# Implications of Einstein-Weyl Causality on Quantum Mechanics

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## 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.Borchers, H.J., Sen, R.N.: Mathematical Implications of Einstein-Weyl Causality. Springer, Berlin (2006)CrossRefGoogle Scholar
- 2.Dyson, F.J.: Divergence of perturbation theory in quantum electrodynamics. Phys. Rev.
**85**, 631 (1952)MathSciNetCrossRefGoogle Scholar - 3.Fraenkel, A.A., Bar-Hillel, Y., Levy, A.: Foundations of Set Theory. North Holland, Amsterdam (1958)MATHGoogle Scholar
- 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.Gottfried, K.: Inferring the statistical interpretation of quantum mechanics from the classical limit. Nature
**405**, 533–536 (2000)CrossRefGoogle Scholar - 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.Wigner, E.P.: The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math.
**13**, 1–14 (1960)CrossRefGoogle Scholar

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