On the Unification of the Constants of Nature

  1. 1.  Embry−Riddle Aeronautical University


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.


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

where h is Planck's constant[4] and Z0 is the charge of an alpha particle (2e). Planck's reduced constant ћ is

which can also be defined with Bohr's radius rB as

where α is the fine structure constant, me 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 rB from an Alpha particle (Z0 = 2= a Helium nucleus and not a Hydrogen nucleus). The adjusted radius r0 for a Helium atom can be deduced from

Eq. (4) as r0 ≈ 0.529177211 × 10−10 m.


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

where is the particle's momentum and v is its speed[6]. With the mass quantized in units of me, 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 f0 is then

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

Eq. (8) suggests v0 ≈ αc. The energy of electromagnetic radiation (E = hf) is simply the product of the electric, magnetic, and frequency quanta;


The Gaussian gravitational constant k0 (not to be confused with the Coulomb constant ke)[7] is

where G is Newton's gravitational constant, T is the orbital period, and M1 and M2 are the masses of the system. Setting the total mass of the system to the mass of an Alpha particle MA (MA = 2MP + 2MN where MP and MN are the proton and neutron masses), the quantized relationship between the Gaussian gravitational constant k0 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 fn 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.


[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

Showing 4 Reviews

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    sidd yadav

    Your shoolders to protect your own fbpasshack.net  account.some people use it to keep in touch.

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    Hontas Farmer
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    The way this kind of thing is usually discussed in quantum gravity research is with the classic consideration of the following question.

    What happens when the Schwarzschild radius of a black hole is the Planck length. 

    Now for all we know such tiny black holes are a fiction.   Helium atoms on the other hand exist.  Without a question they exist.  In that sense this essay is better than most similar writing.

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    John Smith
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    "A short essay that unifies gravity and electromagnetism with a system of natural units based upon the helium atom." -- no, it doesn't.

    This short collection of expressions for physical units says nothing about physics, let alone what the author suggests it does

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      Brent Jarvis

      In the very first equation I took the charge of an alpha particle (helium nucleus) and showed how it was related to the Gaussian gravitational constant in the last equation.

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    John Culpepper
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    Unified Field Theory?!


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