In the last two centuries, physicists have formulated the theory of the atom extensively. All matter is made up of individual particles called “atoms”. Although the Greek root “atom” means indivisible, physicists found that atoms consist of electrons which orbit a nucleus. The electrons can be separated from the nuclei. Hence the atom is not indivisible. Modern physicists find that protons and neutrons can also be further subdivided into particles known as quarks. Each proton and neutron consists of three quarks.

Thus modern physics theorizes that many particles constitute the fundamentals of matter. These particles are of several kinds and combine in various ways to form different kinds of matter. The study of these several particles is called Particle Physics. The main theory which describes the different particles and their various properties is called the Standard Model.

Under the Standard Model, there are 61 fundamental particles (those that have not yet been divided into smaller constituents). These are called elementary particles. They are of three types: quarks, leptons and gauge bosons.

Based on spin, there are two types of particles: fermions and bosons. Fermions are named after scientist Enrico Fermi while bosons are named after Surendra Nath Bose. Fermions are defined as particles with half-integral spin while bosons are particles with whole-integral spin. The spin of a particle is a measure of its intrinsic angular momentum. Spin is a quantum mechanical concept and the spin of a particle usually refers to its spin quantum number. This number multiplied by some constant (usually a multiple of Planck’s constant) gives the particle’s spin angular momentum, a vector quantity. Particles also possess extrinsic angular momentum, which is by virtue of the motion involved in their current quantum state. This is the orbital angular momentum. Adding the spin and orbital angular momentum together gives the particle’s total angular momentum.

Thus a fermion will have a spin quantum number of 1/2, 3/2, 5/2 or any other multiple of 1/2. A boson will have a spin of 0, 1, 2 and all other positive integers. Quarks and leptons are fermions while gauge bosons are bosons. If one considers the probabilities of finding particles in different states, fermions obey Fermi-Dirac statistics while bosons obey Bose-Einstein statistics. Two or more fermions cannot occupy the same quantum state whereas two or more bosons can do so.

The leptons and quarks both have 3 generations with each generation having 2 different types of particles (known as flavors). Thus there are 6 lepton flavors and 6 quark flavors. The two first generation leptons are the electron and the electron neutrino, the second generation leptons are the muon and muon neutrino while the third generation leptons are the tau particle and the tau neutrino. The electron, muon and tau particle are all negatively charged (with a charge of -1) and carry an electrical charge. They carry no color charge. The neutrinos are all neutral and carry no electric charge nor any color charge. All the leptons have a spin of 1/2.

Like spin, electric charge and color charge are intrinsic properties of particles. Electric charge is that charge by virtue of which particles attract and repel each other due to electromagnetic forces. Color charge is that charge by virtue of which particles are glued together by the strong nuclear force. There is yet another intrinsic property of the leptons known as the generational lepton number. The electron lepton number is +1 for electrons and electron neutrinos while it is 0 for all other lepton flavors. Similarly, the tau lepton number is +1 only for tau particles and tau neutrinos while the mu lepton number is +1 only for muons and muon neutrinos. Elsewhere, the tau lepton and mu lepton numbers are 0.

There also exist antiparticles of all the 6 lepton flavors described. The anti-electron (also called the positron) has a positive electric charge (+1) and an electron lepton number of -1. The positron is otherwise identical to the electron in mass, spin, etc. Similarly, the anti-muon is positively charged with a mu lepton number of -1 while the anti-tau particle is positively charged with a tau lepton number of -1. All 3 anti-neutrinos are electrically neutral but have generational lepton numbers of -1. All 12 leptons are colorless (they have no color charge).

The 6 neutrino leptons are essentially massless and only interact via the weak nuclear force. The other 6 leptons are massive with the tau pair the heaviest, the muon pair lighter and the electron pair the lightest. The generations can be understood as follows: the taus decay into muons or electrons, the muons decay into electrons and the electrons do not decay over very long time periods. The physicists today cannot tell whether neutrinos decay or not.

The first generation quarks are the up and down quarks, the second generation quarks are the charm and strange quarks while the third generation quarks are the top and bottom quarks. The up, charm and top quarks are known as the up-type quarks while the other 3 are the down-type quarks. These are collectively the 6 quark flavors. All up-type quarks have an electric charge of +2/3 while all down-type quarks have an electric charge of -1/3. There are 6 anti-quarks corresponding to these 6 quarks with opposite electric charges, eg. the 3 up-type anti-quarks have -2/3, etc. All quarks have a spin of 1/2.

