Abstract
The present paper examines an episode from the historiography of the genesis of general relativity. Einstein rejected a certain theory in the so-called “Zurich notebook” in 1912–13, but he reinstated the same theory for a short period of time in the November of 1915. Why did Einstein reject the theory at first, and why did he change his mind later? The group of Einstein scholars who reconstructed Einstein’s reasoning in the Zurich notebook disagree on how to answer these questions. According to the “majority view”, Einstein was unaware of so-called “coordinate conditions”, and he relied on so-called “coordinate restrictions”. John Norton, on the other hand, claims that Einstein must have had coordinate conditions all along, but that he committed a different mistake, which he would repeat in the context of the famous “hole argument”. After an account of the two views, and of the reactions by the respective opponents, I will probe the two views for weaknesses, and try to determine how we might settle the disagreement. Finally, I will discuss emerging methodological issues.
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Notes
- 1.
- 2.
See the introduction in Janssen et al. (2007a) for remarks on the collaboration between Jürgen Renn, Tilman Sauer, Michel Janssen, John D. Norton, and John Stachel.
- 3.
Stachel (2007) has given an account of the genesis of GR in this form. The present section serves as an introduction; technical details are mostly relegated to footnotes.
- 4.
A detailed account of how the third act unfolded can be found in Renn and Sauer (2007).
- 5.
The collaboration between Einstein and Grossmann resulted in several publications, most importantly the so-called “Entwurf” (“outline”) theory (Einstein and Grossmann 1995), which contains the first detailed exposition of tensor calculus in the context of GR. The Entwurf theory does not yet formulate the final, correct field equations of GR; see Sauer (2014) for an account of Grossmann’s contribution to GR.
- 6.
- 7.
The name was coined by the genesis collaboration; the November tensor became prominent in November 1915. It first appears on p. 22R of the Zurich notebook; see Fig. 9.1. I use the standard pagination; see Janssen et al. (2007a), Klein et al. (1995) for a facsimile of the notebook and Janssen et al. (2007b) for the commentary. Note that a facsimile of the Zurich notebook is also available online at Einstein Archive Online.
- 8.
- 9.
The name was coined by the genesis collaboration. It figures prominently in correspondence between Einstein and Paul Hertz; see, e.g., Renn and Sauer (2007, p.184).
- 10.
Unimodular coordinates require that the determinant of the Jacobian of the coordinate differentials are equal to one.
- 11.
Only Galilean covariance is needed for the Newtonian limit, but it is easy to get Galilean covariance, because the condition is invariant under linear transformations, which implies Galilean covariance. However, Einstein does not eliminate terms from his calculation that would vanish under linear transformations. Therefore, he is not after linear transformations.
- 12.
Einstein used harmonic coordinates to recover the weak field form of the metric in the context of the Ricci tensor. Harmonic coordinates were known in the mathematical literature as “isothermal coordinates” at the time of the notebook.
- 13.
This formulation is used in Norton (2007) for this particular misconception. I will use it as a technical notion in the present paper. It does not apply to the mistake of, say, using coordinate restrictions instead of coordinate conditions.
- 14.
See Norton (2011) for a discussion of the hole argument.
- 15.
The argument for dating the Besso memo is given in Janssen (2007).
- 16.
See Janssen and Renn (2007, Sect. 1.5) for an argument to this effect. This argument is neutral with respect to the disagreement discussed here.
- 17.
Note that Ricci and Levi-Civita (1901) discuss isothermal surfaces.
- 18.
Relevant parts of the modern notion may be discussed elsewhere in the mathematical literature. There are useful remarks on the history of “Euclidean geometry by means of general coordinates” in Veblen (1927, p.66).
- 19.
Note that the two labels are identical in German (up to the capital letter), but translated differently in the commentary; see Janssen et al. (2007b, p.555andp.647).
- 20.
