Implications of Einstein-Weyl Causality on Quantum Mechanics

Chapter
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)

Abstract

An investigation of the topological consequences of Einstein-Weyl causality by others has shown that a denumerable space-time would be admitted, but they were left with an experimentally unresolvable question regarding the nature of the physical line E, e.g., whether E =  R, the real line of mathematics. We propose a nonstandard constructible set-theoretical foundation and find it indeed provides a dense, denumerable space-time that still allows physical functions and their derivatives to be continuous. We show here that this leads to a novel approach to quantum mechanics and, in addition, has important implications for relational space-time and the avoidance of physical infinities.

References

  1. 1.
    Borchers, H.J., Sen, R.N.: Mathematical Implications of Einstein-Weyl Causality. Springer, Berlin (2006)CrossRefGoogle Scholar
  2. 2.
    Dyson, F.J.: Divergence of perturbation theory in quantum electrodynamics. Phys. Rev. 85, 631 (1952)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fraenkel, A.A., Bar-Hillel, Y., Levy, A.: Foundations of Set Theory. North Holland, Amsterdam (1958)MATHGoogle Scholar
  4. 4.
    Gödel, K.: The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis. Ann. Math. Stud., vol. 3. Princeton University Press/Oxford University Press, Princeton/Oxford (1940)Google Scholar
  5. 5.
    Gottfried, K.: Inferring the statistical interpretation of quantum mechanics from the classical limit. Nature 405, 533–536 (2000)CrossRefGoogle Scholar
  6. 6.
    Sen, R.N.: Why is the Euclidean line the same as the real line? Found. Phys. Lett. 12, 325–345 (1999)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wigner, E.P.: The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13, 1–14 (1960)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Johnson SchoolCornell UniversityIthacaUSA

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