acceleration The rate of change of velocity (speed) with time, usually given the symbol a, as in F = ma, or force equals mass times acceleration (Newton’s second law).
anti-particle Identical in mass to an ‘ordinary’ particle but of opposite charge. For example, the anti-particle of the electron (e–) is the positron (e+). The anti-particle of a red quark is an anti-red anti-quark. Every particle in the standard model has an anti-particle. Particles with zero charge are their own anti-particles.
ATLAS Acronym for A Toroidal LHC Apparatus, one of the two main detector collaborations involved in the hunt for the Higgs boson at CERN’s Large Hadron Collider.
atom From the Greek atomos, meaning ‘indivisible’ or ‘uncuttable’. Originally intended to denote the ultimate constituents of matter, the word ‘atom’ now signifies the fundamental constituents of individual chemical elements. Thus, water consists of molecules of H2O, which is composed of two atoms of hydrogen and one atom of oxygen. The atoms in turn consist of protons and neutrons, which are bound together to form a central nucleus, and electrons whose wavefunctions form characteristic patterns called orbitals around the nucleus.
atomism A natural philosophy based on the notion that matter is composed of ultimate, indivisible, uncuttable parts, called atoms. The atomist tradition is most closely associated with the ancient Greek philosophers Leucippus, Democritus, and Epicurus, and the Roman poet and philosopher Lucretius, although atomism also formed part of the philosophy of certain schools in ancient India.
atto A prefix denoting a billion billionth (10−18). An attometre (am) is 10−18 metres, or a thousandth of a femtometre. The radius of a proton is about 850 am. The LIGO gravitational wave observatory is sensitive to displacements of the order of 1 am.
Avogadro’s constant Typically given the symbol NA. Defined as the number of atoms in 12 grams (or 1 mole) of carbon-12. It has the value 6.022 × 1023 per mole.
Avogadro’s hypothesis/law Equal volumes of all gases, at the same temperature and pressure, contain equal numbers of particles (atoms or molecules). This follows because, with fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas present (e.g., as measured by its weight). One mole of gas at a temperature of 273.15 kelvin (0 oC) and pressure of 101.325 thousand Pascals (1 atmosphere) has a volume of about 22.4 litres, and contains 6.022 × 1023 atoms or molecules.
bare mass The hypothetical mass that a particle would possess if it could be separated from the quantum fields which it generates, or with which it interacts. The observed mass of the particle is then the bare mass plus mass generated by interactions with the quantum fields.
baryon From the Greek barys, meaning ‘heavy’. Baryons form a sub-class of hadrons. They are heavier particles which experience the strong nuclear force and include the proton and neutron. They are comprised of triplets of quarks.
Bell’s theorem/inequality Devised by John Bell in 1966. The simplest extension of quantum theory, which resolves the problem of the collapse of the wavefunction and the ‘spooky action-at-a-distance’ that this seems to imply, involves the introduction of local hidden variables which govern the properties and behaviour of quantum particles. Bell’s theorem states that the predictions of any local hidden variable theory will not always agree with the predictions of quantum theory. This is summarized in Bell’s inequality—the predictions of local hidden variable theories cannot exceed a certain maximum limit. But quantum theory predicts results that for certain experimental arrangements will exceed this limit. Bell’s inequality therefore allows a direct experimental test.
beta particle A high-speed electron emitted from the nucleus of an atom undergoing beta radioactive decay. See beta radioactivity/decay.
beta radioactivity/decay First discovered by French physicist Henri Becquerel in 1896 and so named by Ernest Rutherford in 1899. An example of a weak force decay, it involves transformation of a down quark in a neutron into an up quark, turning the neutron into a proton with the emission of a W− particle. The W− decays into a high-speed electron (the ‘beta particle’) and an electron anti-neutrino.
big bang Term used to describe the cosmic ‘explosion’ of spacetime and matter during the early moments in the creation of the universe, about 13.8 billion years ago. Originally coined by maverick physicist Fred Hoyle as a derogatory term, overwhelming evidence for a big bang ‘origin’ of the universe has since been obtained through the detection and mapping of the cosmic microwave background radiation, the cold remnant of hot radiation thought to have disengaged from matter about 380,000 years after the big bang.
billion One thousand million, 109, or 1,000,000,000.
black hole A name popularized (though not, as many suggest, coined) by John Wheeler. A black hole is a region of spacetime containing so much mass-energy that its escape velocity—the speed required to escape its gravitation pull—is greater than the speed of light. This idea actually dates back to the eighteenth century, but came to prominence through the work of Karl Schwarzchild, who in 1916 was the first to derive formal solutions for Einstein’s gravitational field equations. See also Schwarzchild solution/radius.
