Finite Quantum Models: Constructive Approach to Description of Quantum Behavior

TL;DR

This paper shows that quantum behavior can be naturally modeled in finite systems with symmetry groups, simplifying quantum dynamics to permutation operations and enabling constructive analysis with computational tools.

Contribution

It introduces finite quantum models that describe quantum behavior through symmetry and permutation dynamics, avoiding complex interpretational concepts.

Findings

Quantum behavior arises from symmetry properties in finite systems.

Quantum dynamics reduces to permutation dynamics in finite models.

Finite models are amenable to constructive analysis using computer algebra.

Abstract

Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing indistinguishable, i.e. lying on the same orbit of some symmetry group, elements. In this paper we demonstrate, that quantum behavior arises naturally in systems with finite number of elements connected by non-trivial symmetry groups. The "finite" approach allows to see the peculiarities of quantum description more distinctly without need for concepts like "wave function collapse", "Everett's multiverses" etc. In particular, under the finiteness assumption any quantum dynanics is reduced to the simple permutation dynamics. The advantage of the finite quantum models is that they can be studied constructively by means of computer algebra and computational group theory methods.