Spatial Transformations of Atoms

On the basis of fundamental probabilistic arguments, a theory of spatial transitions of atoms in configurations with number of spatial dimensions D = 1, 2, and 3 is proposed. Relations linking the 1 ↔ 3 and 2 ↔ 3 transition probabilities and the mean numbers of atoms in the 1, 2, and 3 configurations are obtained, assuming the existence of only these pairs of spatial configurations, as has been observed in earlier experiments. A similar program was realized in a situation with possible simultaneous existence of all three spatial configurations with these same transitions plus the transitions 1 ↔ 2, and the mean numbers of atoms was also found although the corresponding experiments have still not been performed. All of the conclusions of this work and the adequacy of the implemented approach can be verified in experiments with systems of atoms. In this regard, the possibility of extending the given theory to other (including not-necessarily physical) systems consisting of an invariant number of identical objects that can be found in two or three states is discussed.