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In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world In Mathematics, a diffeomorphism is an Isomorphism of Smooth manifolds It is an Invertible function that maps one Differentiable Invariance is a French journal edited by Jacques Camatte, published since 1968. A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws.

A physical law expressed in a generally covariant fashion takes the same mathematical form in all coordinate systems,[1] and is usually expressed in terms of tensor fields. In Mathematics, Physics and Engineering, a tensor field is a very general concept of variable geometric quantity The classical (non-quantum) theory of electrodynamics is one theory that has such a formulation. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently

Albert Einstein proposed this principle for his special theory of relativity; however, that theory was limited to space-time coordinate systems related to each other by uniform relative motions only, the so-called "inertial frames. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest " Einstein recognized that the general principle of relativity should also apply to accelerated relative motions, and he used the newly developed tool of tensor calculus to extend the special theory's global Lorentz covariance (applying only to inertial frames) to the more general local Lorentz covariance (which applies to all frames), eventually producing his general theory of relativity. A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in In Mathematics, Physics and Engineering, a tensor field is a very general concept of variable geometric quantity A global Lorentz covariance or global Lorentz symmetry is a Global symmetry and a Lorentz symmetry of Space-time. A local Lorentz covariance or local Lorentz symmetry is a Local symmetry of Space-time which reduces locally (i General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 The local reduction of the general metric tensor to the Minkowski metric corresponds to free-falling (geodesic) motion, in this theory, thus encompassing the phenomenon of gravitation. In the mathematical field of Differential geometry, a metric tensor is a type of function defined on a Manifold (such as a Surface in space In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces Gravitation is a natural Phenomenon by which objects with Mass attract one another

Much of the work on classical unified field theories consisted of attempts to further extend the general theory of relativity to interpret additional physical phenomena, particularly electromagnetism, within the framework of general covariance, and more specifically as purely geometric objects in the space-time continuum. Since the 1800s some physicists have attempted to develop a single theoretical framework that can account for the Fundamental forces of nature – a Unified field theory.

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Remarks

The relationship between general covariance and general relativity may be summarized by quoting a standard textbook:[2]

Mathematics was not sufficiently refined in 1917 to cleave apart the demands for "no prior geometry" and for a geometric, coordinate-independent formulation of physics. Einstein described both demands by a single phrase, "general covariance. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical " The "no prior geometry" demand actually fathered general relativity, but by doing so anonymously, disguised as "general covariance", it also fathered half a century of confusion.

A more modern interpretation of the physical content of the original principle of general covariance is that the Lie group GL4(R) is a fundamental "external" symmetry of the world. In Mathematics, a Lie group (ˈliː sounds like "Lee" is a group which is also a Differentiable manifold, with the property that the group Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or Other symmetries, including "internal" symmetries based on discrete groups, now play a major role in fundamental physical theories. In Mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element

Notes

  1. ^ More precisely, only coordinate systems related through sufficiently differentiable transformations are considered.
  2. ^ Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler (1973). Charles W Misner is an American physicist and one of the authors of " Gravitation " Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in gravitation physics John Archibald Wheeler ( July 9, 1911 &ndash April 13, 2008) was an eminent American Theoretical physicist. Gravitation. Freeman, 431. ISBN 0-716-70344-0.  

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This relativity-related article is a stub. In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally This is a list of mathematical topics in relativity, by Wikipedia page In General relativity, a harmonic coordinate x &alpha is one which satisfies the d'Alembert's equation when regarded as a scalar field This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. You can help Wikipedia by expanding it.
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