On the Superposition Principle and its Physics Content

Eftichios Bitsakis

O. М. Kholod

The article considers the tendencies of three principles of quantum mechanics for the micro world (uncertainty principle, additionality or complementarity principle and superposition or superposition principle) as having similarities with the tendencies of analysis of processes occurring in the macro world. The hypothesis is proved during the analysis of the fairy tale “Painted Fox” by Ivan Franko. The aim of the research was to identify, search for and describe the psychological and physical transformations of Fox Mykyta in Ivan Franko’s fairy tale as an explication of the tendencies of the functionality of the principles of quantum mechanics in the macro world. Among the research methods were chosen methods of analysis, synthesis, content analysis on the units of “image” and “theme”. We have chosen the following procedure as the research method: search for publications related to the problem analyzed by us; implementation of content analysis by unit “image” and “theme”; classification of identified fragments of the text of the fairy tale “Painted Fox” according to three criteria: “Compliance with the principle of uncertainty”, “Compliance with the principle of complementarity” and “Compliance with the principle of superposition”. Based on the analysis, it was concluded that the trends reflected in the three principles of quantum mechanics for studying the processes of the micro world (uncertainty, principle of additionality or complementarity and the principle of superposition or superposition) are clearly fixed in macro world processes.

F. Károlyházy

Peter Goetsch, Robert Graham

While the linearity of the Schr\"odinger equation and the superposition principle are fundamental to quantum mechanics, so are the backaction of measurements and the resulting nonlinearity. It is remarkable, therefore, that the wave equation of systems in continuous interaction with some reservoir, which may be a measuring device, can be cast into a linear form, even after the degrees of freedom of the reservoir have been eliminated. The superposition principle still holds for the stochastic wave function of the observed system and exact analytical solutions are possible in sufficiently simple cases. We discuss here the coupling to Markovian reservoirs appropriate for homodyne, heterodyne, and photon counting measurements. For these we present a derivation of the linear stochastic wave equation from first principles and analyze its physical content.

Łukasz Czekaj, Michał Horodecki, Paweł Horodecki +1 more

To explain the conceptual gap between classical and quantum and other, hypothetical descriptions of the world, several principles have been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce an information content principle (ICP) which represents a constrained uncertainty principle. The principle, by taking into account the encoding and decoding properties of a single physical system, is capable of separation, both classicality and quanta from a number of potential physical theories, including hidden variable theories. The ICP, which is satisfied by both classical and quantum theory, states that the amount of nonredundant information which may be extracted from a given system is bounded by a perfectly decodable information content of the system. We show that ICP allows one to discriminate theories which do not allow for correlations stronger than Tsirelson's bound. We show also how to apply the principle to composite systems, ruling out some theories despite that their elementary constituents behave quantumly.