Eur. Phys. J. Plus (2016) 131: 352
https://doi.org/10.1140/epjp/i2016-16352-7

Regular Article

Fundamental constraints on two-time physics

¹ Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, Puebla, Mexico
² Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Mexico

^* e-mail: sadurni@ifuap.buap.mx

Received: 25 April 2016
Accepted: 14 September 2016
Published online: 5 October 2016

Abstract

We show that generalizations of classical and quantum dynamics with two times lead to a fundamentally constrained evolution. At the level of classical physics, Newton’s second law is extended and exactly integrated in a (1 + 2) -dimensional space, leading to effective single-time evolution for any initial condition. The cases 2 + 2 and 3 + 2 are also analyzed. 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.