Exotic Smoothness and Noncommutative Spaces. The Model-Theoretical Approach

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 R4's and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R4'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.