Berlin 2015 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 16: Gravitation

MP 16.3: Vortrag

Donnerstag, 19. März 2015, 12:00–12:20, HFT-FT 101

Defining equidistance in finite and discrete geometries — •Alexander Laska, Benedikt Krüger, and Klaus Mecke — Institut für Theoretische Physik, Staudtstr. 7, 91058 Erlangen

In order to replace the continuous smooth manifold of general relativity by a suitable discrete structure, we tried to practice physics within finite – affine and projective – geometries. They might be the discrete analog to tangential and cotangential spaces to the manifold. In order to implement a lightcone the notion of one quadric per point does not suffice to encode length (and thus causal relations) in all directions. But a pair of quadrics – a biquadric – has to be employed per point. The scope of this talk is to present how and to what extent these biquadrics might encode length, causal relations, and furthermore curvature for arbitrary dimensions and signatures in order to be able to retrieve back the general theory of relativity – or a close approximation – in terms of a continuum limit.