Bohr radius The orbital distance of the electron as measured from the proton in a hydrogen atom. In Bohr’s model of the atom, published in 1913, Bohr calculated this distance from a collection of fundamental physical constants (including Planck’s constant, the speed of light, and the mass and charge of the electron). In Schrödinger’s wave mechanics, the electron is spherically ‘distributed’ within its lowest-energy orbital, but has the highest probability for being found at a distance corresponding to the Bohr radius, a little over 0.0529 nanometres.
Boltzmann constant Typically denoted k or kB. This constant connects the energy (E) of individual particles with temperature (T), such that T = E/kB (or E = kBT), and was actually first introduced by Planck in his derivation of the radiation law. Even the iconic equation connecting entropy (S) and probability (W) which is carved on Boltzmann’s headstone, S = klnW, was derived by Planck, not Boltzmann.
boson Named for Indian physicist Satyendra Nath Bose. Bosons are characterized by integral spin quantum numbers (1, 2, … , etc.) and, as such, are not subject to Pauli’s exclusion principle. Bosons are involved in the transmission of forces between matter particles, and include the photon (electromagnetism), the W and Z particles (weak force), and gluons (colour force). Particles with spin zero are also called bosons but these are not involved in transmitting forces. Examples include the pions and the Higgs boson. The graviton, the hypothetical particle of the gravitational field, is believed to be a boson with spin 2.
bottom quark Also sometimes referred to as the ‘beauty’ quark. A third-generation quark with charge –1⁄3, spin ½ (fermion), and a mass of 4.18 GeV/c2. It was discovered at Fermilab in 1977, through the observation of the upsilon, a meson formed from bottom and anti-bottom quarks.
CERN Acronym for Conseil Européen pour la Recherche Nucléaire (the European Council for Nuclear Research), founded in 1954. This was renamed the Organisation Européenne pour la Recherche Nucléaire (European Organization for Nuclear Research) when the provisional Council was dissolved, but the acronym CERN was retained. CERN is located in the north-west suburbs of Geneva near the Swiss–French border.
charm quark A second generation quark with charge +2⁄3, spin ½ (fermion) and a mass of 1.28 GeV/c2. It was discovered simultaneously at Brookhaven National Laboratory and SLAC in the ‘November revolution’ of 1974 through the observation of the J/ψ, a meson formed from a charm and anti-charm quark.
classical mechanics The system of mechanics embodied in Newton’s laws of motion and the law of universal gravitation, although the study of mechanics predates Newton. The system deals with the influence of forces on the motions of larger, macroscopic bodies at speeds substantially less than light. Although ‘classical’, the system remains perfectly valid today within the limits of its applicability.
classical modern philosophy The philosophy that emerged in Europe in the seventeenth and eighteenth centuries as the grip of the establish Church began to be relaxed is sometimes referred to as ‘classical modern’. It succeeded medieval philosophy. Classical modern philosophers include: René Descartes (born 1596), John Locke (1632), Baruch Spinoza (1632), Gottfried Leibniz (1646), George Berkeley (1685), David Hume (1711), and Immanuel Kant (1724).
CMS Acronym for Compact Muon Solenoid, one of the two detector collaborations involved in the hunt for the Higgs boson at CERN’s Large Hadron Collider.
cold dark matter A key component of the current Λ-CDM model of big bang cosmology, thought to account for about twenty-six per cent of the mass-energy of the universe. The constitution of cold dark matter is unknown, but is thought to consist largely of ‘non-baryonic’ matter, i.e. matter that does not involve protons or neutrons, most likely particles not currently known to the standard model.
collapse of the wavefunction In most quantum systems, the wavefunction of a quantum entity will be delocalized over a region of space (the quantum entity may be here, there, or everywhere within the boundary of the wavefunction), yet when a measurement is made the result is localized to a specific position (the entity is here). Similarly, in a quantum measurement in which a number of different outcomes is possible (such as spin-up or spin-down), it is necessary to form a superposition of the wavefunctions describing these outcomes. The probability of getting a specific result is then related to the square of the amplitude of the corresponding wavefunction in the superposition. In either case, the wavefunction or superposition is said to ‘collapse’. A number of possible outcomes converts to one outcome only, and all the other possibilities disappear.
