ESTABLISHING THE RIEMANNIAN STRUCTURE OF SPACE-TIME BY MEANS OF LIGHT RAYS AND FREE MATTER WAVES

As compared with axiomatic schemes based on the paths of massive point particles, a constructive approach based on the classical limit of the wave mechanics of matter fields has a particular advantage: The locally approximately plane waves do not only define matter rays, but can in addition be subject to interference measurements. These, in contrast to the free-fall experiments, are sensitive to the mass. This makes it possible to further specify the geometry of space-time. Light rays reveal a conformal structure of the space-time manifold. It will be shown that if, in addition, in each point of space-time locally approximately plane matter waves can be realized that are free and massive, the space-time is a Riemann space.