The problem of properties in quantum mechanics

L. E. Ballentine

Pang Xiao‐feng, Feng Yuan-Ping

Linear Quantum Mechanics (LQM): Its Successes and Problems Macroscopic Quantum Effects and Properties of Motion of Quasiparticles The Fundamental Principles and Theories of Nonlinear Quantum Mechanics Wave-Corpuscle Duality of Microscopic Particles (MIP) in the NLQM Nonlinear Interaction and Localization of the MIP Nonlinear Versus Linear Quantum Mechanics The Problems Solving in the NLQM Properties and States of the MIP in Different Nonlinear Systems Nonlinearly Quantum-Mechanical Properties of the Excitons and Phonons Properties of Nonlinear Excitations and Motions for Protons, Polarons and Magnons in Different Systems.

Petr Hájíček

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

Dirk Aerts

We prove that a theory that is different from a classical theory and has the property that orthogonal states of a physical system are compatible states (a property called orthomodularity in axiomatics) cannot describe two separated entities. Quantum mechanics has this property and as a consequence it is impossible to describe two separated entities in quantum mechanics. This is essentially due to the fact that quantum mechanics is too specific a theory. We indicate the direction for a generalization where the problem could be solved.