Quantum Principles and Mathematical Models in Physics and Beyond

While mathematical modeling beyond physics—in biology, neuroscience, psychology, and economics—has been and is still dominated by classical mathematical models (C-models), primarily of probabilistic and statistical nature, quantum mathematical models (Q-models), mathematical models based in the mathematical formalism of quantum theory, have recently acquired currency in mathematical modeling in these areas. This chapter examines some of the reasons for using such models. In order to do so, the author considers the fundamental principles behind these models in quantum physics itself, taking as its point of departure Einstein’s distinction between “constructive” and “principle” theories. Two types of principle thinking in quantum theory will be considered, those defining the initial development of quantum mechanics in 1920s and those of quantum information theory, a more recent and still ongoing development. The principle perspective, the author argues, may help us to understand better a possible and possibly necessary role for quantum mathematical models beyond physics.