World-line
The locus of events in spacetime traced out by a particle as it moves; a 1D curve in the 4D manifold. Massive particles have timelike world-lines; photons have null world-lines; the proper time elapsed on the particle's clock is the arc length of its world-line in the Minkowski metric.
Definition
A world-line is the curve traced through spacetime by a particle as time progresses — the geometric record of its entire history, parametrized by proper time. For a particle at rest in some inertial frame, the world-line is a straight line parallel to that frame's time axis. For a particle in uniform motion, the world-line is straight but tilted relative to the time axis; for an accelerating particle, the world-line is curved. The angle a world-line makes with the time axis is constrained by causality: |dx/dt| ≤ c, so a world-line never tilts more than 45° from the vertical in units where c = 1. The 45° envelope is the local light-cone.
Massive particles trace timelike world-lines (interval invariant ds² > 0 between any two events on them) and have well-defined proper time dτ = √(1 − β²) dt integrated along the curve. Photons trace null world-lines (ds² = 0) — light rays in spacetime — for which proper time does not elapse. Tachyons would have spacelike world-lines (ds² < 0); none have ever been observed, and special relativity makes them causally pathological. Hermann Minkowski introduced the term Weltlinie in 1908; the geometric content is that all of a particle's kinematics lives in the shape of a single curve, and conservation laws translate into geometric constraints on how curves can intersect at collision events.