PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2013 | 11 | 10 | 1212-1220
Article title

On the origin of space

Content
Title variants
Languages of publication
EN
Abstracts
EN
Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension d of space evolves smoothly with time in the range 0 ≤ d(t) ≤ 3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1212-1220
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
Contributors
References
  • [1] K. Miller, B. Ross, An introduction to fractional calculus and fractional differential equations, (Wiley, New York, 1993)
  • [2] S. G. Samko, B. Ross, Integr. Transf. Spec. F. 1, 277 (1993) http://dx.doi.org/10.1080/10652469308819027[Crossref]
  • [3] I. Podlubny, Fractional differential equations, (Academic Press, New York, 1999)
  • [4] R. Hilfer, Applications of fractional calculus in physics, (World Scientific Publ., Singapore, 2000) http://dx.doi.org/10.1142/9789812817747[Crossref]
  • [5] R. Herrmann, Fractional calculus - An introduction for physicists, (World Scientific Publ., Singapore, 2011) http://dx.doi.org/10.1142/8072[Crossref]
  • [6] G. F. Leibniz, Correspondence with l’Hospital manuscript (1695)
  • [7] C. Darwin, On the origin of species by means of natural selection, (John Murray, London, 1859)
  • [8] L. E. S. Ramirez, C. F. M. Coimbra, Int. J. Differential Equations 2010, 846107 (2010)
  • [9] T. Odzijewicz, A. B. Malinkowska, D. F. M. Torres, Operator Theory: Advances and Applications 229 291–301, (Birkhäuser Science, Springer, Berlin, Heidelberg, New York, 2013)
  • [10] T. Odzijewicz, A. B. Malinkowska, D. F. M. Torres, arXiv:1304.5282 [math.OC] (2013)
  • [11] O. von Guericke, Nova (ut vocantur) Magdeburgica de vacuo spatio, (J. Janssonius, Waesberge, Amsterdam, 1672)
  • [12] Th. Kaluza, Zum Unitätsproblem der Physik Sitzungsberichte der Preussischen Akademie der Wissenschaften Physikalisch-mathematischer Klasse (1921) 966
  • [13] O. Klein, Z. Phys. 37, 895 (1926) http://dx.doi.org/10.1007/BF01397481[Crossref]
  • [14] É. Cartan, Comptes Rendus Acad. Sci. 174, 593 (1922)
  • [15] T. W. B. Kibble, J. Math. Phys. 2, 212 (1961) http://dx.doi.org/10.1063/1.1703702[Crossref]
  • [16] A. Lasenby, C. Doran, S. Gull, Phil. Trans. R. Soc. Lond. A 356, 487 (1998) http://dx.doi.org/10.1098/rsta.1998.0178[Crossref]
  • [17] M. Jamil, D. Momeni, R. Myrzakulov, Eur. Phys. J. C D 72, 1959 (2012) http://dx.doi.org/10.1140/epjc/s10052-012-1959-4[Crossref]
  • [18] M. E. Rodriguez, M. J. S. Houndjo, D. Morneni, R. Myrzakulov, Int. J. Mod. Phys. D 22, 1350043 (2013) http://dx.doi.org/10.1142/S0218271813500430[Crossref]
  • [19] K. Karami, M. Jamil, S. Ghaffari, K. Fahimi, R. Myrzakulov, Can. J. Phys. 91, 770 (2013) http://dx.doi.org/10.1139/cjp-2013-0293[Crossref]
  • [20] F. R. Tangherlini, Nuovo Cimento 27, 636 (1963) http://dx.doi.org/10.1007/BF02784569[Crossref]
  • [21] X. F. He, Phys. Rev. B 42 11751 (1990) http://dx.doi.org/10.1103/PhysRevB.42.11751[Crossref]
