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Noncommutative geometry, negative probabilities and Cantorian-Fractal spacetime

Abstract:

The Young's two-slit experiment on a quantum particle is explained within the framework of the noncommutative geometry associated with El Naschie's Cantorian-Fractal transfinite spacetime manifold. The noncommutative nature of Cantorian-fractal spacetime combined with the notion of the inherent negative probability assigned to a Peano-Hilbert loop around the region of slit B, because its orientation is opposite to the Peano-Hilbert loop located in the region around slit A, explains the wave-particle duality of an indivisible quantum particle. Since the noncommutative Cantorian-Fractal spacetime is not a classical space, it further supports the interpretation of the Schrodinger equation as two dual diffusion equations.