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A Non-Riemannian Universe

eigenvalues. The eigenvalues for the field equations are then related to the eigenvalues of the electromagnetic and gravitational fields. The ratio of the latter can be given the physical interpretation of (e/m)2 for an elementary particle. The equations of the paths in a non-Riemannian space are written down. It is shown that there is a parallel solution which applies at all points along the path. This parallel solution makes explicit the form of the equations which does not conserve the vectors along the path. A simple transformation applied to the vectors does produce conserved vectors along the path, and enables a solution for the functional form of their evolution. This allows a redshift in the wavelength of light received from great distances without implying a recession of the emitting source. The redshift would be dependent on the path of evolution and its environment. A conclusion is given that non-Riemannian geometry is capable of generating results of signif icance and interest at both the elementary particle and cosmological levels. Satisfactory answers to physical problems at both levels would be more likely if there were a coherent philosophical basis to the different branches of theoretical physics.