Abstract We present a canonical construction of global observables -sometimes referred to in the literature as macroscopic observables or observables at infinity- in statistical mechanics, providing a unified treatment of both commutative and non-commutative cases. Unlike standard approaches, the framework is formulated directly in the
C∗ C ∗ -algebraic setting, without relying on any specific representation.
In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.
In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.