The Importance of the Empty Set and Noncommutative Geometry in Underpinning the Foundations of Quantum Physics
Ji‐Huan He, Ting Zhong, Lan ping Xu +4 more
Unlike relativity quantum mechanics was not developed originally as a spacetime theory. Noncommutative geometry radically changed the situation. The present work builds upon noncommutative geometry and Cantorian spacetime theories to give a mathematical explanation coupled to a general and obvious physical reasoning for the quantum contra-intuitive results associated with particle wave duality, state vector reduction and related aspects at measurement. In particular we stipulate that a quantum particle is represented by a Cantor point via the dimensions of a Cantorian zero set given by dim (P) = (0,)φ while the quantum wave is represented by the emptiness between disjointed Cantorian points, i.e. a complementary empty Cantorian set of dim (W) = ( 1,)φ − where φ = ( 5 − 1)/2. Measurement interferes with the empty set and renders it non-empty and that accounts in various ways for the wave collapse and the disappearance of the interference fringes.
•Jan 13, 2016•1 citation