Foundations of Physics

, Volume 45, Issue 4, pp 382–403

Timelines and Quantum Time Operators

Original Paper

DOI: 10.1007/s10701-015-9870-0

Cite this article as:
Moyer, C.A. Found Phys (2015) 45: 382. doi:10.1007/s10701-015-9870-0


The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the Hamiltonian as the generator of translations in time to construct time states. Taken together, these states constitute what we call a timeline. Such timelines are adequate for the representation of any physical state, and appear to exist even for the semi-bounded and discrete Hamiltonian systems ruled out by Pauli’s theorem. However, the step from a timeline to a valid time operator requires additional assumptions that are not always met. Still, this approach illuminates the issues surrounding the construction of time operators, and establishes timelines as legitimate alternatives to the familiar coordinate and momentum bases of standard quantum theory.


Time operator Positive, operator-valued measure (POVM) observable Time covariance Time of arrival Recurrence time 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Physics and Physical OceanographyUNC WilmingtonWilmingtonUSA

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