Geometrization of Physics: The Problem of Motion

Abstract The geometrization of physics may be expressed in the context of finding equations of motion for different objects rather than the conventional concept of allocating field variables geometrically. This can be performed by identifying physical quantities in terms of scalars, vectors and tensors described in various geometries that admit a nonvanishing curvature and torsion of space-time. The effect of covariant differentiation may represent the effect of physical fields on the trajectory of objects. We adopt a method in which spinning and charged objects are expressed using a parameter transformation between two nearby paths separated by a deviation vector in Riemannian, non-Riemannian, and Finslerian geometries. Moreover, the concept of parameter transformation is being revisited in the context of Clifford space as a step of combining microphysics and macrophysics.