THE WEYL-CARTAN SPACE PROBLEM IN PURELY AFFINE THEORY

According to Poincare, only the ''epistemological sum of geometry and physics is measurable''. Of course, there are requirements of measurem ent to be imposed on geometry because otherwise the theory resting on this geometry cannot be physically interpreted. In particular, the Wey l-Cartan space problem must be solved, i.e., it must be guaranteed tha t the comparison of distances is compatible with the Levi-Civita trans port. In the present paper, we discuss these requirements of measureme nt and show that in the (purely affine) Einstein-Schrodinger unified f ield theory the solution of the Weyl-Cartan space problem simultaneous ly determines the matter via Einstein's equations. Here the affine fie ld Gamma(kl)(i) represents Poincare's sum, and the solution of the spa ce problem means its splitting in a metrical space and in matter field s, where the latter are given by the torsion tensor Gamma([kl])(i).