On the localization of the gravitational energy

Pinto-Neto, Nelson; Trajtenberg, P. I.

doi:10.1590/s0103-97332000000100020

Cited by 11 publications

(15 citation statements)

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“…The emergence of an additional gauge group deprives of physical meaning the precise quantitative relationship between the effective curved metric and the/a flat background metric, making the flat spacetime(s) elusive (Grishchuk et al, 1984;Norton, 1994;Pinto-Neto and Trajtenberg, 2000), a point made early in little-known work by William Band (Band, 1942b;Band, 1942a) and conceded but still insufficiently attended by Nathan Rosen in his application to gravitational energy localization (Rosen, 1963). Which flat metric underlies the effective curved geometry?…”

Section: (No) Ontology Of Particle Physics Derivationsmentioning

confidence: 99%

“…Thus besides the (here trivial) formal general covariance, one has an additional gauge freedom to alter the flat metric tensor while leaving the curved metric and matter fields alone, or, alternately, to alter the curved metric and matter fields by what looks like a coordinate transformation while leaving the flat metric alone (Grishchuk et al, 1984;Norton, 1994;Pinto-Neto and Trajtenberg, 2000;. If one fixes the coordinates to be Cartesian, then one has η µν = diag(−1, 1, 1, 1) and the additional gauge freedom looks like a coordinate transformation in single-metric General Relativity (at least for transformations connected to the identity).…”

Section: Appendixmentioning

confidence: 99%

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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

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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.

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Section: (No) Ontology Of Particle Physics Derivationsmentioning

confidence: 99%

Section: Appendixmentioning

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

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“…However, quantum decoherence is not yet a complete answer to the measurement problem [6]. It dose not explain the apparent collapse after the measurement is completed, or why all but one of the diagonal elements of the density matrix become null when the measurement is finished [7]. Also, in its developments like the consistence histories approach [8] the important role played by observers is not yet explained [9] and it is not clear how to describe a quantum universe when the background geometry is not classical [10].…”

Section: Introductionmentioning

confidence: 99%

The quantum state of the universe from deformation quantization and classical-quantum correlation

Rashki

Jalalzadeh

2017

Gen Relativ Gravit

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In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-WignerGroenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is described by the Moyal-Wheeler-DeWitt equation which has exact solutions in Moyal phase space, resulting in Wigner quasiprobability distribution functions peaking around the classical paths for large values of scale factor. We show that the Wigner functions of these models are peaked around the non-singular universes with quantum modified density parameter of radiation.

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“…1 A background metric allows introducing a gravitational energy-momentum tensor [17], not merely a pseudotensor. As a result, gravitational energy and momentum are independent of the coordinates but dependent on the gauge [18]. If we want to regard the background metric seriously as a property of space-time and not just treat it as a useful fiction, then the relation between the effective curved metric's null cone and that of the flat background must be considered.…”

Section: Introductionmentioning

confidence: 99%

Universally coupled massive gravity

Pitts

Schieve

2007

Theor Math Phys

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We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The FreundMaheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein's theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way.

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On the localization of the gravitational energy

Cited by 11 publications

References 0 publications

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

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

The quantum state of the universe from deformation quantization and classical-quantum correlation

Universally coupled massive gravity

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