World line

The world line (or worldline) of an object is the path that object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics. The world line (or worldline) of an object is the path that object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics. The concept of a 'world line' is distinguished from concepts such as an 'orbit' or a 'trajectory' (e.g., a planet's orbit in space or the trajectory of a car on a road) 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). 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 relative to the sun. 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 {displaystyle t} , upwards and the space coordinate, say x {displaystyle x} horizontally.As expressed by F.R. Harvey 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. A one-dimensional line or curve can be represented by the coordinates as a function of one parameter. Each value of the parameter corresponds to a point in spacetime and varying the parameter traces out a line. So in mathematical terms a curve is defined by four coordinate functions x a ( τ ) , a = 0 , 1 , 2 , 3 {displaystyle x^{a}( au ),;a=0,1,2,3} (where x 0 {displaystyle x^{0}} usually denotes the time coordinate) depending on one parameter τ {displaystyle au } . A coordinate grid in spacetime is the set of curves one obtains if three out of four coordinate functions are set to a constant.