Particles and Forces

Spin

Before I get into the different types of particle there’s a bit more back story you need. All particles have a property called spin. The spin of a particle has a fixed value that depends only on the type of particle. Spin can also have direction, up or down and the particle carrying the spin can have a handedness, left or right. This gives four possible combinations shown below

spin

I admit, this looks quite confusing but it can be possibly simplified with the help of your own left and right hands. If you get your right hand in a grip position with your thumb sticking straight up then your fingers represent the handedness of the particle, or direction of spin, and your thumb represents whether the particle is orientated up or down. For example, if a clock is thrown with its face directed forwards it’s Left-handed. In order to represent its clock hands motion with your gripped fingers and the overall clock flying through the air motion with your thumb you have to use your left hand.

Types of Particle

Throughout the whole of the known universe there are only 2 types of particle. Particles that make up matter, and particle that carry force. They are the only 2 types found so far. Now you may be thinking that, yes there may only be two categories but I bet they’re filled with hundreds of different subgroups and types. Thankfully this isn’t the case, particles follow specific rules and once you known them everything gets a lot easier.

The two groups are called Fermions and Bosons

Fermions

Fermions are all particles that make up matter. The name comes from the fact that all particles of matter follow a certain set of laws called Fermi-Dirac Statistics, developed by Enrico Fermi and Paul Dirac in 1926.

All fermions in existence possess half integer spin i.e. 1/2, 3/2, 5/2 etc, for example every electron in the universe possesses a spin of 1/2. Fermions also obey the Pauli exclusion principle. This sounds complicated but it’s relatively simple to describe. What it means is that only certain combinations of matter can exist in the same space, more specifically it states that

No two identical fermions may occupy the same quantum state simultaneously

For example take Helium. It’s got a lowest energy shell for the electrons. You can put one electron in easy, however the Pauli Exclusion principle says 2 electrons can’t occupy the same quantum state so the second one has to have the opposite spin. This then allows the 2 electrons because spin is part of the quantum state of the electron, so the two electrons are occupying different quantum states. The spin however can only be one of two things, up or down (+1/2 or -1/2). If for example you had a lithium atom, which has three electrons then the third electron can’t fit into the 1st shell. So to fit it in it has to move up to the next shell. The entire Periodic table is built up from this principle.

There are two different types of fermions, Leptons and Quarks.

Leptons

There are six sub-atomic particles that make up the leptons; the Electron and the Electron Neutrino, the Muon and Muon Neutrino (which are basically heavier versions of the Electron and the Electron Neutrino), and the Tau and the Tau Neutrino (which are heavier versions still). The electron, muon and tau all have charges of -1 whereas all the neutrinos have charges of 0

(1)   \begin{equation*} \begin{tabular}{ c c c c } \hline Lepton Group & Name & Charge & Mass (estimate)\\ \hline 1 & Electron (e) & -1 & 9.10938291\times 10^{-31}kg \\ 1 & Electron Neutrino ($\nu_e$)& 0 & Small, but non-zero \\ 2 & Muon ($\mu$)& -1 & 1.883531\times 10^{-28}kg \\ 2 & Muon Neutrino ($\nu_{\mu}$) & 0 & Small, but non-zero \\ 3 & Tau ($\tau$) & -1 & 3.1675 \times 10^{-27}kg \\ 3 & Tau Neutrino ($\nu_{\tau}$& 0 & Small, but non-zero \\ \end{tabular} \end{equation*}

Quarks

Quarks are the other type of matter particle along with the leptons. Like the leptons there are six quarks, grouped in 3 sets of 2, with each successive group basically just a heavier version of the previous. Like the leptons the quarks in each set have a charge difference of 1, but instead of nice whole numbers the charges of quarks come in fractions of e. The six quarks are named Up, Down, Charmed, Strange, Top and Bottom

(2)   \begin{equation*} \begin{tabular}{ c c c c } \hline Quark Group & Name & Charge & Mass (estimate)\\ \hline 1 & Up (u) & 2/3 & 4.17\times 10^{-30}kg \\ 1 & Down (d) & -1/3 & 9.08\times 10^{-30}kg\\ 2 & Charm (c) & 2/3 & 2.30\times 10^{-27}kg \\ 2 & Strange (s) & -1/3 & 1.78\times 10^{-28}kg \\ 3 & Top (t) & 2/3 & 3.09 \times 10^{-25}kg \\ 3 & Bottom (b) & -1/3 & 7.45 \times 10^{-27}kg \\ \end{tabular} \end{equation*}

Hadrons, Mesons and Baryons

Physicists seem to love their labels and groups. As soon as you put quarks together in groups then the resultant particles are called Hadrons. But the names and classes don’t stop there. If you make a Hadron out of 2 quarks it’s called a Meson and if you make a Hadron out of 3 quarks it called a Baryon.

The reason you get groupings of 2 or 3 quarks is because of their colour. Quarks can be red, green or blue and anti quarks can be anti-red anti-green and anti-blue. The particles aren’t actually coloured (for one thing they’re much smaller than the wavelength of visible light). The “colours” are just labels. Quarks have a property that can take 3 distinct values, so physicists called those values red, green and blue.

