Fundamental Nature of the Fine-Structure Constant
-
2014-03-28 https://doi.org/10.14419/ijpr.v2i1.1817 -
Abstract
Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics.
Keywords: Euler's constant, Fine-structure constant, Fundamental constants, Kepler's equation, Natural philosophy.
-
References
- Barrow, J.D. The Constants of Nature: From Alpha to Omega–the Numbers That Encode the Deepest Secrets of the Universe, New York: Pantheon Books, 2002.
- Miller, A.I. Deciphering the Cosmic Number, New York: W.W. Norton, 2009.
- Uzan, J.P. & Leclercq, B. The Natural Laws of the Universe: Understanding Fundamental Constants, New York: Springer, 2008.
- Fritzsch, H. The Fundamental Constants, Hackensack, NJ: World Scientific, 2009.
- Sommerfeld, A. “On the Quantum Theory of Spectral Lines,” Annals of Physics, 51, 1-94, 125-67 (1916).
- Sommerfeld, A. Atomic Structure and Spectral Lines, London: Methuen, 118, 1923.
- Kragh, H. Niels Bohr and the Quantum Atom, NY: Oxford University Press, 2012.
- Enz, C.P. No Time to be Brief: A Scientific Biography of Wolfgang Pauli, New York: Oxford University Press, 2002.
- Miller, A.I. Early Quantum Electrodynamics: A Source Book, Cambridge, UK: Cambridge University Press, 1995.
- Feynman, R.P. QED: The Strange Theory of Light and Matter, Princeton, NJ: Princeton University Press, 1985.
- Yoshihiro, K. et al. “Determination of the Fine Structure Constant Based on the Quantum Hall Effect,” Progress of Theoretical Physics, 84, 1, 215-223 (1985).
- Nair, R.R. et al. “Fine Structure Constant Defines Visual Transparency of Graphene,” Science, 320, 5881, 1308-1308 (2008) arXiv:0803.3718v1.
- Maciejko, J. et al. “Topological Quantization in Units of the Fine Structure Constant,” Physical Review Letters, 105, 16, 166803 (2010) arXiv:1004.2514v3.
- Kravets, V.G. et al. “Fine Structure Constant and Quantized Optical Transparency of Plasmonic Nanoarrays,” Nature Communications, 3, 640, (2012).
- Mac Gregor, M.H. The Power of Alpha, Hackensack, NJ: World Scientific, 2007.
- Sturm, S., Werth, G. & Blaum, K. “Electron g-Factor Determinations in Penning Traps,” Annals of Physics, 525, 8-9, 620-635 (2013).
- Karshenboim, S. “Recent Progress in Determination of Fundamental Constants and Fundamental Physics at Low Energies,” Annals of Physics, 525, 7, 472–483 (2013).
- Truppe, S., Hendricks, R.J., Tokunaga, S.K., Lewandowski, H.J. Kozlov, M.G. et al. “A Search for Varying Fundamental Constants using Hertz-Level Frequency Measurements of Cold CH Molecules,” Nature Communications, 4, 2600 (2013).
- Hagar, A. & Hemmo, M. “The Primacy of Geometry,” Studies in History and Philosophy of Modern Physics, 44, 3, 357–364 (2013).
- Born, M. “The Mysterious Number 137,” Proceedings of the Indian Academy of Sciences - Section A, 2, 6, 533–561 (1935).
- Blaum, K., Müller, H. & Severijns, N. “Precision Experiments and Fundamental Physics at Low Energies – Part I,” Annals of Physics, 525, 7, A111–A112 (2013).
- Ubachs, W., Vassen, W. et al. “Precision Metrology on the Hydrogen Atom in Search for New Physics,” Annals of Physics, 525, 7, A113–A115, (2013).
- Bouchendira, R. et al. “State of the Art in the Determination of the Fine Structure Constant,” Annals of Physics, 525, 7, 484–492 (2013) arXiv:1309.3393v1.
- Sherbon, M.A. “Wolfgang Pauli and the Fine-Structure Constant,” Journal of Science, 2, 3, 148-154 (2012) SSRN: 2147980.
- Pauli, W. “On the Hydrogen Spectrum from the Standpoint of the New Quantum Mechanics,” Journal of Physics A: Hadrons and Nuclei, 36, 5, 336–363 (1926).
- Schwinger, J. “On Quantum Electrodynamics and the Magnetic Moment of the Electron,” Physical Review, 73, 4, 416-417 (1948).
- Aoyama, T., Hayakawa, M., Kinoshita, T. & Nio, M. “Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant,” Physical Review Letters, 109, 111807 (2012) arXiv:1205.5368v2.
- Weisstein, E.W. “Prime Constant,” MathWorld–A Wolfram Web Resource.
- Finch, S.R. ”Kepler-Bouwkamp Constant,” Mathematical Constants, Cambridge: Cambridge University Press, 428-429, 2003.
- Weisstein, E.W. “Golden Ratio,” MathWorld–A Wolfram Web Resource.
- Stakhov, A. “The Golden Section and Modern Harmony Mathematics,” in Bergum, G.E. et al. Eds. Applications of Fibonacci Numbers, NY: Springer, 393-399, 1998.
- Weisstein, E.W. “Fresnel Integrals,” MathWorld–A Wolfram Web Resource.
- Stakhov, A.P. & Rozin, B.N. “The Golden Section, Fibonacci Series and New Hyperbolic Models of Nature,” Visual Mathematics, 8, 3 (2006).
- Lagarias, J.C. “Euler’s Constant: Euler’s Work and Modern Developments,” Bulletin of the American Mathematical Society, 50, 4, 527-628 (2013) arXiv:1303.1856.
