Below is a list of scientific terms, some of which emerge from the work of Quicycle members. (The definitions relate primarily to physics and chemistry.)
This is not an inter-action. It is just action. It is a force to which there is no resistance, a process that must occur. Example: If there is a changing electric field, there will be a corresponding changing magnetic field associated with it. It is a fundamental process of electro-mass dynamics.
Absolute Relativity (A.R.):
The conscious restriction of thinking to include only elements with the proper fully relativistic form.
An acid is a substance that releases hydrogen (H+) ions into solution when placed in water. An H+ ion is very reactive, being simply a bare proton, and it will attach itself to an electron-rich oxygen atom on the nearest water (H2O) molecule, forming the H3O+ ion. The stronger an acid, the more H+ ions it produces in solution. Hydrochloric acid (HCl) is a strong acid because it releases all of its hydrogen into solution as H+ ions. A weak acid, like vinegar (HC2H3O2), only releases a small percentage. The exposed proton of the H+ ion is the reason that strong acids can be so corrosive. Each H+ ion is desperately seeking an electron in which to clothe its bare proton nucleus. It does so by taking an electron from another substance around it, which results in a (sometimes violent) chemical reaction.
A particle of matter has a corresponding antimatter particle (or antiparticle) that has the same mass but the opposite electric charge.
The proton’s anti-particle is the anti-proton, and it has the same mass as the proton but a negative charge. The anti-particle of the electron is the positron, which has positive charge. While neutrons and neutrinos are electrically neutral, they still have anti-particles, called the anti-neutron and the anti-neutrino.
In the case of the neutron, while it has no overall charge, it is comprised of (according to the standard model) quarks that have charge or (according to the rotating photon model of matter) photon harmonic resonances that outwardly express either their positive or negative electric fields. In the corresponding antiparticles, these resonances rotate in the opposite direction, yielding the opposite charge for charged particles but the same overall neutrality for neutral particles.
According to this model, antimatter is matter that is composed of particles whose internal (photon) structure has opposite quantum ‘spin-handedness’ (chirality), which therefore outwardly expresses the opposite polarity of the internal photon’s electric field.
When a particle and its anti-particle meet, they unlock each other’s internal spin angular momenta, converting their rotating photons to linear photons in a high-energy release called a matter-antimatter annihilation. (See this presentation excerpt, by Arnie Benn, for a conjecture as to the specific sub-quantum mechanism involved.)
Antimatter is encountered in association with nuclear transmutation reactions. According to the rotating photon model of matter, antimatter arises as a result of a nuclear reaction because antimatter particles are the photon resonances that form (and are consumed) in order to conserve photon angular momentum (as well as other quantum numbers) through a nuclear reaction. These antimatter particles can then be consumed in other nuclear reactions or in annihilation reactions with matter particles. They will therefore not have long-term survivability in a universe made of regular matter.
The smallest particle of a pure element. When two or more atoms are bonded together it is called a molecule. All solids, liquids, and gases are made of atoms or molecules. An atom contains a nucleus, a tiny positively charged central region containing protons and neutrons. This is surrounded by an electron cloud, a region of negative charge that fills the space around the nucleus. The positive charge field of the nucleus is thus cancelled by the negative charge field of the electron cloud around it. The charges are therefore balanced, and this stabilizes the atom by achieving a lowest energy state. Protons, neutrons, and electrons are known as subatomic particles. If electrons are added or removed, the atom will no longer be balanced and will have an overall charge. It is then called an ion.
Substances form when atoms group together. Atoms will only bond (or stick together) to the extent that they are attracted to each other. That attraction is based upon the interactions between atoms — whether their electron shells are eager to gain or lose electrons, whether they are charged ions, or whether they specifically do not want to interact with other atoms. The position of an element in the periodic table — in which column and in which row it is found — gives us clues as to its bonding properties.
On the periodic table: most of the elements (on the left side) are considered metals and elements on the far right side are considered non-metals. The dividing line between them is a diagonal ‘staircase’ of elements that are considered semi-metals or metalloids. These include B, Si, Ge, As, Sb, Te & At (as shown below).
Elements become more metallic in character the further they get from the metalloids towards the left bottom corner of the table, and more non-metallic towards the top right corner of the table. The reason for this is that larger atoms and those with fewer outer electrons will give these (valence) electrons more easily, and smaller atoms with almost-full electron shells will attract electrons the most strongly. The right-most column, the Noble gases, are generally unreactive because they are both neutral and have full electron shells. (See Periodic Trends for more detail.)
The main types of atomic bonds are: covalent bonds, network covalent bonds, metallic bonds, and ionic bonds. Covalent bonds occur between non-metal atoms (ex: H2O). Network covalent bonds occur in non-metal crystals (ex: C in diamond). Metallic bonds occur between metal atoms (ex: bronze, Cu+Sn). Ionic bonds form between ions of opposite charge (ex: salt, NaCl) involving a metal atom and a non-metal atom. This is because the difference in their electronegativities is enough to go from simply sharing a pair of electrons in a (covalent) bond to completely stealing the electron (in Ionic bonds).
There are also other bond-like interactions, attractions between atoms and molecules that are weaker than bonds. These are called intermolecular forces.
Atomic mass unit (amu):
For convenience, the mass of atoms is usually considered in terms of the mass of the proton (or neutron). One amu is the same as the mass of a single proton, which is 1.67×10−27 kg. This is not a very convenient number to work with, so, instead of saying that a helium atom has a mass of 6.69×10−27 kg, it is easier to say that helium has a mass of 4 amu. Atomic numbers are not perfect integers because they really represent the average mass of all the different isotopes of an element.
This refers to the size of the atom by referring to the distance from its center to the “edge” of its electron cloud. The “bonding atomic radius” is slightly shorter than the radius of the neutral atom because, when atoms bond, their electron clouds tend to overlap. This makes the radius shorter at that place, and it is calculated by taking half of the bond length — the distance from the nucleus of one atom to the nucleus of the other. The circles in the table below represent the sizes of the atoms when they form covalent bonds. (The colors in this table represent electronegativity.)
Ionic Radius: When atoms become ions, they gain or lose electrons in order to gain full outer electron shells. This causes their sizes to change because the balance of protons to electrons has changed. This changes the effective nuclear charge. In the case of positive ions, the effective nuclear charge will be greater because there are now more protons than electrons. The inward attraction of the electron cloud towards the nucleus is therefore greater, and positive ions are therefore smaller than their neutral atoms. In the case of negative ions, the effective nuclear charge will be smaller because there are now more electrons than protons. Negative ions are therefore larger than their neutral atoms. Some (metal) ions are capable of making more than one type of ion, for example Germanium (Ge) can make a 2+ or 4+ ion. (This is represented by a 2-tone ion color with more than one charge listed. The larger the charge, the smaller the ion.) Notice that some elements, such as Phosphorus (P) and Sulfur (S), can form positive or negative ions.