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, which physicists have chosen to call 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, which get weaker with increasing distance, the colour force acts like a piece of elastic or spring, tethering the quarks together. When the quarks are close together, the elastic or spring is relaxed and the quarks behave as though they are entirely free. But as the quarks are pulled apart, the elastic or spring tightens and keeps the quarks ‘confined’. The strong nuclear force which binds protons and neutrons together inside atomic nuclei results from a kind of ‘leakage’ of the colour force beyond the boundaries of the nucleons.
complementarity The principle of complementarity was devised by Niels Bohr and is a key pillar of the Copenhagen interpretation of quantum mechanics. According to this principle, quantum wave-particles will exhibit wave-like and particle-like behaviour in mutually exclusive experimental arrangements, but it is impossible to devise an arrangement that will show both types of behaviour simultaneously. Such behaviour is, however, not contradictory; it is complementary.
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 – (5i)2—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.
Copenhagen interpretation Developed by Niels Bohr, Werner Heisenberg, and Wolfgang Pauli as a way of thinking about the nature of elementary quantum wave-particles as described by quantum mechanics. Depending on the experimental set-up, such wave-particles will exhibit wave-like or particle-like behaviour. But these behaviours are complementary: in this kind of experiment the wave-particle is a wave, in this other kind of experiment it is a particle and it is meaningless to ask what the wave-particle really is.
cosmic 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 and infrared regions with a temperature of just 2.7 kelvin (–270.5oC), 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, WMAP, and Planck satellites have since studied this radiation in detail.
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 by American physicist Alan Guth in 1980, inflation helps to explain the large-scale structure of the universe that we observe today.
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 Albert Einstein initially resisted the idea that the universe is dynamic—that it could expand or contract—and 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 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 69.1 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 mass of galaxies in the Coma cluster (located in the constellation Coma Berenices). Zwicky observed that the rotation speeds of galaxies near the cluster edge are much faster than predicted from the mass of all the observable galaxies, implying that the mass of the cluster is actually much larger. As much as ninety per cent of the mass required to explain the rotation curve 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.
de Broglie relation Deduced by Louis de Broglie in 1923, this equation relates a wave-like property (the wavelength, λ) of a quantum wave-particle to a particle-like property (linear momentum, p). The relation is λ = h/p, where h is Planck’s constant. For ‘everyday’ objects of macroscopic size (such as a tennis ball), the wavelength predicted by the de Broglie relation is much too short to observe. But microscopic entities such as electrons have measureable wavelengths, typically 100,000 times shorter than visible light. A beam of electrons can be diffracted and will show two-slit interference effects. Electron microscopes are used routinely to study the structures of inorganic and biological samples.
dressed mass The mass derived from a quantum wave-particle’s self-energy, the result of interactions with the system from which it is physically inseparable. For example, an electron acquires self-energy by interacting with its own self-generated electromagnetic field.
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 electrical 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 Joseph John Thompson. The electron is a first-generation lepton with a charge –1, spin ½ (fermion), and mass 0.51 MeV/c2.
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 100W 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 a unified field theory was first achieved by Steven Weinberg and independently by Abdus Salam in 1967–1968.
element The philosophers of Ancient Greece believed that all material substance was 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.
empiricism One of several philosophical perspectives on the acquisition of human knowledge. In an empiricist philosophy, knowledge is firmly linked to experience and evidence—‘seeing is believing’. If we can’t directly experience or acquire even indirect evidence for the existence of an entity, then we have no grounds for believing that it really exists. Such an entity would then be regarded as metaphysical.
Euclidean space Named for the ancient Greek mathematician Euclid of Alexandria. This is the familiar geometry of ‘ordinary’ three-dimensional space, typically described in terms of Cartesian co-ordinates (x,y,z) and in which the angles of a triangle add up to 180o, the circumference of a circle is given by 2π times its radius, and parallel lines never meet.
exclusion principle See Pauli exclusion principle.
femto A prefix denoting a million billionth (10−15). A femtometre (fm) is 10−15 metres, a thousand attometres or a thousandth of a picometre. The radius of a proton is about 0.85 fm.
