worldlines

Worldlines are the histories of physical objects in spacetime. In relativity, spacetime has four dimensions: three spatial and one temporal. A worldline is the continuous curve traced by a pointlike object as it moves through spacetime.

Timelike worldlines correspond to massive particles with speeds less than the speed of light; the tangent to the curve is the four-velocity, and the proper time along the worldline provides a natural parameter for the curve. Null or lightlike worldlines have zero spacetime interval and describe photons or other massless quanta; such curves cannot be parameterized by proper time.

Worldlines can be straight in flat (Minkowski) spacetime, representing inertial motion with constant velocity. Gravitational fields or applied forces bend worldlines, so that accelerated motion or free fall in curved spacetime yields curved worldlines. In general relativity, free-fall worldlines are geodesics, curves that extremize proper time between events.

On a spacetime diagram, the projection of a worldline onto space conveys the object’s instantaneous velocity, while the vertical component relates to the elapsed time. The slope of a worldline reflects speed, and, in natural units, light follows lines at 45 degrees.

Worldlines connect causality and the sequence of events: events on the same worldline can be causally related, while spacelike-separated events cannot influence each other. In quantum contexts, one may speak of histories or path integrals over worldlines or field configurations, rather than a single trajectory.