  "Time" has different meanings in classical general relativity and in quantum
theory. While all choices of a time function yield the same local classical
geometries, quantum theories built on different time functions are not
unitarily equivalent. This incompatibility is most vivid in model systems for
which exact quantum descriptions in different time variables are available. One
such system is a spherically symmetric, thin dust shell. In this essay we will
compare the quantum theories of the shell built on proper time and on a
particular coordinate time. We find wholly incompatible descriptions: whereas
the shell quantum mechanics in coordinate time admits no solutions when the
mass is greater than the Planck mass, its proper time quantum mechanics only
admits solutions when the mass is greater than the Planck mass. The latter is
in better agreement with what is expected from observation. We argue that
proper time quantization provides a superior approach to the problem of time in
canonical quantization.
