Can the universe be represented by a superposition of spacetime manifolds?

In this article it is argued, that the universe cannot be modeled as a space-time manifold. A theorem of geometry provides that null geodesics on a space-time manifold which begin at the same point with the same initial tangent vector are unique. But in reality, light originating from a single point with a given initial direction does not travel along a unique null geodesic path when a massive object attracts it, in particular when the massive object is in an indefinite location. Therefore, the universe cannot be described as a space-time manifold. It is then argued that the universe is a superposition of space-time manifolds, where the manifolds form a Hilbert space over the complex numbers.