On the interaction of mesoscopic quantum systems with gravity

Abstract

We review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non-relativistic expansions of the Klein-Gordon and Dirac equations in the post-Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated. Quantum theory and the gravitational fieldIn this introductory section we shall give a brief review of the relation between quantum theory and gravity. For more details and references we refer to [1].The gravitational interaction is distinguished by the fact that it interacts universally with all forms of energy. It dominates on large scales (relevant for cosmology) and for compact objects (such as neutron stars and black holes). All presently known features of gravitational physics are successfully described by the theory of general relativity (GR), accomplished by Albert Einstein in 1915.1 In this theory, gravity is not interpreted as a force acting on space and in time, but as a representation of the geometry of spacetime. This is a consequence of the equivalence principle stating the (local) equivalence of free fall with the gravity-free case. Mass generates curvature which in turn acts back on the mass. Curvature can also exist in vacuum; for example, it can propagate with the speed of light in the form of gravitational waves. In contrast to other physical theories, spacetime in GR plays a dynamical role and not the role of a rigid background structure.Experimentally, GR is a very successful theory [4]. Particularly impressive examples are the observations of the double pulsar PSR 1913+16 by which the existence of gravitational waves has been verified indirectly. Many interferometers on Earth are now in operation with the goal of direct observations of these waves. This would open a new window to the universe ('gravitational-wave astronomy'). After 40 years of preparation, the ambitious satellite project Gravity-Probe B was launched in April 2004 in order to observe the 'Thirring-Lense effect' predicted by GR. This effect states that a rotating mass (here the Earth) forces local inertial systems in its neighbourhood to rotate with respect to far-away objects. GR has also entered everyday life in the form of the global positioning system GPS; without the implementation of GR, inaccuracies in the order of kilometres would easily arise over the time span of days [5]. A recent survey of GR tests in space can be found in [6] and the references therein. * Corresponding author: e-mail: kiefer@thp.uni-koeln.de 1 Exceptions may be the Pioneer anomaly [2] and the rotation curves of galaxies [3], which could in principle d...

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