Relational mechanics as a gauge theory

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 comp...

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Autor principal:	Ferraro, R.
Formato:	JOUR
Materias:	Mach’s principle Relational mechanics Shape-dynamics
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00017701_v48_n2_p1_Ferraro
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_00017701_v48_n2_p1_Ferraro2023-10-03T13:52:10Z Relational mechanics as a gauge theory Ferraro, R. Mach’s principle Relational mechanics Shape-dynamics 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. Fil:Ferraro, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00017701_v48_n2_p1_Ferraro
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Mach’s principle Relational mechanics Shape-dynamics
spellingShingle	Mach’s principle Relational mechanics Shape-dynamics Ferraro, R. Relational mechanics as a gauge theory
topic_facet	Mach’s principle Relational mechanics Shape-dynamics
description	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.
format	JOUR
author	Ferraro, R.
author_facet	Ferraro, R.
author_sort	Ferraro, R.
title	Relational mechanics as a gauge theory
title_short	Relational mechanics as a gauge theory
title_full	Relational mechanics as a gauge theory
title_fullStr	Relational mechanics as a gauge theory
title_full_unstemmed	Relational mechanics as a gauge theory
title_sort	relational mechanics as a gauge theory
url	http://hdl.handle.net/20.500.12110/paper_00017701_v48_n2_p1_Ferraro
work_keys_str_mv	AT ferraror relationalmechanicsasagaugetheory
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Relational mechanics as a gauge theory

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