Gravitation in the Twilight of Classical Physics: An Introduction

Renn, Jürgen; Schemmel, Matthias

doi:10.1007/978-1-4020-4000-9_10

Cited by 21 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Gauge transformations that can be derived from (25), of course, are more complicated, and even if they were to form a group it would lead to a commutator with a field-dependent gauge parameter ξ α [1,2] . Further, according to classification scheme of Henneaux, Kleinschmidt, Gómez [32], the transformations that follow from (25) seem to be an example of trivial gauge symmetries (i.e.…”

Section: Symmetries Of the Einstein-hilbert Action In The Lagrangian mentioning

confidence: 99%

See 1 more Smart Citation

Remarks on the “Non-canonicity Puzzle”: Lagrangian Symmetries of the Einstein-Hilbert Action

2012

View full text Add to dashboard Cite

Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two formulations, the assumption that the Lagrangians from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Einstein-Hilbert action: diffeomorphism, which follows from the PSS and Dirac formulations, and the one that arises from the ADM formulation. We demonstrate that unlike the diffeomorphism transformations, the ADM transformations (as well as others, which can be constructed for the Einstein-Hilbert Lagrangian using Noether's identities) do not form a group. This makes diffeomorphism transformations unique (the term "canonical" symmetry might be suggested). If the two Lagrangians are to be called equivalent, canonical symmetry must be preserved. The interplay between general covariance and the canonicity of the variables used is discussed.

show abstract

Section: Symmetries Of the Einstein-hilbert Action In The Lagrangian mentioning

confidence: 99%

“…In addition, this identity was known before any connection was made to Euler-Lagrange derivatives of the EH action-this is simply the contracted Bianchi identity[23] 10. For an English translation see[25].…”

mentioning

confidence: 96%

Remarks on the “Non-canonicity Puzzle”: Lagrangian Symmetries of the Einstein-Hilbert Action

2012

View full text Add to dashboard Cite

show abstract

“…Hilbert and later Klein had found that the conserved energy-momentum in General Relativity consists of a term proportional to the Einstein tensor and hence having a value of 0 using the Euler-Lagrange equations (vanishing on-shell, one says) and a term with automatically vanishing divergence (a "curl"). They worked with the most straightforwardly derivable expressions for gravitational energy-momentum: pseudo-tensors and what one now calls the Noether operator (Hilbert, 2007;Klein, 1917;Klein, 1918;Pais, 1982;Olver, 1993;Rowe, 1999;Rowe, 2002;Brading and Brown, 2003). Noether also proved a converse to the "Hilbertian assertion," along with converses to the two theorems associated with her name (Noether, 1918).…”

Section: Introductionmentioning

confidence: 99%

Einstein׳s Equations for Spin 2 Mass 0 from Noether׳s Converse Hilbertian Assertion

Pitts

2016

Studies in History and Philosophy of Science Part B: Studies in

View full text Add to dashboard Cite

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a converse "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom ("ghosts") for stability, along with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form.The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed.

show abstract

“…In the 1910s Nordström proposed a theory of gravity that met the strictures of Special Relativity [1,2,3] by having, at least, Lorentz transformations as well as space-and time-translations as symmetries, as well as displaying retarded action through a field medium, as opposed to Newtonian instantaneous action at a distance. Nordström's scalar gravity was a serious competitor to Einstein's program for some years during the middle 1910s.…”

Section: Introductionmentioning

confidence: 99%

Massive Nordström scalar (density) gravities from universal coupling

Pitts

2010

Gen Relativ Gravit

View full text Add to dashboard Cite

Both particle physics and the 1890s Seeliger-Neumann modification of Newtonian gravity suggest considering a "mass term" for gravity, yielding a finite range due to an exponentially decaying Yukawa potential. Unlike Nordström's "massless" theory, massive scalar gravities are strictly Special Relativistic, being invariant under the Poincaré group but not the conformal group. Geometry is a poor guide to understanding massive scalar gravities: matter sees a conformally flat metric, but gravity also sees the rest of the flat metric, barely, in the mass term. Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source. All are new except the Freund-Nambu theory. The smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities. The ease of accommodating electrons, protons and other fermions using density-weighted Ogievetsky-Polubarinov spinors in scalar gravity is noted.

show abstract

Gravitation in the Twilight of Classical Physics: An Introduction

Cited by 21 publications

References 18 publications

Remarks on the “Non-canonicity Puzzle”: Lagrangian Symmetries of the Einstein-Hilbert Action

Remarks on the “Non-canonicity Puzzle”: Lagrangian Symmetries of the Einstein-Hilbert Action

Einstein׳s Equations for Spin 2 Mass 0 from Noether׳s Converse Hilbertian Assertion

Massive Nordström scalar (density) gravities from universal coupling

Contact Info

Product

Resources

About