Experiment, Entanglement and the Foundations of Quantum Mechanics

Arthur Zajonc

Jürg Martin Fröhlich, Baptiste Schubnel

We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the key problems in a quantum theory of observations and measurements are. In the last part of our essay, we attempt to elucidate the roles played by entanglement between a system and its environment and of information loss in understanding "decoherence" and "dephasing", which are key mechanisms in a quantum theory of measurements and experiments. We also discuss the problem of "time in quantum mechanics" and sketch an answer to the question when an experiment can be considered to have been completed successfully.

Daniel R. Bes

F.J. Duarte, T S Taylor

Edward R. Floyd

Bibliography ............................................................................................................50 Entanglement phenomena offer fine, didactic examples that demonstrate the application of quantum trajectories. Quantum entanglement phenomena are tractable to the quantum trajectory representation. Quantum trajectories render insight into entanglement phenomena of quantum systems. Entanglement is one of the prime features that distinguishes quantum mechanics from classical mechanics. Entanglement implies nonlocality as confirmed by the Aspect experiments [1-3]. Entangled quantum systems have nonclassical correlations that manifest nonlocal behavior for the system. The quantum trajectory representation can describe how entanglement induces nonlocality [4]. Within the foundations of quantum mechanics, a quantum trajectory representation of entangled systems is the key to resolving the nonintuitive behavior of wave packet spreading [4], the which-way paradox of the double-slit experiment [5], and the Einstein-Podolsky-Rosen (EPR) paradox [6].

James K. Freericks

Abstract In this work, we describe strategies and provide case-study activities that can be used to examine the properties of superposition, entanglement, tagging, complementarity, and measurement in quantum curricula geared for teacher training. Having a solid foundation in these conceptual ideas is critical for educators who will be adopting quantum ideas within the classroom. Yet they are some of the most difficult concepts to master. We show how one can systematically develop these conceptual foundations with thought experiments on light and with thought experiments that employ the Stern-Gerlach experiment. We emphasize the importance of computer animations in aiding the instruction on these concepts.