The rainbow color coding (from the previous table) has changed because ions do not have electronegativity values. Ions cannot share electrons in covalent bonds because they have full electron shells. Instead, they simply stick to one another electrostatically in ionic bonds. Notice that the noble gases in group VIII do not form ions because they already have full electron shells, so they will not gain or lose any more. (Kr & Xe can actually bond, but only with the most electrogenative elements like F, O, or Cl. One example is XeF4.)
A base (or alkali) is a substance that attracts and bonds with hydrogen (H+) ions in solution. Most bases are therefore negative ions, like hydroxide (OH–) or hydride (H–), or else they contain atoms with exposed di-electrons (lone pairs), like nitrogen, because these negative charge centers strongly attract positively charged H+ ions.
See atomic bond.
A subatomic particle with an integer quantum spin, meaning a spin of S = 0, 1, 2, etc. All subatomic particles are either a boson or a fermion. Examples of bosons include di-electrons (Cooper Pairs) and photons of light.
This is the wavelength (λC) of a photon that has the same energy as represented by the rest mass/energy of a subatomic particle. The equation that represents this relationship is λC=h/mc. The Compton wavelength is inversely proportional to the mass of the particle, so larger particles have smaller Compton wavelengths. (Compare: De Broglie wavelength)
Covalent bonds occur between non-metal atoms (ex: H2O). Non-metals occupy the right-side columns of the periodic table, and they represent atoms with high electronegativity that strongly attract electrons because they want to complete their almost-filled electron shell. When two non-metal atoms encounter each other, neither will therefore be willing to relinquish an electron. They are therefore forced to share electrons. That way, neither atom feels like it has lost an electron but both feel like they have gained one (or more).
Curie Temperature (Tc):
The temperature at which a ferromagnetic metal loses its permanent magnetization. This occurs because there is so much thermal entropy at this temperature that the spin orientations between unpaired electrons on adjacent atoms are disrupted.
De Broglie Wavelength:
(Pronounced: De-Broyi) This is the wavelength (λB) of a photon that represents the classical momentum of a subatomic particle. The equation that represents this relationship is λB=h/p, where its momentum p=mv. Thus, the larger the momentum (i.e. its mass and/or velocity), the shorter the DeBroglie wavelength. An electron in a matter state that occupies a larger volume will have a larger De Broglie wavelength. (Compare: Compton wavelength)
This is when a substance is repelled from a magnetic field because it contains paired electrons. These paired electrons are in a state of field cancellation with one another. The presence of an external magnetic field will disrupt the coherence of this di-electron state, raising its energy. This causes it to repel away from the field in search of a lower energy state. Copper (Cu) and zinc (Zn) are diamagnetic.
A pair of electrons of opposite spin that have completely superimposed upon one another. This yields a single, coherent, quantum state which brings their magnetic fields into equal and opposite orientations at every point within the di-electron, facilitating almost total magnetic field cancellation. It also facilitates a cancellation of the equal and opposite quantum spins, converting two fermions (with spin 1/2) to one boson (with spin 0). This results in a highly stable and favorable state, in spite of the like-charge electric field repulsion, because it allows for a significant lowering of energy. Examples of di-electrons include the 1s2 shell in helium (He), the covalent bond in the hydrogen molecule (H2), the “lone pair” on the nitrogen atom (N), and the superconducting Cooper pair. For more on electrons, see Understanding electrons.
When a molecule features a covalent bond between atoms of two different elements, their different electronegativities can cause them to share the bonding electrons unequally. The atom that pulls more electron density to its side of the bond will manifest a slight negative-charge bias — a partial charge — and the one that loses some of its electron density from its side of the bond will manifest a slight positive-charge bias. This makes the molecule polar. Polar molecules are also called ‘dipoles’ because they have two opposite ‘poles’ or charge biases on opposite ends of the molecule. This will cause these opposite partially charged ends on adjacent molecules to attract each other. This attraction is not as strong as an actual atomic bond.
See London Dispersion Force.
This is Einstein’s famous formula that relates energy (E) to mass (m), using the square of the speed of light (c2) as the ratio (or conversion factor) between them. Radiant energy and matter are really two forms of the same root-energy ‘stuff.’ If we want to know how much pure energy we get if we convert matter into pure radiant energy, we multiply the mass by the speed of light squared, which is a very large number (9×1016). It also reflects the fact that particles that have mass, such as electrons (see below), are photons of light that are traveling in a circle (or knot) rather than in a straight line. Such self-sustaining photon resonance structures are the essence of matter.
Effective Nuclear Charge (Zeff):
The protons in the nucleus attract the electrons in the electron cloud around it. The more protons in the nucleus and the more electrons in the orbitals, the more strongly the two are attracted towards each other. This shrinks the size of the atom. In general, effective nuclear charge increases as we move to the right in a row on the periodic table, since we are adding both protons and electrons when we move to the next element. This means atoms get smaller as we move to the right in a row on the periodic table. In general, effective nuclear charge decreases as we move down a column (group) on the periodic table, since we are adding electron shells. The outer electrons are further from the nucleus, which both decreases their attraction to it, and the new shell adds diameter to the atom.
The scientific term for light waves, whether they are in the visible part of the spectrum (like the colors of the rainbow) or the invisible part of the spectrum (for example radio waves or gamma rays).
Light waves store part of their energy in an electric field and part of it in a magnetic field, hence the name. In a typical circularly-polarized photon, the electric and magnetic fields spiral around the axis of travel, 90 degrees apart. Since an electric field incites a forward motion, like velocity, and magnetic field incites a rotation (see spacetime), the combination of the two should yield a combined electromagnetic field that spirals as it moves forward. Electromagnetic waves can only travel at the speed of light (c), which is just under 300,000 kilometers per second.
By analogy, whatever bulk water is or is not, it has the property that energy waves can propagate along its surface as water waves. Similarly, whatever spacetime is or is not, it has the property that photons of electromagnetic energy can travel through it as waves (of field differentials). Like most waves, electromagnetic waves have a wavelength (𝜆) and a frequency (𝜈), and the mathematical relationship between these three properties is given by the equation c=𝜆𝜈. This implies that the larger the frequency, the smaller the wavelength, and vice versa, because the speed of light (c) must remain unchanged.
