Geometric uncertainty in non-paraxial interference

Abstract

In this article, a novel meaning for the notion of uncertainty is discussed, within the framework of the non-paraxial interference theory based on confinement in geometric states of space. This novel meaning refers to the fact that, for any set of space states whose vertices are distributed in an arbitrary array of size less than λ/10, both the excitation provided by the geometric potential and the positions of the vertices of the states are completely uncertain, such that the complete set is represented by the Lorentzian well of an individual ground state of space, with vertex at any of the points of the array, even if the set is under the maximum prepared non-locality (i.e., under a strong geometric potential). It is shown that the geometric uncertainty is different but compatible with the Heisenberg uncertainty principle. In fact, geometrical uncertainty establishes both the upper limit of momentum uncertainty and the lower limit of position uncertainty in the Heisenberg principle.