The coupling between electron spin and orbital spin magnetism, spin-orbit coupling, has no classical analog and results in a splitting proportional to α2.
The quantum mystery of the fine structure constant deepened when increasing measurement precision of the electron magnetism found that the electron spin magnetism affected itself. The anomalous electron magnetic moment is due to a quantum self energy that does not have a classical meaning and there is no such self energy for classical gravity force. It was then discovered by Feynman and Schwinger that the fine structure constant nicely predicted that a spinning electron created a counterspinning vacuum electric field with its own magnetism and the fine structure constant defined that coupling.
With higher resolution spectrographs, spectroscopists in the 1800's came to realize that spectral lines showed even further splitting and that spectral splitting came to be known as fine structure. Although not completely understood until Dirac in 1928, electrons can orbit in either spherical or donut-shaped ellipsoid orbits with different orbital angular momentum and phase or orbital magnetism. In fact, electrons exist in superposition states that involve some of all possible states and the interaction of those states splits their degeneracy into what was termed the fine-structure constant by Sommerfeld in 1916, actually the square of the fine-structure constant α2.
An electron in the perfect symmetry of a spherical orbit does not have any average orbital magnetism, but an electron in various donut orbits does have magnetism due to the reduced symmetry of such orbits and that orbital magnetism then couples with the electron spin magnetism. In addition, the intrinsic spins of the electron and proton are also interact and cause the hyperfine splitting observed at even higher resolution as the figure below represents. The quantum underpinnings for the fine-structure constant would have to wait until Dirac in 1928 and by that time, the hyperfine spectral splittings were also discovered.
The key to all of these quantum magnetic interactions turned out to be the fine-structure constant quantum quantum phase, but there is no classical analog to spin orbit coupling and so the fine-structure constant is not part of a classical reality. Indeed, Feynman developed his quantum field theory in 1958 that conveniently used α to represent a perturbation expansion to account for the effect of quantum electron charge on itself.
In fact, there is another common constant called the gyromagnetic ratio, g, which is around two and expresses the difference between classical and quantum rotating charges. The gyromagnetic ratio turns out to be completely determined by a series expansion of α, which then reveals the mystery of the quantum spinning charge with g = 2 reality versus the classical spinning charge with a g = 1 reality.
Somehow the gyromagnetic ratio all by itself embodies the difference between quantum and classical charge motion and there is a similar factor of two that shows up with gravity deflection of light. The equivalent mass from light's momentum deflects light passing near a gravity body like the sun. The gravity deflection of quantum light has twice the angle of an equivalent classical body like a comet or asteroid.
Just like the interaction of photon magnetism with quantum spin in a magnetic field is the result of many exchanges among virtual states, the interaction of photon momentum with gravity is also the result of many photon exchanges among virtual states. It is likely that a similar correspondence with α and gravity occurs for quantum gravity, but a quantum gravity is not yet in common use.
While the CMB emission at 2.7 K represents the hydrogen ionization energy in the early universe, the gravity modes oscillate with a fundamental at around 5e-5 K or 50 ppm of the 2.7 K CMB emission. The CMB gravity modes represent the multipole peaks in the CMB spectrum below.
There are any number of papers that show that α2 varies on the order of 3e-15/yr for astrophysical spectra and 6e-17 for terrestrial atomic clocks and not the 0.26 ppb/yr decoherence rate predicted by quantum aether. Actually the standard cosmology of mainstream science does not recognize any variation in α and the measured variations have not yet been widely accepted. With quantum aether, there is a phase factor for α that is consistent with a variation in α2 that is as reported. Thus the variations of α2 with both astrophysical and high precision atomic time are consistent with the aether decoherence rate of 0.26 ppb/yr.
The key turns out to be a complementary α phase factor that accompanies each oscillating charge dipole that generates a photon of light. Although mainstream science approximates a hydrogen atom with the motion of an electron in orbit around a proton and that motion shows an average velocity of αc, the product of α and the speed of light, c.
This means that the dipole average kinetic energy of the photon from the oscillation is proportional to α2c2. However, there is a neglected phase factor associated with charge motion that is why distant galaxies show the same α2 as we experience in our epoch even though both α and c actually increase at 0.26 ppb/yr. In quantum aether, it is the ratio of c/α that is constant and h becomes the matter scaled Planck's constant h/c2 is the Planck constant in quantum aether.
Although it seems a bit incredible that mainstream science has long misinterpreted the meaning of spectral splittings in distant galaxies, there are many measurements that validate the ongoing decay of matter at 0.26 ppb/yr along with the increase in both gravity and charge forces that complements the decay of matter. Moreover, it is the decoherence of quantum aether that determines and unites the two forces of matter that mainstream science calls gravity and charge.