Abstract
The effect of fractal space time of the quantum particles on the variation of the fine-structure constant α has been studied. The variation of the fine-structure constant has been investigated around De Broglie length λ and Compton length λ c and it has been suggested that the variation may be attributed to the dimensional transition of the particle trajectories between these two quantum domains. Considering the fractal universe with a small inhomogeneity in the mass distribution in the early universe, the variations of the fine-structure constant have been investigated between matter- and radiation-dominated era. The fine-structure constant shows critical behaviour with critical exponent which is fractional and shows a discontinuity. It has been suggested that the variation of the fine-structure constant may be attributed to the intrinsic scale dependence of the fundamental constants of nature.
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References
A. Albrecht et al., Phys. Rev. D 59, 043516 (1999).
J.D. Barrow et al., Phys. Lett. B 443, 104 (1998).
J.D. Barrow et al., Phys. Rev. D 65, 063504 (2002).
P.A.M. Dirac, Nature 139, 323 (1973).
E. Teller, Phys. Rev. 73, 801 (1948).
J.K. Webb et al., Phys. Rev. Lett. 82, 884 (1999).
J.K. Webb et al., Phys. Rev. Lett. 87, 091301 (2001).
J.A. King et al., Mon. Not. R. Astron. Soc. 000, 1 (2012).
M.T. Murphy et al., Mon. Not. Astron. Soc. 327, 1208 (2001).
G. Huey et al., Phys. Rev. D 65, 083001 (2003).
J.D. Barrow et al., Phys. Rev. D 78, 083536 (2008).
J.D. Barrow et al., Astrophys. J. Lett. 532, L87 (2000).
L. Anchordoqui et al., Phys. Lett. B 660, 529 (2008).
J.W. Moffat, arXiv: astro-ph/0109350v2.
J.D. Bakenstein, Phys. Rev. D 25, 1527 (1982).
M.S. Berman, Rev. Mex. Astron. Astrofis. 45, 139 (2009).
H.B. Sanvik et al., Phys. Rev. Lett. 88, 031302 (2002).
C. Cingoz, Phys. Rev. Lett. 98, 040801 (2007).
J.P. Uzan, Rev. Mod. Phys. 75, 403 (2003).
S.N. Banerjee et al., Mod. Phys. Lett. A 12, 537 (1997).
R.P. Feyman, A.R. Hibbs, Quantum Mechanics and Path Integrals (MacGraw-Hill, 1965).
L. Nottale, Fractal spacetime and Microphysics (World Scientific, Singapore, 1992) p. 95.
L. Nottale, Scale Relativity and Fractal Space-Time (Imperial College Press, 2011).
M. Ozer, Mod. Phys. Lett. A 13, 571 (1998).
S. Weinberg, The Three Minutes (Harper Collin, 1993) p. 180.
T. Bank et al., Phys. Rev. Lett. 88, 131301 (2002).
F.J. Culetto, Does Fractal geometry tune electrodynamics’ scales? article in web.
M.S. Naschie, Chaos, Solitons Fractals 10, 1947 (1999).
E. Goldfain, Chaos, Solitons Fractals 17, 811 (2003).
Zhe Chang et al., Eur. Phys. J. C 72, 1838 (2012).
F. Cannatan et al., Am. J. Phys 56, 721 (1988).
M.N. Celerier, L. Nottale, J. Phys. A 37, 931 (2004).
G. t’Hooft, Quantum Grav. 16, 3262 (1999).
L. Susskind, J. Math. Phys. 36, 6377 (1995).
J. Gine, Adv. Stud. Theor. Phys. 6, 485 (2012).
B. Wang et al., Phys. Rev. Lett. 85, 5507 (2000).
G. Veneziano, Phys. Lett. B 454, 22 (1999).
J.P. Mureika, JCAP 05, 021 (2007).
R. Tavakol et al., Phys. Lett. B 469, 37 (1999).
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Bhattacharya, A., Saha, R. & Chakrabarti, B. Fractal space time and variation of fine-structure constant. Eur. Phys. J. Plus 127, 57 (2012). https://doi.org/10.1140/epjp/i2012-12057-3
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DOI: https://doi.org/10.1140/epjp/i2012-12057-3