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Einstein Symposion Berlin pp 320–335Cite as

Mathematical theories and philosophical insights in cosmology

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Notes

  1. M. Born, Experiment and Theory in Physics, Cambridge: at the University Press, 1943.

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  2. A. Einstein, H. und M. Born, Briefwechsel 1916–1955, München: Nymphenburger Verlaashandlung, 1969, p. 203. I thank the Estate of Albert Einstein for allowing me to reproduce the above and the remaining passages of Einstein's writings quoted in this paper.

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  3. Einstein-Born Briefwechsel, 1.c., p. 204.

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  4. See, for example, N. Maxwell, “The rationality of scientific discovery”, Phi. Sci., 41 (1974) 123, 247; J. Agassi, Science in Flux, Dordrecht: Reidel, 1975; L.Laudan, Progress and its Problems, Berkeley: University of California Press, 1977.

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  5. E. A. Milne, Modern Cosmology and the Christian Idea of God, Oxford: Clarendon Press, 1952, p. 50.

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  6. E. A. Milne, Kinematic Relativity, Oxford: Clarendon Press, 1948, p. 39.

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  7. E. A. Milne, Modern Cosmology and the Christian Idea of God, p. 61, compare, however, Kinematic Relativity, p. 93.

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  8. E. A. Milne, Kinematic Relativity, p. 64.

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  9. H. Bondi and T. Gold “The Steady-State Theory of the Expanding Universe”, Mon. Not. R. Astron. Soc., Cambridge: at the University Press, 1960, Chapter XII.

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  10. H. Reichenbach, The Theory of Probability, Berkeley: University of California Press, 1949, paragraph 91.

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  11. M. Bunge, “Cosmology and Magic”, The Monist 47 (1962), 116.

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  12. Compare the sympathetic stance towards the Steady State Theory taken in J. Merleau-Ponty's Cosmologie du XXe Siecle, Paris: Gallimard, 1965.

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  13. A. Einstein, “Prinzipielles zur allgemeinen Relativitätstheorie”, Annalen der Physik, 55 (1918) 241. Cf. E. Kretschmann, “über den physikalischen Sinn der Relativitätspostulate”, Annalen der Physik, 53 (1917) 575.

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  14. G. Holton, Thematic Origins of Scientific Thought, Cambridge, Mass.: Harvard University Press, 1973, Introduction and Chapter 1; The Scientific Imagination, London: Cambridge University Press, 1978, Chapter I.

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  15. J. A. Wheeler, “Mach's Principle as Boundary Condition for Einstein Equations”, in Chiu and Hoffmann, eds, Gravitation and Retativity, New York: W. A. Benjamin, 1964, pp. 303–349.

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  16. Compare A. Einstein, “über das Relativitätsprinzip und die aus demselben gezogenen Folgerunaen”, Jahrb. Radioakt. u. Elektronik, 4 (1907), p. 454; “Zum gegenwärtigen Stande des Gravitations problems”, Phys. Ztschr. 14 (1913), pp. 1254 f., 1260 f., 1265; A. Einstein and M. Grossmann, Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation, Leipzig: Teubner, 1913, p. 6. See also Mach's obituary, by Einstein in Phys. Ztschr., 17 (1916) 101.

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  17. The Leibniz-CZarke Correspondence, edited ... by H. G. Alexander, Manchester: Manchester University Press, 1956.

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  18. E. Mach, Die Mechanik, Darmstadt: Wissenschaftliche Buchgesellschaft, 1963, pp. 216 ff.

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  19. A. Einstein, Annalen der Physik, 55 (1918), p. 243, footnote.

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  20. I. Newton, Philosophiae Naturalis Principia Mathematica, Cambridge, Mass.: Harvard University Press, 1972, vol. I, p. 51.

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  21. E. Cartan, “Sur les variétés à connexion affine et la théorie de la relativité généralisée”, Ann. Ec. Norm. Sup. 40 (1923) 325; 41 (1924) 1.

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  22. “It is contrary to the mode of thinking in science to conceive of a thing (the space-time continuum) which acts itself, but which cannot be acted upon”. A. Einstein, The Meaning of Relativity, Princeton: Princeton University Press, 1956, pp. 55 f.

