Resolving the Mystery of the Fine Structure Constant

  1. 1.  Embry Riddle Aeronautical University

Abstract

A quantized magnetic flux version of Planck's reduced constant is deduced from first principles. The magnetic flux quantum can explain the fine structure constant and the “anomalous” magnetic moment of an electron.

INTRODUCTION


The magnetic flux quantum Φ0[1], [2], [3] is equivalent to,




where e is the unit of elementary charge and h is Planck's constant,




Planck's reduced constant ћ can also be defined from Bohr's radius rB as,




where α is the fine structure constant, me is the rest mass of an electron and c is the speed of light in a vacuum. Combining Eqs. (1) through (3) yields,




It is remarkable that the dimensions in Eq. (4) are balanced by the dimensionless quantity Ð,




AN ELECTRON'S ANOMALOUS MAGNETIC MOMENT


The g−factor for an electron's magnetic moment[4] is,




suggesting that the fine structure constant and an electron's “anomalous” magnetic moment may be related to the the magnetic flux quantum Φ0. Substituting the g−factor for an electron's magnetic moment µe yields,




where LT is an electron's total angular momentum, LS is the angular momentum of its spin and v is its tangential speed. A dimensionless correction factor is not needed with this classical definition since the electron's magnetic moment is related to the magnetic flux quantum Φ0 and not to the electrostatic charge unit e. A special relativistic version of Eq. (7) can then be given as,




where γ is the Lorentz factor and m0 is the rest mass of a particle[5]. The ± sign in Eq. (8) suggests that the rotational direction of a nuclear particle relative to an atomic barycenter may be opposite to the rotational direction of an electron.


WAVE−PARTICLE DUALITY


A particle's wavelength can be determined with de Broglie's matter wave relation[6],




where p is a particle's momentum. Substituting the mass in de Broglie's relation with the mass in Eq. (8) yields,




A particle's frequency f is therefore,




and a wave mechanical version of Eq. (8) can be given as,




where ω is a particle's angular frequency. Since ω = v/r, an alternative system of natural units can be given as,




With this system, a particle's speed can be determined if you know its position!


REFERENCES


[1] "Magnetic flux quantum Φ0". 2010 CODATA recommended values.


[2] Deaver, Bascom; Fairbank, William (1961). "Experimental Evidence for Quantized Flux in Superconducting Cylinders". Physical Review Letters 7 (2): 43−46.Bibcode:1961PhRvL...7...43D. doi:10.1103/PhysRevLett.7.43.


[3] Doll, R.; Näbauer, M. (1961). "Experimental Proof of Magnetic Flux Quantization in a Superconducting Ring". Physical Review Letters 7 (2):

51–52. Bibcode:1961PhRvL...7...51D.doi:10.1103/PhysRevLett.7.51.


[4] Lamb, Willis E. (1952-01-15). "Fine Structure of the Hydrogen Atom. III". Physical Review Letters. 85 (2): 259–276. doi:10.1103/PhysRev.85.259


[5] Marmet, Paul. (2003). “Fundamental Nature of Relativistic Mass and Magnetic Fields”.

http://www.newtonphysics.on.ca/magnetic/


[6] de Broglie, L. (1923). Waves and quanta, Nature 112: 540.


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