Foundations of Physics

, Volume 40, Issue 9–10, pp 1368–1378 | Cite as

Time in Quantum Physics: From an External Parameter to an Intrinsic Observable

  • Romeo Brunetti
  • Klaus Fredenhagen
  • Marc Hoge


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 Schrödinger equation give rise to weights on the enlarged algebra of observables. States in the associated GNS representation correspond to states on the original algebra composed with a completely positive unit preserving map. Application of this map to the functions of the time operator on the large system delivers the positive operator valued maps which were previously proposed by two of us as time observables. As an example we discuss the application of this formalism to the Wheeler-DeWitt theory of a scalar field on a Robertson-Walker spacetime.

Quantum theory Time operator Constraint Partial observables Conditional probabilities in quantum physics Wheeler-De Witt equation 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoPovoItaly
  2. 2.II. Institut für Theoretische PhysikUniversität HamburgHamburgGermany

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