The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of 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 inclusion of the dimension time, and typically encompasses a large area of spacetime wherein paths which are straight perceptually are rendered as curves in space-time 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. The term is now used most often in the context of relativity theories (i.e., special relativity and general relativity).
A world line of an object (generally 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 therefore helical in spacetime (a curve in a four-dimensional space) and does not return to the same point.
Spacetime is the collection of 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 (a topological space that locally resembles Euclidean space near each point).
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In mathematical physics, Minkowski space (or Minkowski spacetime) (mɪŋˈkɔːfski,_-ˈkɒf-) combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics). A four-vector (x,y,z,t) consists of a coordinate axes such as a Euclidean space plus time. This may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally.
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Albert Einstein in 1915 in the form of a tensor equation which related the local (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor).
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of 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 inclusion of the dimension time, and typically encompasses a large area of spacetime wherein paths which are straight perceptually are rendered as curves in space-time to show their (relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions.
Topics covered: Superfluidity in weakly interacting Bose gas, the random phase approximation to the Coulomb interaction in the Jellium model, superconductivity within the random phase approximation, t
This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex