An essay I wrote that explains the fine structure constant, a long-standing enigma in physics, along with much more!

The Fine Structure Constant and Atomic Theory

The fine structure constant is a dimensionless combination of Coulomb’s constant (k), electric charge (e), Planck's constant (h), and the speed of light (c) in the formula ke^2/hc. For any context of units, this constant usually has the same value, approximately 1/137. The maximum quantity of possible paired electron configurations or orbitals in an atom's seven shells is 140, so that a single orbital is approximately 1/140th of an atom. Considering that orbitals may not be distributed with absolute uniformity in the space surrounding an atom, the distinction between number of orbitals and the fine structure constant as possible quantification of an average orbital’s size seems startlingly minor. Can this adjacency of mathematical figures, 137 and 140, explain something about the composition of atoms in addition to the fine structure constant itself?

First of all, modern theory represents electrons as probability distributions enveloping the nucleus rather than minuscule corpuscles revolving at characteristic velocities in likeness to planets of the solar system. This probability distribution model explains why atoms and the molecules they comprise absorb light at various frequencies regardless of the direction from which photons approach them. Electrons occupy the entire bulk of the atom and so respond to perturbations at any point surrounding the nucleus.

The typical rendering of orbital arrangement for visualization purposes is rather arbitrarily plotted on a coordinate plane, as well as biased towards the outer “valence” shell with its primary responsibility for an atom’s bonding properties, but whatever the orientation or motion of electrons in nanoscale space, there is no doubt that the majority of their substance is concentrated in particular regions as the loci of distribution and charge. The shape of atoms is roughly spherical, but internal contours of the electron probability wave with its heterogeneous organization of charge density, altogether occupying most of an atom’s space, are unknown. Plenty of flexibility exists for reimagining atomic structure in a way that transcends the textbook picture, and perhaps an effort such as this can better account for certain material properties.

In the probability wave model, positively charged protons in the nucleus and negatively charged electrons that surround them are not tiny and much tinier points of mass with roughly equivalent densities, but rather vastly different forms of matter. The electron wave takes up most of the space, though perhaps concentrated in as many as 140 orbitals, its centers of charge, while the nucleus is by comparison an extremely dense point of much larger mass, with the space it occupies almost negligible by comparison. If we think of protons and electrons as extremely divergent forms of matter, this better explains some properties of atoms.

We can begin by considering how atoms are separate. The introductory model views atoms as entirely self-contained entities of equal positive and negative charge with likeness to billiard balls, only differing from the classical scale by way of their electromagnetic properties which usually bring them into emergent alignments via chemical bonding. This outlook makes it hard to envision what distinguishes one atom from another, for electron wavicles in even nonreactive molecules would be expected to blend in interference as all waves tend to do rather than bounce off each other in the opposite and equal manner of macroscopic objects. No explanation exists for how electron arrangements in single atoms act like waves and interactions between multiple atoms are like particles. It is as if two incompatible principles, intraatom quantum physics and interatom classical physics, are being applied simultaneously from this casual perspective.

Additionally, the space within which these alleged spheres of balanced charge move would have to be in essence completely vacant of atomic matter, and as the saying goes, “nature abhors a vacuum”. It seems unlikely that matter on Earth could be failing to occupy all available space by some arbitrary principle of radical localization which does not apply at the classical scale. The concepts are not exactly incoherent, but it seems that a more plausible explanation than the existence of fundamental nothingness should be sought. So do we have an alternative that is not as suspect?

Perhaps Earth’s matter does not consist in duality between atomic particularity and the nothingness of an absolute vacuum, but instead a duality between the particlelike constitution of the nucleus and the wavelike constitution of electrons. Rather than collections of distinct electrons orbiting proton clusters amongst the enigma of an empty space devoid of all intrinsic force, this envisions positively charged protons as interspersed in a space-saturating sea of electromagnetic charge. How does a model fare that assigns nuclei some sorts of properties traditionally attributed to atoms, and electrons the properties of an interstitial medium, a relationship arbitrated by electromagnetism?

Firstly, in this schema the distinction between electromagnetic and nucleic matter seems as if it would be equivalent to the difference between quantum and classical dynamics. The nucleus, as a dense point of mass, can be expected to diffuse in the manner traditionally assigned to atoms and molecules, and every nucleus is positively charged so that these like charges repel, which partially restricts their motions. Something along these lines is indicated by the way a drop of aqueous solution with concentrated solute, when introduced to nearly pure water, spreads more slowly as it strays from the initial point of contact. Once classical forces of gravitational pull and friction have been exhausted and the chemistry takes over, nucleic material surrounding the droplet resists protonic diffusion, constraining it to a local region of the total solution with increasing force as it expands.

It is possible that in a liquid the electrons would have similar repulsive effects, making the proposed behavior of a nucleus indistinguishable from a whole atom except by virtue of the fact that rate of diffusion would be expected within a billiard ball model to remain constant or increase rather than decelerate amongst most cases due to the force of greater mass and spatial extension in the solute, or in an enveloping wave model, diffusion would decelerate to a much more extreme degree and in a less particularized way from the repulsive effects of a solution already saturated with negative charge. Additionally, diffusion occurs in solids with their extremely static electron orientations, albeit at lesser rate and in lesser amount, a simultaneity of perpetual motion with extremely rigid stability that can only be explained if tiny nuclei give each other a wide berth as they travel through a relatively expansive electromagnetic matrix.

