100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Development of the Concepts of Space, Time and Space-Time 35Such a construction could involve just the pure gravitational field, i.e., bebased upon just the metric tensor field; or, it could involve the other nongravitationalfield variables if they are present in the region of space-timeunder consideration.I shall not go into further detail here, but end by noting that this problemreappears in all attempts to construct a quantum theory that incorporatesgeneral relativity — a quantum gravity. A typical quantum questionconcerns a process, and takes the form: If one physical quantity has beenfound to have a certain value ‘here’ and ‘now’, what is the probability thatsome (possibly the same) physical quantity will be found to have some othervalue ‘there’ and ‘then’? Again, a quantum gravity question cannot takethis form because ‘here’ and ‘now’, and ‘there’ and ‘then’ somehow have tobe constructed as part of the answer, not part of the question.AcknowledgementI thank Dr. Mihaela Iftime for a careful reading of the manuscript and manyvaluable suggestions for its improvement.References1. J. Ehlers, Über den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie,in Grundlagenprobleme der modernen Physik, eds. J. Nitsch et al.(Bibliographisches Institut, Mannheim, 1981), pp. 65–84.2. A. Einstein, Zur Elektrodynamik bewegter Korper, Annalen der Physik 17,891–921 (1905); Translation from John Stachel et al. (eds.), The CollectedPapers of Albert Einstein, Vol. 2, The Swiss Years; Writings, 1902–1909(Princeton University Press, 1989), p. xxiii.3. A. Einstein, Relativity and the Problem of Space, Appendix V to Relativity:The Special and the General Theory, 15th edn. (Crown, New York, 1952).4. A. Einstein, ’Foreword’ to Max Jammer, Concepts of Space (HarvardUniversity Press, Cambridge, 1954), pp. xi–xvi.5. L. Euler, Reflexions sur l’espace et le temps. Memoir de l’Académie des Sciencesde Berlin 4: 324–333 (1748); Reprinted in Leonhard Euler, Opera Omnia,Series 3, Vol. 2, pp. 376–383; English translation by Soshichi Uchii,Euler on Space and Time, Physics and Metaphysics .6. G. S. Kirk and J. E. Raven, The Presocratic Philosophers (CambridgeUniversity Press, 1957).7. K. Marx, Capital A Critique of Political Economy, Vol. 1 (Penguin, Harmondsworth,1976), Chapter I, Section 4 entitled: “The fetishism of theCommodity and Its Secret,” pp. 163–177.8. J. A. Schouten, Tensor Analysis for Physicists, 2nd edn. (Dover Publications,Mineola, New York, 1989).