Like the lepton number, the quarks have an intrinsic property called the baryon number. All quarks have a baryon number of +1/3 while all anti-quarks have a baryon number of -1/3. Physicists have defined other properties of quarks such as isospin, charm, strangeness, topness and bottomness. These 5 are called the flavor quantum numbers. The isospin of an up quark and down anti-quark is +1/2 while that of an up anti-quark and down quark is -1/2. All other quarks and anti-quarks have an isospin of 0. The charm of the charm quark is +1 and 0 for the other quarks. The strangeness of the strange quark is -1 and 0 for others. The topness of only the top quark is +1 and with the others having 0 topness. The bottomness of only the bottom quark is -1. The corresponding anti-quarks have the relevant quantum numbers negated, eg. the strange anti-quark has strangeness of +1, etc.

Quarks often combine with each other to form larger particles called hadrons. These hadrons are glued together by the strong nuclear force (like atoms are held together by the attractive electromagnetic force). Hadrons are of two types: mesons and baryons. Mesons always consist of a quark and an anti-quark thus having a baryon number of 0. Baryons consist of 3 quarks thus having a baryon number of 1. There can also be anti-baryons which consist of the corresponding anti-quarks (hence having baryon number -1). Concerning spin, mesons are bosons while baryons are fermions. It can be seen that the baryon number of a hadron is found by adding the relevant baryon numbers of the constituent quarks. Similarly, the 5 flavor quantum numbers (isospin, charm, strangeness, topness and bottomness) of hadrons can also be calculated by adding those of the individual constituent quarks.

Examples of baryons include protons and neutrons. Protons are made up of 2 up quarks and 1 down quark. Neutrons are made up of 1 up quark and 2 down-quarks. Anti-protons have 2 up anti-quarks and 1 down anti-quark. Similarly, anti-neutrons have 1 up and 2 down anti-quarks.

While interacting via the electromagnetic or strong nuclear force, the 5 flavor quantum numbers are conserved, eg. suppose some hadrons interact to form new hadrons via the electromagnetic or strong nuclear force, then the total isospin, charm, etc. of all initial particles is equal to the corresponding totals of the final particles. However, these quantum numbers are not conserved when particles interact via the weak nuclear force. In fact, quarks can change from one flavor to another via the weak nuclear force. Some details related to such changes can be studied using a mathematical device known as the CKM Matrix.

Physicists also define the hypercharge of a quark. It is defined as:

Y = C + S + T + B + B’

where Y is the hypercharge, C the charm, S the strangeness, T the topness, B the bottomness and B’ is the baryon number. The electric charge of a particle, Q can be expressed in terms of the hypercharge and the isospin I:

Q = I + 0.5Y

In other words, the electric charge is the sum of the isospin and half the hypercharge. The hypercharge is conserved only by strong nuclear interactions, not weak nuclear interactions. The quark flavor does not change if the hypercharge is conserved.

For a general system consisting of both quarks and leptons, quantitative attributes of the total system such as mass-energy, momentum, electric charge, baryon number and the generational lepton numbers are also conserved during interactions. Of these, the baryon and lepton numbers are conserved most of the times but not all the time.

If one wishes to go into more depth, one could explore other concepts such as the weak isospin, weak hypercharge and their relevance in the electroweak force. While the isospin is a quantum number that relates to the strong nuclear force, the weak isospin is another quantum number that relates to the weak nuclear force. Both leptons and quarks have a weak isospin while only the up and down quarks have an isospin. The weak hypercharge Z is defined such that the electric charge of the particle is the sum of the weak isospin and half the weak hypercharge. The electroweak force is a unification of the weak nuclear and electromagnetic forces. Details can be studied from Wikipedia and other sources. It can be observed that the leptons do not interact via the strong interaction due to the lack of isospin, color charges, charm, strangness, etc.

Besides electric charges, the flavor quantum numbers and the weak isospin, quarks also possess color charges. The color charges are of three types: red, green and blue. The color charges work such that red + green + blue = white or colorless (no color charge). Anti-quarks have anti-colors which serve as complementary colors to the colors. So anti-quarks have three anti-colors: anti-red (or cyan), anti-green (or magenta) and anti-blue (or yellow). Note that red + anti-red = white, etc. Quarks combine into hadrons such that the total color of the hadron is zero. Thus in a meson, a quark with a certain color must combine with an anti-quark with the corresponding anti-color. In a baryon, the three quarks must have the three different colors. In an anti-baryon, the three anti-quarks must have the three anti-colors. Like the electric charge makes particles interact via the electromagnetic force, the color charge makes particles interact via the strong nuclear force.