  • [22] J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, Phys. Lett. B 288, 23 (1992) http://dx.doi.org/10.1016/0370-2693(92)91949-A[Crossref]
  • [23] G. Calcagni, J. High Energy Phys. 2012, 65 (2012) http://dx.doi.org/10.1007/JHEP01(2012)065[Crossref]
  • [24] Z. Merali, Nature 500, 516 (2013) http://dx.doi.org/10.1038/500516a[Crossref]
  • [25] P. Ehrenfest, Proc. Amsterdam Acad. 20 I, 200 (1917) reprinted in M. J. Klein (Ed.), (North Holland Publ. Co., Amsterdam, 1959)
  • [26] M. D. Roberts, arXiv:0909.1171 (2009) [WoS]
  • [27] R. A. El-Nabulsi, Fizika B 19, 103 (2010)
  • [28] U. Debnath, M. Jamil, S. Chattopadhya, Int. J. Theor. Phys. 51, 812 (2012) http://dx.doi.org/10.1007/s10773-011-0961-1[Crossref]
  • [29] S. Chakraborty, U. Debnath, M. Jamil, Can. J. Phys. 90, 365 (2012) http://dx.doi.org/10.1139/p2012-027[Crossref]
  • [30] R. A. El-Nabulsi, Indian J. Phys. 87(2), 195 (2013) http://dx.doi.org/10.1007/s12648-012-0201-4[Crossref]
  • [31] U. Debnath, S. Chattopadhya, M. Jamil, Journal of Theoretical and Applied Physics 7, 25 (2013) http://dx.doi.org/10.1186/2251-7235-7-25[Crossref]
  • [32] R. Herrmann, Int. J. Mod. Phys. B 27, 1350019 (2013) http://dx.doi.org/10.1142/S0217979213500197[Crossref]
  • [33] M. Caputo, Geophys. J. R. Astr. Soc. 13, 529 (1967) http://dx.doi.org/10.1111/j.1365-246X.1967.tb02303.x[Crossref]
  • [34] V. E. Tarasov, Int. J. Math. 18, 281 (2007) http://dx.doi.org/10.1142/S0129167X07004102[Crossref]
  • [35] R. Herrmann, Physica A 389, 4613 (2010) http://dx.doi.org/10.1016/j.physa.2010.07.004[Crossref]
  • [36] R. Herrmann, Gam. Ori. Chron. Phys. 1, 13 (2013)
  • [37] N. Laskin, Phys. Rev. E 66, 056108 (2002) http://dx.doi.org/10.1103/PhysRevE.66.056108[Crossref]
  • [38] P. A. M. Dirac, Scientific American 208, 47 (1963) http://dx.doi.org/10.1038/scientificamerican0563-45[Crossref]
  • [39] A. G. Riess et al., Astron. J. 116, 1009 (1998) http://dx.doi.org/10.1086/300499[Crossref]
  • [40] F. Zwicky, Helv. Phys. Acta 6, 110 (1933), republication: Gen. Relat. Grav. 41, 207 (2009)
  • [41] V. C. Rubin, W. K. Jr. Ford, N. Thonnard, M. S. Roberts, J. A. Graham, Astron. J. 81, 687 (1976) http://dx.doi.org/10.1086/111942[Crossref]
  • [42] V. C. Rubin, N. Thonnard, W. K. Ford, M. S. Roberts, Astron. J. 81, 718 (1976)
  • [43] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions, (Dover Publications, New York, 1965)
  • [44] M. M. Colless et al., (the 2dFGRS team), Mon. Not. R. Astron. Soc. 328, 1039 (2001) http://dx.doi.org/10.1046/j.1365-8711.2001.04902.x
  • [45] M. Jamil, A. R. Muneer, D. Momeni, O. Razina, K. Esmakhanova, J. Phys.: Conf. Ser. 354, 012008 (2012)
  • [46] B. Riemann, (1847) Versuch einer allgemeinen Auffassung der Integration und Differentiation in: H. Weber, R. Dedekind (Eds.) (1892) Bernhard Riemann’s gesammelte mathematische Werke und wissenschaftlicher Nachlass, Teubner, Leipzig, reprinted in Collected works of Bernhard Riemann, Dover Publications, 353 (1953)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0315-0
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.