Physics at the Transition between Bounded and Unbounded Trajectories

The electromagnetic interaction is characterised by discrete states for bound systems in contrast to continuous states for unbound systems. The difference merely arises because the characteristic equations do not exhibit the same behaviour for negative and positive energy parameter values, thus the apparent distinction between bound and unbound states can be considered purely descriptive and completely superficial - there is no indication that bounded and unbounded systems are subject to differing physical laws. However, the remarkable suggestion has been made that there exists a behavioural distinction between bound and unbound states of systems under gravitational influence. This notion is critically evaluated here. At the very basic level, a severe problem is found in defining a local concept of boundedness consistent with the current understanding of the gravitational interaction. Nevertheless it is difficult to exclude the possibility that bound and unbound systems are dynamically distinct, a distinction that may be relevant to existing cosmological and astronomical anomalies.