Quarks exist in groups that have no overall colour charge, so you can get groups that are red+blue+green=white, anti-red+anti-blue+anti-green=white, red+anti-red=white, blue+anti-blue=white or green+anti-green=white, i.e. either 3 quarks or anti quarks together or 1 quark and 1 anti quark together; Baryons and Mesons.

Particles like the proton and neutron are examples of Baryons as they are comprised of 3 quarks, while particles like the \pi^+ and \pi^- are Mesons as they are made from a quark and an anti quark, however all four of them are types of Hadrons.

 Bosons

Bosons are the particles that carry force. They are characterised by having whole integer spin e.g. -1, 0, 1, and don’t obey the Pauli Exclusion Principle, so you can have loads of them in the same space. Each of the fundamental forces of nature has its own Bosons.

For Electromagnetism the force carrier is the Photon. They are sometimes called virtual photons as they only exist for very small intervals of time or space. If an electron gets near another electron it emits a virtual photon which is absorbed by the second electron and lets it know it need to move away.

PF-FeynmanDiagram1

This is a Feynman Diagram, named after the amazing physicist Richard Feynman. Its an easy way of describing or visualising particle interactions. Particles are represented as lines, either straight or wavy, and interactions are depicted as a vertex of the lines. Most of the time the lines will have arrows to show more specifically how the particles are moving. In the above example two electrons move towards each other, then we have the interactions with the boson of the electromagnetic force, then they move away from each other.

For The Strong Nuclear Force the boson is the Gluon. It has zero rest mass and zero charge. Despite there only being one boson for this force it can come in different Colours.

For Gravity the boson is theorised to be the Graviton. Its is thought to have zero rest mass and zero charge but has not been discovered yet.

The Weak Nuclear Force looks like the odd one out. It has three bosons, the W^+, W^- and the Z^0. None of them are massless like the photon, on average they’re about half the mass of a caffeine molecule.

Forces

What is stuff made of? Compounds, molecules, atoms, electrons and quarks. At the moment you can go no further. Forces are the same, there are loads of them about but really there just combinations of 4 fundamental forces. This isn’t enough for most physicists (myself included) and so research has been going on for a long time now to try and find just one description of all of them. James Clerk Maxwell did it with Electricity and Magnetism, so why cant we do it with the rest. Actually we partially have, but more on that later . For now here are the 4 forces.

Gravity

Gravity is the weakest of all the forces, which seems odd at first. It holds planets together and holds them in their orbits. It is also the longest ranged force mainly because it is always attractive. You can easily overcome gravity just by jumping, that’s how weak it is. Gravity is felt by anything with mass. If it has mass, gravity can act on it. Gravity works via the following law

    \[F=-G\frac{m_1m_2}{r^2}\]

It’s an inverse square law so it gets weaker the further you move away, it also gets stronger for objects of larger mass.

Electromagnetism

Electromagnetism is 1 trillion, trillion, trillion times stronger than gravity. However unlike gravity which is always attractive, electromagnetism can be both attractive and repulsive. This is because there are 2 types of electromagnetic “matter”, positive charge and negative charge. Electromagnetism follows the following law

    \[F=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\]

You can see that its very similar to the law for gravity. It’s inversely proportional to distance and is stronger for objects of larger charge. It’s a long ranged force, however the mix of positive and negative charge cancel each other so it’s hardly ever felt on large scale, unlike gravity.

Weak Nuclear Force

Weak Nuclear Force 10 trillion, trillion times stronger than gravity. The weak nuclear force is responsible for all three types of nuclear decay; Alpha, Beta or Gamma. Alpha decay is the emission of a helium nucleus from an atom, Beta decay is when an electron or positron is emitted from an atom, and Gamma decay is the emission of a high energy photon from an atom. The weak nuclear force is the odd one out of all the forces. Firstly because of its bosons. The weak force has three bosons unlike the others which only have one each. The bosons are also unlike the others as they have charge and mass, so much mass in fact that they are heavier that atoms of Rubidium! This is why the force only acts over small distances. In one type of decay an Up quark can emits a W^-, that’s a particle emitting something that is 40,000 times heavier! The weak force is also different as it only affects left handed particles or right handed antiparticles with flavour.

Strong Nuclear Force

Inside a nucleus you have protons and neutrons. Due to the electromagnetic force however all of the protons in the nucleus are pushing each other apart trying to break free, the thing that holds them together is the Strong Nuclear force. Its 100 times stronger that EM, an affects all particles with colour. The Strong Nuclear Force gets stronger with distance however is a very small ranged force only acting over a range of 10^{-15}m

Are There Really 4?

It turn out that most of the forced seem to be just different aspects of the same thing. Electromagnetism and Weak Nuclear Forces have shown that at high enough energies the two forces are the same, called the Electroweak interaction. Above the unification energy of about 100 GeV or 1015 kelvin, they would merge into a single Electroweak force. Work is currently being done on adding the Strong force and then hopefully gravity.

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