fermion Named for Italian physicist Enrico Fermi. Fermions are characterized by half-integral spins (½, 3⁄2, 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 +2⁄3, spin ½ and masses of 1.8-3.0 MeV/c2, 1.28 GeV/c2 and 173 GeV/c2, respectively, and down, strange and bottom with electric charge –1⁄3, spin ½ and masses 4.5–5.3 MeV/c2, 95 MeV/c2 and 4.18 GeV/c2, respectively. The term ‘flavour’ is also sometimes applied to leptons, with the electron, muon, tau, and their corresponding neutrinos distinguished by their ‘lepton flavour’. See lepton.
force Any action that changes the motion of an object. In Isaac Newton’s three laws of motion forces are ‘impressed’, meaning that the actions involve some kind of physical contact between the object and whatever is generating the force (such as another object). The exception to the rule is Newton’s force of gravity, which appears to act instantaneously and at a distance (no obvious contact between gravitating objects, such as the Earth and the Moon). This problem is resolved in Einstein’s general theory of relativity.
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 in 2010 by the International Council for Science Committee on Data for Science and Technology (CODATA) task group is 2.00231930436153. The difference is due to quantum electrodynamic effects.
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 with the movement of massive bodies in a curved spacetime. In general relativity, matter tells spacetime how to curve, and the curved spacetime tells matter how to move.
giga A prefix denoting billion. A giga electron volt (GeV) is a billion electron volts, 109 eV or 1,000 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 and quark–anti-quark pairs created by the colour field.
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 force, and electromagnetism. The effects of gravity are described by Einstein’s general theory of relativity and approximated in Newton’s theory of universal gravitation.
graviton A hypothetical particle which carries the gravitational force in speculative 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 a spin quantum number of 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 comprised 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.
hidden variables The simplest way to modify or extend conventional quantum mechanics to eliminate the collapse of the wavefunction is to introduce hidden variables. Such variables govern the properties and behaviour of quantum wave-particles but by definition cannot be observed directly. If the resulting extension is required to ensure that individual quantum entities possess specific properties at all times (in other words, the entities are ‘locally real’), then the hidden variables are said to be local. If the extension is required to ensure that quantum entities possess specific properties in a collective sense, then the hidden variables may be non-local.
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 1967–1968 by Steven Weinberg and Abdus Salam to account for electro-weak symmetry-breaking. It is now thought that the electro-weak Higgs boson was discovered at CERN’s Large Hadron Collider, a discovery announced on 4 July 2012. It is a neutral, spin-0 particle with a mass of about 125 GeV/c2.
Higgs field Named for English physicist Peter Higgs. A generic term used for any background quantum field added to a 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 Higgs boson 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: Robert Brout, François Englert, Higgs, Gerald Guralnik, Carl Hagen, and Tom Kibble. The mechanism describes how a background quantum field—called the Higgs field—can be added to a field theory to break a symmetry. In 1967–1968 Steven Weinberg and Abdus Salam independently used the mechanism to develop a field theory of the electro-weak force.
Hubble’s law The observation, first reported by American astronomer Edwin Hubble, that distant galaxies recede from us at speeds that are directly proportional to their distances. This relationship is summarized by the equation v = H0D, in which v is the recession speed of the galaxy, D is its distance from Earth and H0 is the Hubble constant, which has a value of 67.7 kilometres per second per megaparsec (based on analysis of Planck satellite mission data reported in 2015).
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.
kaon A group of spin-0 mesons consisting of up, down, and strange quarks and their anti-quarks. These are Κ+ (up-anti-strange), Κ− (strange-anti-up), Κ0 (mixtures of down-anti-strange and strange-anti-down) with masses 493.7 MeV/c2 (Κ±) and 497.6 MeV/c2 (Κ0).
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.
Λ-CDM An abbreviation of Lambda-cold dark matter. Also known as the ‘concordance model’ or the ‘standard model’ of big bang cosmology. The Λ-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 69.1 per cent of the mass-energy of the universe is dark energy (reflected in the size of the cosmological constant, Λ), 26.0 per cent is cold dark matter, leaving the visible universe—galaxies, stars, planets, gas, and dust—to account for just 4.9 per cent.
Leggett inequality Named for English physicist Anthony Leggett as an extension of the logic of Bell’s theorem and Bell’s inequality. The introduction of local hidden variables implies two logical consequences: measurements involving entangled pairs are not affected by the way the experimental apparatus is set up and they are not affected by the results of any measurement that is actually made on one, the other, or both particles in the pair. Leggett defined a class of ‘crypto’ non-local hidden variable theories in which the experimental set up can indeed affect the outcome, but the actual results cannot. Such theories do not predict all the possible results that quantum theory predicts and Leggett was able to develop an inequality that could be subjected to a direct test.