The amount of energy carried by an electromagnetic wave depends on its frequency. This is reflected in the Planck equation for energy, E=h𝜈, in which the higher the frequency (𝜈) of the wave, the more energy (E) it carries. The ratio between energy and frequency is Planck’s constant (h) (where h=6.626×10-34 m2kg/s). High frequency waves, such as ultraviolet waves, are more dangerous than low frequency waves, such as radio waves, because UV waves carry much more energy. They can therefore ionize molecules, disrupt cellular function, or cause radiation burns. From lowest energy to highest, the main types of electromagnetic radiation are: radio, microwave, infrared, visible (red/orange/yellow/green/blue/indigo/violet), ultraviolet, X-ray, gamma ray.
One of the three subatomic particles out of which all atoms are made. (The other two are the proton and the neutron.) An electron is negatively charged and highly stable. Contrary to popular misconception, it is not a point particle but it has a sub-structure that gives rise to its properties. It is made of a single photon of light making two revolutions per wavelength. An electron is thus a self-confined knot of concentrated light energy traveling around itself at the speed of light. It has a toroidal (donut-shaped) sub-structure in (momentum) space, but the charge field of an isolated electron (or an s-orbital electron around a hydrogen or helium atom) manifests as a sphere. As a result of the geometry of this double-loop torus and the circular polarization of the photon, the photon’s negative electric field is pointing outwards at all times, which is what gives the electron its negative charge. An electron is a fermion and has a left-handed spin of S=½, a charge of C=-1.6×10-19 Coulombs, and a mass-energy content of 511 keV. For more on electrons, see Understanding electrons.
This is a measure of how much an atom wants to accept another electron. It is a measure of how much an added electron would stabilize the atom, so it is quantified by how much energy is released when an electron is added. The more negative the energy value, the more the atom wants another electron. Atoms like chlorine (Cl) and fluorine (F) have the largest negative values. If the value is positive, it indicates that the atom’s orbital resonance is so stable that an added electron would be unfavorable and would increase energy. Examples include noble gases, like neon (Ne), or atoms with a full orbital, like zinc (Zn).
When two atoms bond, electronegativity is a measure of how strongly an atom’s nucleus pulls the bonding di-electron toward itself. When there is an electronegativity difference between the two bonding atoms, the more electronegative atom will pull electron density more strongly, resulting in an imbalance in the electron sharing. This results in a polar bond. In general, as we move across the periodic table, the atoms get smaller. This is due to the stronger pull from the nucleus (effective nuclear charge) since it is closer. Therefore, the smaller the atom, the higher its electronegativity. As we move down the periodic table, atoms get larger due to having additional electron shells. This lowers electronegativity because the outer electrons are not as strongly held to the atom. Fluorine (F) has the highest electronegativity on the periodic table and francium (Fr) has the lowest. In the rainbow-colored diagram below, red represents the lowest electronegativity and violet represents the highest. The circles represent the sizes of the atoms (atomic radius) when they form covalent bonds.
A unique, pure substance made up of only one type of atom. The number of protons in an atom’s nucleus determines which element it is, and this is known as its atomic number. The periodic table of the elements lists all 118 known elements in order of their atomic numbers. By way of example, the nuclei of all hydrogen atoms contain 1 proton, all helium nuclei contain two, and so on. The uranium atom has the heaviest naturally-occurring nucleus, and it contains 92 protons. All of the heavier nuclei, from atomic number 93 through 118, do not occur naturally and are created through the application of man-made nuclear technologies (like reactors, for example). They are all naturally unstable, and therefore, radioactive.
A subatomic particle with an odd half-integer quantum spin, meaning a spin of S = 1/2, 3/2, 5/2, etc. All subatomic particles are either a fermion or a boson. Examples of fermions include the electron, proton, and neutron.
This is when a metal, after being exposed to an external magnetic field, can retain its internal magnetic field alignment after the external field is removed. It can therefore act as a permanent magnet. When exposed to an external magnetic field, the unpaired electrons throughout the substance align with the field, and when the field is removed, the electrons are able to maintain their alignment as a result of interactions with one another. Iron (Fe), cobalt (Co), and nickel (Ni) are ferromagnetic. Most other metals are paramagnetic, which means they only hold their magnetic alignment in the presence of an external magnetic field. Without it, their unpaired electrons revert back to random alignments.
( CLICK HERE to watch a clip of Arnie Benn offering a possible explanation of the physical mechanism behind ferromagnetism, on the Demystify Sci podcast.)
The frequency of a wave is a measure of how frequently it passes a given point each second, or put another way, how many wave crests pass a given point each second. If two waves pass every second, the frequency is 2 (waves) “per second,” also known as 2 Hertz (Hz). Frequency is measured in “per second,” which means 1/sec (or s-1). This means that frequency is the inverse (or reciprocal) of time, which is measured in sec/1 (or s1). Frequency represents energy. As reflected in the Planck equation, E=h𝜈, the higher the frequency (𝜈) of an electromagnetic wave, the more energy (E) it carries. (Planck’s constant h = 6.626×10-34 m2kg/s.) High frequency ultraviolet waves are more dangerous than low frequency radio waves because the UV waves carry much more energy. With electromagnetic (light) waves, when frequency (𝜈) increases, wavelength (𝜆) decreases, and vice versa. This is because the speed of light (c) is constant, and the three are related by the equation c=𝜆𝜈. Frequency is also the means by which we measure time, whether the frequency of a pendulum, an atom, or a planetary orbit. Without frequency, there is no time measurement.
Gravity is a very weak force exerted by one mass upon another. In fact, it is about 1038 times weaker than electromagnetism. Isaac Newton’s equation for gravity is F=GMm/r2. This equation describes that the force (F) of attraction exerted by one mass (M) upon another mass (m) gets weaker with (the square of the) distance (r). (The gravitational constant G=6.674×10−11 m3kg−1s−2.) According to Albert Einstein, gravity is caused by the fact that mass distorts spacetime. According to Vivian Robinson, the mechanism by which mass distorts spacetime is via the redshift of photons (see more here). Gravity is caused by a change in the refractive index of space, which is caused by the radial differential of the electric permittivity of space. In turn, this is induced by the high frequency electric field oscillations resulting from the rotating photon structure of protons and neutrons. The high frequency nucleon oscillations add to produce a variation in electric permittivity that produces the same deflection for photons of all frequencies. This approach results in a single, simple equation — an equation of quantum gravity: Fz=GMm/r2e𝛼/r — that derives Newton’s inverse square law as a first approximation, Einstein’s field equations as a second approximation, and the bright torus-shaped accretion disc observed (at r=0.5𝛼) around massive objects and galaxy centers as an exact solution. Gravity is therefore an electromagnetic effect. When mass distorts spacetime strongly, the force of gravity is weakened to slightly less than inverse-square (see more here). That is the reason the orbit of Mercury’s perihelion precesses around the Sun in its direction of travel. (If gravity were stronger than inverse-square, such orbits would regress.)
