Harmonic Oscillator with Time as a Dynamical Variable

We find that a field with oscillations of matter in proper time has the properties of a zero-spin bosonic field. A particle observed in this field is a proper time oscillator. Neglecting all quantum effects, a proper time oscillator can mimic a point mass at rest in general relativity. The spacetime outside a ‘stationary’ proper time oscillator is a Schwarzschild field.