The Question of Simultaneity in Relativity and Quantum Mechanics

Abstract

In relativity, two simultaneous events at two different places are not simultaneous for observers in different Lorentz frames. In the Einstein-Podolsky-Rosen experiment, two simultaneous measurements are taken at two different places. Would they still be simultaneous to observers in moving frames? It is a difficult question, but it is still possible to study this problem in the microscopic world. In the hydrogen atom, the uncertainty can be considered to be entirely associated with the ground-state. However, is there an uncertainty associated with the time-separation variable between the proton and electron? This time-separation variable is a forgotten, if not hidden, variable in the present form of quantum mechanics. The first step toward the simultaneity problem is to study the role of this time-separation variable in the Lorentz-covariant world. It is shown possible to study this problem using harmonic oscillators applicable to hadrons which are bound states of quarks. It is also possible to derive consequences that can be tested experimentally.