**Further Afield**

There are many observations in the quantum world that do not fit into the Standard Model, which may be generously characterized as incomplete. Other physics theories can account for what SM cannot. But they too have flies in their ointment of exposition.

**Lattice World**

In 1928, Paul Dirac described his relativistic approach to characterizing a fermion field. He had in mind electrons, which have both mass and charge.

Within his mathematical solutions, Dirac found the positron, which is the electron’s antiparticle. The positron has the same mass as the electron, but the opposite charge: positive rather than negative. Positrons were experimentally confirmed the year after the Dirac equation appeared, becoming the first antiparticle found.

In 1929, German mathematician and physicist Hermann Weyl showed that Dirac’s equation could be simplified for massless fermions.

The next year, Wolfgang Pauli proposed neutrinos to explain the continuous energy spectrum coming out of radioactive decay. To respect the law of energy conservation, neutrinos had to be chargeless.

Neutrinos were first detected in 1956. Early experimental data suggested that neutrinos lacked mass. From that, it was assumed that Dirac’s neutrinos were merely massless Weyl fermions. Later investigation surmised that the masses of neutrinos are slight, but that remains uncertain.

In 1937, Italian physicist Ettore Majorana took neutrinos to an even more ethereal state, by proposing a class of quanta that was both massless and chargeless. Majorana particles were first glimpsed in 2012.

Whereas Dirac fermions have an antiparticle counterpart, such as electrons and positrons, Majorana fermions are their own antiparticle.

3 distinct classes of fermions have been identified: Dirac (with mass and charge), Weyl (massless, charged), and Majorana (massless, chargeless). What all fermions have in common is the same spin, which is the direction of internal angular momentum relative to the direction of linear momentum. Spin is the property that distinguishes fermions from bosons.

The asymmetrical spin of fermions explains why they cannot occupy the same space at the same time; but bosons can, because their spin is symmetrical. This fermionic limitation is termed the Pauli exclusion principle, which Wolfgang Pauli discovered in 1925.

Don’t think for a Planck moment that fermions always mind their manners. It all depends upon the environment they are in. Fermions might go bosonic when stressed.

The mathematics of existence can be quite slippery. Nature’s fondness for diversity often rides roughshod over textbook behaviors. Such is the case when fermions find themselves in the tight confines of a crystalline space.

Crystals are highly ordered solids which may form any one of 230 distinct lattice structures. Figuring out the extent of lattice space groups was a tour de force of 19th-century crystallography.

In 1930, Werner Heisenberg wondered what would happen if space itself was quantized instead of continuous. Heisenberg was inspired to speculate about a Planck Gitterwelt (lattice world) out of a desire to rid quantum mechanics of the vexatious infinities that kept arising in equations.

(Quantum mechanics’ mathematics was never able to shake off infinity. So, the beautiful symmetries and inscrutable infinities that appear everywhere are purposely broken by spontaneous symmetry breaking, which is a statistical abuse to force equations to behave so that physicists feel comfortable with them.)

What Heisenberg got in Gitterwelt was inexplicably peculiar: electrons might lose their mass, or morph into protons. This strangeness drove him to abandon “this completely crazy idea.”

But Gitterwelt happens. An electron moving through a honeycomb lattice of graphene carbon atoms loses its mass, transforming itself from a Dirac fermion to a Weyl one. If the lattice is superconductive, the electron may drop its charge and change into a Majorana.

Lattices offer even stranger transformations. A Weyl fermion trapped in a lattice world might alter its spin to that of a boson, while still being fermionic in obeying the Pauli exclusion principle. Other quantum oddities of lattice worlds are still being explored.

**Hyperuniformity**

Prime numbers can only be divided by 1 and themselves. The first few primes are 2, 3, 5, 7 and 11. The pattern of primes becomes more sporadic higher in the number line. Though seemingly random in their distribution along the number line, primes have a deeply hidden order.

