UBC Theses and Dissertations
Particle detectors in the theory of quantum fields on curved spacetimes Cant, John Fraser
This work discusses aspects of a fundamental problem in the theory of quantum fields on curved spacetimes - that of giving physical meaning to the particle representations of the theory. In particular, the response of model particle detectors is analysed in detail. Unruh (1976) first introduced the idea of a model particle detector in order to give an operational definition to particles. He found that even in flat spacetime, the excitation of a particle detector does not necessarily correspond to the presence of an energy carrier - an accelerating detector will excite in response to the zero-energy state of the Minkowski vacuum. The central question I consider in this work Is - where does the energy for the excitation of the accelerating detector come from? The accepted response has been that the accelerating force provides the energy. Evaluating the energy carried by the (conformally-invariant massless scalar) field after the Interaction with the detector, however, I find that the detector excitation is compensated by an equal but opposite emission of negative energy. This result suggests that there may be states of lesser energy than that of the Minkowski vacuum. To resolve this paradox, I argue that the emission of a detector following a more realistic trajectory than that of constant acceleration - one that starts and finishes in inertial motion - will in total be positive, although during periods of constant acceleration the detector will still emit negative energy. The Minkowski vacuum retains its status as the field state of lowest energy. The second question I consider is' the response of Unruh's detector in curved spacetime - is it possible to use such a detector to measure the energy carried by the field? In the particular case of a detector following a Killing trajectory, I find that there is a response to the energy of the field, but that there is also an inherent 'noise'. In a two dimensional model spacetime, I show that this 'noise' depends on the detector's acceleration and on the curvature of the spacetime, thereby encompassing previous results of Unruh (1976) and of Gibbons & Hawking (1977).