Foundations of anisotropic relativistic mechanics

Sonego, Sebastiano; Pin, Massimo

doi:10.1063/1.3104065

Cited by 28 publications

(34 citation statements)

References 143 publications

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“…Since then conformal symmetries have been successfully exploited for many physical systems (see, e.g., reviews [15], [16]). Transformations which conformally modify Minkowski metric have been introduced in the context of the special relativity kinematics in the presence of space anisotropy in [17] and [18] (see also [19]). As a matter of fact, those works are not directly related to the subject of the present study as they consider the case of a constant anisotropy degree, not dependent on the frame motion.…”

Section: Conceptual Frameworkmentioning

confidence: 99%

Cosmological models based on relativity with a privileged frame

Burde

2020

Int. J. Mod. Phys. D

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Special relativity (SR) with a privileged frame is a framework, which, like the standard relativity theory, is based on the relativity principle and the universality of the (two-way) speed of light but includes a privileged frame as an essential element. It is developed using the following first principles: (1) Anisotropy of the one-way speed of light in an inertial frame is due to its motion with respect to the privileged frame; (2) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant; (3) A set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of transformations. The correspondingly modified general relativity (GR), like the standard GR, is based on the equivalence principle but with the properly modified space-time local symmetry in which an invariant combination differs from the Minkowski interval of the standard SR. That combination can be converted into the Minkowski interval by a change of space-time variables and then the complete apparatus of general relativity can be applied in the new variables. However, to calculate physical effects, an inverse transformation to the 'physical' time and space intervals is to be used. Applying the modified GR to cosmology yields the luminosity distance -redshift relation corrected such that the observed deceleration parameter can be negative as it was derived from the data for type Ia supernovae. Thus, the observed negative values of the deceleration parameter can be explained within the matter-dominated Friedman-Robertson-Walker (FRW) cosmological model of the universe without introducing the dark energy. A number of other observations, such as Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Background (CMB), that are commonly considered as supporting the late-time cosmic acceleration and the existence of dark energy, also can be well fit to the cosmological model arising from the GR based on the SR with a privileged frame.

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Section: Conceptual Frameworkmentioning

confidence: 99%

Cosmological models based on relativity with a privileged frame

Burde

2020

Int. J. Mod. Phys. D

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“…Electromagnetism is only relevant, if present within the theory, as a way to fix the arbitrary velocity scale, which is then identified with the speed of light. This deep and fascinating result, although well known in the specialized literature, [3][4][5][6][7][8][9][10][11] is not commonly found in textbooks, 12 because its usual proof is rather complicated and uninspiring. It is the purpose of the present paper to present a derivation of the von Ignatowsky result using elementary considerations, which, in our opinion, sheds new light on the result.…”

Section: Introductionmentioning

confidence: 99%

Getting the Lorentz transformations without requiring an invariant speed

Pelissetto

Testa

2015

American Journal of Physics

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The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically necessary. The existence of an invariant speed is \textit{not} a necessary assumption, and in fact is a consequence of the principle of relativity (though the finite value of this speed must, of course, be obtained from experiment). Von Ignatowsky derived this result in 1911, but it is still not widely known and is absent from most textbooks. Here we present a completely elementary proof of the result, suitable for use in an introductory course in special relativity.Comment: 4 pages, 1 figur

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“…Moreover, bimetric constructions can be naturally incorporated in the Finsler framework [32]. Finally, we mention that Finsler geometry can be closely related to the standard-model extension [33]. Before proceeding to the cosmological application of Finsler geometry, in the following subsections we briefly present its basic features.…”

Section: Relativistic Finsler Geometrymentioning

confidence: 99%

Resembling dark energy and modified gravity with Finsler-Randers cosmology

et al. 2013

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In this article we present the cosmological equivalence between the relativistic Finsler-Randers cosmology, with dark energy and modified gravity constructions, at the background level. Starting from a small deviation from the quadraticity of the Riemannian geometry, through which the local structure of General Relativity is modified and the curvature theory is extended, we extract the modified Friedmann equation. The corresponding extended Finsler-Randers cosmology is very interesting, and it can mimic dark-energy and modified gravity, describing a large class of scalefactor evolutions, from inflation to late-time acceleration, including the phantom regime. In this respect, the non-trivial universe evolution is not attributed to a new scalar field, or to gravitational modification, but it arises from the modification of the geometry itself.PACS numbers: 95.36.+x, 04.50.Kd

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Foundations of anisotropic relativistic mechanics

Cited by 28 publications

References 143 publications

Cosmological models based on relativity with a privileged frame

Cosmological models based on relativity with a privileged frame

Getting the Lorentz transformations without requiring an invariant speed

Resembling dark energy and modified gravity with Finsler-Randers cosmology

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