“Primes have multiscale order characterized by dense Bragg peaks.” ~ Italian American scientist Salvatore Torquato et al

Ionizing radiation is an energy transmission strong enough to rip electrons from their atoms. Such energy loses its oomph as it traverses matter. This retarding force is called stopping power. In certain materials, stopping power cumulates, reaching an apex – Bragg peak – before the radiative energy precipitously drops to nothing. English physicist and chemist William Henry Bragg discovered this diffraction pattern in 1903.

Crystals scatter energy in an orderly way characterized by Bragg peaks. Systems exhibiting order at large distances follow a pattern known as hyperuniformity. Besides primes and crystals, hyperuniformity is found in supercooled liquids and glasses, the arrangement of avian vision color-receptor (cone) cells, certain rare meteorites, and in the large-scale structure of the universe.

**The Ground State**

“There is no such thing as a real void.” ~ Carlo Rovelli

The ground state is the lowest-energy state of a quantum-mechanical system, with supposedly zero-point energy. In quantum field theory, the ground state is called the vacuum state, or simply vacuum.

Yet the ground state is far from grounded. Vacuum energy is calculated to be 10^{113} joules per cubic meter: unimaginably enormous power. And this is a comedown from the early universe, when the ground state was even more energetic.

According to classical thermodynamics, the ground state is supposed to be at absolute zero temperature (0 K). That is a theoretical fiction, as the ground state is not a void, or empty space. Virtual particles testify to that.

“Quantum mechanics teaches us that the vacuum is not empty at all, but, on small scales, contains virtual particles, their anti-particles, and the quanta of their interactions.” ~ Italian particle physicist Alessandro Bettini

** The Dance of Spacetime**

In 2017, Chinese physicist Qingdi Wang and his colleagues investigated the gravitational nature of the ground state. What they found was a dynamo of emergence.

“Spacetime is not as static as it appears; it’s constantly moving. This happens at very tiny scales, billions and billions of times smaller even than an electron.” ~ Qingdi Wang

“It’s similar to the waves we see on the ocean. They are not affected by the intense dance of the individual atoms that make up the water on which those waves ride.” ~ Canadian physicist William Unruh

From a fluctuating fabric of spacetime emerges the illusion of a stable cosmos.

**Virtual Particles**

Our 4-dimensional (4D) existence emerges from a holistic dimensionality (HD) which includes extra dimensions (ed). Only a tiny fraction of the mass found in atomic nuclei comes from the quarks within. Over 99% comes from being bound into a hadron.

The glue that holds hadrons together is a swarming stew of virtual particles: subatomic mystery matter that is ed, with only transient 4d appearance. Their energetic interactions multiply the mass that makes up everyday matter.

In adding mass and other attributes to virtually all quantum bits, virtual particles from vacuum are a paradox which physicists cannot explain. The conventional comprehension is that these fleeting waveforms pop in and out of “existence” from the ground state; a rather ridiculous notion. Instead, the virtuosity of virtuality is a demonstration of dimensional phase-shifting.

The ground state is simply the limit boundary to perceptible existence (4D). Its incredible energy, and the virtual horde which incessantly emerges to add heft and vitality to phenomena, is further proof that existence is a chimera.

**Solitons**

In 1834, Scottish engineer John Scott Russell saw a solitary wave in a canal travel for over 8 miles without changing shape or amplitude. Fascinated, Russell reproduced solitons in a wave tank.

Soliton dynamics vary depending upon the medium in which they appear. Solitons arise at both the macroscopic and quantum scales, in both matter (fermions) and pure energy (bosons). Solitons may occur in light beams, magnets, DNA molecules, proteins, and cell membranes.

Superfluidity readily happens in Bose-Einstein condensate (BEC), which is a supercooled dilute gas of bosons. Solitons can arise in a BEC. Atomic BEC always act in a coherent wavelike manner, even when chilled near absolute to create a quantum phase transition.

