  I prefer not to believe in distant parallelism for a number of  reasons. First, my mathematical attitude resists accepting such an  artificial geometry; it is difficult for me to understand the force  that would keep the local tetrads at different points and in rotated  positions in a rigid relationship. There are, I believe, two  important physical reasons as well. In particular, by loosening the  rigid relationship between the tetrads at different points, the gauge factor \(e^{i\lambda}\), which remains arbitrary  with respect to the quantity \(\psi\), changes from a constant to an  arbitrary function of spacetime location; that is, only through the  loosening of the rigidity does the actual gauge invariance become  understandable. Secondly, the possibility to rotate the tetrads at  different points independently from each other, is as we shall see,  equivalent to the symmetry of the energy-momentum tensor or with the  validity of its conservation law.