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If Gravity is Geometry, is Dark Energy just Arithmetic?

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Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional 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 non-Diophantine 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 non-Diophantine 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 miss-match 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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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS nr 56, wydanie 4, strony 1364 - 1381,
ISSN: 0020-7748
Język:
angielski
Rok wydania:
2017
Opis bibliograficzny:
Czachor M.: If Gravity is Geometry, is Dark Energy just Arithmetic?// INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS. -Vol. 56, iss. 4 (2017), s.1364-1381
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1007/s10773-017-3278-x
Bibliografia: test
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Weryfikacja:
Politechnika Gdańska

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