Relativistic causality requires physical influences and controllable information to propagate only within or on the future light cone of their source.
Two events are spacelike separated when no signal traveling at or below the speed of light can connect them. Their temporal order can differ between inertial frames.
For a parent of mass decaying into two freely propagating daughters of equal mass , whose proper survival times are , 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.
Superluminal signalling would transmit controllable information outside the source event's future light cone and would violate relativistic causality.
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