Foundations of Physics

, Volume 43, Issue 1, pp 54–80 | Cite as

Mirror Symmetry and Other Miracles in Superstring Theory

Article

Abstract

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These predictions were made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. I shall attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a considerably high (philosophical) price.

Keywords

String theory Mirror symmetry No miracles argument 

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References

  1. 1.
    Achinstein, P.: Explanation v. prediction: which carries more weight? in: PSA: Proceeding of the Biennial Meeting of the Philosophy of Science Association, vol. 1994. Volume Two: Symposia and Invited Papers, pp. 156–164 (1994) Google Scholar
  2. 2.
    Atiyah, M.F.: The Geometry and Physics of Knots. Cambridge University Press, Cambridge (1990) MATHCrossRefGoogle Scholar
  3. 3.
    Baker, A.: Are there genuine mathematical explanations of physical phenomena? Mind 114, 223–237 (2005) MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ballman, W.: Lectures on Kähler Manifolds. ESI Lectures in Mathematics and Physics. American Mathematical Society, Providence (2006) CrossRefGoogle Scholar
  5. 5.
    Bangu, S.I.: Inference to the best explanation and mathematical realism. Synthese 160, 13–20 (2008) MATHCrossRefGoogle Scholar
  6. 6.
    Brush, S.: Prediction and theory evaluation: the case of light bending. Science 246, 1124–1129 (1989) ADSCrossRefGoogle Scholar
  7. 7.
    Brush, S.: Dynamics of theory change: the role of predictions. in: PSA: Proceeding of the Biennial Meeting of the Philosophy of Science Association, vol. 1994. Volume Two: Symposia and Invited Papers, pp. 133–145 (1994) Google Scholar
  8. 8.
    Brush, S.: Why was relativity accepted? Phys. Perspective 1, 184–214 (1999) MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Candelas, P., Horowitz, G., Strominger, A., Witten, E.: Vacuum configurations for superstrings. Nucl. Phys. B 258, 46–74 (1985) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Cartwright, N., Frigg, R.: String theory under scrutiny. Phys. World 20, 14–15 (2007) Google Scholar
  11. 11.
    Colyvan, M.: Mathematical recreation versus mathematical knowledge. In: Leng, M., Paseau, A., Potter, M. (eds.) Mathematical Knowledge, pp. 109–122. Oxford University Press, Oxford (2007) Google Scholar
  12. 12.
    Cox, D.A., Katz, S.: Mirror Symmetry and Algebraic Geometry. American Mathematical Society, Providence (1999) MATHGoogle Scholar
  13. 13.
    Darwin, C.: The Origin of Species (1859). Collier Press (1962) Google Scholar
  14. 14.
    Dawid, R.: Scientific realism in the age of string theory. Phys. Philos. 11, 1–35 (2007) Google Scholar
  15. 15.
    Dirac, P.A.M.: The evolution of the physicist’s picture of nature. Sci. Am. 208(5), 45–53 (1963) ADSCrossRefGoogle Scholar
  16. 16.
    Engler, G.: Quantum field theories and aesthetic disparity. Int. Stud. Philos. Sci. 15(1), 51–63 (2001) MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Feynman, R.P.: QED. The Strange Theory of Light and Matter. Princeton University Press, Princeton (1988) Google Scholar
  18. 18.
    Field, H.: Science Without Numbers. Basil Blackwell, Oxford (1980) MATHGoogle Scholar
  19. 19.
    Galison, P.: Mirror symmetry: persons, values, and objects. In: Norton Wise, M., et al. (eds.) Growing Explanations: Historical Perspectives on Recent Science, pp. 23–61. Duke University Press, Durham (1999) Google Scholar
  20. 20.
    Green, M., Schwarz, J., Witten, E.: Superstring Theory: Volume 1, Introduction. Cambridge University Press, Cambridge (1988) Google Scholar
  21. 21.
    Greene, B.: Aspects of Quantum Geometry. In: Phong, D.H., Vinet, L., Yau, S.-T. (eds.) Mirror Symmetry III, pp. 1–67. American Mathematical Society, Providence (1999) Google Scholar
  22. 22.
    Hand, E.: String Theory Hints at Explanation for Superconductivity. Nature 25(11), 114008-21 (2009) Google Scholar
  23. 23.
    Hedrich, R.: The internal and external problems of string theory. J. Gen. Philos. Sci. 38, 261–278 (2007) MathSciNetCrossRefGoogle Scholar
  24. 24.
    Hori, K., Katz, S., Klemm, A., Vafa, C., Vakil, R., Zaslow, E.: Mirror Symmetry. American Mathematical Society, Providence (2003) MATHGoogle Scholar
  25. 25.
    Katz, S.: Enumerative Geometry and String Theory. Student Mathematical Library, vol. 32. American Mathematical Society, Providence (2006) Google Scholar
  26. 26.
    Lian, B.H., Liu, K., Yau, S.-T.: The Candelas-de la Ossa-Green-Parkes formula. Nucl. Phys. B: Proc. Suppl. 67(1–3), 106–114 (2000) MathSciNetADSGoogle Scholar
  27. 27.
