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The Rise and Fall of Geometrodynamics

Published online by Cambridge University Press:  28 February 2022

John Stachel
John Stachel*
Affiliation:
Boston University
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Extract

One thing that everyone can agree on is that the subject of geometrodynamics, whatever we interpret it as covering, is inseparably associated with the name of John Wheeler. To discuss the history and current status of geometrodynamics thus necessitates the discussion of the evolution of Wheeler's ideas on the subject. This is not meant to detract, in any way, from the fact that he has been ably assisted in his intellectual Odyssey by a distinguished group of co-workers; most prominently by Charles Misner, whom we have been fortunate to hear today on the subject. Since Professor Wheeler has recently indicated his abandonment of major features of the original geometrodynamic program, as I shall discuss later, I hope he will forgive me the rather dramatic title I have chosen for my talk.

Type
Part I Symposium: Space, Time, and Matter: The Foundations of Geometrodynamics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1972 , 1972 , pp. 31 - 54
Copyright
Copyright © 1974 by D. Reidel Publishing Company

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Footnotes

*

I should like to thank Professor Wheeler for reading the typescript of this paper. His comments have enabled me to avoid misinterpretation of his position on at least one point; he is, of course, not responsible for any remaining misinterpretations or for my critical comments.

**

Research partially supported by the U.S. National Science Foundation.

References

Notes

1a Einstein himself has been claimed for both outlooks. But in at least one comment, he seems to have explicitly disavowed any desire to reduce physics to geometry. In the ‘Autobiographical Notes’, p. 61 (see next note for reference) he warns against imagining that “intervals are physical entities of a special type, intrinsically different from other physical variables (‘reducing physics to geometry’)”.

1b Einstein, A., ‘Autobiographical Notes’, in Schilpp, P. A. (ed.), Albert Einstein: Philosopher-Scientist, Open Court Publishing Co., LaSalle, III., 1970, pp. 71-73.Google Scholar

2 Ibid., pp. 73-75.

3 Ibid., p. 75

4 Ibid., p. 81.

5 Einstein, A., ‘Remarks to the Essays Appearing in This Collective Volume’, ibid., p. 675.Google Scholar

6 An excellent recent reference for such problems is, Hawking, and Ellis, , The Large Scale Structure of Space-Time, Cambridge, 1973.CrossRefGoogle Scholar

7 Misner, , Thorne, and Wheeler, , Gravitation, Freeman, 1973, Chapter 44, pp. 1197-98Google Scholar. I wish to thank Prof. Wheeler for most kindly giving me a preprint copy of Chapter 44 before its appearance in print.

8 J. Wheeler, A., ‘From Mendeleev's Atom to the Collapsing Star’, Boston Studies in the Philosophy of Science, Vol. XI (ed. by Seeger, R. J. and Cohen, R. S.), Dordrecht and Boston, 1974.Google Scholar

9 Ibid., footnotes omitted. Wheeler, in common with most physicists, used the word ‘observation’ here, for what I have called preparations and registrations above. I prefer the less anthropomorphic terms.

10 DeWitt, B. , ‘The Many-Universe Interpretation of Quantum Mechanics’, in B. d'Espagnat (ed.), Foundations of Quantum Mechanics, Academic Press, New York, 1971Google Scholar. This has been reprinted, with a number of other fundamental papers on the subject in DeWitt, B. and Graham, N. (eds.), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press, Princeton, 1973.Google Scholar

11 Ibid., $.212.

12 Ibid., p. 214.

12a Of course, in classical geometrodynamics one can just insert by hand, so to speak, the correct signature for the four-dimensional metric when building up a family of threedimensional spatial metrics from superspace into a four-dimensional Riemannian space time; but one could just as well build in the incorrect signature. The point is that, from the 3-metrics of a family of hypersurfaces in a four-dimensional manifold, one cannot infer the signature of the manifold.

13 Misner, , Thorne, and Wheeler, , Gravitation, Freeman, 1973, Chapter 44, pp. 1203-1205.Google Scholar

14 Ibid., Chapter 44, p. 1206.

15 DeWitt, B. and van Dantzig, D., ‘On the Relation Between Geometry and Physics and the Concept of Space-Time’, in Helvetica Physica Ada, Supplement IV, p. 48.Google Scholar

16 Wheeler, J. A., ‘From Relativity to Mutability’, in Mehra, J. (ed.), The Physicist's Conception of Nature, Dordrecht and Boston, 1973, pp. 233-34.Google Scholar

17 Misner, , Thorne, and Wheeler, , Gravitation, Freeman, 1973, Chapter 44, p. 1208.Google Scholar

18 Ibid., Chapter 44, p. 1212.

19 J. A. Wheeler, see note 16, p. 244.

20 D. van Dantzig, ibid.

21 Stachel, J., ‘A Note on Scientific Practice’, to appear in For Dirk Struik (Boston Studies in the Philosophy of Science, Volume XV, 1974).Google Scholar