Reciprocal symmetry and continuous-discrete and wave-particle description of the same motion

摘要

Description of motion in terms of reciprocal velocity 1/v is as valid as the description in terms of velocity v. We have exploited this freedom to show that continuous and discrete variables are equivalent (and reciprocal) ways of describing the same motion. We have also shown that hyperbolic functions and circular functions are equivalent ways of describing the same motion. Hyperbolic functions give a particle description, and circular functions give a wave description. Therefore, particle and wave are equivalent ways of describing the same motion. Quantum mechanics prefers the wave function representation.