    Lipton, P.: Testing hypotheses: prediction and prejudice. Science 307, 21–22 (2005) CrossRefGoogle Scholar
  28. 28.
    Maddy, P.: Naturalism in Mathematics. Oxford University Press, Oxford (1997) MATHGoogle Scholar
  29. 29.
    Manin, Y.: Reflections on arithmetical physics. In: Dita, P., Georgescu, V. (eds.) Conformal Invariance and String Theory, pp. 293–303. Academic Press, New York (1989) Google Scholar
  30. 30.
    Manin, Y.: Interrelations between mathematics and physics. Soc. Math. Fr. 3, 157–168 (1998) MathSciNetGoogle Scholar
  31. 31.
    McCallister, J.W.: Dirac and the aesthetic evaluation of theories. Methodol. Sci. 23(2), 87–102 (1990) Google Scholar
  32. 32.
    Morrow, J., Kodaira, K.: Complex Manifolds. American Mathematical Society, Providence (1971) MATHGoogle Scholar
  33. 33.
    Musgrave, A.: Logical versus historical theories of confirmation. Br. J. Philos. Sci. 25, 1–23 (1974) CrossRefGoogle Scholar
  34. 34.
    Myers, R.C., Vázquez, S.E.: Quark soup Al Dente: applied superstring theory. Class. Quantum Gravity 25(11), 114008-21 (2008) ADSCrossRefGoogle Scholar
  35. 35.
    Olive, D.I., West, P.C.: Duality and Supersymmetric Theories. Publications of the Newton Institute, No. 18. Cambridge University Press, Cambridge (1999) MATHGoogle Scholar
  36. 36.
    Polchinski, J.: String Theory, vol. 2. Cambridge University Press, Cambridge (2000) Google Scholar
  37. 37.
    Polyakov, A.M.: Quantum geometry of bosonic strings. Phys. Lett. B 103(3), 207–210 (1981) MathSciNetADSGoogle Scholar
  38. 38.
    Polyakov, A.M.: Quantum geometry of fermionic strings. Phys. Lett. B 103(3), 211–213 (1981) MathSciNetADSGoogle Scholar
  39. 39.
    Putnam, H.: What is Mathematical Truth? Reprinted in Mathematics, Matter, and Method, pp. 60–78. Cambridge University Press, Cambridge (1979) Google Scholar
  40. 40.
    Quine, W.V.O.: The philosophical bearing of modern logic. In: Klibansky, R. (ed.) Philosophy in the Mid-Century, vol. 1. Nuova Italia, Florence (1958) Google Scholar
  41. 41.
    Rickles, D., Schindler, S.: Physics as good as sex? Reconsidering the scientific status of string theory (forthcoming) Google Scholar
  42. 42.
    Riordan, M.: Stringing physics along. Phys. World 2007, 38–39 (2007) Google Scholar
  43. 43.
    Schellekens, A.N.: The emperor’s last clothes? Overlooking the string theory landscape. Rep. Prog. Phys. 71, 1–13 (2008) MathSciNetCrossRefGoogle Scholar
  44. 44.
    Schrödinger, E.: The philosophy of experiment. Il Nuovo Cimento 1(1), 5–15 (1955) CrossRefGoogle Scholar
  45. 45.
    Schwarz, J.: Superstrings—an overview. In: Second Aspen Winter Particle Physics Conference, pp. 269–276. The New York Academy of Sciences, New York (1987) Google Scholar
  46. 46.
    Schwarz, J., Scherk, J.: Dual models for non-hadrons. Nucl. Phys. B 81(1), 118–144 (1974) ADSCrossRefGoogle Scholar
  47. 47.
    Smart, J.J.C.: Between Science and Philosophy. Random House, New York (1968) Google Scholar
  48. 48.
    Smolin, L.: The Trouble with Physics. Houghton Mifflin Company (2006) Google Scholar
  49. 49.
    Sober, E.: Mathematics and indispensability. Philos. Rev. 102(1), 35–57 (1993) MathSciNetCrossRefGoogle Scholar
  50. 50.
    Thomson, W.H.: On vortex motion. Trans. R. Soc. Edin. 25, 217–260 (1869) Google Scholar
  51. 51.
    van Fraassen, B.: The Scientific Image. Oxford University Press, Oxford (1980) CrossRefGoogle Scholar
  52. 52.
    Veneziano, G.: String theory: physics or metaphysics? Humana Mente 13, 13–21 (2010) Google Scholar
  53. 53.
    Veneziano, G.: Physics and mathematics: a happily evolving marriage (2010) Google Scholar
  54. 54.
    Whewell, W.: The Philosophy of the Inductive Sciences, vol. 2 (1847), Johnson Reprint Corporation (1967) Google Scholar
  55. 55.
    Yau, S.-T.: Compact three dimensional Kähler manifolds with zero Ricci curvature. In: Bardeen, W.A., White, A. (eds.) Proceedings of the Symposium on Anomalies, Geometry and Topology: Argonne, pp. 395–406. World Scientific, Singapore (1985) Google Scholar
  56. 56.
    Yoneya, T.: Connection of dual models to electrodynamics and gravidynamics. Prog. Theor. Phys. 51(6), 1907–1920 (1973) MathSciNetADSCrossRefGoogle Scholar
  57. 57.
    Yoneya, T.: Quantum gravity and the zero-slope limit of the generalized Virasoro model. Lett. Al Nuovo Cimento 8(16), 951–955 (1973) CrossRefGoogle Scholar
  58. 58.
    Zahar, E.: Why did Einstein’s programme supercede Lorentz’s? Br. J. Philos. Sci. 24, 95–123 (1973) CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Unit for HPSUniversity of SydneySydneyAustralia

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