General Relativity and Gravitation

, Volume 43, Issue 10, pp 2865–2884 | Cite as


  • Gordon Belot
Research Article


Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.


Background-independence General relativity Absolute objects 


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  1. 1.
    Anderson J.: Relativity principles and the role of coordinates in physics. In: Chiu, H.Y., Hoffman, W. (eds) Gravitation and Relativity, pp. 175–194. W.A. Benjamin Inc, New York (1964)Google Scholar
  2. 2.
    Anderson J.: Principles of Relativity Physics. Academic Press, New York (1967)Google Scholar
  3. 3.
    Andersson L.: Momenta and reduction in general relativity. J. Geom. Phys. 4, 289–314 (1987)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Anninos, D., Ng, G.S., Strominger, A.: Asymptotic symmetries and charges in de Sitter space. ArXiv: 1009.4730v1 [gr-qc] (2010)Google Scholar
  5. 5.
    Ashtekar A., Magnon A.: Asymptotically anti-de Sitter space-times. Cl. Quantum Gravit. 1, L39–L44 (1984)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Belot G.: An elementary notion of gauge equivalence. Gen. Relativ. Gravit. 40, 199–215 (2008)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Carlip S.: Quantum Gravity in 2 + 1 Dimensions. Cambridge University Press, Cambridge (1998)zbMATHCrossRefGoogle Scholar
  8. 8.
    Chruściel P., Isenberg J.: Nonisometric vacuum extensions of vacuum maximal globally hyperbolic spacetimes. Phys. Rev. D 48, 1616–1628 (1993)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Ciarlet P., Gratie L., Mardare C.: Intrinsic methods in elasticity: a mathematical survey. Discret. Contin. Dyn. Syst. 23, 133–164 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Crnković v., Witten E.: Covariant description of canonical formalism in geometrical theories. In: Hawking, S., Israel, W. (eds) Three Hundred Years of Gravitation, pp. 676–684. Cambridge University Press, Cambridge (1987)Google Scholar
  11. 11.
    Deligne P., Freed D.: Classical field theory. In: Deligne, P., Etingof, P., Freed, D., Jeffrey, L., Kazhdan, D., Morgan, J., Morrison, D., Witten, E. (eds) Quantum Fields and Strings: A Course for Mathematicians, vol. 1, pp. 137–225. American Mathematical Society, Providence (1999)Google Scholar
  12. 12.
    Diacu F.: Singularities of the N-Body Problem. Les Publications CRM, Montréal (1992)Google Scholar
  13. 13.
    Dirac P.A.M.: Lectures on Quantum Mechanics. Dover, New York (2001)Google Scholar
  14. 14.
    Earman J.: Covariance, invariance, and the equivalence of frames. Found. Phys. 4, 267–289 (1974)MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Friedman M.: Relativity principles, absolute objects, and symmetry groups. In: Suppes, P. (eds) Space, Time, and Geometry, pp. 296–320. Reidel, Dordrecht (1973)CrossRefGoogle Scholar
  16. 16.
    Friedman M.: Foundations of Spacetime Theories. Princeton University Press, Princeton (1983)Google Scholar
  17. 17.
    Geroch R.: Electromagnetism as an aspect of geometry? Already unified field theory—the null case. Annal. Phys. 36, 147–187 (1966)MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Geroch R.: Asymptotic stucture of space-time. In: Esposito, F.P., Witten, L. (eds) Asymptotic Stucture of Space-Time, pp. 1–105. Plenum Press, New York (1977)CrossRefGoogle Scholar
  19. 19.
    Giulini D.: Some remarks on the notions of general covariance and background independence. In: Seiler, E., Stamatescu, I.O. (eds) Approaches to Fundamental Physics: An Assessment of Current Theoretical Ideas, pp. 105–120. Springer, Berlin (2007)Google Scholar
  20. 20.
    Gotay, M., Castrillón López, M.: Covariantizing classical field theories (2010). ArXiv:1008.3170v1 [math-ph]Google Scholar
  21. 21.
    Gotay M., Nester J., Hinds G.: Presymplectic manifolds and the Dirac–Bergmann theory of constraints. J. Math. Phys. 19, 2388–2399 (1978)MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    Gryb S.: A definition of background independence. Cl. Quantum Gravit. 27, 215018 (2010)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Hawking S., Ellis G.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)zbMATHCrossRefGoogle Scholar
