2011/07/31 by Vladimir V. Kornyak · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Computer science #Constructive #Fractal and DNA sequence analysis #Impossibility #Invariant (physics) #Mathematics #Neutrino Physics Research #Observable #Origins and Evolution of Life #Permutation (music) #Physics #Pure mathematics #Quantum #Quantum dynamics #Quantum mechanics #Quantum process #Relational quantum mechanics #Theoretical physics #hep-th #math-ph #math.GR #math.MP #quant-ph
paper · pdf · doi:10.1088/1742-6596/343/1/012059
published in Journal of Physics Conference Series 343, 012059 (IOP Publishing) · 15 pages, talk at the conference "Mathematical Modeling and Computational Physics" Stara Lesna, High Tatra Mountains, Slovakia, July 4 - 8, 2011; v.2, some refinements of text
arxiv created 2011/08/31 · openalex publication_date 2012/02/08 · arxiv updated 2012/02/15 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
We analyse quantum concepts in a constructive finite background. Introduction of continuum or other actual infinities into physics leads to non-constructivity without any need for them in description of empirical observations. We argue that quantum behavior is a natural consequence of symmetries of dynamical systems. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution — only information about invariant combinations of such objects is available. General mathematical arguments imply that any quantum dynamics can be reduced to a sequence of permutations. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants. We demonstrate that for description of quantum phenomena there is no need to use such non-constructive number system as complex numbers. It is sufficient to employ the cyclotomic numbers — a minimal extension of the natural numbers which is suitable for quantum mechanics.