When an object vibrates or when waves interact, if their frequencies are multiples of one another then some of their nodes can overlap perfectly where they meet. The waves then reinforce each other and stabilize themselves into a single symmetrical wave state. Such a harmonic resonance state represents a lower energy state for a system since the waves can now share energy. They will therefore naturally seek out this state if they can. One example of a harmonic resonance would be the wave state set up on a guitar or a violin string when they are played, since multiple harmonics are sounding simultaneously, their waves superimposed along the string. Another occurs when a wine glass is shattered by a sound wave whose resonance matches perfectly with its interior volume. If the sound wave carries enough power, the vibrations it induces in the glass structure can destabilize it, causing it to crack or shatter. Subatomic particles like protons or electrons are also harmonic resonance states involving the rotating photons of various energies that make them up. Overall, quantum states can only be stable and coherent if they are in a state of harmonic resonance. Since there are no stable states between harmonics, it means that harmonic states will be intrinsically quantized. Mathematically, the term ‘harmonic’ means that the wave equations satisfy the double differential of themselves (where ∇2=0).
The directed space-space-space volume element in M.A.R.T. The element can be outwardly-directed, like the spines on a hedgehog, or — a somewhat less comfortable image (for the hedgehog) — inwardly-directed.
When different orbitals in the same electron shell, like an s-orbital and a p-orbital, resonate together since they are occupying the same volume of space. This combination of their electron densities changes their shape in order to achieve greater symmetry and stability. (See Understanding Electrons: Hybridization for more detail.) Boron (B) is the first element on the periodic table that experiences hybridization of its electron shell.
A hydrogen bond is a dipole-dipole force that is particularly strong. Since it involves a hydrogen (H) atom, and since it is the strongest of the intermolecular forces (see bonds), it is referred to as a hydrogen bond. It is not a bond, however, but rather a meaningful electrostatic dipole attraction. The reason its polarity is so strong is because the hydrogen atom is bonded to either nitrogen (N), oxygen (O), or fluorine (F), the three most electronegative atoms on the periodic table. As such, when they bond with hydrogen, they pull so much electron density from it that it creates a very strong dipole. These strong dipoles then interact with one another strongly, and as a result, they have many important chemical properties. Examples include water (H2O), ammonia (NH3), hydrofluoric acid (HF), or the A-T & G-C connections holding DNA’s double helix together. As such, without hydrogen bonding there would be neither liquid water at room temperature on Earth, nor DNA-based life forms to take note of the fact.
The consideration of a complete quantum system, including source, observer, and that which is common between them.
An atom that has either lost or gained one or more electrons. This means there is no longer a balance between the positive protons in the nucleus and the negative electrons enveloping it. The atom therefore has an overall charge. If it lost electrons it will be a positive ion (also known as a cation). If it gained electrons it will be a negative ion (also known as an anion).
In nature, crystals (like salt or quartz) are made of ions. While the term can refer to either positive or negative ions, it is often used to refer to positive ions, as in the case of cosmic rays, for example. Electromagnetic radiation that has enough energy to knock electrons free from atoms is called ionizing radiation. This also makes it hazardous to biological tissue, since changing the charge of a molecule in the body will affect the chemical role it plays.
When a polar and covalently bonded molecule encounters an ion, there will be an attraction between them that will usually be stronger than a dipole-dipole attraction, given that an ion involves a full charge rather than the partial charge of a polar molecule. An example is salt water. When salt (NaCl) is exposed to water (H2O) molecules, which are strongly polar (see hydrogen bonding), the attraction between them causes the salt ions to become separated from the solid salt crystal. This process is called dissolving, and a salt solution is formed.
Ionic bonds occur between metal and non-metal atoms (ex: NaCl). Metals (like Na) occupy the left-side columns of the periodic table, and they represent atoms with low electronegativity that are willing to relinquish one or more outer electrons in order to reach the stability of a full electron shell. Non-metals (like Cl) occupy the right-side columns, and they represent atoms with high electronegativity that strongly attract electrons because they want to complete their almost-filled electron shell. When a metal and a non-metal atom encounter each other, the non-metal will take one or more electrons from the metal. Both therefore achieve the stability of full electron shells, but, since they are charged, they stick together because of their opposite electric charges.
See atomic radius.
This is the amount of energy needed to remove an electron from an atom, to overcome the attraction from its nucleus. (An analogy might be giving a rocket enough thrust to escape a planet’s gravity.) The higher the ionization energy, the harder it is to remove the electron. The lower the ionization energy, the easier it is to remove the electron. The most reactive elements will be those with either low or high ionization energies. This is because they will either be eager to donate an electron or steal an electron (respectively) in a chemical reaction. In general, ionization energy increases as we move to the right in a row on the periodic table, since effective nuclear charge is increasing (see above). In general, ionization energy decreases as we move down a column (Group) on the periodic table, since the valence electrons are further from the nucleus and therefore less strongly attracted to it.
Intermolecular Forces (IMF):
Intermolecular forces are forces of attraction that exist between noble gas atoms or covalently bonded molecules. There are three forms of IMF attraction, based on the types of atoms or molecules involved, and they are generally not as strong as bonds. The main types of intermolecular forces that hold atoms or molecules together are: dispersion forces, dipole-dipole attraction, hydrogen ‘bonding’, and ion-dipole attractions.
Atoms of the same element that have different masses are called isotopes. An element is defined by how many protons it contains in its nucleus. But it can have varying numbers of neutrons, which changes its mass but does not affect its charge because neutrons are neutral. By way of example, the three hydrogen isotopes are protium (1H1), deuterium (1H2), and tritium (1H3).
Some isotopes are stable but others are radioactive. By way of example, uranium has two primary isotopes, the more stable 92U238 and the radioactive 92U235. Over 99% of uranium atoms have a mass of 238 atomic mass units, and only less than 1% have a mass of 235 amu. This is the reason uranium atoms must be separated in a centrifuge in order to collect enough 92U235 for use in a reactor or a bomb.
London Dispersion Force:
When two (neutral) atoms or molecules approach each other, their electron clouds experience mutual repulsion. This causes the electrons on both of them to shift slightly so that a weak polarity is induced. If there are enough electrons present (because the atoms are larger), this polarity can become quite meaningful. If temperatures are low enough to minimize particle movement, this temporary polarity can be enough to stick particles together to form a solid. Example: iodine (I2) molecules at room temperature form a solid, though not bromine (Br2) molecules, which form a liquid, or chlorine (Cl2) molecules, which form a gas. This is because, the fewer electrons they have, the weaker the dispersion forces between them. Liquids feature particles with weaker forces holding them together, while gases have little to no appreciable cohesion between particles.
