Spacelike distance between daughter decay events ($d^2/c^2=(M^2/m^2){\tau }_1{\tau }_2-({\tau }_1+{\tau }_2{)}^2$)

For a parent of mass $M$ decaying into two freely propagating daughters of equal mass $m$, whose proper survival times are ${\tau }_1,{\tau }_2$, the separation of their decay events has the displayed spacelike squared length when positive. It follows from their invariant relative four-velocity contraction. The distance in a simultaneous inertial frame is therefore independent of the laboratory boost of the parent; when the expression is not positive such a simultaneous frame does not exist.