Colour charge. A property possessed by quarks in addition to flavour (up, down, strange, etc.). Unlike electric charge, which comes in two varieties – positive and negative – colour charge comes in three varieties – red, green, and blue. Obviously, the use of these names does not imply that quarks are ‘coloured’ in the conventional sense. The colour force between quarks is carried by coloured gluons.
Colour force. The strong force responsible for binding quarks and gluons together inside hadrons. Unlike more familiar forces, such as gravity and electromagnetism, the colour force exhibits asymptotic freedom – at the asymptotic limit of zero separation, quarks behave as though they are entirely free. The strong nuclear force which binds protons and neutrons together inside atomic nuclei is thought to be a ‘hang-over’ of the colour force binding quarks inside the nucleons.
Complex number. A complex number is formed by multiplying a real number by the square-root of –1, written i. The square of a complex number is then a negative number for example, the square of 5i is –25. Complex numbers are used widely in mathematics to solve problems that are impossible using real numbers only.
Conservation law. A physical law which states that a specific measureable property of an isolated system does not change as the system evolves in time. Measureable properties for which conservation laws have been established include mass-energy, linear and angular momentum, electric and colour charge, isospin, etc. According to Noether’s theorem, each conservation law can be traced to a specific continuous symmetry of the system.
Cooper pair. When cooled below its critical temperature, electrons in a superconductor experience a weak mutual attraction. Electrons with opposite spin and momentum combine to form Cooper pairs, which move through the metal lattice cooperatively, their motion mediated or facilitated by lattice vibrations. Such pairs of electrons have spin 0 or 1 and are therefore bosons. Consequently, there is no restriction on the number of pairs that can occupy a single quantum state, and at low temperatures they can ‘condense’, building the state to macroscopic dimensions. The Cooper pairs in this state experience no resistance as they pass through the lattice and the result is superconductivity.
Cosmic inflation. A rapid exponential expansion of the universe thought to have occurred between 10–36 and 10–32 seconds after the big bang. Discovered in the context of GUTs by American physicist Alan Guth in 1980, inflation helps to explain the large-scale structure of the universe that we observe today.
Cosmic microwave background radiation. Some 380,000 years after the big bang, the universe had expanded and cooled sufficiently to allow hydrogen nuclei (protons) and helium nuclei (consisting of two protons and two neutrons) to recombine with electrons to form neutral hydrogen and helium atoms. At this point, the universe became ‘transparent’ to the residual hot radiation. Further expansion has shifted and cooled this hot radiation to the microwave region with a temperature of just 2.7 K (–270.5 °C), a few degrees above absolute zero. This microwave background radiation was predicted by several theorists and was discovered accidentally by Arno Penzias and Robert Wilson in 1964. The COBE and WMAP satellites have since studied this radiation in detail.
Cosmic rays. Streams of high-energy charged particles from outer space which wash constantly over the earth’s upper atmosphere. The use of the term ‘ray’ harks back to the early days of research on radioactivity, when directed streams of charged particles were referred to as ‘rays’. Cosmic rays are derived from a variety of sources, including high-energy processes occurring on the surface of the sun and other stars, and as-yet unknown processes occurring elsewhere in the universe. The energies of cosmic ray particles are typically between 10 MeV and 10 GeV.
Cosmological constant. In 1922 Russian theorist Alexander Friedmann found solutions to Einstein’s gravitational field equations that describe a universe in which space-time is expanding. Einstein had initially resisted the idea that space-time could expand or contract and had fudged his equations to produce static solutions. Concerned that conventional gravity would be expected to overwhelm the matter in the universe and cause it to collapse in on itself, Einstein had introduced a ‘cosmological constant’ – a kind of negative or repulsive form of gravity – to counteract the effect. When evidence accumulated that the universe is actually expanding, Einstein regretted his action, calling it the biggest blunder he had ever made in his life. But, in fact, further discoveries in 1998 suggested that the expansion of the universe is actually accelerating. When combined with satellite measurements of the cosmic microwave background radiation these results have led to the suggestion that the universe is pervaded by ‘dark energy’, accounting for about 73 per cent of the mass-energy of the universe. One form of dark energy requires the reintroduction of Einstein’s cosmological constant.