The “Mathematics of Absolute Relativity Theory”
An evolving Clifford-Dirac algebra designed to encapsulate Absolute Relativity. It aims to develop to a solution of Hilbert’s 6th. It is named in memory and honor of founding Quicyclist, Dr. Martin van der Mark. (See Williamson Equation below. See also: Computational Tools. For a detailed presentation by John Williamson on the subject, see Absolute Relativity Theory: A Proposed Solution To Hilbert’s 6th .)
Magnetic Susceptibility (χm):
This is a measure of how strongly an element will be attracted (or repelled) by an external magnetic field. A negative value means the element is diamagnetic — it has all of its electrons paired and it repels from an external magnetic field. A positive value means the element is paramagnetic — it has unpaired electrons and it is attracted into an external magnetic field.
A force of attraction or repulsion resulting from the flow of electric current or the spin of a charged particle. According to both the Williamson-van der Mark and Robinson models, subatomic particles are made of self-confined knots of electromagnetic radiation. In the toroidal, double-loop rotation of the electron, for example, chirality is immediately a characteristic of the system, and this naturally divides ‘spin reactions’ (magnetism) into two complementary forms that we call north and south. They are simply the two relative chiral orientations of the rotating electromagnetic flow.
In an electron, the (instantaneous) north magnetic pole lies along the axis running through the center of the torus, in the direction of the thumb in a left-handed chiral rotation. South lies in the opposite direction along the same axis. In an isolated electron, the magnetic field averages to zero (due to the electron’s spin). The magnetic moment of the electron emerges in the presence of an external field, which breaks the internal spherical symmetry of an isolated electron.
This magnetic spin then extends its influence into the spacetime around it, distorting its magnetic permeability (μ0), which causes other magnetic fields to respond when they encounter this distortion. The magnetic fields of other nearby electrons will therefore interact with this electron’s field in such a way that north repels north but attracts south. This ultimately derives from the fact that angular momenta are either working together, lowering energy (attraction), or working against each other, increasing energy (repulsion).
Unpaired electrons therefore have magnetic fields as a result of their spins and that of the photons that constitute them. When the unpaired electrons throughout a metal crystal align their magnetic spins, the crystal as a whole manifests a macro-magnetic field. One example of this is an iron (Fe) ferromagnet. When electrons pair up, on the other hand, they superimpose in a way that finds them perfectly anti-parallel, and this cancels out their magnetic fields. One example of this is the electron shell of a helium (He) atom. This pair is no longer attracted towards other magnetic fields, but rather, repels them. This is called diamagnetism, and it happens in order to maintain the pair’s perfect field cancellation, which is their lowest energy state.
On the periodic table, elements on the left side are considered metals and elements on the right side are considered non-metals. The dividing line between them is a diagonal ‘staircase’ of elements that are considered semi-metals or metalloids. These include B, Si, Ge, As, Sb, Te & At. Elements become more metallic in character the further they get from the metalloids towards the left bottom corner of the table. The reason for this is that larger atoms will give their outer electrons more easily because they are further from the nucleus and therefore less strongly bound to it. (See Periodic Trends for more detail.) Metallic bonds occur between metal atoms (ex: bronze, Cu+Sn).
Metallic bonds occur between metal atoms (ex: bronze, Cu+Sn, or pure silver, Ag). Metals occupy the left-side columns of the periodic table, and they represent atoms with low electronegativity that are willing to relinquish one or more outer electrons in order to reach the stability of a full electron shell. When many metal atoms occur together as a solid crystal, they are able to share their outer-shell electrons, which become delocalized. this forms a background matrix of electron density in which the now-positive and full-shell atomic cores remain suspended. They are held in place by their mutual repulsion, as well as their attraction to the 3-dimensional ‘electron gas’ in which they are suspended.
On the periodic table, the elements B, Si, Ge, As, Sb, Te & At are considered semi-metals or metalloids because they lie between the metals and non-metals on the periodic table. This gives them unique properties as a result.
A combination of two of more atoms bonded together. Simple examples include the hydrogen molecule (H2), the oxygen molecule (O2), and the water molecule (H2O). More complex examples include protein and DNA molecules, which can contain hundreds or even thousands of atoms.
Neel Temperature (TN):
The temperature at which the electrons in an antiferromagnetic metal lose their alternating spin alignments and they become paramagnetic. This means they will be able to align in the same direction as an external magnetic field. It occurs because there is enough thermal entropy at this temperature that the spin orientations between unpaired electrons on adjacent atoms can be disrupted.
Network covalent bond:
Network covalent bonds occur between non-metal atoms that form solid crystals (ex: C in diamond). Non-metals occupy the right-side columns of the periodic table, and they represent atoms with high electronegativity that strongly attract electrons because they want to complete their almost-filled electron shell. When many non-metal atoms occur together in a crystal, none will be willing to relinquish an electron. They are therefore forced to share electrons. That way, none of the atoms feel like they have lost an electron but all feel like they have gained one (or more). With multi-directional covalent bonds being formed by each atom with those around it, network covalent bonds form extremely stable and strong structures, resulting in some of the hardest materials on the planet. Diamond is an example, a crystal made of a network of carbon atoms bonded in a perfect tetrahedral crystal lattice.
The neutron is one of the three subatomic particles that make up all atoms. (The other two are the proton and the electron.) Neutrons carry no overall charge and are found in the central nucleus of the atom along with the protons. Protons and neutrons each have more than 1,800 times more mass than an electron.
According to the standard model of physics, the neutron is believed to be a composite particle made up of three quarks — two ‘down’ quarks and one ‘up’ quark — that are held together by a binding energy. The quarks constitute about 1% of the neutron’s mass-energy and the binding energy contributes the remaining 99%.
According to The Robinson Model of Nuclear Binding, like all subatomic particles, the neutron is made of a photon of light of the appropriate energy making two revolutions per wavelength. While a charged particle like the proton will be made of a circularly-polarized photon, a neutral particle like the neutron will be made of a plane-polarized photon. The neutron’s lack of charge arises from the plane-polarization of its inner photon. The orientation of its electric field, as it makes its double loop rotation, is such that the positive and negative fields alternate pointing outwards. While each resonant element within the neutron’s structure has charge, the overall result is a net neutral particle. As a result of its plane-polarization, an isolated neutron is not stable. It usually decays within 15 minutes, splitting into a proton, an electron, and an anti-neutrino. (The latter is the means by which the angular momentum of all the particles involved in the transition is conserved.) When bound to a proton within a nucleus, however, a neutron is stable as a result of the resonance and field sharing between the particles.
