Boundary conditions, semigroups, quantum jumps, and the quantum arrow of time

• Published in: Journal of physics. Conference series 2015-04, Vol.597 (1), p.12018
• Main Author: Bohm, Arno
• Format: Article
• Language: English
• Subjects: Acoustic scattering; Asymmetry; Boundary conditions; Hilbert space; Mathematical analysis; Physics; Quantum theory; Theorems
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/597/1/012018

Experiments on quantum systems are usually divided into preparation of states and the registration of observables. Using the traditional mathematical methods (the Hilbert space and Schwartz space of distribution theory), it is not possible to distinguish mathematically between observables and states. The Hilbert space as well as Schwartz space boundary conditions for the dynamical equations lead by mathematic theorems (Stone-von Neumann) to unitary group with -∞ < t < ∞. But in the experimental set-up, one clearly distinguishes between the preparation of a state and the registration of an observable in that state. Furthermore, a state must be prepared first before an observable can be measured in this state (causality). This suggests time asymmetric boundary conditions for the dynamical equations of quantum theory. Such boundary conditions have been provided by Hardy space in the Lax-Phillips theory for electromagnetic and acoustic scattering phenomena. The Paley-Wiener theorem for Hardy space then leads to semi-group and time asymmetry in quantum physics. It introduces a finite "beginning of time" t0 for a time asymmetric quantum theory, which have been observed as an ensemble of finite times t(i)0, the onset times of dark periods in the quantum jump experiments on a single ion.