The Large Numbers in a Quantized Universe

ABSTRACT

The article relates to decades-old problem of the mysterious coincidence of various Large numbers of magnitude ranging from 10^{40} to 10^{120} which sometimes appears in cosmology and quantum physics. Using well-known classical relations as well as the ideal Schwarzschild solution the exact relations of various large numbers, fine structure constant α and were found. The new Largest number law is claimed. The hypothetical approximations of the Hubble parameter—68.7457(82) km/s/Mpc, Hubble radius—14.2330(17) Gly, and some others were proposed. The exact formulae supporting P. Diracs Large number hypothesis and H. Weyls proposition were found. It is shown that all major physical constants with length dimension (from Compton wave length of universe through Planck and atomic scale up to Hubble sphere radius) could be derived from each other, and the table of the specific conversion rules has been developed. The model shows that Eddington-Weinberg relation can be transformed to precise identity. It is shown that both Bekenstein universal entropy bound and Hooft-Susskind holographic entropy bound are equal to the Largest number doubled.

Cite this paper

Y. Ryazantsev, "The Large Numbers in a Quantized Universe,"*Journal of Modern Physics*, Vol. 4 No. 12, 2013, pp. 1647-1653. doi: 10.4236/jmp.2013.412205.

Y. Ryazantsev, "The Large Numbers in a Quantized Universe,"

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[1] H. Weyl, Annalen der Physik, Vol. 359, 1917, pp. 117-145. http://dx.doi.org/10.1002/andp.19173591804

[2] H. Weyl, “The Open World Yale,” Oxbow Press, Oxford, 1989.

[3] H. Weyl, “Space Time Matter,” Methuen, Dover, 1952.

[4] A. S. Eddington, “The Math. Theory of Relativity,” Cambridge University Press, Cambridge, 1924.

[5] A. S. Eddington, “Fundamental Theory,” Cambridge University Press, Cambridge, 1946.

[6] P. C. W. Davies, “The Accidential Universe,” Cambridge University Press, Cambridge, 1982.

[7] S. Lloyd, “Computational Capacity of the Universe,” 2001.

[8] L. Smolin, “The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next,” Mifflin, Houghton, 2006.

[9] S. Ray, U. Mukhopadhyay and P. P. Ghosh, Large Number Hypothesis: A Review, 2007.

[10] K. A. Tomilin, Issledovaniya po Istorii Fiziki i Mekhaniki, Vol. 141, 1999.

[11] P. A. M. Dirac, Nature, Vol. 139, 1937, p. 323.

http://dx.doi.org/10.1038/139323a0

[12] P. A. M. Dirac, Proceedings of the Royal Society A, Vol. 165, 1938, p. 199.

[13] P. A. M. Dirac, Nature, Vol. 1001, 1937, pp.

[14] E. A. Milne, Proceedings of the Royal Society A, Vol. 158, 1937, p. 324.

[15] P. J. Mohr, B. N. Taylor and D. B. Newell, The 2010 CODATA Recommended Values of the Fundamental Physical Constants, National Institute of Standards and Technology, Gaithersburg, 2011.

http://physics.nist.gov/constants

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[17] J. Casado, Connecting Quantum and Cosmic Scales by a Decreasing-Light-Speed Model, 2004.

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http://dx.doi.org/10.1103/PhysRev.73.801

[19] S. Weinberg, “Gravitation and Cosmology,” Wiley, New York, 1972.

[20] J. D. Bekenstein, Physical Review D, Vol. 23, 1981, pp. 287-298. http://dx.doi.org/10.1103/PhysRevD.23.287

[21] G. Hooft, “Dimensional Reduction in Quantum Gravity,” In: Salam-Festschrifft, A. Aly, J. Ellis and S. Randjbar-Daemi , Eds., World Scientific, Singapore, 1993.

[22] L. Susskind, Journal of Mathematical Physics, Vol. 36, 1995, p. 6377. http://dx.doi.org/10.1063/1.531249