Happy Thanksgiving! :-)
Roman V. Buniy and Stephen D.H. Hsu
For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.It may come as a surprise to many physicists that Schrodinger evolution in large isolated quantum systems leads generically to macroscopic superposition states. For example, in the familiar Brownian motion setup of a ball interacting with a gas of particles, after sufficient time the system evolves into a superposition state with the ball in macroscopically different locations. We use von Neumann's 1929 Quantum Ergodic Theorem as a tool to deduce this dynamical result.