While in the case of the electron, the internal photon traces a toroidal path in (momentum) space as it completes its double-loop rotation, in the case of the neutron, it is a little more complex. Since the neutron contains more than 1,800 times the mass-energy of the electron, according to the Robinson Model its rotating photon resonance also contains higher energy harmonics of its fundamental rotation — 1/3rd, 1/9th, and 1/27th harmonics. These charged harmonics resonate in the equatorial plane while the (toroidal) magnetic field loops around in the axial direction.
Since quarks have never been isolated and seem to occur only in their groupings of three, the photon harmonics of the Robinson Model may provide insight into why quarks do not occur except as part of such a stable resonance.
In atoms, neutrons are very important, not simply because they separate the positive protons — whose like charges repel — but because they actually bind the protons together electrostatically. The exterior 1/27th photon harmonic of the neutron is negative, and binds to the positive exterior resonance of the proton through an overlapping ‘division-by-zero’ attraction. As a result of being made of a rotating photon, a neutron has a quantum spin of S=½. The mass of the neutron (939.6 MeV) is very similar to (though slightly larger than) the combined masses of the proton (938.3 MeV) and electron (0.511 MeV). The difference in their masses represents the difference in energy between the neutron state and the electro-proton state that is the hydrogen (H) atom.
The neutrino is the smallest stable subatomic particle. It has no charge, no magnetic moment, a spin of S=½, and an exceedingly small mass-energy content of the order of 10-4 eV. That energy corresponds to the peak energy of the cosmic microwave background radiation temperature of ~2.7°K. Cosmological neutrinos constitute by far the most common component of the universe with a density of about 1012 neutrinos per cubic meter (see more here). Like the electron, it is comprised of a single photon of the appropriate energy making two revolutions per wavelength. Neutrinos can travel at very high speeds approaching the speed of light. While they do not easily interact with matter, neutrinos can be either captured or released during the process of one subatomic particle morphing into another. When a neutron decays into a proton and an electron, for example, a neutrino is also produced as a by-product of the reaction, and it will have a spin opposite to that of the electron. This is the means by which the angular momentum (spin) of all the particles involved in the transition is conserved. In addition, the universe is literally completely filled with neutrinos. Like electrons, neutrinos are not point particles. They are rotating photon loops, just like all other particles, and they have size. There are over a million cosmic neutrinos in every cubic millimeter of space, and each one has a radius of about 2 millimeters. That provides a continuous effect through all of space, a ‘substrate’ with the same quantum spin as the electron, through which all photons must travel.
On the periodic table, elements on the left side are considered metals and elements on the right side are considered non-metals. The dividing line between them is a diagonal ‘staircase’ of elements that are considered semi-metals or metalloids. These include B, Si, Ge, As, Sb, Te & At. Elements become more non-metallic towards the top right corner of the table. The reason for this is that smaller atoms with almost-full electron shells will attract electrons the most strongly. The right-most column, the Noble gases, are generally unreactive because they are both neutral and have full electron shells. (See Periodic Trends for more detail.) Covalent bonds occur between non-metal atoms (ex: H2O).
A region of space occupied by electron density. There are several different types of orbitals that vary in size and shape. The simplest is a sphere that envelops the nucleus, known as an s-orbital.
This is when a substance is attracted to a magnetic field because it contains one or more unpaired electrons. In the presence of an external magnetic field, the magnetic field of an unpaired electron will cause it to align with the magnetic field. This causes cancellation of magnetic field to occur between the electron and the direction of the field, and the substance will therefore experience an attraction into the magnetic field. Many molecules, such as dioxygen (O2), and most metals are paramagnetic.
( CLICK HERE to watch a clip of Arnie Benn explaining the physical mechanism behind paramagnetism, on the Demystify Sci podcast.)
A chart containing all of the elements that have been discovered. They are arranged in order of their number of protons (atomic number), as well as in rows and columns. These reflect the periodic nature of their properties — that those in the same column exhibit similar properties, and those in the same row exhibit similar trends in their properties. This structure was first discovered by Russian chemistry professor, Dmitri Mendele’ev, in 1869
The scalar unit element in MART. It has the same physical dimension as the magnetic field but transforms as a rest-mass rather than a field.
A quantum (or ‘packet’ or bullet) of light energy. Electromagnetic radiation travels in discreet packets called photons. It does not travel in a continuous stream, as we might imagine when we look at a beam of light or a laser. There are usually so many photons being released so rapidly by a light source that it only gives the impression of being a continuous beam. In a typical circularly-polarized photon, the electric and magnetic fields spiral around the axis of travel, 90 degrees apart. The fields complete one revolution around the axis for every wavelength. This gives the photon a quantum spin = 1, making it a boson. The spin of a photon can also be excited up to higher spin states, but they can only be integer spin states, for instance S = 2, 3, 4, etc.
If an atom or molecule has asymmetry in its electron cloud so that one side has more electron density than the other, it will feel partially positive on one end and partially negative on the other end. This separation of charges is called polarity, and it gives such atoms or molecules forces of attraction and repulsion that are meaningful, though not quite as strong as full ionic charges. Polar molecules are therefore attracted to one another. If the electron cloud is symmetrical or identical on opposite sides of the atom or molecule, then it will be non-polar. (Non-polar molecules are only slightly attracted to one another as a result of London Dispersion forces.)
If atoms in a molecule share the electrons is a bond equally (because they are the same atom), then such bonds will be non-polar and therefore purely covalent in nature. If the electrons in a bond are shared unequally (by different atoms), the bond will be polar. The more unequally shared, the more polar the bond. If the sharing becomes so unequal that one atoms ends up stealing the electron completely from the other, ions will result, and an ionic bond will form as a result of the strong electrostatic attraction between the (full) charges.
A positively charged subatomic particle, identical to the electron, except that it has the opposite charge. It is the electron’s ‘anti-particle,’ and this illustrates the concept of antimatter. It is ‘anti’ in the sense of its charge being opposite, and it also has opposite spin. Like the electron, it is made of a single photon of light making two revolutions per wavelength. A positron is thus a self-confined knot of concentrated light energy traveling around itself at the speed of light, and it therefore has a toroidal (donut-shaped) sub-structure in (momentum) space. As a result of the geometry of this double-loop torus, the photon’s positive electric field is pointing outwards at all times, which is what gives the positron its positive charge. When an electron and a positron meet, they unlock each other’s photons’ angular momenta, converting their rotating photons to linear photons in an explosion of pure energy called a matter-antimatter annihilation. A positron has a right-handed spin of S=½, a charge of C=+1.6×10-19 Coulombs, and a mass-energy content of 511 keV.
