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Abstract
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in natural sciences. A change of realization of arithmetic, without altering the remaining structures of a given equation, plays the same role as a symmetry transformation. An appropriate construction of arithmetic turns out to be particularly important for dynamical systems in fractal space-times. Simple examples from classical and quantum, relativistic and nonrelativistic physics are discussed, including the eigenvalue problem for a quantum harmonic oscillator. It is explained why the change of arithmetic is not equivalent to the usual change of variables.
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s40509-015-0056-4
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- Category:
- Articles
- Type:
- publikacja w in. zagranicznym czasopiśmie naukowym (tylko język obcy)
- Published in:
-
Quantum Studies : Mathematics and Foundations
no. 3,
edition 2,
pages 123 - 133,
ISSN: 2196-5609 - Language:
- English
- Publication year:
- 2016
- Bibliographic description:
- Czachor M.. Relativity of arithmetic as a fundamental symmetry of physics. Quantum Studies : Mathematics and Foundations, 2016, Vol. 3, iss. 2, s.123-133
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s40509-015-0056-4
- Verified by:
- Gdańsk University of Technology
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