The Science of Existence – Electrons


An electron is a particle and a wave; it is ideally simple and unimaginably complex; it is precisely understood and utterly mysterious; it is rigid and subject to creative disassembly. No single answer does justice to reality. ~ Frank Wilczek

Swirling in an orbital cloud around a nucleus, at a distance 10,000 times that of the nucleus’ diameter, are perfectly round, negatively charged electrons. An electron has a mass estimated at 1/1,836th of a proton.

Individual electron orbitals are limited to pairs. An electron pair comprises 2 electrons in the same orbital, albeit with opposite spins.

The Pauli exclusion principle forbids fermions from simultaneously occupying the same space. Electrons are fermions. Despite the Pauli exclusion principle, there is a distinct probability of an electron being inside the nucleus of an atom.

To fly together, members of an electron pair have different angular momentums – a different spin makes for an orbital twin.

Electrons commonly escape their atomic bond and become free electrons, at least temporarily. Electron transitions between bound and free characterize chemical reactions.

An electron in motion generates a magnetic field in its wake; whence electromagnetism. Electrons possess a magnetic dipole moment: a polarity like a bar magnet. Supposedly, that is because an electron is a spinning smear of charge. Elementary electromagnetism stipulates that this creates a magnetic dipole field. The more complex actuality is not understood.

That electrons have an electric dipole moment is strongly suspected. Confirming that by isolating an electron has proven tricky.

A free electron will accelerate under the influence of an electric field and crash into whatever is in its path. This is handy for recruiting electrons into employment, but self-defeating for measuring elusive electron properties. So, experiments to date aimed at determining whether electrons have an electric dipole moment have been thwarted.

An electron having an electric dipole moment might doom the Standard Model. Consider time-reversal symmetry.

Supposedly, the laws of physics stay the same if time ran backward. But for a spinning electron, the north and south poles would swap. An electric dipole would accumulate charge at one pole; the inverse of which does not happen with time running forward. So, an electron with an electric dipole moment would violate time-reversal symmetry.

That would not be a first. Mesons are known CP violators and do not respect time-reversal symmetry. But to have the star of electromagnetism and the cornerstone of chemistry blithely skirt the fundamental principles of the Standard Model would bring the model’s reign to an end.

“The strength of the electron’s magnetic field provides perhaps the most stringent and brilliantly successful comparison of theory and experiment in all of physical science, whereas the value of the electric field has never been measured. It is a mystery even to theory.” ~ Frank Wilczek

There is a great irony at the heart of electronics. At a practical level, electrons provide a steady charge. At a more fundamental level, that charge is immeasurable.

There are also limits to electron reliability. Semiconductor fabrication has reached the point of nano wires only a hundred atoms wide. At that point, electrons behave like quantum waves. Electrodes to control electron flow create a mountainous terrain that electrons struggle with.

“They bash against the walls, and sometimes reflect from the flanks of the mountain pass. They also sense each other’s presence.” ~ Dutch quantum physicist Casper van der Wal

At the quantum level, electron flow is an incredibly complex interaction of various physical phenomena: indescribable by any single formula. Depending upon the environment, electrons may scurry about, with eddies that create resistance among themselves, or may flow with no friction whatsoever.

Maxwell’s unified field theory of electromagnetism is neat packaging that does not always apply. In some environs, the electrical and magnetic properties of electrons are divisible. Electrons may behave as fractional particles: splitting into a magnet and an electrical charge which can move freely and independently of each other. Electrons’ magnetic moment may split into 2 halves and move apart, albeit with extra-dimensional linkage.

Electrons amply illustrate how little we know about how existence is constructed.


The bottom line of a ‘normal’ atom is no charge: the positive protons and negative electrons balance out. Thankfully, ionic heretics are everywhere.


“The removal of an electron from the surface of an atom – that is, the ionization of the atom – means a fundamental structural change in its surface layer.” ~ German physicist Johannes Stark

An ion is an atom or molecule with an electrical imbalance owing to an unequal number of protons and electrons. Ions are promoters of chemical reactions.