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/c2, 105.7 MeV/c2, and 1.78 GeV/c2, 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 collider, designed to produce 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 and 8 TeV, produced evidence which led to the discovery of the Higgs boson in July 2012. After a two-year shutdown, it began operations in 2015 at a collision energy of 13 TeV.
mass In classical mechanics, the mass of a physical object is a measure of its resistance to changes in its state of motion under the influence of an applied force, assumed to be related to the ‘quantity of matter’ that it contains. As such, it is a ‘primary’ quality of material substance. In special relativity and quantum physics, our understanding of the nature of mass changes quite dramatically. Mass becomes a measure of the energy content of an object (m = E/c2), and the mass of elementary particles is traced to the energies associated with different kinds of quantum fields.
mass renormalization See renormalization.
mechanical philosophy A branch of seventeenth-century natural philosophy concerned with the establishment of a particularly mechanistic view of nature. The approach of the mechanical philosophers was determinedly reductionist—the properties and behaviour of all natural objects (including living creatures) can be understood in terms of mechanical principles. The mechanical philosophers ushered in the modern scientific era, and included: Francis Bacon (born 1561), Galileo Galilei (1564), Johannes Kepler (1571), Pierre Gassendi (1592), Robert Boyle (1627), Christian Huygens (1629), and Isaac Newton (1642).
mega A prefix denoting million. A mega electron volts (MeV) is a million electron volts, 106 eV.
meson From the Greek mésos, meaning ‘middle’. Mesons are a sub-class of hadrons. They experience the strong nuclear force and are composed of quarks and anti-quarks.
mole A standard unit for the amount of a chemical substance, defined as the amount which contains as many atoms or molecules of the substance as there are carbon atoms in 12 grams of carbon-12 (6.022 × 1023). It is approximately equal to the atomic or molecular weight of the substance in grams. The name is derived from ‘molecule’. See also Avogadro’s constant.
molecule A fundamental unit of chemical substance formed from two or more atoms. A molecule of oxygen consists of two oxygen atoms, O2. A molecule of water consists of two hydrogen atoms and one oxygen atom, H2O.
muon A second-generation lepton equivalent to the electron, with a charge –1, spin ½ (fermion), and mass 105.7 MeV/c2. First discovered in 1936 by Carl Anderson and Seth Neddermeyer.
Nambu–Goldstone boson Massless, spin-0 particles created as a consequence of spontaneous symmetry-breaking, first discovered by Yoichiro Nambu in 1960 and elaborated by Jeffrey Goldstone in 1961.
natural minima, or minima naturalia The ancient Greek philosopher Aristotle hypothesized that there must be ‘smallest parts’—natural minima—into which a naturally occurring substance could be divided without losing its essential character. Such smallest parts are not atoms. In Aristotle’s philosophy they would still be imbued with the form of the substance and can in principle be further divided. However, any further division results in a loss of form—what remains can no longer be considered to be the original substance.
neutrino From Italian, meaning ‘small neutral one’. Neutrinos are the chargeless, spin ½ (fermion) companions to the negatively charged electron, muon, and tau. The neutrinos 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. Neutrino oscillation solves the solar neutrino problem—the problem that the numbers of neutrinos measured to pass through the Earth are inconsistent with the numbers of electron neutrinos expected from nuclear reactions occurring in the Sun’s core. It was determined in 2001 that only thirty-five per cent of the neutrinos from the Sun are electron neutrinos—the balance are muon and tau neutrinos, indicating that the neutrino flavours oscillate as they travel from the Sun to the Earth.
neutron An electrically neutral sub-atomic particle, first discovered in 1932 by James Chadwick. The neutron is a baryon consisting of one-up and two-down quarks with spin ½ and mass 939.6 MeV/c2.
Noether’s theorem Developed by Amalie Emmy Noether in 1918. The theorem connects the laws of conservation with specific continuous symmetries of physical systems and the theories that describe them, used as a tool in the development of new theories. The conservation of energy reflects the fact that the laws governing energy are symmetric to continuous changes in time. For linear momentum, the laws are symmetric to continuous changes in spatial position. For angular momentum, the laws are symmetric to the angle of direction measured from the centre of the rotation.
nucleus The dense region at the core of an atom in which most of the atom’s mass is concentrated. Atomic nuclei consist of varying numbers of protons and neutrons. The nucleus of a hydrogen atom consists of a single proton.
