A short essay that unifies gravity and electromagnetism with a system of natural units that are based upon a Helium nucleus (Alpha particle). Alternative definitions for Planck's constant and the fine structure constant are deduced and the standard gravitational parameter of a Helium nucleus is shown to be directly proportional to the square of its electromagnetic frequency.

A short essay that unifies gravity and electromagnetism with a system of natural units that are based upon a Helium nucleus (Alpha particle). Alternative definitions for Planck's constant and the fine structure constant are deduced and the standard gravitational parameter of a Helium nucleus is shown to be directly proportional to the square of its electromagnetic frequency.

INTRODUCTION





The magnetic flux quantum Φ 0 is equivalent to[1], [2], [3]











where h is Planck's constant[4] and Z 0 is the charge of an alpha particle (2e). Planck's reduced constant ћ is











which can also be defined with Bohr's radius r B as











where α is the fine structure constant, m e is the mass of a Beta particle, and c is the speed of light in a vacuum. Combining Eqs. (1) through (3) yields











Bohr, however, did not deduce his radius r B from an Alpha particle (Z 0 = 2e = a Helium nucleus and not a Hydrogen nucleus). The adjusted radius r 0 for a Helium atom can be deduced from

Eq. (4) as r 0 ≈ 0.529177211 × 10−10 m.





WAVE−PARTICLE DUALITY AND A NEW DEFINITION FOR THE FINE STRUCTURE CONSTANT





A particle's wavelength λ can be determined with de Broglie's matter wave equation











where p is the particle's momentum and v is its speed[6]. With the mass quantized in units of m e , a Beta particle's ground state wavelength relative to the electric and magnetic flux quanta of a Helium nucleus can be deduced from Eqs. (4) & (5) as











The Beta particle's ground state frequency f 0 is then











and a wave mechanical definition for the fine structure constant can be given as











Eq. (8) suggests v 0 ≈ αc. The energy of electromagnetic radiation (E = hf) is simply the product of the electric, magnetic, and frequency quanta;











CONCLUSION





The Gaussian gravitational constant k 0 (not to be confused with the Coulomb constant k e ) [7] is











where G is Newton's gravitational constant, T is the orbital period, and M 1 and M 2 are the masses of the system. Setting the total mass of the system to the mass of an Alpha particle M A (M A = 2M P + 2M N where M P and M N are the proton and neutron masses), the quantized relationship between the Gaussian gravitational constant k 0 and the electromagnetic frequency of an Alpha particle can be given as











The standard gravitational parameter µ for the Alpha particle is therefore











and the energy of its electromagnetic frequency is











Could Eq. (13) help explain dark energy? The nuclear frequency f n of an atom would then be











where n is the nuclear mass number relative to a Helium nucleus. For Hydrogen, n = ½, Helium, n = 1, Lithium, n = 1½, Beryllium, n = 2, etcetera.





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] Barrow, John D. (2002) “The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe”, Pantheon Books, ISBN 0-375-42221-8





[5] Eisberg, Robert (1974). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. New York: John Wiley & Sons Inc. pp. 114–117. ISBN 978-0-471-23464-7.





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





[7] Gauss, Carl Friedrich; Davis, Charles Henry (1857). Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections. Little, Brown and Company, Boston., atGoogle books