Gaseous ions are highly reactive. They relatively rare on Earth: appearing only in flames, lightning, sparks, and other plasmas. The energy required to remove electrons from gaseous atoms or ions is termed ionization energy or ionization potential.

Liquid or solid-state ions naturally occur when salts interact with a solvent, such as water, and are more stable than gaseous ions, owing to energy and entropy changes as ions move away from each other to interact with the liquid (or solid). Stabilized ions are commonly found at low temperatures, such as in dissolved salts in cold seawater.


Electrons are construed to swirl in orbital layers – shells – defined by their relative quantum energy state. The energy ranges of shells can overlap. Generally, more energetic electrons move in orbitals farther from an atom’s nucleus. But electrons can store some energy before getting so excited that they feel obliged to migrate to another shell.

Like an electronic Matryoshka doll, a shell may have subshells. While it is commonly stated that same-shell electrons have the same energy, that is an approximation. But electrons in the same subshell are equally energetic.

Shell layering is related to atomic spectral lines (electron energy level changes). These energetic relations are a product of quantum interactions and are an hd phenomenon. Electrons in different shells exchange status information to favor a coherent spin alignment of all electrons in their atom.

As atom size increases, more electrons whiz about it. Some electrons in heavier elements attain velocities approaching the speed of light. This increases relativistic mass, causing certain inner orbitals to contract and stabilize; which, in turn, destabilizes outer orbitals and provokes their expansion.

(More specifically, electron velocity is correlated with its effective nuclear charge, which is the net positive charge experienced by an electron in any atom with multiple electrons.)

The relativistic effects of electrons in heavier atoms contribute to their attributes. Gold has its characteristic amber color because of it. Mercury is a liquid at room temperature owing to the relativistic speed of its electrons.

Electron orbitals have a wavelike existence. Their position at any point in time is only a probability.

“Today, instead of thinking of electrons as microscopic planets circling a nucleus, we now see them as probability waves sloshing around the orbits like water in some kind of doughnut-shaped tidal pool governed by Schrödinger’s equation.” ~ American physicist James Trefil

 The Atomic Void

“By convention sweet, by convention bitter, by convention hot, by convention cold, by convention color, but in reality atoms and void.” ~ Democritus

An atom’s electron swirl is a long way away from its nucleus. In 1913, Niels Bohr constructed a model of hydrogen-1 and figured that its radius – the distance from proton to electron – was 100,000 times the size of the nucleus. Heavier atoms are more compact: nuclei gain girth but the orbits of electrons are constrained.

Measured across the electron cloud, a typical atom, such as carbon, is 10–8 cm: 1/10-millionth of a millimeter. The diameter of a nucleus is about 10–12 cm. This is 1/10,000th of the diameter of the atom in which the nucleus resides. Most atoms have electrons whirling in a cloud at a distance somewhat over 10,000 times the radius their nuclei. These numbers are proximate, as electrons move in probabilistic orbits, and nuclei themselves restlessly skitter about.

An atom is 99.999+% empty space, albeit seething with ed energy. If a hydrogen proton were a tennis ball, 6.35 centimeters in diameter, its electron would be 6.35 kilometers away. If devoid of void, all the matter in the universe would fit within the size of a single pea, less than 1 cm in diameter.


Electrons coursing through materials normally encounter electrical resistance: opposition to the flow of an electric current. The resistance is typically only partly successful.

How well a substance allows electron flow falls into 2 categories: conductor and resistor. Temperature affects conductivity and resistance.

In being a lattice of atoms, metals are inherently good conductors. A positive ionic lattice engenders outer shell electrons to disassociate from their parent atoms, creating an electron sea that flows with the force: an electrical current.

