Relational mechanics as a gauge theory

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• 作者：Rafael Ferraro
• 关键词：Relational mechanics ; Mach’s principle ; Shape ; dynamics
• 刊名：General Relativity and Gravitation
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：48
• 期：2
• 全文大小：555 KB
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  8.Barbour, J.B., Pfister H. (eds.): Einstein Studies, vol. 6: Mach’s Principle: From Newton’s Bucket to Quantum Gravity. Birkhäuser: Boston (1995)
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  23.Kuchař, K.V.: In: Kunstatter, G., Vincent, D., Williams, J. (eds.) Proceedings of the 4th. Canadian Conference on General Relativity and Relativistic Astrophysics. World Scientific: Singapore (1992)
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  25.Mercati, F.: A Shape Dynamics Tutorial. arXiv:​1409.​0105 (2014)
  26.Anderson, E.: The problem of time and quantum cosmology in the relational particle mechanics arena. arXiv:​1111.​1472v3 (2011)
  27.Einstein, A.: Ann. Phys. 354, 769–822 (1916) (English translation In: H.A. Lorentz, A. Einstein, H. Minkowski, H. Weyl, The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Dover Publications: New York (1952))
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• 作者单位：Rafael Ferraro (1) (2)
  
  1. Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Sucursal 28, Casilla de Correo 67, 1428, Buenos Aires, Argentina
  2. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428, Buenos Aires, Argentina
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Relativity and Cosmology
  Differential Geometry
  Quantum Physics
  Astronomy, Astrophysics and Cosmology
  
• 出版者：Springer Netherlands
• ISSN：1572-9532

文摘

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 \(\mathbf{P}\), intrinsic angular momentum \(\mathbf{J}\) and intrinsic inertia tensor \(\mathbf{I}\). 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).