The status of Time in the Quantum Theory remains even today a largely open question. In particular, the existence of a Quantum Time Operator that would describe the distribution of decay times of an unstable quantum system (in analogy with the Position operator that is associated to the position distribution) remained a polemichal question during several decades. Recently, we conceived experimental proposals involving CP violating processes (of single mesons and entangled pairs of mesons) that can be considered as crucial experiments aimed at testing the existence of a Quantum Time Operator. In the present paper, we shall present a similar proposal that can be realized with a single trapped ion. These proposals aim at bringing fundamental problems related to the status of Time in the Quantum Theory to the realm of experimental physics.
A New Look at the Position Operator in Quantum Theory
