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Worldline
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 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. The term is now used most often in the context of relativity theories (i.e., special relativity and general relativity). Usage in physics A world line of an object (generally approximated as a point in space, e.g., a partic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Electrodynamics of Moving Bodies", the theory is presented as being based on just Postulates of special relativity, two postulates: # The laws of physics are Invariant (physics), invariant (identical) in all Inertial frame of reference, inertial frames of reference (that is, Frame of reference, frames of reference with no acceleration). This is known as the principle of relativity. # The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance. The first postulate was first formulated by Galileo Galilei (see ''Galilean invariance''). Background Special relativity builds upon important physics ide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Diagram
A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations. The history of an object's location through time traces out a line or curve on a spacetime diagram, referred to as the object's world line. Each point in a spacetime diagram represents a unique position in space and time and is referred to as an event. The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General theory of relativity, relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time in physics, time, or four-dimensional spacetime. In particular, the ''curvature of spacetime'' is directly related to the energy and momentum of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations. Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Time
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line. The proper time interval between two events depends not only on the events, but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to arc length in Euclidean space). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated ( inertial) clock between the same two events. The twin paradox is an example of this effect. By conventio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path (topology)
In mathematics, a path in a topological space X is a continuous function from a closed interval into X. Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be path-connected. Any space may be broken up into path-connected components. The set of path-connected components of a space X is often denoted \pi_0(X). One can also define paths and loops in pointed spaces, which are important in homotopy theory. If X is a topological space with basepoint x_0, then a path in X is one whose initial point is x_0. Likewise, a loop in X is one that is based at x_0. Definition A ''curve'' in a topological space X is a continuous function f : J \to X from a non-empty and non-degenerate interval J \subseteq \R. A in X is a curve f : , b\to X whose domain , b/math> is a compact non-degenerate interval (meaning a is homeomorphic to , 1 which is why a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Fall
In classical mechanics, free fall is any motion of a physical object, body where gravity is the only force acting upon it. A freely falling object may not necessarily be falling down in the vertical direction. If the common definition of the word "fall" is used, an object moving upwards is not considered to be falling, but using scientific definitions, if it is subject to only the force of gravity, it is said to be in free fall. The Moon is thus in free fall around the Earth, though its orbital speed keeps it in orbit of the Moon, very far orbit from the Earth's surface. In a roughly uniform gravitational field gravity acts on each part of a body approximately equally. When there are no other forces, such as the normal force exerted between a body (e.g. an astronaut in orbit) and its surrounding objects, it will result in the sensation of weightlessness, a condition that also occurs when the gravitational field is weak (such as when far away from any source of gravity). The ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal completed the next year, after a regulatory review. Thus, Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ... Well-known products include the '' Methods in Enzymology'' series and encyclopedias such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Sheet
In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in which it propagates, and the presence of long-range background fields (such as gauge fields) are encoded in a two-dimensional conformal field theory defined on the worldsheet. For example, the bosonic string in 26 dimensions has a worldsheet conformal field theory consisting of 26 free scalar bosons. Meanwhile, a superstring worldsheet theory in 10 dimensions consists of 10 free scalar fields and their fermionic superpartners. Mathematical formulation Bosonic string We begin with the classical formulation of the bosonic string. First fix a d-dimensional flat spacetime (d-dimensional Minkowski space), M, which serves as the ambient space for the string. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
