Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in GeneralCovariant Quantum Theories

摘要

The authors consider the cluster of problems raised by the relation between thenotion of time, gravitational theory, quantum theory and thermodynamics; in particular, the authors address the problem of relating the 'timelessness' of the hypothetical fundamental general covariant quantum field theory with the 'evidence' of the flow of time. By using the algebraic formulation of quantum theory, the authors propose a unifying perspective on these problems, based on the hypothesis that in a generally covariant quantum theory the physical time-flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system ('thermal time hypothesis'). The authors implement this hypothesis by using a key structural property of von Neumann algebras; the Tomita-Takesaki theorem, which allows to derive a time-flow, namely a one-parameter group of automorphisms of the observable algebra, from a generic thermal physical state. The authors study this time-flow, its classical limit, and the authors relate it to various characteristic theoretical facts, as the Unruh temperature and the Hawking radiation. The authors also point out the existence of a state-independent notion of 'time'.