World line From Wikipedia, the free encyclopedia (Redirected from Worldline) General relativity Spacetime curvature.png G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu} Introduction Mathematical formulation Resources · Tests Fundamental concepts[hide] Special relativity Equivalence principle World line · Riemannian geometry Phenomena[show] Equations[show] Advanced theories[show] Solutions[show] Scientists[show] Spacetime[show] v t e In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" (such as an orbit in space or a trajectory of a truck on a road map) by the time dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their (relatively) more absolute position states — to reveal the nature of special relativity or gravitational interactions. The idea of world lines originates in physics and was pioneered by Hermann Minkowski. The term is now most often used in relativity theories (i.e., special relativity and general relativity). However, world lines are a general way of representing the course of events. The use of it is not bound to any specific theory. Thus in general usage, a world line is the sequential path of personal human events (with time and place as dimensions) that marks the history of a person[1] — perhaps starting at the time and place of one's birth until one's death. The log book of a ship is a description of the ship's world line, as long as it contains a time tag attached to every position. The world line allows one to calculate the speed of the ship, given a measure of distance (a so-called metric) appropriate for the curved surface of the Earth. Contents [hide] 1 Usage in physics 2 World lines as a tool to describe events 2.1 Trivial examples of spacetime curves 2.2 Tangent vector to a world line, four-velocity 3 World lines in special relativity 3.1 Simultaneous hyperplane 4 World lines in general relativity 5 World lines in literature 6 See also 7 References 8 External links Usage in physics[edit] 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 t, upwards and the space coordinate, say x horizontally. As expressed by F.R. Harvey A curve M in [spacetime] 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.[2] 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.