The proton is one of the three subatomic particles that make up all atoms. (The other two are the neutron and the electron.) Protons are stable, carry a positive charge, and are found in the central nucleus of the atom along with the neutrons. Protons and neutrons each have more than 1,800 times the mass of an electron.
According to the standard model of physics, the proton is believed to be a composite particle made up of three quarks — two ‘up’ quarks and one ‘down’ quark — that are held together by a binding energy. The quarks constitute about 1% of the proton’s mass-energy and the binding energy contributes the remaining 99%.
According to The Robinson Model of Nuclear Binding, like all subatomic particles, the proton is made of a photon of light of the appropriate energy making two revolutions per wavelength. While in the case of the electron, the internal photon traces a toroidal path in (momentum) space as it completes its double-loop rotation, in the case of the proton, it is a little more complex. Since the proton contains about 1,836 times more mass-energy than the electron, its rotating photon resonance also contains higher energy harmonics of its fundamental rotation — 1/3rd and 1/9th harmonics. These charged harmonics resonate in the equatorial plane while the (toroidal) magnetic field loops around in the axial direction.
Since quarks have never been isolated and seem to occur only in their groupings of three, the photon harmonics of the Robinson Model may provide insight into why quarks do not occur except as part of such a stable resonance.
Protons are important because atoms of a given element are identified according to their number of protons. This is called the atomic number, and the periodic table of the elements is laid out in order of atomic number. The first element on the periodic table, hydrogen, has 1 proton. The second element, helium, has 2 protons, and so on. It is also the presence of the protons in the central nucleus that attracts electrons to the atom, specifically in order to neutralize their charge. Neutrons are attracted into the mix not only in order to separate the protons from one another (since their like positive charges repel one another) but to bind the protons together (since, according to the Robinson Model of Nuclear Binding, the exterior resonance of the neutron is negative).
As a result of being made of a rotating double-loop photon, a proton is a fermion and has a quantum spin of S=½. It has a mass-energy content of 938.3 MeV and carries a charge of +1.6×10-19 Coulombs. According to the Robinson Model, the proton’s charge arises from the fact that the orientation of its internal circularly-polarized photon’s electric field, as it makes its double-loop rotation, is such that the positive field polarity is outwardly directed for the majority of its harmonic oscillations, and in particular, for the inner- and outermost ones. This results in a net positive charge for the particle.
‘Quantum’ means ‘countable.’ It means that something happens in integer units. It also implies that changes must occur in discrete steps rather than in a smooth, continuous gradient. These ‘quantum leaps’ of change mean that the process or system is quantized. Stairs and piano keyboards are examples of things that are quantized. Ramps and violins are not. The fundamental reason for quantization is that waves resonate in multiples of their wavelengths, rather than at arbitrary points in between. Subatomic particles are made of photons that make double-loop rotations. They are only stable if their rotations are in multiples of double-loops. A “quantum” of light is called a photon, and it is the amount of electromagnetic energy that is emitted, transmitted, or absorbed in a quantum inter-action. A photon can even have a very high energy, which means that each packet of energy at that wavelength carries a large amount of energy. An example is the gamma ray. Electron clouds in atoms can also only manifest certain discrete electron states. This is because each electron is an identical unit, and because their interactions result in discrete, resonant, stationary wave states. Electron clouds transition between adjacent energy states by emitting or absorbing whole photons (or electrons) — one quantum at a time.
The science that describes light, subatomic particles, and their quantum interactions. It is based upon the idea that all interactions are quantized. Particles and energy states can be described by equations called wave-functions, since they are resonant wave states that are made up of photons.
The 4-dimensional analog of the “Hedgehog” (see above).
(Pronounced like ‘bicycle,’ but with a ‘Qu.’)
A contraction of the words “Quantum Bicycle.” It represents the turning, twisting, and tumbling motion of an electron (or positron) in free (4D) spacetime.
It is also short for ‘The Quantum Bicycle Society,’ whose website you are currently perusing .
In the nucleus of an atom, protons, which carry a positive charge, will repel each other unless they are held together by bonding electrostatically to neutrons, whose outer regions carry negative charge (see The Robinson Model of Nuclear Binding). The balance between protons and neutrons in the nucleus is therefore very important. If a nucleus has either too many or too few neutrons, it lacks stability, and it may therefore begin ejecting or transmuting some of its subatomic particles in order to reach a stable configuration. This is called radioactivity, and it involves the ejection (or sometimes the absorption) of one or more subatomic particles or a photon of electromagnetic radiation, or both, from the nucleus. Alpha radiation occurs when two protons and two neutrons are ejected in a cluster with a 2+ charge called an alpha particle. (It is identical to the nucleus of a helium atom.) Beta radiation occurs when a neutron in the nucleus morphs into a proton by ejecting an electron and a neutrino. In the case of gamma radiation, only a (gamma ray) photon will be emitted. A radioactive decay therefore usually results in the atom turning into a different element. Almost all of the radioactive atoms on the periodic table are those with the highest atomic numbers (and largest nuclei).
This is a measure of how readily an atom will give or take electrons in order to achieve greater stability and symmetry. If it has a low ionization energy and wants to lose electrons, a high ionization energy and wants to gain electrons, or if it has a high electron affinity and thus a strong desire to gain electrons, it will react vigorously with other elements in order to make those electron exchanges.
This refers to the stretching of the wavelength of light radiation. It can be caused by the Doppler effect or by photon interactions with mass and gravity. The Doppler effect occurs when a light source is getting further away, either because we are moving away from it or it is moving away from us. This causes its wavelength to appear longer and its frequency to therefore appear lower. The longer wavelengths of visible light lie at the red end of the rainbow spectrum, hence the name.
Redshift can also result from a photon interacting with (or moving away from) a gravitational field. Photons have inertial mass, and they are therefore affected by gravity. Such interactions will reduce their energy. A reduction in energy means a reduction in frequency, and since the speed of light is constant, this results in an increase in wavelength (see more here).
Root-energy (as in ‘square-root’ energy) refers to quantities that need to be ‘squared’ in order to represent an energy density. These include field-level elements such as electric field, magnetic field, and the quantum mechanical wave function, ψ. (In quantum mechanics, energy density is proportional to ψ†ψ.)
All 16 elements of the 𝚵𝒢 term in the Williamson equation represent root energies, at the level of field.
