Noumen Mechanics: a Program

Noumen Mechanics (NM): geometric synthesis between Relativistic Mechanics (RM) and Quantum Mechanics (QM) based on a more fundamental approach to RM. Events (1905) are geometric points in Minkowski space-time M$^{4}$, noumens (1972) in C$^{4}$, M$^{4}$ complex extension. A noumen is a chiral entity containing more information than an event, thus suggesting doing physics in C$^{4}$ instead of M$^{4}$. Three main principles: \textit{Representation duality:} M$^{4}$= C$^{4\ast }$xC$^{4}$ since Sl(2;C) acts on C$^{4}$ and is the fundamental representation of the Lorentz group. \textit{Homogeneous hypercomplex space:} C$^{4}$ and M$^{4}$ are quotient spaces of homogeneous spaces CC$^{4}$ and MM$^{4}$. A geometric point is represented by a homogeneous class; the coefficients of homogeneity $\lambda $ is its electroweak charge in CC$^{4}$, and $\mu =\vert \lambda \vert ^{2}$ its mass in MM$^{4}$. \textit{Analytic function of physical points:} Physical points are bounded sets of geometric points, noumens in C$^{4}$, events in M$^{4}$, with the resulting electroweak charge and mass. \textit{Phase 1}: gain a deeper understanding of the mathematical sources of QM and RM. Two main NM results: bound electrons do not radiate; C$^{4}$/M$^{4}$ is the solution to physics hierarchy problem. \textit{Phase 2}: apply new concepts to nuclear physics, following Pauli's interpretation (1936) of Fermi's weak-interaction constant (1934).