World Library  
Flag as Inappropriate
Email this Article

General covariance

Article Id: WHEBN0000681875
Reproduction Date:

Title: General covariance  
Author: World Heritage Encyclopedia
Language: English
Subject: General relativity, Event symmetry, Symmetry (physics), History of general relativity, Einstein aether theory
Collection: Diffeomorphisms, Differential Geometry, General Relativity
Publisher: World Heritage Encyclopedia
Publication
Date:
 

General covariance

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. 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. The classical (non-quantum) theory of electrodynamics is one theory that has such a formulation.

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." 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. 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.

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.

Contents

  • Remarks 1
  • See also 2
  • Notes 3
  • References 4
  • External links 5

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." 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. Other symmetries, including "internal" symmetries based on compact groups, now play a major role in fundamental physical theories.

See also

Notes

  1. ^ More precisely, only coordinate systems related through sufficiently differentiable transformations are considered.
  2. ^  

References

  • O'Hanian, Hans C.; & Ruffini, Remo (1994). Gravitation and Spacetime (2nd ed.). New York: W. W. Norton. . section 7.1 See  

External links

  • General covariance and the foundations of general relativity: eight decades of dispute, by J. D. Norton (file size: 4 MB)
    re-typeset version (file size: 460 KB)


This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.