In the author’s own words this paper is a philosophical essay. It is not mathematically deductive and too abstract and speculative to be regarded as a research paper in physics.
The starting point is the characterization of Lorentz invariance by an invariant Radon measure \(\rho\) in \(R^8\) with support on the union \(S\) of all light cones in \(R^4.\) A geometrical interpretation of \(\rho\) is provided by a discrete set \(\mathcal{L}\) of lightlike vectors which is very dense in \(S.\) These vectors and fields of vortices formed by them are hypothesized to be the fundamental physical objects. The vortex fields correspond to ”Clifford forms”, i.e. fields with values in the Clifford algebra defined by the Minkowski metric. The central idea is the definition of a simple stochastic process (involving the ”junction” and ”disjunction” of lightlike vectors) which gives the density of \(\mathcal{L}\) on S corresponding to \(\rho.\) The statement of stochastic equilibrium is just the (Kähler-)Dirac equation. Matter waves are considered to be objectively existent, emanating from well-defined ”generating points”. The latter and the consideration of the complex tensor products of Clifford forms give rise to far-reaching speculations about the emergence of the fundamental interactions and other elementary particles besides the electron (namely the photon, muon and two neutrinos) within the geometrical framework outlined above.