Quantum-like Representation of Macroscopic Configurations

TL;DR

This paper introduces a quantum-like probabilistic model that represents macroscopic configurations using wave functions, providing new insights into quantum logic and potential applications in various scientific fields.

Contribution

It develops a quantum-like representation algorithm (QLRA) that maps probabilistic data into complex or hyperbolic Hilbert spaces for macroscopic systems.

Findings

Macroscopic configurations can be represented with wave functions.

The model clarifies some foundational questions in quantum mechanics.

Potential applications in biology, sociology, and psychology.

Abstract

The aim of this paper is to apply a contextual probabilistic model (in the spirit of Mackey, Gudder, Ballentine) to represent and to generalize some results of quantum logic about possible macroscopic quantum-like (QL) behaviour. The crucial point is that our model provides QL-representation of macroscopic configurations in terms of complex probability amplitudes -- wave functions of such configurations. Thus, instead of the language of propositions which is common in quatum logic, we use the language of wave functions which is common in the conventional presentation of QM. We propose a quantum-like representation algorithm, QLRA, which maps probabilistic data of any origin in complex (or even hyperbolic) Hilbert space. On the one hand, this paper clarifyes some questions in foundations of QM, since some rather mystical quantum features are illustrated on the basis of behavior of macroscopic systems. On the other hand, the approach developed in this paper may be used e.g. in biology, sociology, or psychology. Our example of QL-representation of hidden macroscopic configurations can find natural applications in those domains of science.