Finite Quantum Models: Constructive Approach to Description of Quantum Behavior

Details Finite Quantum Models: Constructive Approach to Description of Quantum Behavior Finite Quantum Models: Constructive Approach to Description of Quantum Behavior

2010-10-16

arxiv.org/abs/1010.3370v2

Physics

Mathematical Physics

v2: English translation added, some changes in text, English version 16 pages, Russian version 18 pages, submitted to "Zapiski

Scientific paper

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.

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