• The ‘time of occurrence’ in quantum mechanics

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    • Keywords


      Time operator; spectral condition; Pauli’s theorem; time of occurrence of an event; continuous measurements; positive-operator-valued measures; timeenergy uncertainty relation; time of arrival of photons

    • Abstract


      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 event associated with the system. However, while the observables normally encountered in quantum theory (and characterized by self-adjoint operators or projection-valued measures) correspond to instantaneous measurements, a time of occurrence measurement involves continuous observations being performed on the system to monitor when the event occurs. It is argued that a time of occurrence observable should be represented by a positive-operator-valued measure on the interval over which the experiment is carried out. It is shown that while the requirement of time-translation invariance and the spectral condition rule out the possibility of a self-adjoint time operator (Pauli’s theorem), they do allow for time of occurrence observables to be represented by suitable positive-operator-valued measures. It is also shown that the uncertainty in the time of occurrence of an event satisfies the time-energy uncertainty relation as a consequence of the time-translation invariance, only if the time of occurrence experiment is performed on the entire time axis.

    • Author Affiliations


      M D Srinivas1 R Vijayalakshmi1 2

      1. Department of Theoretical Physics, University of Madras, Guindy Campus, Madras - 600 025, India
      2. E. D. P. Department, Bharat Petroleum Corporation Limited, Ballard Estate, Bombay - 400 038, India
    • Dates

  • Pramana – Journal of Physics | News

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