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Timelines and Quantum Time Operators

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Abstract

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.

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  1. Department of Physics and Physical Oceanography, UNC Wilmington, Wilmington, USA

    Curt A. Moyer

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  1. Curt A. Moyer
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Correspondence to Curt A. Moyer.

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Moyer, C.A. Timelines and Quantum Time Operators. Found Phys 45, 382–403 (2015). https://doi.org/10.1007/s10701-015-9870-0

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