Then we must determine what the so-called electromagnetic matrix commonly attributed to electrons consists in. We can easily rule out the orbiting particle model of electron behavior in space, for this would result in a tangled mess akin to solar systems colliding, with matter in a constantly explosive state. Even if electrons orbit so rapidly that they resemble a swarm of bees, one would not expect this to much effect the trajectories of nuclei with protons that are two thousand times larger than an individual electron, just as a swarm of as many as 280 bees would not be expected to levitate a boulder no matter how fast the bees fly. At any rate, electron behavior is much less haphazard than the chaos of an account such as this suggests, for the quantitative precision of photon absorption and emission by electrons in atoms implies an arrangement of extreme orderedness, more like a synchronous overall shape with oscillations centered on specific frequencies, analogous in their discreteness to the harmonics of vibrating guitar strings.

A wavicle model seems more plausible at first glance because it describes how electrons can take up so much space amongst atoms, but if electron waves with negative charge envelop nuclei in a state of permeating tension, it is difficult to imagine how the experimentally confirmed phenomenon of dynamic equilibrium can happen in a solution at constant temperature, for negative charges of equivalent kinetic energy would be expected to hover or jimmy in a state of global tension rather than radically displace each other. This is not as much of a theoretical barrier in the case of solids because their molecules might conceivably vibrate in almost fixed locations, but the dynamic diffusion of liquids and gases, during which molecules rapidly exchange places and spread out on macroscopic scales until they achieve homogeneity, seems impossible. Why will a wave-saturated mass of liquid or gas molecules quickly diffuse over large distances in the absence of external forces any more than a bucket packed tight with billiard balls, regardless of internal motions at the subatomic scale?

The photoelectric effect is also mystifying in this wavicle model, for it is not apparent how an electron can quantum jump to a different energy level. We might imagine electron orbital transition as reminiscent of kaleidoscopes, a single, entirely blended shape which permutes as energy content and wavicle quantities variegate, but this would render distinct spectral absorption/emission lines unlikely. One expects assortments of synthetic orbital complexes in an atom to evince more of a block spectrum comprised of intensities that vary with a fair amount of theoretically predictable continuity rather than a wide range of substantially separated frequencies, for conversions between these hybrid arrangements would occur with a relatively smooth, fluid holism rather than as many abrupt, choppy disjunctions. Orbitals seem to be highly delineated and at least semi-independent entities with properties that are unique to each electron or electron pair in each atom. And why must much more massive, fermionic electrons respond to nearly massless, bosonic photons in the first place as well as spontaneously generate electromagnetic radiation as they move?

Electrons of course ionize, emitted by atoms as a relatively localized wavicle packet or circular ring, but it is not at all certain that this resembles their structure when fixated within an atom. Experiments would have to be designed to verify the following, but perhaps electrons do not exist as a distinct category of fermionic particle at all while inside atoms, instead being a perturbation of the electromagnetic field that gives it a sort of emergent, more complex architecture while under the nucleus’ sphere of influence. If nuclei are not inert, but engage in a currentlike, rotational or oscillating motion, they might produce something akin to magnetic field lines in adjacent electromagnetic fields that arrange negative charge into specific patterns and perhaps mutate these fields while the nuclei diffuse. Orbitals would then be loci of charge concentration within an amorphous electromagnetic field of precise mathematical organization, and transformation into more excited or ground states a reconfiguration of these so-called orbitals.

It is evident that orbitals are in a dynamic state of perpetual flux as they emit and absorb free photons, a process which would be causally conjuncted to the dynamism of nucleic motion. In this model, spontaneous electromagnetic radiation is generated as a natural extension of fluxing by an orbital’s constituent form of matter that is of essentially the same type as a photon, but more densely compacted while moving in complex standing wave formations.

This models orbitals as something like slots of core concentration within the electromagnetic field that are elicited by nuclei, and each orbital harbors the energetic equivalent of two free “electron” wavicles coupled in some kind of complementary, probably opposite motion as per the Pauli exclusion principle. Whenever a photon is absorbed or emitted by an orbital, the structure of the entire complex of orbitals changes, but each orbital fluxes independently enough that it generates a unique spectral signature.

An orbital is defined by four properties: average bosonic rate of flux (c, the speed of light), electric charge (e), base unit of energy transfer (h, Planck’s constant), and Coulomb’s constant (k) which scales up to size the total electric charge per units of fluxing energy transference; hence the formula ke^2/hc.

This “size” is the compounded substance and force phenomena characterizing single orbitals, of which there are 140 within an atom, all close enough in their two electron slotting structure that the total can be approximated by the quantity 137. Each nucleus of whatever girth takes up roughly the same negligible space relative to a whole atom, and apparently generates almost the same overall orbital pattern since this fine structure term is nearly an absolute constant. The deviation from 140 is a mystery, but might be explainable as a result of slight variations in electromagnetic concentrating that depend on which core “orbital” slots are simultaneously occupied.

The model can possibly account for significantly higher ionization energy in smaller elements such as hydrogen despite their much less massive nucleus: the electromagnetic field within an atom might need to travel through every orbital’s energy state before it liberates from protonic matter, so that ionization in closer orbitals is more impeded. Because orbitals are usually bound up in chemical bonds or blocked as inner energy levels, tremendous energetic input is typically requisite for these electromagnetic concentrations to be fully freed from the nucleus, so ionization packs quite a punch that in combination with forces of electric charge in the environment is responsible for the relatively dense, “electron” nature of this material while transiting outside an atom.

When modeling matter of the kind we find on Earth, the fine structure constant shows up as a term that represents the constitution of electromagnetic divisibility internal to an atom. This is a quantitative parameterization of the average size of single orbitals, approximately 1/137 of 140 orbitals.