2015/12/31 by E. Piceno, A. Rosado, E. Sadurní · 7 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Classical mechanics #Classical physics #Mathematical physics #Mathematics #Observability #Physics #Planck #Planck constant #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Theoretical physics #Time evolution #Uncertainty principle #Unitary state #hep-th #quant-ph
paper · pdf · doi:10.1140/epjp/i2016-16352-7
published in The European Physical Journal Plus 131(10) (Springer Science+Business Media) · 13 pages, 1 figure. This version close to published paper
openalex publication_date 2016/10/01 · arxiv created 2016/10/03 · arxiv updated 2016/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in 1+2 dimensional space, leading to effective single-time evolution for any initial condition. In the domain of quantum mechanics, we follow strictly the hypothesis of probability conservation by extending the Heisenberg picture to unitary evolution with two times. As a result, the observability of two temporal axes is constrained by a generalized uncertainty relation involving level spacings, total duration of the effect and Planck's constant.