving observers exactly when its laboratory propagation <unit vector> $\mathbf n$ obeys the displayed condition. Indeed, measured <angular frequency> is $-k\cdot U=\gamma\omega_{\mathrm{lab}}(1-\mathbf n\cdot\mathbf v/c)$, and equal laboratory <Lorentz factors> cancel. Thus the permitted directions form a <great circle> on the <unit sphere>. In the plane of the two laboratory <velocities>, only the internal <angle bisector> line remains. The <velocity> information alone fixes neither direction along that line nor coplanarity of the ray.
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