Phase Space Quantum Mechanics and the Quantum-Classical Relation

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Phase-Space Quantum Mechanics and the Quantum-Classical Relation Quantum mechanics (QM) describes physics at short, "microscopic'' distances. Classical mechanics (CM) applies at macroscopic scales. Each works eminently well in its regime. The quantum-classical (QC) relation, however, is not well understood. For example, if one imagines moving from the microscopic to the macroscopic, QM does not morph into CM. Even worse, the so-called classical limit becomes singular, and it is difficult to understand how classical can emerge from quantum. I propose a research program aimed at understanding the QC relation better. Improved understanding would represent an advance in the foundations of physics. It would also be important for many experiments now being done and the technology being developed in the QC regime. My work uses phase space quantum mechanics (PSQM). It is the formulation of QM best suited to studying the QC relation. Both PSQM and CM live in phase space, for example, and neither uses operators. Hybrid QC systems point to problems. Many different systems exist in nature that appear to be composed of a quantum part interacting with a classical part. Example: quantum electrons and classical nuclei in a molecule. However, attempts to formulate consistent dynamics for hybrid QC systems have failed. Recently, I attacked this problem in the framework of PSQM. My student Amin and I rederived and generalized key previous results. Furthermore, we introduced a composition product for hybrid observables that made a consistent dynamics possible. In a 2nd paper, we applied the results to a simple model, providing a blueprint for applications to other physical systems. The first and largest part of my research proposal capitalizes on this advance. Our methods will be applied to more and more complex systems, approaching physicality, and eventually, making predictions about experiments. Additional effects have been conjectured to play a role in the emergence of CM from QM. These include measurement uncertainties, thermal effects, decoherence by interaction with the environment, and spontaneous state collapse. All will be studied in PSQM, for eventual use of our results in distinguishing them experimentally. If QM is valid at all scales, then macroscopic quantum systems, "Schrodinger cats'', must exist. An intense hunt is now underway for them. Included is a search for measures of macroscopic quantumness. Many measures of quantumness have been constructed in PSQM. I propose to investigate their dependence on various notions of size, in order to identify candidate measures of macroscopic quantumness. A second aim of my proposed research is to improve and generalize the methods and tools of PSQM. For example, recent work generalizes the Wigner function to quasiprobability distributions for arbitrary sets of operators. I plan to investigate if other elements of PSQM, like a star product, can also be introduced.