The Vacuum as Imaginary Space. The Unreasonable Effectiveness of Complex Numbers

Abstract

The background to the article is the classic and quantum understandings of the vacuum and the use of imaginary numbers in quantum models. The purpose of the article is to outline the possible understanding of the vacuum as imaginary space always coupled with the real space in the complex space of complex numbers. This understanding relates to the duality real-potential, collapsed–collapsible, and superimpositions of waves-phenomena as in quantum mechanics. The incomputability of the imaginary parts may represent the physical meaning of the permanent potential pending nature of the vacuum. The presence of imaginary numbers in models may be intended as warranty that it is not possible to compute definitive results, but it is possible to have pending multiple equivalences and superimpositions as in quantum physics and emergent collective processes in complexity. We consider how much the complexity (i.e., the study of emergence and chaos) may be considered related to and represented by complex numbers (i.e., properties of their dual variables and their collapsibility in real numbers). The usage of imaginary numbers may also be intended as the expression or manifestation of something we do not understand yet, as it was for the indemonstrability of the fifth Euclidian postulate and the unavailability of a distribution law for prime numbers. We conclude that a new global understanding is necessary and capable of explaining what we understand as the unreasonable effectiveness of complex numbers.