An Outline to model Light Propagation in a Space with Torsion

Investigating motion in a space with torsion is everything else than trivial – common differential geometry seems impractical to describe it, and what kind of a real medium is twisted and can carry a traveler? We try to model such a space by sending light through two successive, tilted slits onto the stretch of a hyperbolic paraboloid and calculate its propagation with Huygens elementary waves. For narrow slits at least the classical paths of the light rays follow the twisted surface, while the „nonclassical“ paths of the elementary waves after the second slit know nothing about this confinement of the classic rays. So we hope to construct a mixed space, partly flat and partly with torsion and see what we get. The calculation using Landau II §59 (DgaO-Proc.2016) leads to numerical results with six parameters – the slit distance, tilt angle, slit width of the second slit, and the three coordinates of the test point. We discuss the results of the theory and their problems; experiments with a Mach-Zehnder interferometer are in preparation.