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The Physical Significance of the Fine-Structure Constant
Frederick David Tombe,
Northern Ireland, United Kingdom,
sirius184@hotmail.com
1st December 2024
Abstract. The physical significance of the fine-structure constant, 1/137, also known as
the Sommerfeld constant, has not as yet been realized by the scientific establishment.
This article will hence seek to solve the mystery in connection with the structure of the
electromagnetic wave-carrying medium.
Planck’s Constant and Angular Momentum
I. It was demonstrated in, “The Apparent Dual Nature of Electromagnetic
Waves”, [1], how the reduced Planck’s constant, ℏ, referred to as h-bar, is in fact
the angular momentum of the rotating electron-positron dipoles that comprise
the electromagnetic wave-carrying medium. The equation,
ℏ = 2mcr (1)
applies where m is the mass of both an electron and a positron. These
dipoles each consist of an electron and a positron in mutual circular orbit, but
they are not held in orbit by electrostatic attraction. Instead, they are hemmed
into their orbits by the centrifugal pressure pushing in on them from all sides by
their immediate neighbours in the equatorial plane, [2]. The radius, r, of these
orbits has to be 0.1932 picometres, hence leading to a circumference of 1.213
picometres, this being exactly half of the Compton wavelength, while the
circumferential speed, c, of the electrons and positrons is equal to the speed of
light. See, “The Double Helix Theory of the Magnetic Field”, [3], [4].
Meanwhile, it was shown in Section IV of, “The Double Helix Theory of
the Magnetic Field”, [3], how the outward centrifugal pressure in one of these
compressed dipole orbits has a centrifugal potential energy equal to 2mc2, this
being the energy, 1.02MeV, of the gamma photons that are needed to split one
of these dipoles apart, [5].
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Electrostatic Potential Energy
II. The mutual electrostatic potential energy associated with the force of
attraction between the electrons and positrons in each dipole is expressed by the
equation,
V = e2/4πε0r (2)
where e is the electric charge of both an electron and a positron, ε0 is the
permittivity of space, and r is the radius of the orbit, this being 0.1932
picometres.
The Ratio of the Two Kinds of Potential Energy
III. Consider the ratio, α, of the electrostatic potential energy in Section II to
the centrifugal potential energy in Section I. This ratio takes the form,
α = e2/(4πε0r × 2mc2) (3)
Substituting the reduced Planck’s constant equation (1) into equation (3)
leads to,
α = e2/(4πε0ℏc) (4)
This is the fine-structure constant equal to 1/137.
Conclusion
IV. The fine-structure constant, equal to 1/137, also known as the Sommerfeld
constant, is simply the ratio between the electrostatic potential energy and the
centrifugal potential energy in the rotating electron-positron dipoles that fill all
of space and which comprise the electromagnetic wave-carrying medium. The
dipoles in question each constitute an electron in circular orbit with a positron,
where the circumference is exactly half of the Compton wavelength, and where
the circumferential speed is equal to the speed of light. In the absence of this
arrangement, there could be no other way to explain the connection, as is
implied by the fine-structure constant, between the speed of starlight and the
charge of an electron at a point in space where the starlight is passing through.
Space has to be filled with rotating electron-positron dipoles in order to make
any sense out of the fine-structure constant.
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References
[1] Tombe, F.D., “The Apparent Dual Nature of Electromagnetic Waves”, (2021)
https://www.researchgate.net/publication/356194121_The_Apparent_Dual_Nature_of_Electr
omagnetic_Waves
[2] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, chapter 4, pp.
100-102, (1910)
“All space, according to the younger Bernoulli, is permeated by a fluid aether, containing an
immense number of excessively small whirlpools. The elasticity which the aether appears to
possess, and in virtue of which it is able to transmit vibrations, is really due to the presence
of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to
dilate, and so presses against the neighbouring whirlpools.”
[3] Tombe, F.D., “The Double Helix Theory of the Magnetic Field”, (2006)
Galilean Electrodynamics, vol. 24, number 2, p.34, (March/April 2013)
https://www.researchgate.net/publication/295010637_The_Double_Helix_Theory_of_the_M
agnetic_Field
[4] Tombe, F.D., “The Double Helix and the Electron-Positron Aether”, (2017)
https://www.researchgate.net/publication/319914395_The_Double_Helix_and_the_Electron-
Positron_Aether
[5] Tombe, F.D., “The Positronium Orbit in the Electron-Positron Sea”, (2020)
https://www.researchgate.net/publication/338816847_The_Positronium_Orbit_in_the_Electr
on-Positron_Sea