REVIEW
Some remarks on the notions of general covariance and background independence
General Relativity and Quantum Cosmology · Submitted 22 Mar 2006 · 27 references
Pith's verdict: A historically sharp correction to Einstein's 1913 scalar-gravity argument, with a small unproven step that deserves a fix but doesn't sink the point.
T0 · AI review
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Referee report
The paper
The paper claims
Einstein's 1913 Gedankenexperiment against scalar gravity is not convincing because it neglects the energy cost of lifting the stress in the shaft walls.
The reading
What carries the argument
The load-bearing object in the historical part is the interaction-energy term (43), $E_{\rm interaction}=\int_D(\Phi/c^2)T_{\rm matter}\,d^3x$, which couples the scalar gravitational potential to the trace of the matter energy-momentum tensor and accounts for the weight of stress. In the definitional part, the central machinery is the distinction between covariance (the whole equation, background included, is transformed) and invariance (the background stays fixed), together with Anderson's local 'absolute structure' criterion for identifying background fields; the paper shows through examples that this criterion is either trivializable or misclassifies physical fields.
Extended reading notes
Core claim
The paper makes two central claims. First, no workable definition of general covariance or background independence has been given that would make either a non-trivial selection principle for physical theories. Second, Einstein's 1913 Gedankenexperiment does not show that Poincaré-invariant scalar gravity violates energy conservation. In the model theory $\square\Phi=-\kappa T$ with action (30), the total energy has field, matter, and interaction contributions, and the interaction term $E_{\rm interaction}=\int_D(\Phi/c^2)T_{\rm matter}\,d^3x$ is exactly the weight of stress. During the raising phase of the cycle the shaft walls carry the same sideways stress the box walls carried while lowering, and lifting that stress distribution costs energy even though the shaft material does not move. Including this term converts Einstein's claimed net gain into the identity (44), so the cycle conserves energy. The paper's conclusion is stated directly: 'I conclude that Einstein's argument is not convincing.'
Load-bearing premise
The conclusion depends on the standard formula (39) being the correct way to count energy in the coupled scalar-matter system; if energy has to be defined differently, the balance (44) is not guaranteed.
Editorial extensions
If this is right
- Einstein's 1913 Gedankenexperiment should not be cited as a valid argument that scalar gravity is internally inconsistent, and therefore not as a necessary historical step toward general covariance.
- Within trace-coupled scalar gravity, moving a stressed container through a gravitational potential conserves energy only if the potential energy of the stress distribution in all supporting structures is counted.
- Diffeomorphism invariance plus the absence of absolute structures cannot serve as a precise binary criterion for background independence.
- The experimental rejection of scalar gravity rests on its predictions, such as the wrong perihelion precession and the absence of light deflection, not on an energy-conservation inconsistency.
Reading between the lines
- My inference: the same stress-weight accounting should apply to any thought experiment that moves a stressed container in a gravitational field, and equation (43) gives a concrete test for when such terms are negligible.
- My inference: the definitional part suggests that background independence is best treated as a dynamical or degree-like property rather than a binary label, so it cannot by itself settle competition between quantum-gravity programs.
- My inference: one could extend the model to non-linear scalar-tensor theories to check whether the identity (44) survives back-reaction, since the paper's linear model refutes Einstein's argument but does not establish conservation in every such theory.
Original abstract
In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange argument that Einstein put forward in his 1913 "Entwurf paper" with M. Grossmann to discredit scalar theories of gravity in order to promote general covariance.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange argument that Einstein put forward in his 1913 "Entwurf paper" with M. Grossmann to discredit scalar theories of gravity in order to promote general covariance.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange argument that Einstein put forward in his 1913 "Entwurf paper" with M. | contribution 0.70 | 0.39 | 0.05 | asserted 0.46 |
| s1 | Grossmann to discredit scalar theories of gravity in order to promote general covariance. | contribution 0.81 | 0.08 | 0.05 | asserted 0.91 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:gr-qc/0603087 by the authors.
References
How the literature uses it
40 arXiv papers cite this in 51 sentences
Papers citing it · 34 sentences without a confident label
Cites it as background 15 papers
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This addresses the relational horn [ref] of the Absolute versus Relational (Motion) Debate [ref] , often contemporarily also referred to as `seeking Background Independence' [ref] .
Absolute versus Relational Debate: a Modern Global Version · Introduction · 0.95
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This addresses the relational horn [ref] of the Absolute versus Relational (Motion) Debate [ref] , often contemporarily also referred to as `seeking Background Independence' [ref] .
Shape Theory. III. Comparative Theory of Backgound Independence · Aspect 1: Configurational Relationalism · 0.84
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As will appear below, (substantive) general covariance does play a key role, albeit as a lemma rather than a premise, but generalized relativity of motion does not play any role[The concept of general covariance has become problematic especially in the last decade [ref] .
Einstein's Equations for Spin $2$ Mass $0$ from Noether's Converse Hilbertian Assertion · Introduction · 0.87
Discussion
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