World-Line

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 It might be outdated or ideologically biased.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 x_o-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

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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.

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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.

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