Timelike

Two events are timelike-separated when their invariant interval satisfies s² = c²Δt² − Δx² − Δy² − Δz² > 0 — equivalently, when their spatial separation is small enough that a sub-c signal can traverse it within their time difference. Timelike-separated events lie inside one another's light-cone, so a clock can be carried from one event to the other along a timelike world-line. The proper time elapsed on that clock between them is Δτ = √(s²)/c; in the inertial frame where the two events occur at the same spatial point, Δτ equals the coordinate time difference Δt, and that frame is the rest frame of the carried clock.

The temporal ordering of timelike-separated events is frame-independent: every inertial observer agrees on which event came first, because no Lorentz boost can flip Δt > 0 to Δt < 0 inside the light-cone. This is the structural basis of relativistic causality — cause precedes effect in every frame, and "the future" is a well-defined absolute concept for any event (the interior of its future light-cone). A massive particle's world-line is everywhere timelike — its tangent four-velocity has positive norm c² — and the proper time integrated along the world-line is the time measured on the particle's own clock. Timelike intervals are the regime in which classical mechanics and relativistic dynamics live.