Einstein, Gödel, and the Mathematics of Time
We consider exotic spacetimes in the sense of differential geometry, and then state genericity, undecidability and incompleteness results about general relativity, with the nature of time and the existence of some kind of “cosmic time” as central questions.
KeywordsIntersection Form Global Time Force Extension Smooth Structure Differentiable Structure
This paper collects some results from an ongoing research program with N. C. A. da Costa, whom we heartily thank for criticisms and comments. We must also thank C. M. Doria for his remarks on our results.
The ongoing research program that led to this text has been sponsored by the Advanced Studies Group, Production Engineering Program, COPPE – UFRJ, Rio, Brazil.
FAD wishes to thank the Institute for Advanced Studies at the University of São Paulo for partial support of this research project; we wish to acknowledge support from the Brazilian Academy of Philosophy and its chairman Professor J. R. Moderno. Both authors thank Professors R. Bartholo, C. A. Cosenza and S. Fuks for their invitation to join the Fuzzy Sets Lab at COPPE–UFRJ and the Philosophy of Science Program at the same institution.
FAD acknowledges partial support from CNPq, Philosophy Section.
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