Contributions to the mathematical study of models from classical and quantum physics

Simona Rota Nodari

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.

Vladimir Anashin

Clymer, NY, USA, Richard Joseph Oldani

All of the mathematical formulations of quantum mechanics describe the interaction between radiation and atoms, but we show here that only Einstein has been able to establish a solid logical connection with classical theory. His methods are used to interpret the other mathematical models by requiring that observables be described in a physically-defined coordinate system and that there be strict adherence to the conservation of momentum. The properties of momentum exchange are included in a quantum oscillator, or clock, by replacing the non-relativistic Hamiltonian model with a relativistically correct Lagrangian model. Equal contributions are assigned to photon, electron, and nucleus; and field boundaries are defined that coincide with the electron shells. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The Lagrangian model accounts for the 720 degree rotation of a wave function as an initial 360 degree electromagnetic wave cycle (photon absorption) followed by a second wave cycle (photon emission), yielding two wave cycles to correspond with one complete electron cycle. The abstract space of quantum mechanics is replaced by a real classical space.

David A. Edwards

A. Mangoni