Boundary Conditions for the Dynamical Equations of Quantum Mechanics

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over - ∞ < t < +∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t ₀: t ₀ ≤ t < +∞, for which the mathematicians would choose t ₀ = 0,¹ but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time t₀ⁱ for an ensemble of individual quanta.