The fabric of space and time, whatever it actually is, has two basic properties that we consider: its electrical permittivity (ε0) and its magnetic permeability (μ0). The former describes the extent to which spacetime can hold (or allow the passage of) electric fields, and the latter, the same for magnetic fields. The two properties are intimately related to the speed of light (c) because light is electromagnetic and interacts with space both electrically and magnetically. It can only travel because of its electric and magnetic interactions with spacetime. The three properties are related according to the equation ε0μ0=1/c2.
The term spacetime also relates to the fact that space and time are part of the same ‘stuff’ and cannot be separated, something that may seem unintuitive since we tend to think of time and space as separate things. Spacetime is also distorted by the presence of mass, which gives rise to gravity. Relativity also describes how aspects of space and time appear to become distorted under certain conditions so that the speed of light should appear constant to every observer in every reference frame.
Mathematically, it is interesting to note that different forms of energy interact with spacetime in different ways. The three variables of space are x, y, z, and the one variable of time is t. Spacetime is therefore 4-dimensional: x, y, z, t (and their inverses). The underlying nature of electric field is that it is a (3-component) flow, a rate of change of space by time (dx/dt, dy/dt and dz/dt), like velocity. The underlying nature of the (three component) magnetic field is that it is a twist, a rate of change of space by perpendicular space (dx/dy, dy/dz and dz/dx). No t. It makes things go around in a circle. Angular momentum (spin) is the rate of change of momentum with respect to perpendicular space, taking the form of d/dx(dy/dt).
The process of a photon being reflected back out into space from Earth. (If we could hear at the speed of light, it may also be the sound it makes.)
Many subatomic particles have spin because they are made of a confined photon of light traveling in a circle, a double-loop rotation, at the speed of light (see electron). This is angular momentum at the quantum level. In the case of a charged particle, such as the electron, the (circularly polarized) photon of light making up the particle also has an intrinsic angular momentum because it spirals as it travels. According to the Williamson-van der Mark model (see more here), electrons may also contain a third level of angular momentum, since the photon’s intrinsic spin should cause the ring-shaped structure to tumble in order to conserve angular momentum (depending on the presence of an external magnetic field). According to the Robinson model, only charged particles contain intrinsic photon spin because they are made of circularly polarized photons. Neutral particles are made of plane polarized photons, and their angular momentum therefore arises entirely from their photon’s double-loop rotation (see more here).
An absolutely relativistic quantum mechanics that does not begin with the particle as an axiom, but investigates the substructure of subatomic particles that give rise to their properties. It is built upon the theory of absolute relativity forwarded by John G. Williamson and Martin B. van der Mark, and is encapsulated by the Williamson equation 𝒟𝜇𝚵𝒢 = 0, where 𝒟𝜇 is a Dirac-Clifford four-vector derivative, and 𝚵𝒢 is the root-energy in sixteen spacetime forms including a Lorentz-invariant scalar ‘point’ mass-energy. This is termed the mathematics of absolute relativity (M.A.R.T.), represented by this equation, as well as quantum inversion. (See Absolute Relativity Theory: A Proposed Solution To Hilbert’s 6th for a detailed presentation by John Williamson on the subject.)
The stupidly-strong force holding the electron together. (Formerly known as the ‘Poincaré stresses.’) If you doubt it, smash an electron into a proton at high GeV and see who’s left standing. Unscathed.
A quantity measured in terms of the regular vibrations or oscillations — the frequency — of a harmonic system. Typical examples include using the revolutions of the Earth around the Sun to designate a year, or the vibrations of a cesium atom in an atomic clock to designate a second. The reason that time is measured in seconds (sec) is because frequency is measured in “per second”s (1/sec), and an event’s duration is the inverse of how frequently it occurs.
Time is also not a separate ‘thing,’ but is intimately interconnected with the concept of space (see spacetime). Since all radiation and matter in the universe are made of photons, and since all photons are energy waves of a specific frequency traveling at the speed of light, Relativity will affect our perception of frequency, and therefore, also our perception of the flow of time.
( CLICK HERE to watch a clip of John Williamson explaining ‘time’ on the Demystify Sci podcast.)
The distance from the beginning of one wave to the beginning of the next — the length of one complete cycle of a wave. With electromagnetic (light) waves, when wavelength (𝜆) increases, frequency (𝜈) decreases, and vice versa. This is because the speed of light (c) is constant, and the three are related by the equation c=𝜆𝜈.
𝒟𝜇𝚵𝒢 = 0
where 𝒟𝜇 is a Dirac-Clifford four-vector derivative, and 𝚵𝒢 is the root-energy in its 16 spacetime forms, which includes a Lorentz-invariant scalar ‘point’ mass-energy (see below).
It is a fully relativistic equation containing a set of coupled linear differential equations, and requiring no further relativistic corrections. It is a non-commutative Clifford-Dirac algebra, a quaternion-like algebra, which is essential for accurately representing rotations in four dimensional (x, y, z, and t) spacetime. This equation lies at the heart of the Mathematics of Absolute Relativity Theory, or MART (see above). (For a short overview of the Williamson equation, see this excerpt from Arnie Benn’s presentation on the mathematics of sub-quantum spin (min: 49:35). For a detailed presentation by John Williamson on the subject, see Absolute Relativity Theory: A Proposed Solution To Hilbert’s 6th.)
The 16 root-energy spacetime forms included within the 𝚵𝒢 term are divided into four 3-dimensional sets and four 1-dimensional sets, yielding 16 dimensions. These 16 dimensions are all (only) different mathematical combinations of the 4 dimensions of spacetime, x, y, z, and t — along with their inverses (x-1, y-1, z-1, and t-1). For example, the dx/dt effect of an electric field upon a charge can also be represented, by way of simplifying its dimensionality, as xt-1.
The 16 root-energy spacetime forms are:
αi is vector (potential) (x, y, or z)
αij is the bi-vector magnetic field (xy-1 or yz–1 or zx-1)
α0i is the bi-vector electric field (xt-1 or yt–1 or zt-1)
α0ij is the tri-vector spin ‘field’ (x-1yt-1 or y-1zt–1 or z-1xt-1)
α0 is time (t)
αP is ‘pivot’ (root-mass) — in this model, mass is a dynamic term
α123 is tri-vector, a ‘directed 3-volume’ element (x, y, and z)
α0123 is a ‘quadri-vector’ or pseudo-scalar, a ‘directed 4-volume’ element (x, y, z, and t)
The full expansion of the terms:
By way of example, the highlighted terms above represent the three α0ij quantum spin components.
This underscores the power of this new absolute relativistic sub-quantum mechanics, as well as the dynamical detail to which the Williamson equation allows us to gain access. It takes our understanding of matter and energy to the next level — to the sub-quantum level.
The following diagram represents the mathematical transformations that occur within the dynamics of MART.