On the Topological Nature of Fundamental Interactions

A thought experiment is proposed to unify quantum mechanics and general relativity. The central paradigm is that space-time {\it topology} is ultimately responsible for the Heisenberg uncertaintly principle. It is found that Plankian space-time exhibits a complicated, but also definite, multiply connected character. In this framework, an analysis of the interactions in Nature is presented. I. The Universal ground state of the constructed theory derives from the properties of the topological manifold $Q=2T^3\oplus 3S^1\times S^2$, which has 23 intrinsic degrees of freedom, discrete $Z_3$ and $Z_2\times Z_3$ internal groups, an SU(5) gauge group, and leads to a U(1) symmetry on a lattice. The structure of $Q$ provides a unique equation motion for the mass-energy and particle rest mass wave functions. In its excited state the Universe is characterized by a lattice of three-tori, $L(T^3)$. The topological identifications present in this structure, a direct reflection of the Heisenberg uncertainty principle, provide the boundary conditions for solutions to the equation of motion, and suggest an interpretation for the conceptually difficult concept of quantum mechanical entanglement. II. In the second half of the paper the (observable) properties of $Q$ and $L(T^3)$ are investigated. One reproduces the standard model, and the theory naturally contains a Higgs field with possible inflation. The electron and its neutrino are identified as particle ground states and their masses, together with those of all other known particles, are predicted. A mass of $m_{\rm H}=131.6$ GeV is found for the Higgs boson. [Abridged]