The Pauli Objection

Foundations of Physics 47 (12):1597-1608 (2017)
  Copy   BIBTEX

Abstract

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 concluded that constructing a general a time operator is impossible. Here we show how the Pauli argument fails when one uses an external system to track time, so that time arises as correlations between the system and the clock. In this case, the time operator is conjugate to the clock Hamiltonian and not to the system Hamiltonian, but its eigenvalues still satisfy the Schrödinger equation for arbitrary system Hamiltonians.

Similar books and articles

Timelines and Quantum Time Operators.Curt A. Moyer - 2015 - Foundations of Physics 45 (4):382-403.
Canonical Proper-Time Dirac Theory.Tepper L. Gill - 1998 - Foundations of Physics 28 (10):1561-1575.
The continuous spectra of quantum operators.Boris Leaf - 1982 - Foundations of Physics 12 (6):583-606.
Quantum mechanics in discrete space and angular momentum.T. S. Santhanam - 1977 - Foundations of Physics 7 (1-2):121-127.
From time operator to chronons.B. Misra - 1995 - Foundations of Physics 25 (7):1087-1104.
Change in Hamiltonian general relativity from the lack of a time-like Killing vector field.J. Brian Pitts - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 47:68-89.

Analytics

Added to PP
2017-09-09

Downloads
114 (#151,368)

6 months
39 (#93,002)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Juan Leon
Consejo Superior De Investigaciones Científicas

Citations of this work

No citations found.

Add more citations

References found in this work

Relational quantum mechanics.Carlo Rovelli - 1996 - International Journal of Theoretical Physics 35 (8):1637--1678.
Time in Quantum Gravity: An Hypothesis.Carlo Rovelli - 1991 - Physical Review D 43 (2):451–456.
Time in quantum mechanics: a story of confusion.Jan Hilgevoord - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):29-60.
Time in quantum mechanics: a story of confusion.Jan Hilgevoord - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):29-60.
An axiomatic formulation of the Montevideo interpretation of quantum mechanics.Rodolfo Gambini, Luis Pedro García-Pintos & Jorge Pullin - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (4):256-263.

View all 13 references / Add more references