- Weisstein, E.W. “Silver Constant,” MathWorld–A Wolfram Web Resource.
- Huntley, H.E. “The Golden Ellipse,” The Fibonacci Quarterly, 12, 1, 38-40 (1974).
- Weisstein, E.W. “Laplace Limit,” MathWorld–A Wolfram Web Resource.
- Cariglia, M. & Araújo, E.S. “Dynamical Symmetries of the Kepler Problem,” European Journal of Physics, 34, 5, 1307 (2013) arXiv:1309.6913.
- Nucci, M.C. & Leach, P.G.L. “The Harmony in the Kepler and Related Problems,” Journal of Mathematical Physics, 42, 746 (2001).
- Rogers, H.H. “Symmetry Transformations of the Classical Kepler Problem,” Journal of Mathematical Physics, 14, 1125–1129 (1973).
- Dahl, J.P. “Physical Origin of the Runge-Lenz Vector,” Journal of Physics A: Mathematical and General, 30, 19, 6831 (1997).
- Wulfman, C.E. “On the Dynamical and Geometrical Symmetries of Keplerian Motion,” Journal of Physics A: Mathematical and Theoretical, 42, 18, 185301 (2009).
- Tse, W.K. & MacDonald, A.H. “Magneto-Optical Faraday and Kerr Effects in Topological Insulator Films and in Other Layered Quantized Hall Systems,” Physical Review, B84, 205327 (2011) arXiv:1108.3858v1.
- Shimano, R. et al. “Quantum Faraday and Kerr Rotations in Graphene,” Nature Communications, 4, 1841 (2013).
- Burinskii, A. “The Dirac-Kerr-Newman Electron,” Gravitation and Cosmology, 14, 4, 2, 109-122 (2008) arXiv:hep-th/0507109v4.
- Weisstein, E.W. “Hyperbolic Cotangent,” MathWorld–A Wolfram Web Resource.
- Li, C., Ji, A. & Cao, Z. “Stressed Fibonacci Spiral Patterns of Definite Chirality,” Applied Physics Letters, 90, 164102, (2007).
- Hanneke, D. et al. “New Measurement of the Electron Magnetic Moment and the Fine Structure Constant,” Physical Review Letters, 100, 120801 (2008).
- Hanneke, D. et al. “Cavity Control of a Single-Electron Quantum Cyclotron: Measuring the Electron Magnetic Moment,” Physical Review, A83, 5, 052122 (2011).
- Pfister, H. & King, M. “The Gyromagnetic Factor in Electrodynamics, Quantum Theory and General Relativity,” Classical and Quantum Gravity, 20, 1, 205, (2003).
- Greiner, W., Neise, L. & Stöcker, H. Thermodynamics and Statistical Mechanics, New York: Springer, 216, 1997.
- Weisstein, E.W. “Hyperbolic Cosecant,” MathWorld–A Wolfram Web Resource.
- Sloane, N.J.A. “Reciprocal Fibonacci Constant,” The On-Line Encyclopedia of Integer Sequences, OEIS: A079586.
- Weisstein, E.W. “Lemniscate Constant,” MathWorld–A Wolfram Web Resource.
- Heyrovska, R. “Golden Ratio Based Fine Structure Constant and Rydberg Constant for Hydrogen Spectra,” International Journal of Sciences, 2, 3, 28-31 (2013).
- Weisstein, E.W. “Gauss’s Constant,” MathWorld–A Wolfram Web Resource.
- Beringer, J. et al. (Particle Data Group) “Review of Particle Physics - Gauge and Higgs Bosons,” Physical Review, D86, 1 (2012).
- CMS Collaboration, “Properties of the Observed Higgs-like Resonance using the Diphoton Channel,” PAS CMS HIG-13-016 (2013) cds.cern.ch/record/1558930.
- Mohr, P.J., Taylor, B.N. & Newell, D.B. “CODATA Recommended Values of the Fundamental Physical Constants,” Reviews of Modern Physics, 84, 4, 1527 (2012).
- Weisstein, E.W. “Golden Angle,” MathWorld–A Wolfram Web Resource.
- Munteanu, M.I. “From Golden Spirals to Constant Slope Surfaces,” Journal of Mathematical Physics, 51, 7, 073507, 1-9, (2010) arXiv:0903.1348v1.
- Antognini, A. et al. “Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen,” Science, 339, 6118, 417–420 (2013).
- Weisstein, E.W. “Silver Ratio,” MathWorld–A Wolfram Web Resource.
- Reese, S. & Sondow, J. “Universal Parabolic Constant,” The On-Line Encyclopedia of Integer Sequences, OEIS: A103710.
- Weisstein, E.W. “Hyperbolic Secant,” MathWorld–A Wolfram Web Resource.
- Sachs, M. Quantum Mechanics from General Relativity, New York: Springer, 1986.
- Weisstein, E.W. “Omega Constant,” MathWorld–A Wolfram Web Resource.
- Valluri, S.R, Jeffrey, D.J. & Corless, R.M. “Some Applications of the Lambert W Function to Physics,” Canadian Journal of Physics, 78, 9, 823-831 (2000).
- Weisstein, E.W. “Lambert W-Function,” MathWorld–A Wolfram Web Resource.
- Schweber, S.S. QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga, Princeton, NJ: Princeton University Press, 1994.
-
Downloads
-
How to Cite
Sherbon, M. (2014). Fundamental Nature of the Fine-Structure Constant. International Journal of Physical Research, 2(1), 1-9. https://doi.org/10.14419/ijpr.v2i1.1817Received date: 2014-01-24
Accepted date: 2014-02-23
Published date: 2014-03-28