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Dependence relations in general relativity

  • Antonio VassalloEmail author
Paper in Philosophy of the Natural Sciences

Abstract

The paper discusses from a metaphysical standpoint the nature of the dependence relation underpinning the talk of mutual action between material and spatiotemporal structures in general relativity. It is shown that the standard analyses of dependence in terms of causation or grounding are ill-suited for the general relativistic context. Instead, a non-standard analytical framework in terms of structural equation modeling is exploited, which leads to the conclusion that the kind of dependence encoded in the Einstein field equations is a novel one.

Keywords

Dependence relation Grounding Causation Laws of nature General relativity Spacetime Geodesic motion Structural equation modeling 

Notes

Acknowledgments

Many thanks to Carl Hoefer, Vassilis Livanios, Al Wilson, and two anonymous referees for their comments on earlier drafts of this paper. Ça va sans dire, I am solely responsible for any remaining frown-inducing material. Also, I acknowledge financial support from the Spanish Ministry of Science, Innovation and Universities, fellowship IJCI-2015-23321.

References

  1. Audi, P. (2012). A clarification and defense of the notion of grounding. In Correia, F., & Schnieder, B. (Eds.) Metaphysical Grounding: Understanding the structure of reality, Chapter 3 (pp. pp. 101–121): Cambridge University Press.Google Scholar
  2. Bartels, A. (2013). Why metrical properties are not powers. Synthese, 190, 2001–2013.CrossRefGoogle Scholar
  3. Bennett, K. (2011). Construction area (no hard hat required). Philosophical Studies, 154, 79–104.CrossRefGoogle Scholar
  4. Bird, A. (2009). Structural properties revisited. In Handfield, T. (Ed.) Dispositions and causes, Chapter 8. Oxford University Press (pp. 215–241).Google Scholar
  5. Blanchard, T., & Schaffer, J. (2017). Cause without default. In Beebee, H., Hitchcock, C., Price, H. (Eds.) Making a difference, Chapter 10 (pp. 175–214): Oxford University Press.Google Scholar
  6. Brown, H., & Lehmkuhl, D. (2016). Einstein, the reality of space, and the action-reaction principle. In Ghose, P. (Ed.) Einstein, Tagore and the Nature of Reality, Chapter 1 (pp. 9–36): Routledge.Google Scholar
  7. Bruni, M., Matarrese, S., Mollerach, S., Sonego, S. (1997). Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond. Classical and Quantum Gravity, 14(9), 2585–2606.CrossRefGoogle Scholar
  8. Correia, F., & Schnieder, B. (Eds.). (2012). Metaphysical Grounding: Understanding the structure of reality. Cambridge: Cambridge University Press.Google Scholar
  9. Curiel, E. (2000). The constraints general relativity places on physicalist accounts of causality. Theoria, 15(1), 33–58.Google Scholar
  10. Curiel, E. (2015). If metrical structure were not dynamical, counterfactuals in general relativity would be easy. arXiv:1509.03866.
  11. Dowe, P. (2000). Physical causation. Cambridge University Press.Google Scholar
  12. Earman, J. (1989). World enough and space-time. Absolute versus relational theories of spacetime. The MIT Press.Google Scholar
  13. Ehlers, J., Pirani, F., Schild, A. (1972). The geometry of free fall and light propagation. In O’Reifeartaigh, L., Ehlers, J., Pirani, F., Schild, A. (Eds.) (pp. 63–84): Clarendon Press.Google Scholar
  14. Hehl, F., von der Heyde, P., Kerlick, G., Nester, J. (1976). General relativity with spin and torsion: Foundations and prospects. Reviews of modern physics, 48(3), 393.CrossRefGoogle Scholar
  15. Hoefer, C. (2014). Mach’s principle as action-at-a-distance in GR: The causality question. Studies in History and Philosophy of Modern Physics, 48, 128–136.CrossRefGoogle Scholar
  16. Jaramillo, J., & Lam, V. (2018). Counterfactuals in the initial value formulation of general relativity. The British Journal for the Philosophy of Science, axy066.  https://doi.org/10.1093/bjps/axy066. http://philsci-archive.pitt.edu/15067/.
