  We study the quantum properties of an oscillator in proper time. This proper
time oscillator is a particle model with mass that is on shell. Its internal
time can be treated as a self-adjoint operator. The displaced time and
displaced time rate of the oscillator obey an uncertainty relation resembling
the one between position and momentum, which is different from the usual
energy-time uncertainty relation. In addition, we demonstrate that a matter
field with proper time oscillators satisfies the Klein-Gordon equation. It has
properties of a zero-spin quantum field. The formulations adopted permits a
more symmetrical treatment between time and space in a matter field.