Dark matter. Discovered in 1934 by Swiss astronomer Fritz Zwicky as an anomaly in the measured masses of galaxies in the Coma Cluster (located in the constellation Coma Berenices) based on the observed motions of the galaxies near the cluster edge compared with the number of observable galaxies and the total brightness of the cluster. These estimates of the masses of the galaxies differed by a factor of 400. As much as 90 per cent of the mass required to explain the size of the gravitational effects appeared to be ‘missing’, or invisible. This missing matter was called ‘dark matter’. Subsequent studies favour a form of dark matter called ‘cold dark matter’. See cold dark matter.
Deep inelastic scattering. A kind of particle scattering event in which much of the energy of the accelerated particle (for example, an electron) is channelled into the destruction of the target particle (for example, a proton). The accelerated particle recoils from the collision with considerably less energy and a spray of different hadrons is produced.
Degree of freedom. The number of dimensions that are accessible to a system or in which the system is free to move. A classical particle is free to move in three spatial dimensions. However, photons are massless particles with spin 1 and, as such, are constrained to only two dimensions, manifested as left and right circular polarization or vertical and horizontal polarization. In the Higgs mechanism, massless bosons may gain a third degree of freedom by absorbing a Nambu–Goldstone boson, see Figure 14, p. 89.
Eightfold Way. A scheme for classifying the ‘zoo’ of particles known around 1960 in the form of two ‘octets’, developed by Murray Gell-Mann and independently by Yuval Ne’eman. The patterns are based on a global SU(3) symmetry and are formed by mapping the particles according to their electric charge or total isospin vs. strangeness (see Figure 10, p. 69). The patterns were eventually explained by the quark model (Figure 12, p. 82).
Electric charge. A property possessed by quarks and leptons (and, more familiarly, protons and electrons). Electric charge comes in two varieties – positive and negative – and the flow of negative charge is the basis for electricity and the power industry.
Electromagnetic force. Electricity and magnetism were recognized to be components of a single, fundamental force, through the work of several experimental and theoretical physicists, most notably English physicist Michael Faraday and Scottish theoretician James Clerk Maxwell. The electromagnetic force is responsible for binding electrons with their nuclei inside atoms, and binding atoms together to form the great variety of molecular substances.
Electron. Discovered in 1897 by English physicist J.J. Thompson. The electron is a first-generation lepton with a charge –1, spin ½ (fermion), and mass 0.51 MeV.
Electron volt (eV). An electron volt is the amount of energy a single negatively charged electron gains when accelerated through a one-volt electric field. A 100 W light bulb burns energy at the rate of about 600 billion billion electron volts per second.
Electro-weak force. Despite the great difference in scale between the electromagnetic and weak nuclear forces, these are facets of what was once a unified electro-weak force, thought to prevail during the ‘electro-weak epoch’, between 10–36 and 10–12 seconds after the big bang. The
combination of electromagnetic and weak nuclear forces in an SU(2)×U(1) field theory was first achieved by Steven Weinberg and independently by Abdus Salam in 1967–68.
Element. The philosophers of Ancient Greece believed that all material substance is composed of four elements – earth, air, fire, and water. A fifth element, variously called the ether or ‘quintessence’, was introduced by Aristotle to describe the unchanging heavens. Today, these classical elements have been replaced by a system of chemical elements. These are ‘fundamental’ in the sense that chemical elements cannot be transformed one into another by chemical means, meaning that they consist of only one type of atom. The elements are organized in a ‘periodic table’, from hydrogen to uranium and beyond.
Exclusion principle. See Pauli exclusion principle.
Fermion. Named for Italian physicist Enrico Fermi. Fermions are characterized by half-integral spins (, etc.) and include quarks and leptons and many composite particles produced from various combinations of quarks, such as baryons.
Flavour. A property which distinguishes one type of quark from another, in addition to colour charge. There are six flavours of quark which form three generations up, charm, and top with electric charge , spin ½, and masses of 1.7–3.3 MeV, 1.27 GeV, and 172 GeV, respectively, and down, strange, and bottom with electric charge , spin ½, and masses 4.1–5.8 MeV, 101 MeV, and 4.19 GeV, respectively. The term flavour is also applied to leptons, with the electron, muon, tau, and their corresponding neutrinos distinguished by their ‘lepton flavour’. See lepton.
