The Pauli Objection

@article{Len2017ThePO,
  title={The Pauli Objection},
  author={Juan Le{\'o}n and Lorenzo Maccone},
  journal={Foundations of Physics},
  year={2017},
  volume={47},
  pages={1597-1608}
}
Schrödinger’s equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli… 
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References

SHOWING 1-10 OF 77 REFERENCES
Entangled Histories
We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we
Time in Quantum Theory
  • H. Zeh
  • Physics
    Compendium of Quantum Physics
  • 2009
I. In general, time is used in quantum theory as an external ('classical') concept. So it is assumed, as in classical physics, to exist as a controller of all motion – either as absolute time or in
The ‘time of occurrence’ in quantum mechanics
Apart from serving as a parameter in describing the evolution of a system, time appears also as an observable property of a system in experiments where one measures ‘the time of occurrence’ of an
Time in quantum gravity: An hypothesis.
  • Rovelli
  • Physics
    Physical review. D, Particles and fields
  • 1991
TLDR
It is shown that a natural extension of canonical Heisenberg-picture quantum mechanics is well defined and can be used to describe the "non-Schr\"odinger regime," in which a fundamental time variable is not defined.
Relativity quantum mechanics with an application to Compton scattering
The new quantum mechanics, introduced by Heisenberg and since developed from different points of view by various authors, takes its simplest form if one assumes merely that the dynamical variables
Generalized uncertainty relations: Theory, examples, and Lorentz invariance
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or
Time as a Quantum Observable, Canonically Conjugated to Energy, and Foundations of Self-Consistent Time Analysis of Quantum Processes
Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper
Evolution without evolution: Dynamics described by stationary observables
Because the time parameter in the Schrodinger equation is not observable, energy apparently obeys a superselection rule in the same sense that charge does. That is, observables must all commute with
Time in Quantum Physics: From an External Parameter to an Intrinsic Observable
In the Schrödinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the
...
...