World line

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 inclusion of the dimension time, and typically encompasses a large area of spacetime wherein paths which are straight perceptually are rendered as curves in spacetime to show their (relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions.

The idea of world lines was originated by physicists and was pioneered by Hermann Minkowski.

Below an equivalent definition will be explained: A world line is either a time-like or a null curve in spacetime.

The world line of the Earth is therefore helical in spacetime (a curve in a four-dimensional space) and does not return to the same point.

An event is then represented by a point in a Minkowski diagram, which is a plane usually plotted with the time coordinate, say

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.

A one-dimensional line or curve can be represented by the coordinates as a function of one parameter.

More properly, a world line is a curve in spacetime that traces out the (time) history of a particle, observer or small object.

One usually uses the proper time of an object or an observer as the curve parameter

Two world lines that start out separately and then intersect, signify a collision or "encounter".

Without the existence of a metric (this is important to realize) one can imagine the difference between a point

So far a world line (and the concept of tangent vectors) has been described without a means of quantifying the interval between events.

The basic mathematics is as follows: The theory of special relativity puts some constraints on possible world lines.

The structure of spacetime is determined by a bilinear form η, which gives a real number for each pair of events.

For instance, the traditional electro-static force described by Coulomb's law may be pictured in a simultaneous hyperplane, but relativistic relations of charge and force involve retarded potentials.

A metric exists and its dynamics are determined by the Einstein field equations and are dependent on the mass-energy distribution in spacetime.

Again the metric defines lightlike (null), spacelike, and timelike curves.

Any timelike curve admits a comoving observer whose "time axis" corresponds to that curve, and, since no observer is privileged, we can always find a local coordinate system in which lightcones are inclined at 45 degrees to the time axis.

World lines of free-falling particles or objects (such as planets around the Sun or an astronaut in space) are called geodesics.

However, although not widely appreciated, it has been known since Feynman[2] that many quantum field theories may equivalently be described in terms of world lines.

He wrote A popular description of human world lines was given by J. C. Fields at the University of Toronto in the early days of relativity.

As described by Toronto lawyer Norman Robertson: Kurt Vonnegut, in his novel Slaughterhouse-Five, describes the worldlines of stars and people: Almost all science-fiction stories which use this concept actively, such as to enable time travel, oversimplify this concept to a one-dimensional timeline to fit a linear structure, which does not fit models of reality.

Author Oliver Franklin published a science fiction work in 2008 entitled World Lines in which he related a simplified explanation of the hypothesis for laymen.

[11] In the short story Life-Line, author Robert A. Heinlein describes the world line of a person:[12] Heinlein's Methuselah's Children uses the term, as does James Blish's The Quincunx of Time (expanded from "Beep").

A visual novel named Steins;Gate, produced by 5pb., tells a story based on the shifting of world lines.

World lines and other physical concepts like the Dirac Sea are also used throughout the series.

Neal Stephenson's novel Anathem involves a long discussion of worldlines over dinner in the midst of a philosophical debate between Platonic realism and nominalism.

Absolute Choice depicts different world lines as a sub-plot and setting device.

A space armada trying to complete a (nearly) closed time-like path as a strategic maneuver forms the backdrop and a main plot device of "Singularity Sky" by Charles Stross.