  17. Katzav, J. (2013). Dispositions, causes, persistence as is, and general relativity. International studies in the philosophy of science, 27(1), 41–57.CrossRefGoogle Scholar
  18. Lam, V. (2011). Gravitational and non-gravitational energy: the need for background structures. Philosophy of Science, 78, 1012–1023. http://philsci-archive.pitt.edu/8372/.CrossRefGoogle Scholar
  19. Lee, J. (2009). Manifolds and differential geometry. American Mathematical Society.Google Scholar
  20. Lehmkuhl, D. (2008). Is spacetime a gravitational field?. In Dieks, D. (Ed.) The ontology of spacetime, Volume 2 of Philosophy and foundations of physics, Chapter 5 (pp. 83–110): Elsevier B.V.Google Scholar
  21. Lehmkuhl, D. (2011). Mass-energy-momentum in general relativity. only there because of spacetime?. British Journal for the Philosophy of Science, 62(3), 453–488. http://philsci-archive.pitt.edu/5137/.CrossRefGoogle Scholar
  22. Leuenberger, S. (2014). Grounding and necessity. Inquiry, 57(2), 151–174.CrossRefGoogle Scholar
  23. Livanios, V. (2008). Bird and the dispositional essentialist account of spatiotemporal relations. Journal for General Philosophy of Science, 39, 383–394.CrossRefGoogle Scholar
  24. Livanios, V. (2017). Science in metaphysics. Palgrave Macmillan.Google Scholar
  25. McKitrick, J. (2005). Are dispositions causally relevant? Synthese, 144, 357–371.CrossRefGoogle Scholar
  26. Mellor, H. (1995). The facts of causation. Routledge.Google Scholar
  27. Misner, C., Thorne, K., Wheeler, J. (1973). Gravitation. W.H. Freeman and Company.Google Scholar
  28. Pearl, J. (2000). Causality: Models, Reasoning, and Inference. Cambridge University Press.Google Scholar
  29. Read, J. (2018). Functional gravitational energy. The British Journal for the Philosophy of Science, axx048.  https://doi.org/10.1093/bjps/axx048.
  30. Schaffer, J. (2016). Grounding in the image of causation. Philosophical Studies, 173, 49–100.CrossRefGoogle Scholar
  31. Tamir, M. (2012). Proving the principle: Taking geodesic dynamics too seriously in Einstein’s theory. Studies in History and Philosophy of Modern Physics, 43, 137–154.CrossRefGoogle Scholar
  32. Vassallo, A. (2016). A metaphysical reflection on the notion of background in modern spacetime physics. In Felline, L., Ledda, A., Paoli, F., Rossanese, E. (Eds.) New Directions in Logic and the Philosophy of Science (pp. 349–365): College Publications. arXiv:1602.06254.
  33. Vassallo, A., & Hoefer, C. (2019). The metaphysics of Machian frame-dragging. In Beisbart, C., Sauer, T., Wüthrich, C. (Eds.) Thinking about space and time, Einstein Studies: Birkhäuser. arXiv:1901.10766.
  34. Wald, R. (1984). General Relativity. The University of Chicago Press.Google Scholar
  35. Westland, C. (2015). Structural Equation Models. Springer.Google Scholar
  36. Wilson, A. (2017). Metaphysical causation. Noûs.  https://doi.org/10.1111/nous.12190.CrossRefGoogle Scholar
  37. Wilson, A. (2018). Grounding entails counterpossible non-triviality. Philosophy and Phenomenological Research, 96(3), 716–728.CrossRefGoogle Scholar
  38. Wilson, A. (2019). Classifying dependencies. In Glick, D., Darby, G., Marmodoro, A. (Eds.) The Foundation of Reality: Fundamentality, Space and Time: Oxford University Press.Google Scholar
  39. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford University Press.Google Scholar
  40. Woodward, J. (2008). Mental causation and neural mechanisms. In Hohwy, J., & Kallestrup, J. (Eds.) Being reduced: New essays on reduction, explanation, and causation, Chapter 12 (pp. 218–262): Oxford University Press.Google Scholar
  41. Woodward, J. (2016). Causation and manipulability. The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/win2016/entries/causation-mani/.

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.LOGOS-BIAP, Department of PhilosophyUniversity of BarcelonaBarcelonaSpain

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