Abstract
The geometric basis for the effects of gravitation is traced from the relative orientation structure of pseudo-orthonormal basis vectors on the world line of a material point of interest. The effect of gravitation is specified by a principle of quasi-inertia. The relative basis structure is viewed in terms of a field frame and the effects of gravitation are then expressed by means of a force in this fixed (quasi-inertial) frame. This frame is generalized to a regional space and equations of motion for the nongeodesic particle motion under the influence of gravitation are obtained. The conditions that this regional space actually has the physical significance of an observer space are used to arrive at field equations. These field equations are used to solve for tensor gravitational fields entering in the equations of motion for the case applicable to the gravitational red-shift, the mercury perihelion shift, and the deflection of light by the sun. The usual Einstein-Schwarzschild results are obtained. The unity of the present view of the geometric basis of the effects of gravitation and that of the Lorentz force as described byRiesz are also briefly indicated.
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