Abstract

Although highly predictive in their respective macroscopic and microscopic domains of applicability, General Relativity and quantum mechanics are mathematically incompatible, perhaps most markedly in assumptions in their formalisms concerning the nature of space and time. In perspective we already have a conceptual structure that links the local, macroscopic frame and the remote, apparently microscopic frame. A mathematical principle is invoked as a natural limit on D(n), so that effects which are clearly perspectival at D=3 become ‘more real’ (effectively observer-independent) with each D(n) increment. For instance, the apparently microscopic becomes the effectively microscopic and scale extremes are juxtaposed, so that black holes are local, macroscopic vanishing-points, in a similar way to that in which in projective geometry the point at infinity is incorporated into the foreground.  (In other words, a black hole is a blown-up ‘Planck-scale’ singularity.) Characteristics of the earthbound frame are applied to D>3, suggesting a physical basis for entanglement, and perspectival interpretations of quantum gravity, dimensional reduction and the information paradox.  We claim that the familiar processes whereby multiple physical states become describable by a single state in which composition information appears to be lost (e.g., ‘falling into a black hole’, the state of quantum linearity, and the state of freefall) are all examples of effective convergence of a space or n-surface to a single point of perspective.

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