The torsion-free de Sitter reducible metric linear connection on a five-dimensional manifold is studied in conjunction with a method of constructing spacetime via a partially restricted reference cross section of the bundle of linear frames described in earlier publications. It leads to the equation Rαβ = (1/l)gαβ where l is a fundamental length, assumed to be the Planck length. It also yields the Einstein vacuum equations on the constructed spacetime. Using the Feynman formulation of quantum mechanics together with a dimension reduction by unrestricted transformation of the reference cross section, a geometrical model for quantum non-locality is described. The dimension reduction is then applied to the Schwarzschild solution of Einstein's equations which is found to contain the quantum plane rotation associated with a particle at rest.
Journal of Physics A: Mathematical and Theoretical Vol. 40, Issue 32, p. F805-F816