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Abstract:

Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the resulting equations of motion are valid in any frame. The compensating terms provide inertial forces depending on the total momentum P, intrinsic angular momentum J and intrinsic inertia tensor I. Therefore, the privileged frames where Newton’s equations are valid (Newtonian frames) are completely determined by the matter distribution of the universe (Machianization). At the Hamiltonian level, the gauge invariance leads to first class constraints that remove those degrees of freedom that make no sense once the absolute space has been eliminated. This reformulation of classical mechanics is entirely relational, since it is a dynamics for the distances between particles. It is also Machian, since the rotation of the rest of the universe produces centrifugal effects. It then provides a new perspective to consider the foundational ideas of general relativity, like Mach’s principle and the weak equivalence principle. With regard to the concept of time, the absence of an absolute time is known to be a characteristic of parametrized systems. Furthermore, the scale invariance of those parametrized systems whose potentials are inversely proportional to the squared distances can be also gauged by introducing another compensating term associated with the intrinsic virial G (shape-dynamics). © 2016, Springer Science+Business Media New York.

Registro:

Documento: Artículo
Título:Relational mechanics as a gauge theory
Autor:Ferraro, R.
Filiación:Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Sucursal 28, Casilla de Correo 67, Buenos Aires, 1428, Argentina
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Mach’s principle; Relational mechanics; Shape-dynamics
Año:2016
Volumen:48
Número:2
Página de inicio:1
Página de fin:22
DOI: http://dx.doi.org/10.1007/s10714-016-2018-5
Título revista:General Relativity and Gravitation
Título revista abreviado:Gen. Relativ. Gravit.
ISSN:00017701
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00017701_v48_n2_p1_Ferraro

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Citas:

---------- APA ----------
(2016) . Relational mechanics as a gauge theory. General Relativity and Gravitation, 48(2), 1-22.
http://dx.doi.org/10.1007/s10714-016-2018-5
---------- CHICAGO ----------
Ferraro, R. "Relational mechanics as a gauge theory" . General Relativity and Gravitation 48, no. 2 (2016) : 1-22.
http://dx.doi.org/10.1007/s10714-016-2018-5
---------- MLA ----------
Ferraro, R. "Relational mechanics as a gauge theory" . General Relativity and Gravitation, vol. 48, no. 2, 2016, pp. 1-22.
http://dx.doi.org/10.1007/s10714-016-2018-5
---------- VANCOUVER ----------
Ferraro, R. Relational mechanics as a gauge theory. Gen. Relativ. Gravit. 2016;48(2):1-22.
http://dx.doi.org/10.1007/s10714-016-2018-5