At first we derive a field equation by means of essentially geometry free demands, that is, by means of a Cauchy-problem, superposition principle, finite propagation speed and a conservation law. These requirements characterise a symmetric hyperbolic system of partial differential equations of first order.

The Geometry of Matter Fields

Axiomatic physical derivations of the mathematical picture of spacetime used in General Relativity, which are based on the primitive concepts of free fall and light propagation, have led in a direct, convincing manner only to a Weyl spacetime; a further reduction to the usual Lorentzian manifold required postulates which are much less convincing In this paper we present a new postulate within a more recent spacetime axiomatics, by which there the Lorentzian spacetime is reached in a different way The theory is based on similar basic notions with more emphasis on clock parametrizations; no quantumtheoretical reasonings are used A very natural construction of the spacetime metric is the basis for the postulate which is essentially a compatibility condition for parametrizations of worldlines The result motivates a renewed search for a better way of reduction in the mentioned theories and can guide it

Distinguishability of Weyl- from Lorentz-spacetimes by classical physical means

If one tries to build axiomatically the Einsteinian theory of gravitation by means of the basic concepts «event, light ray and freely falling particle», one arrives at a Weyl and not at a Riemann spacetime. However, Audretsch has recently proved the following remarkable theorem: if one assumes that the motion of the particle is governed by Dirac, or Klein-Gordon, wave equation, the above Weyl space-time degenerates into a Riemann space-time. In this paper, we give a synthetic—and more general—proof of Audretsch’s result.

Weylian geometry and first-order wave equations

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Weylian geometry and first-order wave equations