“In no moment do atoms of BEC become classical particles; they always behave as waves that evolve in synchrony with each other.” ~ Chinese quantum physicist Cheng Chin

Under certain conditions, fermions may also experience frictionless flow. But, to attain superfluidity, fermions must first turn into bosons. They do so by forming entangled pairs which adopt the requisite spin.

What all solitons exhibit are startling robustness in their coherence. Solitons can encounter each other and still maintain their integrity.

“Equations with soliton solutions have a profound mathematical structure.” ~ English mathematician Mason Porter

**The Stability of Existence**

Under the Standard Model, the Higgs boson is a grainy chunk of the Higgs field, which permeates all space. Elementary particles gain their mass by bathing in the ubiquitous Higgs field; a constant process called the Higgs mechanism.

The relationship is circular in its entanglement. While other particles gather mass by their immersion in the Higgs field (the Higgs mechanism), the Higgs boson depends upon those particles for its own existence. Unsurprisingly, the heaviest fermion – the top quark – has the largest impact on the mass of the Higgs boson.

Physicists use the measurement of particle masses, and properties of the Higgs field, to deduce the stability of existence; a conclusion related to the energy of the ground state. What they conclude, according to the set of equations that define the Standard Model, is that spacetime is in a precarious predicament. The stability of the universe is at risk from a treacherous vacuum, which may at any time move to a lower energy state, instantaneously wiping out existence.

“If the Higgs mass and the top quark mass were a little bit different, we would either be in a completely stable vacuum or in an unstable vacuum that would have decayed a long time ago. The world seems to be on an edge. We don’t have enough precision to say whether our vacuum is stable or not.” ~ American astrophysicist Sean Carroll

**Ghost Fields**

In the Standard Model, the masses of bosons are modified via interrelations with other bosons and fermions. This creates what are called ghost fields. Continually perturbing the ground state, matter radiates over these ghost fields, stirring up what has been termed quantum foam.

Boson-fermion interactions are called ghost fields because they are presumed to not exist. Ghost fields are instead treated as a computational tool: a mathematical necessity to maintain consistency in the Standard Model.

But then, ghost fields originate the virtual particles that appear 4d out of the ground state that comprises only vacuum energy. Virtual particles are now taken for granted as existing.

There is a paradox in granting virtual particles existence but considering their creator – ghost fields – to be a fictional construct. It portrays the Standard Model as purely mathematical mumbo-jumbo, despite SM’s many points of convergence with actuality.

Ghost fields play a critical role in producing a loopy hierarchy of particles in SM, thus creating considerable complexity in the Standard Model construct. This hierarchy problem prompted theoretical physicists to derive a more elegant mathematical solution, called supersymmetry (SUSY).

Alas, several SUSY predictions are contradicted by evidence. For example, supersymmetry predicts that electrons have a slightly oval deformation, owing to their having an electric dipole moment, which has yet to be found. Instead, electrons are perfectly spherical.

Supersymmetry is not the only alternative to the Standard Model. Another – string theory – predates SM. While not mainstream, string theory and its offshoot, brane theory, have many adherents.

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Before winging into strings, a brief digression on quanta that aren’t, but act as if they are.

** Quasiparticles**

“These particles are just smoke and mirrors, handy mathematical tricks and nothing more. Or are they?” ~ English physicist Andrea Taroni

Quasiparticles are emergent phenomena that behave as quanta but are illegitimate in the sense of being a fermion or boson per se. Quasiparticles are to quantum mechanics what epigenetics is to genetics: potent, but not quite kosher. Both illustrate the deep, entangled intricacy that characterizes Nature.

Quasiparticles are employed to explain oscillations, which are the fluctuations in fields. Phonons explain mechanical vibrations. Plasmons are quantized plasma oscillations. Magnons quantize the waveform which personifies the spin property of all quanta. Excitons are the quantized excitement of nothingness (holes) that exist after electrons have departed.

**String Theory**

In 1907, Einstein suggested that solids came about from vibrating particles, now termed phonons. Einstein was guessing. The structure of atoms was not discovered until 1911.

