Proper time operator and its uncertainty relation

Abstract

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.

11 pages. Published version

References in corpus (8)

• Big-Bang Nucleosynthesis
• Heisenberg's Uncertainty Principle
• Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam
• How to Introduce Time Operator
• Time as a quantum observable
• Tunneling times with covariant measurements
• Existence and nonexistence of an intrinsic tunneling time
• Self-Adjoint Time Operator of a Quantum Field