Gauge symmetry. A name coined by German mathematician Hermann Weyl. When applied to quantum field theories, a ‘gauge’ is chosen to which the equations are invariant – arbitrary changes in the gauge make no difference to the predicted outcomes. The link between gauge symmetry and conservation laws (see conservation law and Noether’s theorem) means that the correct choice of gauge symmetry can lead to a field theory which will automatically respect the need for conservation of the property under study.
Gauge theory. A gauge theory is one based on a gauge symmetry (see gauge symmetry). Einstein’s general theory of relativity is a gauge theory which is invariant to arbitrary changes in the space-time coordinate system (the ‘gauge’). Quantum electrodynamics (QED) is a quantum field theory which is invariant to the phase of the electron wavefunction. In the 1950s developing quantum field theories of the strong and weak nuclear forces became a matter of identifying the conserved quantity and hence the appropriate gauge symmetry.
General relativity. Developed by Einstein in 1915, the general theory of relativity incorporates special relativity and Newton’s law of universal gravitation in a geometric theory of gravitation. Einstein replaced the ‘action-at-a-distance’ implied in Newton’s theory of universal gravitation with the movement of massive bodies in a curved space-time. In general relativity, matter tells space-time how to curve, and the curved space-time tells matter how to move.
g-factor. A constant of proportionality between the (quantized) angular momentum of an elementary or composite particle and its magnetic moment, the direction the particle will adopt in a magnetic field. There are actually three g-factors for the electron: one associated with its spin, one associated with the angular momentum of the electron orbital motion in an atom, and one associated with the sum of spin and orbital angular momentum. Dirac’s relativistic quantum theory of the electron predicted a g-factor for electron spin of 2. The value recommended by the CODATA task group in 2006 is 2.0023193043622. The difference is due to quantum electrodynamic effects.
Giga. A prefix denoting billion. A giga electron volt (GeV) is a billion electron volts, 109 eV, or 1000 MeV.
Gluon. The carrier of the strong colour force between quarks. Quantum chromodynamics requires eight, massless colour force gluons which themselves carry colour charge. Consequently, the gluons participate in the force rather than simply transmit it from one particle to another. Ninety-nine per cent of the mass of protons and neutrons is thought to be energy carried by gluons.
Grand unified theory (GUT). Any theory which attempts to unify the electromagnetic, weak, and strong nuclear forces in a single structure is an example of a grand unified theory. The first example of a GUT was developed by Sheldon Glashow and Howard Georgi in 1974. GUTs do not seek to accommodate gravity; theories that do are generally referred to as Theories of Everything (TOEs).
Gravitational force. The force of attraction experienced between all mass-energy. Gravity is extremely weak, and has no part to play in the interactions between atoms, sub-atomic, and elementary particles which are rather governed by the colour force, weak nuclear force, and electromagnetism. The force of gravity is described by Einstein’s general theory of relativity.
Graviton. A hypothetical particle which carries the gravitational force in quantum field theories of gravity. Although many attempts have been made to develop such a theory, to date these have not been recognized as successful. If it exists, the graviton would be a massless, chargeless boson with spin 2.
Hadron. From the Greek hadros, meaning thick or heavy. Hadrons form a class of particles which experience the strong nuclear force and are therefore composed of various combinations of quarks. This class includes baryons, which are composed of three quarks, and mesons, which are composed of one quark and an anti-quark.
Higgs boson. Named for English physicist Peter Higgs. All Higgs fields have characteristic field particles called Higgs bosons. The term ‘Higgs boson’ is typically reserved for the electro-weak Higgs, the particle of the Higgs field first used in 1967–68 by Steven Weinberg and Abdus Salam to account for electro-weak symmetry-breaking. Something that looks very much like the electro-weak Higgs boson was discovered at CERN’s Large Hadron Collider on 4 July 2012. It is a neutral, spin 0 particle with a mass of 125 GeV.
