The incorporation of quantum mechanics into gravitational dynamics introduces perplexing issues into modern physics. In contrast to other interactions like electromagnetism, the classical trajectory of a gravitating system is independent of the mass coupling to the gravitational field. As previously discussed, this allows the gravitation of arbitrary test particles to be described in terms of local geometry only, the basis of general relativity. Thus, the geometrodynamics of classical general relativity are most directly expressed using localized geodesics. However, quantum dynamics incorporate measurement constraints that disallow complete localization of physical systems. A coherent quantum system is not represented by a path or a classical trajectory; rather, it self-interferes throughout regions. This complicates the use of classical formulations in describing inherently quantum processes.

In addition, the equations of general relativity are complex and non-linear in the interrelations between sources and geometry, which makes solutions of even classical systems complicated. The key to describing complex systems is to determine the most useful set of parameters and coordinates that give concise predictive explanations of those systems. This chapter will develop tools for examining quantum behaviors in gravitating systems.

Quantum coherence and gravity

The behaviors of quantum objects in Minkowski space-time are well understood, despite a lack of consensus on the various interpretations (Copenhagen, many worlds, etc.) of the underlying fundamentals of the quantum world, or concerns of the completeness of quantum theory. There have also been tests of systems modeled by equations that involve both Newton's gravitational constant GN and Planck's constant ħ, as described in Section 2.3.1.