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The Idea of Structureless Points and Whitehead’s Critique of Einstein

  • Joachim Stolz
Chapter
Part of the Synthese Library book series (SYLI, volume 236)

Abstract

It is no exaggeration to say that since Euclid’s famous definition of points (as without parts and with no magnitude), this idea had been an almost unquestioned assumption at the basis of geometry and theoretical physics. The idea of structureless or extensionless points had been accepted as elementary. But elementarity may not be the same as logical simplicity or physical simplicity. There are at least two beautiful examples from recent History of Science to illustrate this. During the last two decades two age-old presumptions of science have been questioned and in some sense replaced. Firstly Fractal Geometry showed e.g. that the concept of dimensions is by no means necessarily connected with whole numbers like 1, 2, 3 or 4.1 Algorithmic geometries became an immensely rich extension of the classical conception. But I’m not going to elaborate on this. Secondly during the development of physics in our century the elementarity of points became questionable. Within quantum theory and later due to the models of unification (especially string theories) it turned out that the theory of relativity is in some sense still classical. Super String Theory2 is an actual candidate for a Unified Theory of elementary forces after the Grand Unified Theories or alternative candidates like Super Symmetry or Super Gravity had not been as successful as hoped for. One basic problem is still the incompatibility of Relativity and Quantum Theories. Relativity is geometrically a “classical” theory. But the Uncertainty Principle demands e.g. that points in quantummechanical description cannot be local objects. It is very interesting to see that basic structures of Relativity and Quantum Theories are pointing to such geometrical presumptions.

Keywords

Quantum Theory Grand Unify Theory Total Solar Eclipse Firing Line Super Gravity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    Compare e.g. Benoit Mandelbrot: The Fractal Geometry of Nature. New York 1983. german transi.: Die fraktale Geometrie der Natur. Basel 1987. ch.12, p.12 1ff.Google Scholar
  2. 2.
    For a non-technical reading see Frederick David Peat: Superstrings and the search for the theory of everything. Chicago 1988. german transi.: Superstrings. Kosmische Fäden. Die Suche nach der Theorie, die alles erklärt. Hamburg 1989.Google Scholar
  3. 8.
    A. N. Whitehead: On Mathematical Concepts of the Material World; Philos. Trans. Roy. Soc. Lond. A 205 (1906), 465–525 quoted as MC.Google Scholar
  4. 7.
    A. N. Whitehead: “La Theorie Relationniste De L’Espace”; Revue de Metaphysique et de Morale 23 (1916), 423–454; quoted as TR. Whitehead’s Relational Theory of Space: Text, Translation, and Commentary; Philosophy Research Archives 5 (1979), 676–777; Translation (711–741) and Commentary (742–777) by Patrick J. Hurley; Translation quoted as RTS.Google Scholar
  5. 9.
    A. N. Whitehead: An Enquiry concerning the Principles of Natural Knowledge; 1st edn. 1919, 2nd edn. 1925, repr. Cambridge 1955. Part III, esp. ch. viii. and The Concept of Nature; 1st edn. 1920, repr. Cambridge 1971. ch. IV.Google Scholar
  6. it A. N. Whitehead: “Space, Time, and Relativity”; Proceedings of the Aristotelian Society 16 (1915), 104–129, quoted as STR.Google Scholar
  7. 12.
    See for (1.) STR 117f, for (2.) STR 108ff, 125f, for (3.) STR 121f, and for (4.) STR 107f.Google Scholar
  8. 13.
    Hermann Weyl: Philosophie derMathematik und Naturwissenschaft. München 1990 (6th repr.; 1st edn. 1928, enl. amer. edn. 1949), p.121; amer. transi.: Philosophy of Mathematics and Natural Science. New York 1963, p. 90f.Google Scholar
  9. 14.
    See e.g. Donald Franklin Moyer: “Revolution in Science: The 1919 Eclipse Test of General Relativity”; in: B. Kursunoglu et al. eds.: On the Path of Albert Einstein. New York 1979, pp. 55–101.Google Scholar
  10. 15.
    A. N. Whitehead: “A Revolution in Science”; The Nation (November 15, 1919), 232–233 (233).Google Scholar
  11. 16.
    A. N. Whitehead: “Einstein’s Theory. An Alternative Suggestion”; The Times Educational Supplement (February 12, 1920), p. 83 a-d; quoted as ET. Repr. in A. N. Whitehead: Essays in Science and Philosophy. 1st edn. 1947, repr. New York 1968; pp.332–342; quoted as ESP.Google Scholar
  12. 20.
    ET 83 d; ESP 342; A. N. Whitehead: The Principle of Relativity with Applications to Physical Science. Cambridge 1922; pp. 78ff; quoted as PRP.Google Scholar
  13. 21.
    A. S. Eddington: “A Comparison of Whitehead’s and Einstein’s Formulae”; Nature 113 (1924), p.192. see also John L. Synge: The Relativity Theory of A. N. Whitehead. University of Maryland 1951, esp. pp. 12–14.Google Scholar
  14. 22.
    Clifford M. Will: “Einstein on the firing line”; Physics Today 25 (Oct., 1972), 23–29 and in theoretical generality Clifford M. Will: “The Confrontation between General Relativity and Experiment: An Update”; Physics Reports 113, No. 6 (1984), 345–422 (but excluding Whitehead, see p.369); see also Charles W. Misner, Kip S. Thorne, John A. Wheeler: Gravitation. San Francisco 1972; 429ff, 1067 and 1124 pro and contra Whitehead.Google Scholar
  15. 23.
    See J. D. North: The Measure of the Universe. A History of Modern Cosmology. Oxford 1965; pp. 190–197.Google Scholar
  16. 24.
    Clifford M. Will: “Einstein on the firing line”, loc. cit., p. 28 and Charles W. Misner et al., op. cit., p. 1067.Google Scholar
  17. 25.
    Kurt Gödel: “A Remark about the Relationship between Relativity Theory and Idealistic Philosophy”; in: P. A. Schilpp, ed.: Albert Einstein: Philosopher-Scientist. LaSalle, Ill., 1949; pp. 557–562; and Kurt Gödel: “An Example of a new cosmological solution of Einstein’s Field equations of gravitation”; Rev. Mod. Physics 21 (1949), 447–450.Google Scholar
  18. 29.
    Albert Einstein: Grundzüge der Relativitätstheorie. Ist edn. 1922, enl. edn. 1956, repr. Braunschweig 1984, pp. 162f. engl. trans].: The Meaning of Relativity. 1st edn. 1922, rev. edn. 1956, repr. London 1980; pp. 157f.Google Scholar
  19. 30.
    On algebraic approaches in Quantum Theory see e.g. Hans Primas: Chemistry, Quantum Mechanics and Reductionism; 1st edn. 1981, Berlin, Heidelberg 1983; eh. 4; on Relativity Theory see e.g. the remarks of Jürgen Ehlers: “Einstein’s Theory of Gravitation”; in: Einstein Symposion Berlin. Berlin 1979; pp. 10–35 (10 and 32 n. 2); and P. Yodzis: “An Algebraic Approach to Classical Spacetime”; Proc. Roy. Irish Acad. A75 (1975), 37–47.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Joachim Stolz
    • 1
  1. 1.Universität DortmundGermany

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