Temporal Vibrations in a Quantized Field

Abstract

In quantum theory, space and time are treated differently. Matter in a quantum field can have vibration in the spatial directions but not in the temporal direction. By restoring symmetry between space and time, we show that a system with matters vibrating in time has the properties of a zero-spin bosonic field. The real scalar field describing this system obeys the Klein-Gordon equation and Schrödinger equation. It must be quantized under the constraint that a particle’s mass is on shell. In addition, the internal time of this system can be represented by a self-adjoint operator. The spectrum of this operator spans the entire real line despite the Hamiltonian of the system is bounded from below.