Principle stating that physical laws are the same in all coordinate systems
In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of 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. While this concept is exhibited by general relativity, which describes the dynamics of spacetime, one should not expect it to hold in less fundamental theories. For matter fields taken to exist independently of the background, it is almost never the case that their equations of motion will take the same form in curved space that they do in flat space.
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In theoretical physics, generalcovariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical...
Covariance in probability theory and statistics is a measure of the joint variability of two random variables. The sign of the covariance, therefore,...
constructed using tensors, general relativity exhibits generalcovariance: its laws—and further laws formulated within the general relativistic framework—take...
and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square...
revisited the concept of generalcovariance and discovered that the hole argument was flawed. When Einstein realized that generalcovariance was tenable, he quickly...
through space". Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely...
Gauge symmetries can be viewed as analogues of the principle of generalcovariance of general relativity in which the coordinate system can be chosen freely...
mechanics — usually a one-loop diagram—that invalidates the generalcovariance of a theory of general relativity combined with some other fields.[citation needed]...
In physics, the principle of covariance emphasizes the formulation of physical laws using only those physical quantities the measurements of which the...
statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals...
diagram — that implies that the classically valid generalcovariance and gauge symmetry of a theory of general relativity combined with gauge fields and fermionic...
equation in manifestly covariant form is useful because it guarantees generalcovariance upon quick inspection. If an equation is manifestly covariant, and...
symmetry (generalcovariance implies a conserved stress tensor; a "gravitational anomaly" represents a quantum breakdown of generalcovariance, and should...
Causal dynamical triangulation Coordinate-free Quantum field theory Generalcovariance Rickles, Dean (2008). "Who's Afraid of Background Independence?"....
2013-04-24. E. J. Post (1962). Formal Structure of Electromagnetics: GeneralCovariance and Electromagnetics. Dover Publications Inc. ISBN 978-0-486-65427-0...
The eddy covariance (also known as eddy correlation and eddy flux) is a key atmospheric measurement technique to measure and calculate vertical turbulent...
doi:10.1093/bjps/37.2.232. Norton, John D (1993). "Generalcovariance and the foundations of general relativity: eight decades of dispute" (PDF). Rep....
Analysis of covariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable...
an effect in quantum mechanics that invalidates the generalcovariance of some theories of general relativity Konishi anomaly, the violation of the conservation...
'generalcovariance' was used in the early formulation of general relativity, but the principle is now often referred to as 'diffeomorphism covariance'...
ISBN 0-7167-2327-1. E. J. Post (1962). Formal Structure of Electromagnetics: GeneralCovariance and Electromagnetics. Dover Publications Inc. ISBN 978-0-486-65427-0...
arXiv:1902.08997. Grimmer, Daniel (May 2022). "A Discrete Analog of GeneralCovariance -- Part 2: Despite what you've heard, a perfectly Lorentzian lattice...
referred to as generalcovariance, and equations with this property are referred to as written in the covariant form. Generalcovariance is a special case...
the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such...
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