Foundations of Classical Physics

Lajos Diósi

Lloyd Motz, David W. Kraft

Nina Culver

In this thesis we explore the mathematical foundations that unite physics at a quantum scale, quantum mechanics, with a macroscopic scale, classical mechanics. We seek to understand the mathematical motivation behind the quantum-classical correspondence and how it unites two seemingly different theories of the physical world. We show how this correspondence binds the Hamiltonian theory of classical physics to the Hilbert space theory in quantum mechanics, and establish a way to translate between classical observables and quantum operators, using the Fourier transform. These approaches to “quantizing” a physical state can be applied generally to a wide variety of observable quantities in classical mechanics.

Karim P. Y. Thébault

This Element explores the formal and conceptual foundations of phase space formulations of classical and quantum mechanics. It provides an overview of the core mathematical and physical content of Hamiltonian mechanics, stochastic phase space mechanics, contact Hamiltonian mechanics, and open and closed quantum mechanics on phase space. The formal material is unified via three interpretative themes relating to structured possibility spaces, Liouville's theorem and its failure, and the classical and quantum notions of open and closed systems. This Element book is intended for researchers and graduate students in the philosophy and foundations of physics with an interest in the conceptual foundations of physical theory.

Carlo Jacoboni

Thomas Brown