Motion of a body in general relativity

Geroch, Robert; Jang, Pong Soo

doi:10.1063/1.522416

Cited by 90 publications

(127 citation statements)

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“…7 Ehlers and Rudolph go on to explain in a parenthetical that For this reason the mathematically elegant argument given in (Geroch and Jang, 1975) is physically not very enlightening, in our opinion. We will return to this point in section 4.1.…”

Section: Geodesic Dynamicsmentioning

confidence: 95%

“…Shrinking the body down to in nitesimal volume results in a singular charge density, and extending the particle still results in having to grapple with non-analytically expressible expansions of the e ects that the particle's own eld has on its motion. 7 Ehlers and Rudolph go on to explain in a parenthetical that For this reason the mathematically elegant argument given in (Geroch and Jang, 1975) is physically not very enlightening, in our opinion. We will return to this point in section 4.1.…”

Section: Whither Test Particles?mentioning

confidence: 95%

“…49 The rst result by Geroch and Jang (1975) considers sequences of ostensible energy-momentum tensor elds of ever narrowing support. More precisely, Geroch and Jang's theorem can be formulated as follows:…”

Section: Geroch-jang Particlesmentioning

confidence: 99%

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Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

Tamir

2012

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

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In his initial formulation of the general theory of relativity, Einstein's proposal that freely falling gravitating massive bodies follow geodesic paths was submitted as an independent fundamental principle. By adopting this geodesic principle to supply the theory's law of motion, Einstein was immediately able to recover both the free-fall motion of bodies in non-relativistic regimes and the previously anomalous precession of the perihelion of Mercury. Over the last century numerous ostensible proofs claiming to have derived the geodesic principle from Einstein's eld equations have been developed. As a result physicists and philosophers of science alike frequently herald Einstein's theory for having the unique distinction of being able to derive its dynamical law of motion from its own eld equations.In this paper I critically survey the multiple attempts to derive the geodesic principle in the context of Einstein's theory. Grouping these results into three major families, which I refer to as (1) limit operation proofs, (2) 0 th -order proofs, and (3) singularity proofs, I argue that none of these strategies successfully demonstrates the geodesic principle, canonically interpreted as a dynamical law that massive bodies must actually follow geodesic paths in Einstein's theory.Speci cally, I argue for the following three claims: First, limit operation proofs fail to demonstrate that massive bodies are ever guaranteed to follow geodesic paths. Second, on the contrary 0 thorder proofs demonstrate that extended massive bodies generically deviate from uniformly geodesic paths. Moreover, the only potentially extended distributions of matter and energy that fail to avoid a uniform geodesic evolution are highly unstable, deviating from such motion under arbitrary perturbations of their angular momentum (or higher order moments). Third, thanks to certain mathematical theorems concerning distribution theory, alternative representations of massive bodies as unextended point particles must result either in precluding the possibility of coupling the particle to the spacetime metric in a way that is coherent with Einstein's eld equations or in having to excise the particle (and its would-be path) from spacetime entirely. This three pronged argument reveals that not only does the geodesic law of motion fail to be a deductive consequence of the eld equations, but also any attempt to canonically interpret the geodesic principle in such a way requires * In the following, M will be taken to be a smooth, orientable, four-dimensional manifold, and (M, g ab ) will be referred to as a Lorentzian spacetime if g ab is a smooth metric of signature (+, −, −, −) de ned on M. Excepting quoted material all further notational conventions follow that of (Wald, 1984).1 Forthcoming: Studies in History and Philosophy of Modern Physics that either the gravitating body is not massive, its existence violates Einstein's eld equations, or it does not exist within the spacetime manifold at all (let alone along a geodesic).Having rejected the canonical in...

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Section: Geodesic Dynamicsmentioning

confidence: 95%

Section: Whither Test Particles?mentioning

confidence: 95%

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Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

Tamir

2012

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

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“…There is a long-standing view, originally due to Einstein, that the geodesic principle has a special status in GR that arises because it can be understood as a theorem, rather than a postulate, of the theory. (It turns out that capturing the geodesic principle as a theorem in GR is non-trivial, but a result due to Bob Geroch and Pong Soo Jang (1975) 1 Thank you to David Malament and Jeff Barrett for helpful comments on a previous version of this paper and for many stimulating conversations on this topic. Thank you, too, to helpful audiences in Paris, Wuppertal, and London, ON, especially John Manchak, Giovanni Valente, Craig Callendar, Alexei Grinbaum, Harvey Brown, David Wallace, Chris Smeenk, Wayne Myrvold, Erik Curiel, and Ryan Samaroo.…”

Section: Introductionmentioning

confidence: 99%

“…For a classic treatments of the problem, including a review of early approaches, see Dixon (1964) and Carmeli (1982). Geroch and Jang (1975) offer brief but insightful comments about the difficulties facing some of the most intuitively obvious ways of capturing the geodesic principle in the introductory remarks of their paper. A particularly prominent alternative approach involves the use of generalized functions, or distributions.…”

Section: Introductionmentioning

confidence: 99%

On the status of the geodesic principle in Newtonian and relativistic physics

Weatherall

2011

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

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Inertial Motion, Explanation, and the Foundations of Classical Spacetime Theories

Weatherall

2017

Towards a Theory of Spacetime Theories

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I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to "explain" inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of "explain" is rather different from what one might have expected. This sense of explanation is connected with a view of theories-I call it the "puzzleball view"-on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions.

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Motion of a body in general relativity

Abstract: A theorem due to

Cited by 90 publications

References 10 publications

Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

On the status of the geodesic principle in Newtonian and relativistic physics

Inertial Motion, Explanation, and the Foundations of Classical Spacetime Theories

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