Higgs field. Named for English physicist Peter Higgs. A generic term used for any background energy field added to a quantum field theory to trigger symmetry-breaking through the Higgs mechanism. The existence of the Higgs field used to break the symmetry in a quantum field theory of the electro-weak force is strongly supported by the discovery of the new particle at CERN.
Higgs mechanism. Named for English physicist Peter Higgs, but also often referred to using the names of other physicists who independently discovered the mechanism in 1964. One alternative name is the Brout–Englert–Higgs–Hagen–Guralnik–Kibble – BEHHGK, or ‘beck’ mechanism, after the physicists Robert Brout, François Englert, Peter Higgs, Gerald Guralnik, Carl Hagen, and Tom Kibble. The mechanism describes how a background field – called the Higgs field – can be added to a quantum field theory to break a symmetry of the theory. In 1967–68 Steven Weinberg and Abdus Salam independently used the mechanism to develop a field theory of the electro-weak force.
Inflation. See cosmic inflation.
Isospin. Also known as isotopic or isobaric spin. Introduced by Werner Heisenberg in 1932 to explain the symmetry between the newly discovered neutron and the proton. Isospin symmetry is now understood to be a subset of the more general flavour symmetry in hadron interactions. The isospin of a particle can be calculated from the number of up- and down-quarks it contains (see p. 81).
Kaon. A group of spin-0 mesons consisting of up-, down-, and strange-quarks and their anti-quarks. These are K+ (up-anti-strange), K– (strange-anti-up), and K0 (mixtures of down-anti-strange and strange-anti-down) with masses 494 MeV (K±) and 498 MeV (K0).
Lambda-CDM. An abbreviation of lambda-cold dark matter. Also known as the ‘Standard Model’ of big bang cosmology. The lambda-CDM model accounts for the large-scale structure of the universe, the cosmic microwave background radiation, the accelerating expansion of the universe, and the distribution of elements such as hydrogen, helium, lithium, and oxygen. The model assumes that 73 per cent of the mass-energy of the universe is dark energy (reflected in the size of the cosmological constant, lambda), 22 per cent is cold dark matter, leaving the visible universe – galaxies, stars, and known plane
ts – to account for just 5 per cent.
Lamb shift. A small difference between two electron energy levels of the hydrogen atom, discovered by Willis Lamb and Robert Retherford in 1947. The Lamb shift provided an important clue which led to the development of renormalization and ultimately quantum electrodynamics.
LEP. Acronym for Large Electron–Positron collider, the predecessor of the LHC at CERN.
Lepton. From the Greek leptos, meaning small. Leptons form a class of particles which do not experience the strong nuclear force and combine with quarks to form matter. Like quarks, leptons form three generations, including the electron, muon, and tau, with electric charge –1, spin ½, and masses 0.51 MeV, 106 MeV, and 1.78 GeV, respectively, and their corresponding neutrinos. The electron, muon, and tau neutrinos carry no electric charge, have spin ½, and are believed to possess very small masses (necessary to explain the phenomenon of neutrino oscillation, the quantum-mechanical mixing of neutrino flavours such that the flavour may change over time).
LHC. Acronym for Large Hadron Collider. The world’s highest-energy particle accelerator, capable of producing proton–proton collision energies of 14 TeV. The LHC is 27 kilometres in circumference and lies 175 metres beneath the Swiss–French border at CERN near Geneva. The LHC, operating at proton–proton collision energies of 7 TeV and subsequently 8 TeV, provided the evidence which led to the discovery of a new, Higgs-like boson in July 2012.
Luminosity. The luminosity of a beam of particles in an accelerator is the number of particles per unit area per unit time multiplied by the opacity of the beam target (a measure of the impenetrability of the target to the particles). Of particular interest is the integrated luminosity, which is simply the integral (sum) of the luminosity over time, usually reported in units of per square centimetre (cm−2) or inverse barns (1024 cm–2). The number of collisions which result in a particular elementary particle reaction is then just the integrated luminosity multiplied by the cross-section (in units of cm2) for the reaction, which is a measure of its likelihood.
Higgs:The invention and discovery of the 'God Particle' Page 19
