  We study the properties of a quantum field with time as a dynamical variable.
Temporal vibrations are introduced to restore the symmetry between time and
space in a matter field. The system with vibrations of matter in time and space
obeys the Klein-Gordon equation and Schrodinger equation. The energy observed
is quantized under the constraint that a particle's mass is on shell. This real
scalar field has the same properties of a zero-spin bosonic field. Furthermore,
the internal time of this system can be represented by a self-adjoint operator
without contradicting the Pauli's theorem. Neutrino can be an interesting
candidate for investigating the effects of these temporal and spatial
vibrations because of its extremely light weight.