Yet Einstein’s phonon serendipity hit a note that resonated. Phonons are relevant to characterizing several exotic thermodynamic phenomena. A phonon is a quasiparticle that represents the excited state which brings electrons together into an entangled Cooper pair, which synchronously perform miraculous feats like superconductivity.

“Phonons are not actually real. They are really just a way of simplifying a very complicated problem.” ~ English physicist Jon Goff

Phonons were formally conceptualized by Russian physicist Igor Tamm in 1932 as the particle form of wave/particle fields working at a specific vibration.

The first string theory was proposed in 1926, during the swirl of the quantum revolution provoked by the uncertainty principle. The idea was lost, only to be rediscovered decades later.

In 1968, Italian physicist Gabriele Veneziano was working with the Euler Beta function: an equation used to characterize scattering amplitude. He noticed that it could explain particle reactions involving the strong nuclear force, which binds together the nuclei of atoms. Others then realized that the equation made sense to them when they thought of subatomic particles as connected by infinitesimal strings, vibrating their tiny hearts out.

The concept was controversial. Shortly thereafter, the Standard Model swept aside strings as the great explainer of particle interactions. That did not deter physicists from continuing to pluck at string theory.

String theory conceptualizes subatomic particles as infinitesimally thin strings, vibrating through a holistic dimensionality (HD) that has more than 4 dimensions.

The “string” in string theory seems somewhat misleading, as the significance is that quantized fields have resonances at distinct frequencies, harmonically interacting with their brethren. Vibe theory sounds more appropriate.

In 1995, American particle theorist Edward Witten, who had been fiddling strings for over a decade, had a vision of unifying the variant quantum field theories. The result was M-theory, which postulates 11 dimensions of spacetime: 10 of space and 1 of time. ‘M’ stood for membrane.

M-theory is naturally extensible in the number of dimensions. In M-theory, a single string may be a membrane of greater dimensions.

String theorists Petr Horava and Joseph Polchinski independently extended M-strings into higher-dimensional objects: D-branes (a Horava term). Among other things, D-brane theory attempts to characterize string endpoints.

D-branes add rich mathematical texture to M-theory, paving the way for constructing more intricate cosmological models with greater explanatory power. Numerous braneworld (brane cosmology) models have emerged.

String theory has been derided by partisans for its lack of track record. But the theory has been able to explain liquidity experimentally found at trillion-Kelvin conditions, and near absolute zero. Meantime, the Standard Model stood mute. The hot quark soup and ultracold lithium broth exhibited collective behavior, flowing with the lowest possible viscosity. String theory successfully modeled these phenomena as strongly coupled particles, linked by ripples traveling extra-dimensionally.

**Nonlocality**

“The statistical predictions of quantum mechanics are incompatible with separable predetermination.” ~ John Stewart Bell

Quantum mechanics has an obvious deficiency: its mechanics. Quantifying quantum phenomena is the elephant in the room of interpreting quantum theory.

Measuring fundamental particles is an existential oxymoron. Watching a wave function collapse is a probabilistic event. The math itself is nontrivial, and the appropriateness of the bandied equations contentious.

But some quantum field phenomena have been seen. The most inexplicable is nonlocality: what Einstein called “spooky action at a distance.”

Our world works on the principle of locality: that an object can only be affected by its immediate surroundings. In contrast, nonlocality is the notion that distance is ultimately an illusion.

A 1935 paper by Einstein and 2 other physicists posited a paradox over quantum uncertainty: that either locality or uncertainty must be true. Empirically minded Einstein opted for locality (and certainty), thereby concluding that the wave function must be an incomplete description.

Despite upsetting the apple cart of classical physics with his relativity theories, Einstein still preferred the cosmos as comfortably commonplace. After all, relativity only applied when traveling near the speed of light, or at the scale of galactic expanse. These realms were practically abstract.