  24. 24.
    Henneaux M., Teitelboim C.: Quantization of Gauge Systems. Princeton University Press, Princeton (1992)zbMATHGoogle Scholar
  25. 25.
    Janssen, M.: No success like failure …: Einstein’s quest for general relativity, 1907–1920 (2008). Phil-Sci archive: 00004377Google Scholar
  26. 26.
    Janssen, M., Schulmann, R., Illy, J., Lehner, C., Kormos-Buchwald, D. (eds): The Collected Papers of Albert Einstein, vol. 7. The Berlin Years: Writings, 1918–1921. Princeton University Press, Princeton (2002)Google Scholar
  27. 27.
    Kolář I., Michor P., Slovák J.: Natural Operations in Differential Geometry. Springer, Berlin (1993)zbMATHGoogle Scholar
  28. 28.
    Lee J., Wald R.: Local symmetries and constraints. J. Math. Phys. 31, 725–743 (1990)MathSciNetADSzbMATHCrossRefGoogle Scholar
  29. 29.
    Louko J., Marolf D.: The solution space of 2 + 1 gravity on \({\mathbb{R} \times {T} \sp 2}\) in Witten’s connection formulation. Cl. Quantum Gravit. 11, 311–330 (1994)MathSciNetADSzbMATHCrossRefGoogle Scholar
  30. 30.
    Marsden J., Hughes T.: Mathematical Foundations of Elasticity. Dover, New York (1994)Google Scholar
  31. 31.
    Meusburger C.: Cosmological measurements, time, and observables in (2 + 1)-dimensional gravity. Cl. Quantum Gravit. 26, 055006 (2009)MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    Norton J.: Einstein, Nordström, and the early demise of Lorentz-covariant, scalar theories of gravity. Arch. Hist. Exact Sci. 45, 17–94 (1992)MathSciNetADSzbMATHCrossRefGoogle Scholar
  33. 33.
    Norton J.: General covariance and the foundations of general relativity: eight decades of dispute. Rep. Prog. Phys. 56, 791–858 (1993)MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    Olver P.: Applications of Lie Groups to Differential Equations, 2nd edn. Springer, Berlin (1993)zbMATHCrossRefGoogle Scholar
  35. 35.
    Pitts B.: Absolute objects and counterexamples: Jones-Geroch dust, Toretti constant curvature, tetrad-spinor, and scalar density. Stud. Hist. Philos. Mod. Phys. 37, 347–371 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Ravndal, F.: Scalar gravitation and extra dimensions. In: Cranström, C., Montonen, C. (eds.) Proceedings of the Gunnar Nordström Symposium of Theoretical Physics, pp. 151–164. The Finnish Society of Sciences and Letters, Helsinki (2004)Google Scholar
  37. 37.
    Rovelli C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  38. 38.
    Sachs R., Wu H.H.: General Relativity for Mathematicians. Springer, Berlin (1977)zbMATHCrossRefGoogle Scholar
  39. 39.
    Sklar L.: Philosophy and Spacetime Physics. University of California Press, Berkeley (1985)Google Scholar
  40. 40.
    Smolin L.: The present moment in quantum cosmology: Challenges to the argument for the elimination of time. In: Durie, R. (eds) Time and the Instant: Essays in the Physics and Philosophy of Time, pp. 112–143. Clinamen, Manchester (2001)Google Scholar
  41. 41.
    Smolin L.: The case for background independence. In: Rickles, D., French, S., Saatsi, J. (eds) The Structural Foundations of Quantum Gravity, pp. 196–239. Oxford University Press, Oxford (2006)CrossRefGoogle Scholar
  42. 42.
    Sorkin R.: An example relevant to the Kretschmann–Einstein debate. Mod. Phys. Lett. A 17, 695–700 (2002)MathSciNetADSzbMATHCrossRefGoogle Scholar
  43. 43.
    Straumann, N.: Reflections on gravity (2000). ArXiv:astro-ph/0006423v1Google Scholar
  44. 44.
    Torre C.: Covariant phase space formulation of parameterized field theories. J. Math. Phys. 33, 3802–3811 (1992)MathSciNetADSzbMATHCrossRefGoogle Scholar
  45. 45.
    Wolf J.: Spaces of Constant Curvature, 5th edn. Publish or Perish, Wilmington (1984)Google Scholar
  46. 46.
    Zuckerman G.: Action principles and global geometry. In: Yau, S.T. (eds) Mathematical Aspects of String Theory, pp. 259–284. World Scientific, Singapore (1987)Google Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MichiganAnn ArborUSA

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