A Mathematical Preparation for Phenomenon Noumenon Theory

This paper proposes an observation model based on phenomenon space and noumenon space and its related mathematics. This model proposes that observation is essentially a dimensional reduction operation on the system being observed, which causes the observation dimension of the entity to be pushed into imaginary space, rendering it unobservable. This leads to a series of preparatory mathematics for the phenomenon-noumenon theory (Hereinafter referred to as noumenon mathematics). It can serve as a shared mathematical framework for research at the physical level. Observation operators form the cornerstone of this mathematics: ˆOnk : Rn → iRk ×Rn−1 (i is imaginary unit) This operation may bring some interesting directions and discussions to fundamental theoretical physics.