Foundations of Physics

, Volume 48, Issue 5, pp 558–578 | Cite as

On Gravitational Energy in Newtonian Theories

  • Neil Dewar
  • James Owen Weatherall
Part of the following topical collections:
  1. Philosophical Aspects in the Foundations of Physics


There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton–Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.


Gravitational energy Newton-Cartan theory Geometrized Newtonian gravitation General relativity Gravitational stress Gravitational mass-momentum Newtonian Weyl tensor 



This paper is partially based upon work supported by the National Science Foundation under Grant No. 1331126. We are grateful to David Malament for helpful conversations about the material presented here, including suggesting the form of Eq. (23); to Erik Curiel for discussions about conformal invariance in the context of geometrized Newtonian gravitation; and to David Wallace for discussions of these and related ideas. The manuscript was improved by comments from James Read and two anonymous referees. Weatherall is grateful for feedback from an audience at the 18th UK/European Foundations of Physics Conference in London, UK.


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Authors and Affiliations

  1. 1.Munich Center for Mathematical PhilosophyLMU MunichMunichGermany
  2. 2.Department of Logic and Philosophy of ScienceUniversity of CaliforniaIrvineUSA

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