It would be desirable to get a better systematic understanding of the role of errors in this episode. Such an understanding might be gained on the basis of the so-called “dynamical inferential conception” of the application of mathematics, proposed in Räz and Sauer (2015). This framework systematizes different kinds of mistakes that can be made in the context of applying mathematics to empirical problems.
References
Bianchi, L. 1910. Vorlesungen über Differentialgeometrie, 2 ed. Teubner.
Einstein, A., and M. Grossmann. 1995. Entwurf einer verallgemeinerten relativitätstheorie und einer theorie der gravitation, 302–343. In Klein et al. (1995).
Janssen, M. 2007. What did Einstein know and when did he know it? A besso memo dated August 1913, 785–838. In Janssen et al. (2007b).
Janssen, M., Norton, J.D., Renn, J., Sauer, T., and J. Stachel. 2007a. The genesis of general relativity. Vol. 1. Einstein’s Zurich notebook: Introduction and source. Dordrecht: Springer.
Janssen, M., Norton, J.D., Renn, J., Sauer, T., and J. Stachel. 2007b. The genesis of general relativity. Vol. 2. Einstein’s Zurich notebook: Commentary and essays. Dordrecht: Springer.
Janssen, M., and J. Renn. 2007. Untying the knot: How Einstein found his way back to field equations discarded in the Zurich notebook, 839–925. In Janssen et al. (2007b).
Klein, M.J., Kox, A.J., Renn, J., and R. Schulmann (eds.). 1995. The collected papers of Albert Einstein, volume 4: The Swiss years: Writings, 1912–1914. Princeton, NJ: Princeton University Press.
Norton, J.D. 2005. A conjecture on Einstein, the independent reality of spacetime coordinate systems and the disaster of 1913. In The universe of general relativity, volume 11 of Einstein studies, ed. A.J. Kox, and J. Eisenstaedt, 67–102. Basel, Boston, Berlin: Birkhäuser.
Norton, J.D. 2007. What was Einstein’s “Fateful Prejudice”?, 715–83. In Janssen et al. (2007b).
Norton, J.D. 2011. The hole argument. http://plato.stanford.edu/entries/spacetime-holearg/.
Räz, T., and T. Sauer. 2015. Outline of a dynamical inferential conception of the application of mathematics. Studies in History and Philosophy of Modern Physics 49: 57–72.
Renn, J. 2004. Standing on the shoulders of a dwarf: General relativity: A triumph of Einstein and Grossmann’s erroneous “entwurf” theory. In In the shadow of the relativity revolution, Preprint 271, 5–20, Berlin: Max Planck Institute for the History of Science.
Renn, J. (ed.). 2007. The genesis of general relativity (4 vols.). Dordrecht: Springer.
Renn, J., and T. Sauer. 2007. Pathways out of classical physics. Einstein’s double strategy in his search for the gravitational field equation, 113–312. In Janssen et al. (2007a).
Ricci, M., and T. Levi-Civita. 1901. Méthodes de calcul différentiel absolu et leurs applications. Mathematische Annalen 54: 125–201.
Sauer, T. 2014. Marcel Grossmann, and his contribution to the general theory of relativity. In Proceedings of the 13th Marcel Grossmann meeting on recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theory, ed. Jantzen, R.T., Rosquist, K., and R. Ruffini. Singapore: World Scientific. arXiv:1312.4068.
Stachel, J. 2007. The first two acts, 81–112. In Janssen et al. (2007a).
Veblen, O. 1927. Invariants of quadratic differential forms. Cambridge: Cambridge University Press.
Wright, J.E. 1908. Invariants of quadratic differential forms. New York: Hafner Publishing Co.
Acknowledgments
I thank John Norton and Raphael Scholl for comments on previous drafts of the paper, and Tilman Sauer for comments and fruitful discussions concerning the genesis of GR.
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Räz, T. (2016). Gone Till November: A Disagreement in Einstein Scholarship. In: Sauer, T., Scholl, R. (eds) The Philosophy of Historical Case Studies. Boston Studies in the Philosophy and History of Science, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-319-30229-4_9
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