Spacetime Structure Explored by Elementary Particles : Microscopic Origin for the Riemann-Cartan Geometry

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Abstract
The metric condition and the symmetry of affine connexions are both a priori assumed by General Relativity without much justification. To provide a basis for this, we present a new approach to spacetime structure, taking as probes elementary particles of spin 1/2, baryons and leptons including neutrinos which define `neutrino null cone'. Thus our approach is much finer than the usual ones using classical particles and quite opposite to spinor formulation of General Relativity as it stands. Assuming the most general form of metric spinor and spinor connexion which includes two gauge fields, we mathematically deduce (1) the metric tensor and (2) the semimetric condition. By virtue of the Eötvös-type null experiments, we find that fermion-number gauge field interacts with matter too weakly to be detected. Furthermore, it it shown that scale gauge field neither couples to the elementary particles, nor the electromagnetic field. We are thus led to the Riemann geometry with torsion, first introduced by Cartan independently of spin concept. There is no evidence whatsoever to exclude torsion. We conclude, therefore, that torsion must seriously be taken into account, in particular when and where classical General Relativity seems to break down.

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