Colloquium: Age, the Complement of Energy
Tue 12 Aug 08 12:00pm - 1:00pm
Location: Hercus Theatre, University of Melbourne
Presented by Professor David T. Pegg, School of Biomolecular and Physical Sciences, Griffith University, Brisbane, Australia
Position is the quantum mechanical complement of momentum. Angular orientation is the complement of angular momentum. Phase is the complement of photon number. What is the complement of energy? Is it time? Unfortunately time is not an observable, that is, it is not a property of the system and cannot be represented by an operator as can the observables mentioned above. The complement of energy must have dimensions of time but must also be an observable. A suitable name for this quantity would be “age”, but does such a quantity exist? We show that it does and can be represented both by a probability-operator measure and by an Hermitian operator. The energy-age uncertainty relation is slightly more complicated than the momentum-position relation but is readily interpretable. The rate of change of age with time depends on the system and on its state. For example the age of an oscillator, or a rotator, in a suitable state increases directly as the time (as defined by the parameter in the Schroedinger equation). This is why the rotating earth and a pendulum make good clocks. For other systems and states, ageing can be slowed; indeed a system in an energy eigenstate does not age at all.