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Fundamental constraints on two-time physics

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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.

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Author information

Authors and Affiliations

  1. Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, Puebla, Mexico

    E. Piceno

  2. Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Mexico

    A. Rosado & E. Sadurní

Authors
  1. E. Piceno
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  2. A. Rosado
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  3. E. Sadurní
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Correspondence to E. Sadurní.

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Piceno, E., Rosado, A. & Sadurní, E. Fundamental constraints on two-time physics. Eur. Phys. J. Plus 131, 352 (2016). https://doi.org/10.1140/epjp/i2016-16352-7

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