Inrelativistic physics,Lorentz symmetry orLorentz invariance, named after the Dutch physicistHendrik Lorentz, is an equivalence of observation or observational symmetry due tospecial relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within aninertial 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 underlyingspacetime manifold. Lorentz covariance has two distinct, but closely related meanings:
Anequation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the terminvariant 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 theprinciple 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 differentinertial frames of reference.
Onmanifolds, the wordscovariant andcontravariant 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 fromgeneral relativity, refers to Lorentz covariance applying onlylocally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to coverPoincaré covariance and Poincaré invariance.
In general, the (transformational) nature of a Lorentz tensor[clarification needed] can be identified by itstensor order, which is the number of free indices it has. No indices implies it is a scalar, one implies that it is a vector, etc. Some tensors with a physical interpretation are listed below.
In standard field theory, there are very strict and severe constraints onmarginal and relevant Lorentz violating operators within bothQED and theStandard Model. Irrelevant Lorentz violating operators may be suppressed by a highcutoff scale, but they typically induce marginal and relevant Lorentz violating operators via radiative corrections. So, we also have very strict and severe constraints on irrelevant Lorentz violating operators.
Similar to the approximate Lorentz symmetry of phonons in a lattice (where the speed of sound plays the role of the critical speed), the Lorentz symmetry of special relativity (with the speed of light as the critical speed in vacuum) is only a low-energy limit of the laws of physics, which involve new phenomena at some fundamental scale. Bare conventional "elementary" particles are not point-like field-theoretical objects at very small distance scales, and a nonzero fundamental length must be taken into account. Lorentz symmetry violation is governed by an energy-dependent parameter which tends to zero as momentum decreases.[4] Such patterns require the existence of aprivileged local inertial frame (the "vacuum rest frame"). They can be tested, at least partially, by ultra-high energy cosmic ray experiments like thePierre Auger Observatory.[5]
The laws of physics are symmetric under adeformation of the Lorentz or more generally, thePoincaré group, and this deformed symmetry is exact and unbroken. This deformed symmetry is also typically aquantum group symmetry, which is a generalization of a group symmetry.Deformed special relativity is an example of this class of models. The deformation is scale dependent, meaning that at length scales much larger than the Planck scale, the symmetry looks pretty much like the Poincaré group. Ultra-high energy cosmic ray experiments cannot test such models.
Very special relativity forms a class of its own; ifcharge-parity (CP) is an exact symmetry, a subgroup of the Lorentz group is sufficient to give us all the standard predictions. This is, however, not the case.
Models belonging to the first two classes can be consistent with experiment if Lorentz breaking happens at Planck scale or beyond it, or even before it in suitablepreonic models,[6] and if Lorentz symmetry violation is governed by a suitable energy-dependent parameter. One then has a class of models which deviate from Poincaré symmetry near the Planck scale but still flows towards an exact Poincaré group at very large length scales. This is also true for the third class, which is furthermore protected from radiative corrections as one still has an exact (quantum) symmetry.
Even though there is no evidence of the violation of Lorentz invariance, several experimental searches for such violations have been performed during recent years. A detailed summary of the results of these searches is given in the Data Tables for Lorentz and CPT Violation.[7]
Lorentz invariance is also violated in QFT assuming non-zero temperature.[8][9][10]
^Luis Gonzalez-Mestres (1997-05-26). "Absence of Greisen-Zatsepin-Kuzmin Cutoff and Stability of Unstable Particles at Very High Energy, as a Consequence of Lorentz Symmetry Violation".Proceedings of the 25th International Cosmic Ray Conference (Held 30 July - 6 August).6: 113.arXiv:physics/9705031.Bibcode:1997ICRC....6..113G.
^Huang, Lunan; McCormick, Timothy M.; Ochi, Masayuki; Zhao, Zhiying; Suzuki, Michi-To; Arita, Ryotaro; Wu, Yun; Mou, Daixiang; Cao, Huibo; Yan, Jiaqiang; Trivedi, Nandini; Kaminski, Adam (2016). "Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2".Nature Materials.15 (11):1155–1160.arXiv:1603.06482.Bibcode:2016NatMa..15.1155H.doi:10.1038/nmat4685.PMID27400386.S2CID2762780.
