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in relativity theory, a geometrical representation of the four-dimensional “trajectory” of a mass point (particle) in space-time or in its equivalent, Minkowski space, independent of the frame of reference. Each point on the world-line is a “world-point” or “event” that indicates the position of the particle—in space coordinates x1 = x, x2 = y, and x3 = z—and the instant of time t corresponding to this position; the time t is related to the time coordinate x0 of four-dimensional space-time by the equation x0 = ct, where c is the velocity of light. A world-line parallel to the x0-axis represents a particle at rest.
In the special theory of relativity, the world-line of a particle moving uniformly and linearly is given by a straight line inclined at a certain angle θ (<45°) relative to the xo-axis. This angle depends on the velocity v (tan θ = v/c); an angle of 45° corresponds to the world-line of light. The world-line of a nonuniformly moving particle is a curve. In the presence of a gravitational field (in the general theory of relativity), the world-lines of light and of a freely moving particle are curved.
G. A. ZISMAN