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Space-Time and Isomorphism

Published online by Cambridge University Press:  28 February 2022

Brent Mundy
Brent Mundy*
Affiliation:
Syracuse University
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Extract

Leibniz indiscernibility argument: If the points of space or space-time are real, then shifting everything by a geometric symmetry transformation f (e.g., translation or rotation) produces a physically different situation, since the same bodies or events now occupy different points: whatever occupied point p now occupies the distinct point fp. This may violate identity of indiscernibles, or other principles of verifiability or theoretical parsimony.

Leibniz’s f was a symmetry of Euclidean space E, so the argument seems inapplicable to the inhomogeneous space-times of GTR. However, the underlying manifold M always possesses symmetries f, so one may take f also to move the geometric structure across M, along with the physical objects and events. The resulting variant models still represent physically distinct worlds, since the objects and geometric structure formerly at p are now at fp. Indeed there is more variability, since M has far more symmetries than E.

Type
Part XIII. Spacetime
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1992 , Issue 1: Volume One: Contributed Papers 1992 , 1992 , pp. 515 - 527
Copyright
Copyright © 1992 by the Philosophy of Science Association

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References

Borsuk, K., and Szmielew, W. (1960), Foundations of Geometry. Amsterdam: North Holland.Google Scholar
Butterfield, J. (1988), “Albert Einstein Meets David Lewis”, in PSA 1988, volume 2, Fine, A. and Leplin, J. (eds.). East Lansing: Philosophy of Science Association, pp.65-81.Google Scholar
Earman, J. (1989), World Enough and Space-Time. Cambridge: MIT Press.Google Scholar
Earman, J.. and Norton, J (1987), “What Price Spacetime SubstantivalismTThe Hole Story”, British Journal of Philosophy of Science 38,515-525.Google Scholar
Ehlers, J., Pirani, F.A.E., and Schild, A. (1972), “The Geometry of Free Fall and Light Propagation”, in General Relativity; Papers in Honour ofJ. L. Synge, O'Raifeartaigh, L., (ed.). Oxford: Clarendon Press, p. 63-84.Google Scholar
Eisenhart, L. (1926), Riemannian Geometry. Princeton: Princeton University Press.Google Scholar
Field, H. (1980), Science Without Numbers. Princeton: Princeton University Press.Google Scholar
Maudlin, T. (1988), “The Essence of Space-Time”, in PSA 1988, volume 2, Fine, A. and Leplin, J. (eds.). East Lansing: Philosophy of Science Association, pp.82-91.Google Scholar
Norton, J. (1988), “The Hole Argument”, in in PSA 1988, volume 2, Fine, A. and Leplin, J. (eds.). East Lansing: Philosophy of Science Association, pp.56-64.Google Scholar
Robb, A.A. (1936), Geometry of Time and Space. Cambridge, Cambridge U.P.Google Scholar
Woodhouse, N. (1973), “On the Differentiable and Causal Structure of Spacetime”, Journal of Mathematical Physics 14,495-501.CrossRefGoogle Scholar
Zeeman, E.C. (1964), “Causality Implies the Lorentz Group”, Journal of Mathematical Physics 5,490-493.CrossRefGoogle Scholar