Theories of Gravitation in the Twilight of Classical Physics

Renn, Jürgen; Schemmel, Matthias

doi:10.1007/978-0-8176-4940-1_1

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…Initially Hilbert followed Einstein in this belief (see the proofs of his first note in Ref. [108]).…”

Section: Some Brief Early Historymentioning

confidence: 99%

“…thus it is a conserved "current" on shell (i.e., when the field equations are satisfied). Substituting ( 86) into (108) gives the explicit expression…”

Section: The Translational Noether Currentmentioning

confidence: 99%

“…61,98 e Einstein and Hilbert had quite different agendas; 112,115,136,141 Hilbert in his Foundation of Physics papers, based on the work of Einstein and Mie, was using his axiomatic method with the objective of finding a unified field theory of gravity and electromagnetism. 15,28,58,108,109,114 July 28, 2015 0:26 World Scientific Review Volume -9.75in x 6.5in 100GR˙Ch4˙150726v1 page 5Gravitational energy for GR and Poincaré gauge theories:a covariant Hamiltonian approach 5 l The sign in this expression is dictated by the condition for positive energy determined by the Hamiltonian using our local Minkowski signature convention: Pµ = (−E/c, p).…”

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confidence: 99%

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Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Chen

Nester

Tung

2017

One Hundred Years of General Relativity

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Our topic concerns a long standing puzzle: the energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy-momentum and angular momentum/center-of-mass momentum (CoMM). It is known that these quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. In the first part of this work we review some early history, much of it not so well known, on the subject of gravitational energy in Einstein's general relativity (GR), noting especially Noether's contribution. In the second part we review (including some new results) much of our covariant Hamiltonian formalism and apply it to Poincaré gauge theories of gravity (PG), with GR as a special case. The key point is that the Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and, furthermore it determines the boundary conditions for the dynamical variables. Energy-momentum and angular momentum/CoMM are associated with the geometric symmetries under Poincaré transformations. They are best described in a local Poincaré gauge theory. The type of spacetime that naturally has this symmetry is Riemann-Cartan spacetime, with a metric compatible connection having, in general, both curvature and torsion. Thus our expression for the energy-momentum of physical systems is obtained via our covariant Hamiltonian formulation applied to the PG. d One reason was his famous "hole" argument. 61,98 e Einstein and Hilbert had quite different agendas; 112,115,136,141 Hilbert in his Foundation of Physics papers, based on the work of Einstein and Mie, was using his axiomatic method with the objective of finding a unified field theory of gravity and electromagnetism. 15,28,58,108,109,114 July 28, 2015 0:26 World Scientific Review Volume -9.75in x 6.5in 100GR˙Ch4˙150726v1 page 5Gravitational energy for GR and Poincaré gauge theories:a covariant Hamiltonian approach 5 l The sign in this expression is dictated by the condition for positive energy determined by the Hamiltonian using our local Minkowski signature convention: Pµ = (−E/c, p).

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“…Initially Hilbert followed Einstein in this belief (see the proofs of his first note in Ref. [108]).…”

Section: Some Brief Early Historymentioning

confidence: 99%

“…thus it is a conserved "current" on shell (i.e., when the field equations are satisfied). Substituting ( 86) into (108) gives the explicit expression…”

Section: The Translational Noether Currentmentioning

confidence: 99%

mentioning

confidence: 99%

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Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Chen

Nester

Tung

2017

One Hundred Years of General Relativity

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“…A local field theory would be ideal. Eventually, with some help from Einstein, Gunnar Nordström had a satisfactory scalar theory [Renn and Schemmel, 2007], at least prior to the observed bending of light. This theory was fully in accord with Special Relativity, in the sense of being a local field theory with (at least) invariance under the Poincaré group of translations and Lorentz boosts and rotations-though in fact the group is larger, as will appear shortly.…”

Section: The Neglected Rivalrymentioning

confidence: 99%

Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang–Mills and Gravitational Theories

Pitts¹

2011

The British Journal for the Philosophy of Science

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Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang-Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy.

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“…16 These identities -one for each arbitrariness in the choice of a coordinate -were later recognized as the contracted Bianchi ones. Hilbert had already derived them in 1915 (Hilbert, 1915) in a somewhat 'convoluted' manner which was not understood at the time and which keeps modern historians busy (Renn and Stachel, 2007;Sauer, 1999). One can find in Rowe (2002) an interesting discussion on the 'memory loss' of Göttingen circles about the Italian differential geometry which explains why they struggled with these identities and also why the latter were rediscovered a certain number of times.…”

Section: Introductionmentioning

confidence: 99%

On the wonderfulness of Noether's theorems, 100 years later, and Routh reduction

Leone

2018

Preprint

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This paper is written in honour of the centenary of Emmy Amalie Noether's famous article entitled Invariante Variationsprobleme. It firstly aims to give an exposition of what we believe to be the most significant and elegant issues regarding her theorems, through the lens of classical mechanics. Despite the limitation to this field, we try to illustrate the key ideas of her work in a rather complete and pedagogical manner which, we hope, presents some original aspects. The notion of symmetry coming naturally with the idea of simplification, the last part is devoted to the interplay between Noether point symmetries and the reduction procedure introduced by Edward John Routh in 1877. Le temps d'apprendre à vivre il est déjà trop tardLouis Aragon

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Theories of Gravitation in the Twilight of Classical Physics

Cited by 4 publications

References 18 publications

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang–Mills and Gravitational Theories

On the wonderfulness of Noether's theorems, 100 years later, and Routh reduction

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