Full Description
This book describes a promising approach to problems in the foundations of quantum mechanics, including the measurement problem. The dynamics of ensembles on configuration space is shown here to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian. Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices and quantum matter fields interacting gravitationally with a classical spacetime.
Contents
Part I General Properties of Ensembles on Configuration Space: Introduction.- Observables, Symmetries and Constraints.- Interaction, Locality and Measurement.- Thermodynamics and Mixtures on Configuration Space.- Part II Axiomatic Approaches to Quantum Mechanics: Quantization of Classical Ensembles via an Exact Uncertainty Principle.- The Geometry of Ensembles on Configuration Space.- Local Representations of Rotations on Discrete Configuration Spaces.- Part III: Hybrid Classical-Quantum Systems.- Hybrid Quantum-Classical Ensembles.- Consistency of Hybrid Quantum-Classical Ensembles.- Part IV: Classical Gravitational Fields and Their Interaction with Quantum Fields.- Ensembles of Classical Gravitational Fields.- Coupling of Quantum Fields to Classical Gravity.- Variational Derivatives and Integrals.
