Time in Quantum Mechanics

Jan Hilgevoord and David Atkinson

in The Oxford Handbook of Philosophy of Time

Published in print April 2011 | ISBN: 9780199298204
Published online September 2011 | e-ISBN: 9780191728372 | DOI:

Series: Oxford Handbooks in Philosophy

Time in Quantum Mechanics

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Unlike classical mechanics, quantum mechanics assumes the famous Heisenberg uncertainty relations. One of these concerns time: the energy–time uncertainty relation. Unlike the canonical position–momentum uncertainty relation, the energy–time relation is not reflected in the operator formalism of quantum theory. Indeed, it is often said and taken as problematic that there is not a so-called “time operator” in quantum theory. This chapter sheds light on these questions and others, including the absorbing matter of whether quantum mechanics allows for the existence of ideal clocks. The second section notes that quantum mechanics does not involve a special problem for time, and that there is no fundamental asymmetry between space and time in quantum mechanics over and above the asymmetry which already exists in classical physics. The third section studies time operators in detail. The fourth section discusses various uncertainty relations involving time.

Keywords: time operators; classical mechanics; quantum mechanics; Heisenberg uncertainty relations; ideal clocks

Article.  8373 words. 

Subjects: Philosophy of Science ; Metaphysics

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