Particle physics is the science of dividing reality into smaller and smaller pieces: particles. In the classical world, materials and forces appear continuous (able to be subdivided infinitely) but they are actually quantized into fundamental indivisible units. Atomic theory teaches that ordinary matter is composed of molecules which are in turn composed of atoms held together by the electromagnetic force. Ordinary atoms are in turn composed of nuclei and electrons bound together by an exchange of photons (quanta of the electromagnetic force). Note that in particle physics, forces are modeled as exchanges of particles. Particles cannot move faster than a finite celerity constant so that there are no instantaneous forces at a distance. Ordinary nuclei are then composed of nucleonic baryons (protons and neutrons) bound together by an exchange of mesons (primarily pions) or the residual strong nuclear force. Baryons and mesons are collectively called hadrons. Hadrons are composed of partons: quarks, antiquarks, and gluons. In an ordinary hadron, quarks and/or antiquarks are bound by an exchange of gluons (quanta of the strong nuclear force). Electrons, photons, quarks, antiquarks, and gluons are all believed to be elementary particles (elementons) which means that they cannot be further subdivided. There are some theories that postulate that elementons are composed of smaller particles such as preons but there is currently no evidence of or theoretical need for this.
One of the most popular "theories of everything" is membrane theory or M-theory. M-theory postulates that everything in the Universe is composed of two-dimensional objects called membranes that vibrate and rotate in eleven-dimensional spacetime. The additional dimensions are compactified or made very small so that the classical Universe has only four macroscopic dimensions (length, width, height, and time). Superstrings are the one-dimensional equivalents of membranes but M-theory has since superceded string theory. It was eventually proven that membranes (supermembranes) and strings (superstrings) are just different mathematical formulations of the same fundamental object. "Super-" refers to the supersymmetric variants. Supersymmetry is now widely regarded as necessary for unification so that all membranes should be supermembranes. Membranes are theoretical objects and alternatives to M-theory exist. The primary theoretical necessity of membranes is to avoid singularities (massive objects of zero size and thus infinite density). Since membranes have nonzero surface area and are fundamental objects, they cannot be compressed or contracted to zero size.
Particles are generally classified by their spins (quantized rotational angular momenta, s = L/ħ) with integer-spin particles being called bosons and fractional-spin particles being called fermions. Spin is quantized as multiples of one half of the Dirac constant or rationalized Planck constant (ħ). Bosons obey Bose-Einstein statistics which allows many bosons to occupy identical quantum states. This behavior causes bosons to be responsible for what in classical physics is called force and energy, such as the phenomena of light, electricity, and magnetism (photons of electromagnetic force or energy) or gravity (gravitons of gravitational force or energy). Fermions obey Fermi-Dirac statistics which requires that each fermion be in a unique quantum state. This behavior causes fermions to form what is classically known as matter. The structure and subdivision of matter discussed previously is specifically because individual fermions are held apart into unique quantum states and then bound together by bosons sharing quantum states. Bosons are further subdivided into three classes based on their spins: scalar bosons have spin zero, vector bosons have spin one, and tensor bosons have spin two.
Supersymmetry is a theory that unifies bosons and fermions. Supersymmetry is required to exist by many "theories of everything" including M-theory. The first major unification in theoretical physics was between electricity and magnetism when they were realized as two different manifestations of a single electromagnetic force. Light was then shown to be an additional manifestation of electromagnetism, existing as ondulations in the electromagnetic field. Years later, the electromagnetic force and the weak nuclear force were likewise shown to be two different manifestations of a single electroweak force. This provided the fuel for theoretical physicists to pursue a grand unification theory (GUT) that could unify the newfound electroweak force with the strong nuclear force and eventually to merge together a grand unified force with the gravitational force into a single theory of quantum gravity. Eventually it was realized that both grand unification and M-theory typically required supersymmetry in order to work.
Supersymmetry proposes that every known elementon has a supersymmetric partner (superpartner) with a difference in spin number of ½ (one angular momentum quantum) but otherwise identical except for mass. Doubling overnight the number of particles predicted to exist might seem a bit outrageous but this has already happened several times in physics history. The first such doubling was with the discovery of antimatter. Every known elementon has an antimatter partner (antielementon) that is identical in every way except with opposite electric charge and the unique property that when an antiparticle meets its matter counterpart, they annihilate into photons. This is because antimatter can be interpreted as matter moving backward in time so that annihilation can be thought of as what happens when the particle meets itself (an ominous warning to time travelers). Likewise every quark comes in three different generations, each of which comes in three different color charges, each of which comes with its own antimatter partner, each of which also has a supersymmetric partner. The way to think of this is as unfolding symmetries. Each symmetry mirrors the particles in different ways to create reflections except that the reflections have different properties from the originals such as a change in electric charge number, color charge number, or spin number.
The table below illustrates the symmetries between leptons, quarks, antileptons, antiquarks, sleptons, squarks, antisleptons, and antisquarks. Leptons are nonsupersymmetric fermionic (half-spin) elementons with zero color charge (c = 0) whereas quarks are nonsupersymmetric fermionic (half-spin) elementons with nonzero color charge (c ≠ 0). Antileptons and antiquarks are the antiparticles of leptons and quarks. Sleptons and squarks are scalar (spin-zero) bosons as the supersymmetric partners to half-spin leptons and quarks. Antisleptons and antisquarks are then the antiparticles of sleptons and squarks with the same scalar zero spin but opposite electric charge. Antimatter particles are indicated with a macron whereas supersymmetric particles are indicated with a tilde. Electric charge numbers are in superscript. Note how the sign (polarity) of the electric charge flips from positive to negative when reflecting between matter and antimatter and then also note how the electric charge changes by ±1 when reflecting from the bottom half of the table (charged leptons and down-type quarks) to the top half of the table (neutral leptons and up-type quarks). Supersymmetry just extends this folding out one more time with a change in spin number instead of a change in electric charge number.
| ν̃τ0 | ν̃μ0 | ν̃e0 | ũ+2/3 | c̃+2/3 | t̃+2/3 | s = 0 |
|---|---|---|---|---|---|---|
| ν̅̃τ0 | ν̅̃μ0 | ν̅̃e0 | ū̃−2/3 | c̄̃−2/3 | t̄̃−2/3 | s = 0 |
| ν̅τ0 | ν̅μ0 | ν̅e0 | ū−2/3 | c̄−2/3 | t̄−2/3 | s = −½ |
| ντ0 | νμ0 | νe0 | u+2/3 | c+2/3 | t+2/3 | s = +½ |
| τ−1 | μ−1 | e−1 | d−1/3 | s−1/3 | b−1/3 | s = −½ |
| τ̅+1 | μ̅+1 | ē+1 | d̄+1/3 | s̄+1/3 | b̄+1/3 | s = +½ |
| τ̅̃+1 | μ̅̃+1 | ē̃+1 | d̄̃+1/3 | s̄̃+1/3 | b̄̃+1/3 | s = 0 |
| τ̃−1 | μ̃−1 | ẽ−1 | d̃−1/3 | s̃−1/3 | b̃−1/3 | s = 0 |
| c = 0 | c = 0 | c = 0 | c ≠ 0 | c ≠ 0 | c ≠ 0 |