In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".[1]
Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings:
A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e., they transform under the trivial representation).
An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame; this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame. This condition is a requirement according to the principle of relativity; i.e., all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.
On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Both covariant and contravariant four-vectors can be Lorentz covariant quantities.
Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance.
^Russell, Neil (2004-11-24). "Framing Lorentz symmetry". CERN Courier. Retrieved 2019-11-08.
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laboratory through space". Lorentzcovariance, a related concept, is a property of the underlying spacetime manifold. Lorentzcovariance has two distinct, but...
the special theory's global Lorentzcovariance (applying only to inertial frames) to the more general local Lorentzcovariance (which applies to all frames)...
closely related, have subtle and important differences. Understanding Lorentzcovariance is simplified by keeping in mind the geometric character of the process...
universal Lorentzcovariance, or, equivalently, on the single postulate of Minkowski spacetime. Rather than considering universal Lorentzcovariance to be...
Hendrik Antoon LorentzLorentz oscillator model Lorentzcovariance Modern searches for Lorentz violation Heaviside–Lorentz units Lorentz-violating electrodynamics...
the speed of light in vacuum. (See also: Lorentzcovariance.) It is possible to derive the form of the Lorentz transformations from the principle of relativity...
principle of relativity, the principle of general covariance, geodesic motion, local Lorentzcovariance (the laws of special relativity apply locally for...
Principle of relativity Lorentzcovariance General covariance E.J.Post, Formal Structure of Electromagnetics: General Covariance and Electromagnetics, Dover...
including gravitation. He corrected some mistakes of Lorentz and proved the Lorentzcovariance of the electromagnetic equations. However, he used the...
the subsequent development of theoretical physics, because manifest Lorentzcovariance (time and space components of quantities enter equations in the same...
}\right)^{-1}m\omega \psi _{\rm {R}}^{*}(x)} which is exactly the same Lorentzcovariance property noted earlier. Thus, the linear combination, using an arbitrary...
This is because the proof of Goldstone's theorem requires manifest Lorentzcovariance, a property not possessed by the radiation gauge. Wikinews has news...
However, in quantum electrodynamics, consistency with the principle of Lorentzcovariance and with the magnitude of the Planck constant suggests a much larger...
{\displaystyle F_{ab}\,=\,\nabla _{a}A_{b}\,-\,\nabla _{b}A_{a}.} Lorentzcovariance Introduction to the mathematics of general relativity C. B. Parker...
the restricted Lorentz group. This relationship is widely used to express the Lorentz invariance of the Dirac equation and the covariance of spinors. In...
around the observer (represented by the point). The principle of local Lorentzcovariance, which states that the laws of special relativity hold locally about...
argued that Min could be replaced by Lin – experimentally testable Lorentzcovariance. The free will theorem states: Given the axioms, if the choice about...
fields. Goldstone's theorem only applies to gauges having manifest Lorentzcovariance, a condition that took time to become questioned. But the process...
especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution...
^{2}}{{\partial t}^{2}}}} Maxwell's equations in the language of tensors makes Lorentzcovariance clear. We introduce electromagnetic tensors and preliminary four-vectors...
within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski...
obtained full Lorentzcovariance of the electrodynamic equations. Criticizing Lorentz's 1904 theory, Abraham (1904) held that the Lorentz contraction of...
In physics, a covariance group is a group of coordinate transformations between frames of reference (see for example Ryckman (2005)). A frame of reference...
derivatives, and they need to be first order partial derivatives for Lorentzcovariance. The Dirac operator and Dirac slash of the 4-momentum is given by...
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