Abstract
We present a deductive theory of space-timewhich is realistic, objective, and relational. It isrealistic because it assumes the existence of physicalthings endowed with concrete properties. It is objective because it can be formulated without anyreference to knowing subjects or sensorial fields.Finally, it is relational because it assumes thatspace-time is not a thing, but a complex of relationsamong things. In this way, the original program ofLeibniz is consummated, in the sense that space isultimately an order of coexistents, and time is an orderof successives. In this context, we show that the metric and topological properties ofMinkowskian space-time are reduced to relationalproperties of concrete things. We also sketch how ourtheory can be extended to encompass a Riemannianspace-time.
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REFERENCES
Alexander, H. G., ed. (1983). Leibniz-Clarke Correspondence, Manchester University Press, Manchester, U.K.
Basri, S. A. (1966). A Deductive Theory of Space and Time, North-Holland, Amsterdam.
Blumenthal, L. (1965). Geometría Axiomática, Aguilar, Madrid.
Borges, J. L. (1967). Ficciones, Losada, Buenos Aires.
Bourbaki, N. (1964). Topologie Générale, Fascicule de Résultats, Hermann, Paris.
Bunge, M. (1977). Treatise of Basic Philosophy. Ontology I: The Furniture of the World, Reidel, Dordrecht.
Bunge, M. (1979). Treatise of Basic Philosophy. Ontology II: A World of Systems, Reidel, Dordrecht.
Bunge, M., and García Máynez, A. (1977). International Journal of Theoretical Physics, 15, 961.
Carnap, R. (1928). Der logische Aufbau der Welt [English translation: The Logical Structure of the World, University of California Press, Berkeley (1967)].
Covarrubias, G. M. (1993). International Journal of Theoretical Physics, 32, 2135.
Galilei, G. (1945). Dialogues Concerning Two New Sciences, H. Crew and A. de Sabio, transl., Dover, New York.
Garay, J. (1995). International Journal of Modern Physics A, 10, 145.
Gibbs, P. (1996). International Journal of Theoretical Physics, 35, 1037.
]Kelley, J. (1962). Topología General, EUDEBA, Buenos Aires.
Landau, L. D., and Lifshitz, E. M. (1967). Théorie du Champ, MIR, Moscow.
Misner, C., Thorne, K., and Wheeler, J. A. (1973). Gravitation, Freeman, San Francisco.
Perez Bergliaffa, S. E., Romero, G. E., and Vucetich, H. (1993). International Journal of Theoretical Physics, 32, 1507.
Perez Bergliaffa, S. E., Romero, G. E., and Vucetich, H. (1996). International Journal of Theoretical Physics, 35, 1805.
Rey Pastor, J., Pi Calleja, P. y Trejo, C. (1952), Análisis Matemático, Vol. I, Kapelusz, Buenos Aires.
Salomaa, A. (1973). Formal Languages, Academic Press, Boston.
Tegmark, M. (1997). Classical and Quantum Gravity, 14, L69.
Thron, W. J. (1966). Topological Structures, Holt, Rinehart and Winston, New York.
Weinberg, S. (1972). Relativity and Gravitation, Wiley, New York.
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Bergliaffa, S.E., Romero, G.E. & Vucetich, H. Toward an Axiomatic Pregeometry of Space-Time. International Journal of Theoretical Physics 37, 2281–2298 (1998). https://doi.org/10.1023/A:1026662624154
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DOI: https://doi.org/10.1023/A:1026662624154