The study of color charge is known as Quantum Chromodynamics (QCD). The corresponding study of the electric charge of elementary particles is Quantum Electrodynamics (QED). Each quark can have any of the three colors while each anti-quark can have any of the three anti-colors. Thus taking 6 quark flavors along with their anti-particles and 3 colors (or anti-colors), there are 36 quarks. As for the quark generations, the third generation quarks i.e. the top and bottom quarks are the heaviest and most unstable. The charm and strange quarks are lighter and relatively more stable. The up and down quarks are the lightest and most stable. Generally, top and bottom quarks decay into 2nd generation or 1st generation quarks while charm and strange quarks decay into 1st generation quarks. Some details of quark decays via the weak interaction can be studied using the CKM Matrix.

Totally there are 48 elementary fermions: 12 leptons and 36 quarks. The remaining are the elementary bosons, known as gauge bosons or force carriers. These are 13 in total, 12 of which represent 3 fundamental forces or interactions and the remaining 1 is the Higgs boson. These force carriers are the particles which make the fermions interact with each other, eg. electrons are repelled from each other because they interact with each other via photons, etc. Out of the first 12, there are 8 gluons corresponding to 8 different color states, 3 types of weak nuclear interaction gauge bosons and 1 photon. The gluons aid in the strong nuclear interaction amongst quarks and hadrons. The photon aids in the electromagnetic interaction between particles. The 3 weak nuclear interaction bosons are the W+, W- and Z bosons. The W+ and W- bosons are electrically charged (with +1 and -1 respectively) and can be considered a particle anti-particle pair. The Z boson is electrically neutral and can be considered its own anti-particle. These 3 aid in the weak nuclear interaction between particles. Modern physicists sometimes combine the electromagnetic and weak interactions into one electroweak interaction.

The most recent particle found by physicists is the Higgs boson, which is believed to cause the mass of all particles in the universe to arise. Thus there are totally 61 elementary particles under the standard model, 12 leptons, 36 quarks and 13 gauge bosons. Of the 12 leptons, there are 3 generations, 2 flavors in each generation and each flavor has a particle and an anti-particle. Of the 36 quarks, there are 3 generations, 2 flavors, each flavor has a particle anti-particle pair and each of these can have three colors or anti-colors. Of the 13 gauge bosons, there are 8 gluons, 1 W boson particle anti-particle pair, 1 Z boson, 1 photon and 1 Higgs boson.

The standard model explains the force carriers of only 3 of the 4 fundamental forces. These 3 are the strong nuclear force, the weak nuclear force and the electromagnetic force. The gravitational force is not explained. Although some physicists postulate the graviton to be a corresponding gauge boson, this has not yet been widely accepted as a part of the standard model.

One can study in detail the properties of each particle and the ways in which the particles interact with each other, combine to form larger particles and decay into other particles. Particle Physics is indeed a vast field where one is more dazzled by how much more there is to learn than what has already been found by physicists.

The information provided in this article is incomplete and very basic due to my lack of knowledge and should be verified from a more knowledgeable source. I largely consulted Wikipedia while preparing this article. Those who wish to learn more should do the same and also consult the works of Particle Physics experts or other Particle Physics books.

As a side note, the Jain theory of atoms is actually quite interesting. They have defined an atom (Paramanu) as the fundamental unit of matter which is completely indivisible. The atom occupies only one infinitesimal space-unit (Pradesha).

These atoms combine to form larger molecules (Skandhas). These molecules can combine to form yet larger molecules or they can break up into their constituents. Thus matter continuously undergoes fission and fusion.

Some molecules are made up of a few countable atoms, some are made of an uncountable number of atoms and some are made of infinite atoms. One space-point has the capacity to support infinite atoms at once.

Perhaps the elementary particles particle physicists have discovered today are merely larger “molecules” that can be further divided into yet tinier constituents which could in turn be further divided. Perhaps we need to infinitely divide an electron into more fundamental particles until we reach the undivided atom the Jains speak of. Nevertheless I do hope we all see the day when our knowledge can grasp that undivided atom.