The nonclassical features of quantum mechanics are reproduced using models constructed with a classical theory — general relativity. The inability to define complete initial data consistently and independently of future measurements, nonlocality, and the non-Boolean logical structure are reproduced by these examples. The key feature of the models is the role of topology change. It is the breakdown of causal structure associated with topology change that leads to the apparently nonclassical behavior. For geons, topology change is required to describe the interaction of particles. It is therefore natural to regard topology change as an essential part of the measurement process. This leads to models in which the measurement imposes additional nonredundant boundary conditions. The initial state cannot be described independently of the measurement and there is a causal connection between the measurement and the initial state.