World line

A line in space-time which is the space-time trajectory of a material point. Introduce a local coordinate system , in some domain of space-time, and let the point lie on a world line . is called a world point; it describes the event that at time the material point has space coordinates . The concept of an event, and the related concepts of a world point and a world line are among the basic notions of relativity theory, adding to the concept of a material point borrowed from classical mechanics. Usually one considers smooth (or piecewise-smooth) world lines. The world line of a material point with positive rest mass is a time-like curve. The world line of a material point with zero rest mass (such as a non-quantum model of a photon and other elementary particles of mass zero) is an isotropic line. An arbitrary point of space-time is considered as a world point, that is, a (potential) event, and each time-like or isotropic line as the (possible) world line of some material point. The world line of a material point not under the influence of non-gravitational fields is, according to the geodesic hypothesis, a space-time geodesic. The unit tangent vector to a world line is a four-dimensional velocity vector; in local coordinates it has the form

where

See also Minkowski space.

References

[a1]	E.F. Taylor, J.A. Wheeler, "Space-time physics" , Freeman (1963)
[a2]	A.S. Eddington, "The mathematical theory of relativity" , Cambridge Univ. Press (1960)
[a3]	P.G. Bergmann, "Introduction to the theory of relativity" , Dover, reprint (1976)
[a4]	D.F. Lawden, "Tensor calculus and relativity" , Methuen (1962)