This paper considers 4-dimensional manifolds upon which there is a Lorentz metric h and a symmetric connection Γ and which are originally assumed unrelated. It then derives sufficient conditions on h and Γ (expressed through the curvature tensor of Γ) for Γ to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provid...

The new quantum principle of a time machine that is not using a smooth timelike loops in Lorentz manifolds is described. The proposed time machine is based on the destruction of interference of quantum superposition states in the Wheeler superspace.