The flow in conductors is not smooth, as individual electrons suffer scatter due to destructive interference of free electron waves to non-correlating ion potentials – a 4D phenomenon with ED interactions behind it. These collisions transfer energy from an electron to a metal ion, causing the ion to vibrate more vigorously. The result is resistance, manifest as heat.

 Bad Metals

“Metals conduct electricity because they contain electrons that are free to move through the material. In bad metals the electrons seem to reversibly disappear and reappear.” ~ American solid-state physicist Rafael Jaramillo

Theoretically, the hotter the metal, the worse it conducts electricity. Most metals obey this inverse relationship between temperature and conductivity. But some do not. These conductive miscreants are termed bad metals.

At high temperatures, the electrons in bad metals ought to violate Heisenberg’s uncertainty principle, rendering them nonconductive. But they refuse to bow to uncertainty. Instead, bad metals invoke extra-dimensional effects to keep their electrons flowing.

“Electron-electron interactions are so strong in bad metals.” ~ American physicist Ray Osborn


Electrons lose their individual identities in superconductors, in which electrons pair up to form a pervasive sea. Thus, electrons become their own antiparticles. ~ Frank Wilczek

Helium was first liquefied in 1908 by Dutch physicist Heike Kamerlingh Onnes, who studied the resistance of solid mercury when supercooled. Mercury is the only metal that is liquid at room temperature; hence its nom de plume: quicksilver. In 1911, Onnes discovered that at 4.2 K, quicksilver got quicker: shedding electric resistance entirely.

Normally, the pull of one passing electron is drowned out by ion vibrations. Cooling a metal down can lessen ionic wiggles enough that an electron’s gentle tug can be felt by another, and so the 2 electrons form a Cooper pair:  entranced to dance together via a pied-piper phonon. The temperature below which a material becomes superconducting is called its critical temperature.

A Cooper pair passing through are attractive to the ions in a superconductive metal. The metal ions stray as far toward the electron’s wake as their lattice structure allows. This distorts the crystal for a short time, creating a concentrated positive charge that encourages free electrons in the vicinity to pair up and join the flow. (Most inorganic solids, including metals, are polycrystals: a plenitude of microscopic crystals (crystallites) fused together.)

Once paired, electrons stop behaving as ordinary matter particles and enter a collective hd quantum state, where they become entangled; oblivious to the ions, and so lose no energy bumping into them. Current passes through the crystal without resistance.

Superconductivity is zero electrical resistance, resulting from electrons overcoming their mutual repulsion and pairing up, creating a coherent flow. Electrons act oddly on their way to flowing freely. In crystals that become superconductive when cooled, electrons become 1,000 times more massive than normal as they become entangled. These hot-to-trot heavy electrons are actually composite objects, mixing opposite behaviors together: localized bonding to individual atoms and freely flitting between atoms in the lattice.

Entangled electrons can become so obese that they refuse to budge: freezing into a magnetized state while stuck at an atom, spinning in unison. Tweaking the crystal composition can charm the fat electrons to dance in superconducting entanglement as the crystal is cooled.

Superconductivity is a full-blown quantum field party, characterized by the Meissner effect: the complete expulsion of magnetic field lines from the inside of a superconductor as it transitions to a superconducting state. Owing to the Meissner effect, a magnet put over a superconducting substance levitates. The electromagnetic free energy of the superconductor approaches zero, creating a repulsion of objects with intense magnetic field lines, like the repulsion between a magnet and a diamagnetic object.

Absence of resistance does not make a magnet grow fonder; quite the opposite. Magnetism surrenders to superconductivity.

As antiferromagnetism breaks down, superconductivity appears, encouraging electrons to pair up and flow freely. Long-range magnetism – where atoms align their magnetic moments – ceases in giving way to superconductivity. This abdication belies a deeper connection.

“Magnetism is the quantum glue underlying the emergence of superconductivity.” ~ Dirk Morr

The electromagnetism in the electrons involved in superconductive substances bifurcates into an electric charge and a magnet. American physicist Peter Anderson suggested the fractionalization of electron properties (“fractional particles”) as facilitating superconductivity in 1987. Altering the interactivity of magnetism is key to superconductivity.

