Heidelberg 2022 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Classical and quantum gravity

MP 10.1: Vortrag

Donnerstag, 24. März 2022, 16:15–16:35, MP-H5

Space - Time - Matter: Finite Projective Geometry as a Quantum World with Elementary Particles — •Klaus Mecke — Institut für Theoretische Physik, Universität Erlangen-Nürnberg

A unified theory for space-time and matter might be based on finite projective geometries instead of differentiable manifolds and fields. In contrast to general relativity the metric is given over a finite Galois field which defines neighbors in the finite set of points. Due to the projective equivalence of all quadratic forms in finite projective geometries this world exhibits necessarily a 4-dimensional, locally Lorentz-covariant space-time with a gauge symmetry G(3)xG(2)xG(1) for points at infinity which represent elementary particle degrees of freedom. Thus, matter appears as a geometric distortion of an inhomogeneous field of quadrics and physical properties of the standard model such as spins and charges seem to follow from its finite geometric structure in a continuum limit. The finiteness inevitably induces a fermionic quantization of all matter fields and a bosonic for gauge fields. The main difference to Einstein’s general theory of relativity is the use of finite fields instead of real numbers to parametrize points of events.

K. Mecke, Biquadrics configure finite projective geometry into a quantum spacetime, EPL 120, 10007 (2017).