World Line - Usage in Physics

Usage in Physics

In physics, a world line of an object (approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresponding to the history of the object. A world line is a special type of curve in spacetime. Below an equivalent definition will be explained: A world line is a time-like curve in spacetime. Each point of a world line is an event that can be labeled with the time and the spatial position of the object at that time.

For example, the orbit of the Earth in space is approximately a circle, a three-dimensional (closed) curve in space: the Earth returns every year to the same point in space. However, it arrives there at a different (later) time. The world line of the Earth is helical in spacetime (a curve in a four-dimensional space) and does not return to the same point.

Spacetime is the collection of points called events, together with a continuous and smooth coordinate system identifying the events. Each event can be labeled by four numbers: a time coordinate and three space coordinates; thus spacetime is a four-dimensional space. The mathematical term for spacetime is a four-dimensional manifold. The concept may be applied as well to a higher-dimensional space. For easy visualizations of four dimensions, two space coordinates are often suppressed. The event is then represented by a point in a Minkowski diagram, which is a plane usually plotted with the time coordinate, say, upwards and the space coordinate, say horizontally. As expressed by F.R. Harvey

A curve M in is called a worldline of a particle if its tangent is future timelike at each point. The arclength parameter is called proper time and usually denoted τ. The length of M is called the proper time of the worldline or particle. If the worldline M is a line segment, then the particle is said to be in free fall.

A world line traces out the path of a single point in spacetime. A world sheet is the analogous two-dimensional surface traced out by a one-dimensional line (like a string) traveling through spacetime. The world sheet of an open string (with loose ends) is a strip; that of a closed string (a loop) is a volume.

Once the object is not approximated as a mere point but has extended volume, it traces out not a world line but rather a world tube.