Abstract
We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial ℝ4. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between “localized” exotic small R 4's and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R 4's localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in means which may enforce a kind of decoherence.
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Król, J. Exotic Smoothness and Noncommutative Spaces. The Model-Theoretical Approach. Foundations of Physics 34, 843–869 (2004). https://doi.org/10.1023/B:FOOP.0000022189.71690.34
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DOI: https://doi.org/10.1023/B:FOOP.0000022189.71690.34