Whereas atomic magnetism vanishes with superconductivity, local magnetic moments become more powerful, as the electrons in individual atoms synchronize. Superconductivity is a transformation of the turbulent flow of an electron sea into coherence by ordering quantum spin.

Relatively high-temperature superconductivity has been shown in insulators. Intuitive expectation would be that conductors would become more conductive when cooled. One would not expect that insulators would reverse themselves, flipping from resisting to superconducting.

The search for high-temperature superconductivity in hydrogen-rich compounds hinges on a theory that, under certain circumstances, elements that have low atomic masses can contribute to high critical temperatures. Hydrogen, being the lightest element, is optimal for high critical temperatures.  ~ American physicist James Hamlin

Temperature is not the only variable affecting potential superconductive materials. Applied pressure matters. Under pressure (specifically, 16,000 times atmospheric pressure (1.6 Gpa)), iron selenides superconduct at 30–32 K. Pressed further, superconductivity disappears at 9 Gpa, only to reappear at 12.4 Gpa. Yet the basic structure of the compound is retained throughout the pressuring.

More recent research has focused on the internal structure of Cooper pairs. Cooper pairs in “conventional” superconductors spin in opposite directions, resulting in the pair having zero spin.

In more exotic “triplet” superconductors, spins line up, such that a Cooper pair carries some spin of its own. Lanthanum-nickel-carbon (LaNiC2) and lanthanum-nickel-gallium (LaNiGa2) are exemplary triplet superconductors.

Unlike conventional superconductors, triplet superconductors are not ferromagnetic. The magnetic moments of the Cooper pairs themselves create the magnetism favorable to superconductivity.

Non-unitary triplet pairing bootstraps itself into superconductivity via quantum spin liquidity generated by emergent superconductivity. This is a superconducting analogue of how magnetism develops in ferromagnetic metals.

Superconductivity appears in divergent materials at different temperatures owing to their magnetic properties and tendency to become a better conductor of electricity in certain directions. Subatomic alignment matters.

Superconductivity shows how the electromagnetic force is highly variable, depending upon material and ambient conditions. Superconductivity remains a mysterious demonstration of 4d effects from hd interactions.

Emergence, the coming into being through evolution, is an important concept in modern condensed-matter physics. Superconductivity is a classic example of emergence in the realm of quantum matter: as the energy scale decreases, the effective electron–electron interactions responsible for Cooper pairing, and thus superconductivity, evolves from the elementary microscopic Hamiltonian through unanticipated modifications.

“This evolution is why it is so difficult to derive superconductivity from first principles. Finding the microscopic mechanism of Cooper pairing means discovering the nature of the ultimate effective electron–electron interaction at the lowest energy scales.” ~ Scottish Irish American physicist Séamus Davis & Taiwanese American physicist Dung-Hai Lee

 Fractal Superconductivity

There are various classes of superconducting substances, each with a different molecular structure at the atomic bonding level. Researchers create novel superconductors by manipulating atomic arrangements.

The oxygen in a copper-oxide semiconductor settles into a fractal pattern when superconducting. The more fractal, the better the superconductor’s performance.

Fractals are a mathematical construct, displaying a self-similar pattern that is scale indifferent. In fractals, similar patterns may be discerned regardless of how closely a fractal is examined.

Fractals repeatedly appear in Nature, from lightning bolts to shorelines to cauliflower heads. A snapshot of the solar wind shows a fractal signature, imposed by the magnetic field of the Sun.


Insulators are materials with inherent resistance. In contrast, superinsulators, which were discovered in 2008, absolutely resist electrical conductivity.

Cooper pairs avoid each other in superinsulators. They instead generate enormous electrical forces that oppose penetration of current into the material. A superinsulator is the exact opposite of a superconductor.