The factual accuracy of part of this article is disputed. The dispute is about The role of general covariance in gtr has been hotly disputed since 1920, and this article is entirely inadequate, even incorrect in places, e.g. Mach's principle. Image File history File links Stop_hand. ...
Please see the relevant discussion on the talk page.

In theoretical physics, general covariance (also known as diffeomorphism covariance) is the invariance of the form of physical laws under arbitrary coordinate transformations. More precisely, this means that physical laws take the same mathematical form in all coordinate systems whose metric can be locally reduced everywhere to the Minkowski form ( Minkowski metric) under a coordinate transformation. The principle of general covariance was formulated by Einstein who wanted to extend the Lorentz covariance in Special Relativity to non-inertial frames. All known physical theories such as electrodynamics must necessarily have a generally covariant formulation. This article or section contains information that has not been verified and thus might not be reliable. ... Theoretical physics employs mathematical models and abstractions, as opposed to experimental physics, in an attempt to understand Nature. ... In mathematics, a diffeomorphism is a kind of isomorphism of smooth manifolds. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... In mathematics a metric or distance is a function which assigns a distance to elements of a set. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... ‹The template below has been proposed for deletion. ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

The general principle of relativity as used in Einstein's general theory of relativity is that the laws of physics must take the same form in all reference frames. This is an extension of the special principle of relativity. Albert Einstein, photographed by Yousuf Karsh in 1948. ... General relativity (GR) or general relativity theory (GRT) is the theory of gravitation published by Albert Einstein in 1915. ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... The special principle of relativity is an assumption of Einsteins theory of special relativity that states that the laws of physics must take the same form in all inertial reference frames. ...

The “general principle” was defined by Ernst Mach as the principle that all forms of motion between bodies can be said to be purely relative. Ernst Mach Ernst Mach (February 18, 1838 – February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the Mach number and the optical illusion known as Mach bands. ...

Modern textbooks tend to define the general principle as being the principle that all relationships between frames of reference can be said to be purely relative.

This change in emphasis from physical “bodies” to more abstract “frames” allows a simpler derivation of a general theory of relativity, avoiding some of the complicating factors that are expected to arise at small scales with real bodies (e.g. quantum mechanics). For a non-technical introduction to the topic, please see Introduction to Quantum mechanics. ...

External links

• General covariance and the foundations of general relativity: eight decades of controversy, by J. D. Norton

Reference

• O'Hanian, Hans C.; & Ruffini, Remo (1994). Gravitation and Spacetime (2nd edition). New York: W. W. Norton. ISBN 0-393-96501-5. See section 7.1.

See also

• Lorentz covariance
• Covariance and contravariance
• List of mathematical topics in relativity