Abstract
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are nonunique. The examples of fourdimensional spaces, R^4 and (−L/2,L/2)^4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a nonDiophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the ‘natural’ Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the nonDiophantine formalism. When the ‘natural’ formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating expansion. The effect is clearly visible also in solutions of the Friedman equation with vanishing cosmological constant. All of this suggests that phenomena attributed to dark energy may be a manifestation of a missmatch between the arithmetic employed in mathematical modeling, and the one occurring at the level of natural laws. Arithmetic is as physical as geometry.
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 Category:
 Articles
 Type:
 artykuł w czasopiśmie wyróżnionym w JCR
 Published in:

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
no. 56,
edition 4,
pages 1364  1381,
ISSN: 00207748  Language:
 English
 Publication year:
 2017
 Bibliographic description:
 Czachor M.: If Gravity is Geometry, is Dark Energy just Arithmetic?// INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS. Vol. 56, iss. 4 (2017), s.13641381
 DOI:
 Digital Object Identifier (open in new tab) 10.1007/s107730173278x
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