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Transformation of coordinates [8] between a rotating Earth-based frame x, y, z and a nonrotating Sun-based frame X, Y, Z. The origins of the frames are shown as coinciding to ease understanding of relative directions.
Source publication
![Figure 3. Transformation of coordinates [8] between a rotating...](publication/346326329/figure/fig3/AS:1022679104643076@1620837107903/Transformation-of-coordinates-8-between-a-rotating-Earth-based-frame-x-y-z-and-a_Q320.jpg)
In this paper, we use the classical limit of the Standard-Model Extension to explore some generic features of Lorentz violation. This classical limit is formulated at the level of undergraduate physics. We first discuss the general equations of motion and then concentrate on three specific systems. First, we consider the theoretical aspects of pend...
Context in source publication
Context 1
... SME coefficient c yy is a component of a tensor with respect to a coordinate system x, y, z that rotates with Earth, and thus changes as the Earth rotates. In order to clarify the time dependence of c yy , we change coordinates to a non-rotating frame X, Y, Z, seen in Figure 3, commonly used in studies of Lorentz violation [7,8,17]. Using the rotation matrix described in [8], the time dependence of c yy and the period T can be explicitly written ...
Citations
... It is not possible to conduct experiments at such a scale. Violation of Lorentz symmetry could provide a key to experimental probes at the Planck scale [52]. If Lorentz invariance is violated at the Planck scale, it is likely that there must be an interpolation at much lower energy so that a small amount of Lorentz violation should be present at all energies [53]. ...
The quantum tunneling radiation of scalar particles near the event horizon of Kerr-de Sitter black hole is investigated in three systems of coordinates namely naive coordinate system, Painleve coordinate system and Eddington coordinate system using Lorentz violation theory in curved space time. The Klein-Gordon equation of scalar particles is transformed into Hamilton-Jacobi equation by using Lorentz violation theory in curved space time. We observe that due to Lorentz violation theory, the expressions of Hawking temperatures, the Bekenstein-Hawking entropies and heat capacities near the event horizon of Kerr-de Sitter black hole are modified. The Hawking temperatures, entropies and heat capacities increase or decrease depending upon the choices of ether like vectors uα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^\alpha $$\end{document}.
... However, relative to those anisotropy measurements, there is a significant loss of sensitivity, because the Earth's orbital speed is only v ⊕ ≈ 10 −4 . At this slow speed, the effective anisotropy coefficient in the moving lab is c (jk) = c (jk) + v ⊕ [v j c (0k) +v k c (0j) ], wherev is the instantaneous direction of the planet's motion and the unprimed c νμ are as measured in the rest frame of the Solar System [37]. So there is a loss of four orders of magnitude in sensitivity to the c (0j) , and there would be a loss of four more in potential sensitivity to the isotropic c 00 for these kinds of terrestrial experiments. ...
Experimental tests of Lorentz violation are important to our understanding of fundamental physics, and interest in them has picked up a great deal in the twenty-first century. For some of the most natural forms of Lorentz violation involving electrons and positrons, there are competing bounds coming from high-energy astrophysical observations and laboratory tests with optical atomic clocks. I discuss the advantages and limitations of both these approaches and how they may evolve in the future.
... This generalizes the modifications from d = 4 violations found in Refs. [69] and [70]. The velocity-dependent C tensor can be expanded in spin-weighted spherical harmonics. ...
... Note that the C [1] zρ coefficient combination also depends on the Euler angles. A demonstration of the above rotation is provided in Ref. [70], where the effects of d = 4 violations on binary systems are simulated. ...
The effects of Lorentz and CPT violations on macroscopic objects are explored. Effective composite coefficients for Lorentz violation are derived in terms of coefficients for electrons, protons, and neutrons in the Standard-Model Extension, including all minimal and nonminimal violations. The hamiltonian and modified Newton's second law for a test body are derived. The framework is applied to free-fall and torsion-balance tests of the weak equivalence principle and to orbital motion. The effects on continuous media are studied, and the frequency shifts in acoustic resonators are calculated.
... This generalizes the modifications from d = 4 violations found in Refs. [69,70]. ...
... Note that the C [1] zρ coefficient combination also depends on the Euler angles. A demonstration of the above rotation is provided in Ref. [70], where the effects of d = 4 violations on binary systems are simulated. ...
The effects of Lorentz and CPT violations on macroscopic objects are explored. Effective composite coefficients for Lorentz violation are derived in terms of coefficients for electrons, protons, and neutrons in the Standard-Model Extension, including all minimal and non-minimal violations. The hamiltonian and modified Newton’s second law for a test body are derived. The framework is applied to free-fall and torsion-balance tests of the weak equivalence principle and to orbital motion. The effects on continuous media are studied, and the frequency shifts in acoustic resonators are calculated.
We present a 3+1 formulation of the effective field theory framework called the standard model extension in the gravitational sector. The explicit local Lorentz and diffeomorphism symmetry breaking assumption is adopted, and we perform a Dirac-Hamiltonian analysis. We show that the structure of the dynamics presents significant differences from general relativity and other modified gravity models. We explore Hamilton’s equations for some special choices of the coefficients. Our main application is cosmology, and we present the modified Friedmann equations for this case. The results show some intriguing modifications to standard cosmology. In addition, we compare our results to existing frameworks and models, and we comment on the potential impact to other areas of gravitational theory and phenomenology.