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  23. See, e.g., S. Weinberg, Gravitation and Cosmology New York: Wiley, 1972, pp. 133–135, 151–155; D. Lovelock, “The Einstein tensor and its generalizations”, J. math. physics, 12 (1971) 498.

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  24. A. Einstein, “Prinzipielles zur allgemeinen Relativitätstheorie”, Annalen der Physik, 55 (1918), p. 243; W. de Sitter, “On Einstein's Theory of Gravitation and its astronomical consequences”, Monthly Not. R. Astr. Soc., 78 (1917) 3.

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  25. Quoted in G. Holton, “Mach, Einstein, and the Search for Reality”, Boston Studies in the Philosophy of Science, VI, p. 194, n. 24.

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  26. Einstein-Born Briefwechsel (quoted in note 2), p. 258.

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  27. F. M. Cornford, “The Invention of Space”, in Essays in Honour of Gilbert Murray, London: Allen & Unwin, 1936, pp. 215–235.

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  28. M. Bunge, Treatise on Basic Philosophy, vol. 3, Ontology I, Dordrecht: Reidel 1977.

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  29. B. Riemann, “über die Hypothesen, welche der Geometrie zugrunde liegen”, Abh. K. Ges. d. Wiss..zu Göttingen, Bd. 13 (1867).

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  30. I. Kant, Allgemeine Naturgeschichte und Theorie des Himmels, Königsberg/Leipzig: J. F. Petersen, 1755.

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  31. I. Kant, Kritik der reinen Vernunft, Riga: J. F. Hartknoch, 1781, pp. 424 ff., 517 ff., etc.

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  32. A. Einstein, “Kosmologische Betrachtungen zur Allgemeinen Relativitätstheorie” Preuss. Ak. d. Wiss., Sitzber. 1917, Pt. 1, pp. 142–152. Cf. Riemann, “über die Hypothesen...”, p. 22.

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  33. B. G. Schmidt, “A new definition of singular points in General Relativity”, J. Gen. ReZ. and Grav. 1 (1971) 269. Cf. S. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge: at the University Press, 1973, p. 259.

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  34. Die philosophischen Schriften von G. W. Leibniz, hrg. von C. J. Gerhardt, Hildesheim: Olms 1965, vol. 7, p. 302.

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  35. The reason for this interpretation is clearly explained by Max Jammer in his Concepts of Mass in classical and modern physics, Cambridge Mass.: Harvard University Press, 1961, pp. 205 f.

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  36. Kant, Kritik der reinen Vernunft, (1781), p. 158.

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  37. S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge: at the University Press, 1973, p. 189; my italics.

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  38. H. Schmidt in J. Math. Phys., 7 (1966) 494.

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  39. Hawking and Ellis, l.c., p. 189.

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  40. Hawking and Ellis, l.c., p. 266, cf. S. W. Hawking and R. Penrose, “The singularities of gravitational collapse and cosmology”, Proc. Roy. Soc. London, A 314 (1970) 529.

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  41. Hawking and Ellis, 1.c., p. 206.

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  42. See, e. g., P. Lorenzen, “Die allgemeine Relativitätstheorie als eine Revision der Newtonschen Gravitationstheorie”, Philos. Naturalis, 17 (1978), p. 9. On protophysics see G. Böhme (ed.), Protophysik Frankfurt: Suhrkamp, 1976.

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  43. E. Husserl, Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie, Haag: Nijhoff, 1954, p. 29.

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  44. Born an Einstein, 25. 8. 1923; Briefwechsel, 1.c., p. 117.

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  45. J. A. Wheeler, Geometrodynamics, New York: Academic Press, 1962. Cf. R. W. Fuller and J. A. Wheeler, “Causality and multiply connected space-time”, Phys. Rev., 128 (1962) 919–929.

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  1. Universidad de Puerto Rico, USA

    Roberto Torretti

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  1. Roberto Torretti
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H. Nelkowski A. Hermann H. Poser R. Schrader R. Seiler

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Torretti, R. (1979). Mathematical theories and philosophical insights in cosmology. In: Nelkowski, H., Hermann, A., Poser, H., Schrader, R., Seiler, R. (eds) Einstein Symposion Berlin. Lecture Notes in Physics, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09718-X_81

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  • DOI: https://doi.org/10.1007/3-540-09718-X_81

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