  The above argument for the necessity of geometric fields also holds for 3-velocity and 3-acceleration, denoted respectively by \(\xi^{\alpha}_{1}\) and \(\xi^{\alpha}_{2}\).  The transformation law for the 3-acceleration is much more complicated than that of the 4-acceleration. However, analogous to the case of 4-acceleration, the transformation law of 3-acceleration is linear and is inhomogeneous in the 3-acceleration variable \(\xi^{\alpha}_{2}\).  Consequently, there does not exist a unique standard of zero 3-acceleration that is intrinsic to the differential topological structure of spacetime. The standard of zero 3-acceleration must be provided by a geodesic 3-acceleration field or geodesic directing field, or what Weyl calls the guiding field. The guiding field is also referred to as the projective structure of spacetime and is denoted by \(\Pi^{\alpha}_{2}(x^{i}, \xi^{\alpha}_{1}\)). It is a function of spacetime location and the 3-velocity, both variables of which are independent of the 3-acceleration, as is required. Since the transformation law of the projective structure \(\Pi^{\alpha}_{2}(x^{i}, \xi^{\alpha}_{1}\)) has the same inhomogeneous form as the 3-acceleration \(\xi^{\alpha}_{2}\), the difference 