In response to Einstein’s 1935 paper, Irish physicist John Stewart Bell tackled the quantum measurement problem in 1964; whence arose Bell’s theorem.

Science in general, and physics in particular, long assumed that both locality and objectivity were both true.

Locality means that distance affects the probability of interactions. Locality is colloquially codified in the everyday concept of cause and effect.

Objectivity insists that reality is ultimately objective, and therefore independent of observation. With special relativity, Einstein suggested that existence was subjective.

Bell’s theorem stated that either locality or objectivity had to go. In opting for the uniformity of objective reality, Bell pitched locality.

Ironically striving to spite his own theory of special relativity, Einstein struggled to the end of his days for a theory to uphold causality, protesting the view that there is no objective physicality other than that which is revealed through quantum-mechanical formalism.

In squaring off the principle of locality against counterfactual definiteness, Bell’s theorem went the other way: stating that some quantum effects travel faster than light ever can, thus violating locality.

Bell’s theorem painted special relativity into a corner; rendering it applicable only at the macro scale, and irrelevant at the quantum level. Then even that corner was painted over in the 21st century, by nonlocality showing up in the ambient world.

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Cause and effect is how we understand physics in the everyday (ambient) sense. In physics, causality as predictable is called counterfactual definiteness (CFD).

CFD goes to measurement repeatability: whether what has happened in the past is a statistical indicator of the future. Locality goes along with sequential causality: cause resulting in effect.

At the quantum level, CFD butts heads with locality, by stating that past probability as indicative of the future is a chimera. Instead, uncertainty always reigns.

Here we have a basic conflict. In the physics of existence, either certainty or uncertainty is true. The two are mutually exclusive.

Bell’s theorem showed that quantum uncertainty was a certainty: the principle of locality breaks down at the quantum level. Einstein was appalled: “No reasonable definition of reality could be expected to permit this.”

Later findings demonstrated that nonlocality functions at the macroscopic level too. With spooky-action-at-a-distance a reality, superluminal (faster-than-light) effects exist. Bell’s theorem of nonlocality/entanglement is considered a fundamental principle of quantum mechanics, having been supported by a substantial body of evidence.

“Nonlocality is so fundamental and so important for our worldview of quantum mechanics.” ~ Swiss quantum physicist Nicolas Gisin

The supposed trade-off between locality and objective reality is a false one. While strict quantum locality has been disproven, there is no proof that existence is actually objective. It just appears that way as a social convention: we consider the world “objective” when others agree with us; and so, objectivity is taken axiomatically, just as locality was for so long.

“If quantum physics hasn’t profoundly shocked you, you haven’t understood it yet.” ~ Niels Bohr

**Entanglement**

That one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. ~ Isaac Newton

Basic notions in physics depend upon a time continuum: cause preceding effect. The principle of locality must exist for cause and effect to work. If causality is kicked aside, such as with simultaneous (“spooky”) action at a distance, locality is violated. With nonlocality a well-established fact, quantum entanglement has repeatedly been demonstrated.

The fundamental properties of chemistry rely upon entanglement. Solids form, and retain their solidity, via quantum entanglement of the electrons in the material. Superconductivity works through entangled electron pairs.

Superluminal communication presents a challenge to theoretical physics that has not been resolved. It is a dilemma that can never be met by insisting upon the universe as a 4D closed system; an axiom of which Newton and Einstein were so confident, but simply is not so.

A practical pointer to time as an emergent property occurs by entangling particles that don’t exist at the same time. In other words, nonlocality can also be nontemporal.

A scheme termed entanglement swapping – chaining entanglement through time between subatomic particle pairs – has been demonstrated, using 4 photons.

Entanglement demonstrates that time, as well as space, is emergent: constantly coming into being, as contrasted to preexisting and incrementally evolving, as it appears to us.

“Space and time will end up being emergent concepts; i.e. they will not be present in the fundamental formulation of the theory and will appear as approximate semiclassical notions in the macroscopic world.” ~ Israeli physicist Nathan Seiberg