Erlangen 2026 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Geometry, Black Holes, Universality

MP 9.2: Vortrag

Donnerstag, 19. März 2026, 11:30–11:45, KH 02.013

Finite Projective Physics: the world as a process of events — •Klaus Mecke — Universität Erlangen-Nürnberg, Germany

Modern physics is based on the assumption that natural phenomena are the result of force fields and elementary particles moving in a continuous space-time, whereby the dynamics can be described mathematically using differential equations. An alternative to this substance ontology is the assumption that phenomena are processes of elementary events that are causally linked to each other, so that space, time, and matter properties emerge from fundamental process relations. This process ontology - proposed by Alfred North Whitehead - can be formulated mathematically as a finite projective geometry of event points, whereby the dynamics is simply given by local quadratic forms, i.e., by a finite metric field. The task remains to derive from this geometric structure the dynamical laws that are known to be empirically adequate. To this end, finite projective analogues of classical mechanics (time dependence), electrodynamics (spatial gauge fields), and quantum mechanics (random particle events) are formulated and their equivalence to standard analytical theories is demonstrated in the continuum limit. The origin of important concepts such as Legendre transformation, gauge symmetry, and commutator relations can be explained by fundamental features of finite projective geometry, which characterizes any event process. Finally, the possibility of a unified theory of general relativity and quantum field theory of elementary particles is outlined, in which finite projective geometry is the basic structure instead of a differentiable Riemannian manifold.

Keywords: Finite Geometry; Projective Geometry; Quadratic Forms; Classical Physics; Quantum Field Theory