Wyszukiwarka
Abstrakt
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.
Cytowania
-
4
CrossRef
-
0
Web of Science
-
1 0
Scopus
Cytuj jako
Pełna treść
- Wersja publikacji
- Accepted albo Published Version
- Licencja
-
otwiera się w nowej karcie
Słowa kluczowe
Informacje szczegółowe
- 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
-
więcej (15) mniej
- Czachor, M.: Relativity of arithmetic as a fundamental symmetry of physics. Quantum Stud.: Math. Found. 3, 123-133 (2016). arXiv:1412.8583 [math-ph] otwiera się w nowej karcie
- Aerts, D., Czachor, M., Kuna, M.: Crystallization of space: Space-time fractals from fractal arithmetic. Chaos, Solitons and Fractals 83, 201-211 (2016). arXiv:1506.00487 [gr-qc] otwiera się w nowej karcie
- Aerts, D., Czachor, M., Kuna, M.: Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus. Chaos, Solitons and Fractals 91, 461-468 (2016). arXiv:1603.05471 [math-ph] otwiera się w nowej karcie
- Aerts, D., Czachor, M., Kuna, M.: Fractal arithmetic and calculus on Sierpiński sets. arXiv:1606.01337 [math.GN] otwiera się w nowej karcie
- Baird, J.C., Noma, E.: Fundamentals of Scaling and Psychophysics. Wiley, New York (1978)
- Norwich, K.H.: Information, Sensation, and Perception. Academic Press, San Diego (1993) otwiera się w nowej karcie
- Czachor, M.: Information processing and Fechner's problem as a choice of arithmetic. In: Burgin, M., Hofkirchner, W. (eds.) Information Studies and the Quest for Transdisciplinarity: Unity in Diversity. World Scientific, Singapore (2016). arXiv:1602.00587 [q-bio.NC] otwiera się w nowej karcie
- Fechner, G.T.: Elemente der Psychophysik. Breitkopf und Hartel, Leipzig (1860)
- Burgin, M.: Non-Diophantine Arithmetics, Ukrainian Academy of Information Sciences Kiev. (in Russian) (1997) otwiera się w nowej karcie
- Burgin, M.: Introduction to projective arithmetics. arXiv:1010.3287 [math.GM] (2010) otwiera się w nowej karcie
- Benioff, P.: New gauge field from extension of space time parallel transport of vector spaces to the underlying number systems. Int. J. Theor. Phys. 50, 1887 (2011) otwiera się w nowej karcie
- Benioff, P.: Fiber bundle description of number scaling in gauge theory and geometry. Quantum Stud. Math. Found. 2, 289 (2015). arXiv:1412.1493 otwiera się w nowej karcie
- Benioff, P.: Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities. Quantum Inf. Proc. 15, 1081 (2016). arXiv:1508.01732 otwiera się w nowej karcie
- Jackson, J.D.: Classical Electrodynamics. Wiley, New York (1962)
- Hartle, J.B.: Gravity. An Introduction to Einstein's General Relativity. San Francisco, Benjamin Cummings (2003)
- Weryfikacja:
- Politechnika Gdańska
wyświetlono 111 razy