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Do We Need a Fifth Dimension in Quantum Mechanics?

Abstract:
We come to the conclusion in this article that we need an extra imaginary coordinate to describe the curvature induced by mass in three-dimensional volume and to solve the dilemma of whether the electron does occupy some volume before it collapses to a point after the measurement. We also give a new metric for the five-dimensional case. We are in agreement with Kaluza-Klein theory and modern string theories that a loop should be formed in the higher dimensions.