The Role of Mathematics in Physical Sciences and Dirac’s Methodological Revolution

  • Giovanni Boniolo
  • Paolo Budinich

Abstract

In our paper, avoiding any strong metaphysical commitment on the world, we face the topic of the interplay between mathematics and physics by starting from a semiotic approach. It will be shown that it allows us to insert in a unitary and coherent framework answers to questions such as: Why mathematics is physics? What is the role of mathematics in physics? Why is mathematics effective in physical sciences? In the second part of the paper, and by utilizing what discussed in the first one, we analyse what we call Dirac’s methodological revolution, according to which to do good and new physics we must first work on good and promising mathematics. Finally, we exemplify Dirac’s methodological revolution by recalling the role of the mathematical theory of simple spinors in constructing new perspectives for theoretical physics.

Key words

mathematics physics semiotic methodological revolution spinor 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Browder, F. E., 1976, Does pure mathematics have a relation to the sciences?, American Scientist 64: 542–549.Google Scholar
  2. Budinich, P., 2002, From the geometry of pure spinors with their division Algebrasto Fermion physics, Foundations of Physics 32: 1347–1398.CrossRefGoogle Scholar
  3. Cartan, É., 1937, Leçons sur la Théorie de Spineur, Hermann, Paris.Google Scholar
  4. Chevalley, C., 1954, The Algebraic Theory of Spinors, Columbia University Press, New York.Google Scholar
  5. Dirac, P. M. A., 1931, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. 133.Google Scholar
  6. Dirac, P. A. M., 1958, The Principle of Quantum Mechanics, Oxford University Press, Oxford.Google Scholar
  7. Dyson, F. J., 1964, Mathematics in the physical sciences, Scientific American 129: 128–145.Google Scholar
  8. Einstein, A., 1934, The World as I See It, Covici-Friede, New York.Google Scholar
  9. Hertz, H. R., 1894, Die Prinzipien der Mechanik (In neuem Zusammenhange dargestellt), Johann Ambrosius Barth, Leipzig.Google Scholar
  10. Koyré, A. 1948, Du monde de 1’ “a-peu-près” a l’univers de la precision, Critique 28.Google Scholar
  11. Lorentz, H. A., 1915/2004, The Theory of Electrons, Dover, New York.Google Scholar
  12. Mackey, G. W., 1963, Mathematical Foundations of Quantum Mechanics, Benjamin, New York.Google Scholar
  13. Miller, A. I., 1981, Albert Einstein’s Special Theory of Relativity, Addison Wesley Reading, Mass.Google Scholar
  14. Peirce, C. S., 1895, That categorical and hypothetical propositions are one in essence, with some connected matter, in Collected Papers of Charles Sanders Peirce, ed. by C. Hartshorne, P. Weiss and A. Burks, Harvard University Press, Cambridge (Mass.), 2.332-339 and 2.278-280.Google Scholar
  15. Quine, W. V. 0., 1976, Whither physical objects?, Boston Studies in the Philosophy of Science 36: 497–504.Google Scholar
  16. von Neumann, J., 1932, Mathematische Grundlagen der Quantenmechanik, English transl. Princeton University Press, Princeton 1955.Google Scholar
  17. Wigner, E., 1960, The unreasonable effectiveness of mathematics in the natural sciences, Communication on Pure and Applied Mathematics 13: 1–14; now in E. Wigner, Symmetries and Reflections, Indiana University Press, Bloomington 1967, pp. 222–237.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Giovanni Boniolo
    • 1
  • Paolo Budinich
    • 2
  1. 1.University of PadovaPadovaItaly
  2. 2.The Abdus Salam International Centrefor Theoretical PhysicsTriesteItaly

Personalised recommendations