# World-Line

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## World-Line

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

References in periodicals archive ?
So, paradoxes emerging from pastward time travel would only be possible if the composite world-lines of time travelers embedded in the past could be made to change, move, or disappear.
The Synge-Weber equation is the generalization of equation (2.8) for that case where the particles, each having the rest-mass [m.sub.0], are moved along non-geodesic world-lines, determined by the equation
In this case the world-lines deviation equation takes the form
7 Expressing Synge-Weber equation (the world-lines deviation equation) in the terms of physical observable quantities, and its exact solutions
These systems are described by the world-lines deviation equation--the Synge equation of geodesic deviation (2.8) if these are two free particles, and the Synge-Weber equation (2.12) if the particles are connected by a force of non-gravitational nature.
The greater their velocity with respect to the space reference and the observer, the greater the deviation between the time flow on both world-lines. Thus measurement of time deviations between two particles in gravitational waves and gravitational inertial waves would be easier in experiments where the particles move at high speeds.
But if we wish to obtain solutions to the world-lines deviation equation, we need to express the quantity [D.sup.2][[eta].sup.[alpha]]/[ds.sup.2] and also [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in terms of the Christoffel symbols and their derivatives.
We merely need to obtain exact solutions to the world-lines deviation equation, applied to detectors of that kind which this experiment uses.
Therefore, using the world-lines deviation theory developed here in the terms of physically observable quantities, we are going to:
Anyway in this classical problem of General Relativity two interacting particles moved along both neighbour geodesic and non-geodesic world-lines are disentangled.
1) moving along neighbour geodesic world-lines [GAMMA](v) and [GAMMA](v + dv), where v is a parameter along the direction orthogonal to the geodesics (it is taken in the plane normal to the geodesics).
Let us consider the entanglement condition d[tao] = 0 in connection with the world-lines deviation equations.

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