Pauli exclusion principle Discovered by Wolfgang Pauli in 1925. The exclusion principle states that no two fermions may occupy the same quantum state (i.e., possess the same set of quantum numbers) simultaneously. For electrons in atoms, this means that only two electrons can occupy a single atomic orbital provided that they possess opposite spins.
perihelion If a planet were to describe a circular orbit around the Sun, then there would obviously be no change in the distance between the Sun and the planet as it moves around its orbit. However, the planets of the solar system describe elliptical orbits with the Sun at one focus. This means that the distance between the Sun and the planet does change. The perihelion is the point in the orbit at which the planet is closest to the Sun. The aphelion is the point at which the planet is furthest from the Sun. At its perihelion, the Earth is about 147.1 million kilometres from the Sun. At aphelion it is 152.1 million kilometres from the Sun.
perturbation theory A mathematical method used to find approximate solutions to equations that cannot be solved exactly. The offending equation is recast as a perturbation expansion: the sum of a potentially infinite series of terms which starts with a ‘zeroth-order’ expression involving no interaction which can be solved exactly. To this is added additional interaction (or perturbation) terms representing corrections to first-order, second-order, third-order, etc. In principle, each term in the expansion provides a smaller and smaller correction to the zeroth-order result, gradually bringing the calculation closer and closer to the actual result. The accuracy of the final result then depends simply on the number of perturbation terms included in the calculation.
photon The elementary particle underlying all forms of electromagnetic radiation, including light. The photon is a massless, spin-1 boson, which acts as the carrier of the electromagnetic force.
pion A group of spin-0 mesons formed from up and down quarks and their anti-quarks. These are π+ (up-anti-down), π– (down-anti-up) and π0 (a mixture of up-anti-up and down-anti-down), with masses 139.6 MeV/c2 (π±) and 135.0 MeV/c2 (π0). The pions can be thought of as the ‘carriers’ of the strong force binding protons and neutrons inside the atomic nucleus, representing a kind of ‘leakage’ of the colour force binding quarks inside the protons and neutrons beyond the boundaries of these particles. First hypothesized by Japanese physicst Hideki Yukawa in 1935.
Planck constant Denoted h. Discovered by Max Planck in 1900. The Planck constant is a fundamental physical constant which reflects the magnitudes of quanta in quantum theory. For example, the energies of photons are determined by their radiation frequencies according to the relation E = hν, energy equals Planck’s constant multiplied by the radiation frequency. Planck’s constant has the value 6.626 × 10−34 Joule-seconds.
Planck length The ultimate unit of length, derived from a collection of fundamental physical constants as √(hG/2πc3), where h is Planck’s constant, G is Newton’s gravitational constant and c is the speed of light. It has the value 1.616 × 10−35 m. The Planck length helps to define the Planck scale, along with the Planck mass √(hc/2πG), about 2.177 × 10−8 kg, and the Planck time √(hG/2πc5), the time taken for light to travel the Planck length, 5.391 × 10−44 s.
positron The anti-particle of the electron, denoted e+, with a charge +1, spin ½ (fermion), and mass 0.511 MeV/c2. The positron was the first anti-particle to be discovered, by Carl Anderson in 1932.
primary quality A concept developed by the classical modern and mechanical philosophers in the seventeenth century, most closely associated with English philosopher John Locke. The primary qualities of an object are independent of observation and include things like solidity, extension (in three-dimensional space), motion, number, and so on. See also Secondary quality.
proton A positively charged sub-atomic particle ‘discovered’ and so named by Ernest Rutherford in 1919. Rutherford actually identified that the nucleus of the hydrogen atom (which is a single proton) is a fundamental constituent of other atomic nuclei. The proton is a baryon consisting of two-up and one-down quarks with spin ½ and mass 938.3 MeV/c2.
quantum A fundamental, indivisible unit of properties such as energy and angular momentum. In quantum theory, such properties are recognized not to be continuously variable but to be organized in discrete packets or bundles, called quanta. In quantum field theory the use of the term is extended to include particles. Thus, the photon is the quantum particle of the electromagnetic field. This idea can be extended beyond the carriers of forces to include matter particles themselves. Thus, the electron is the quantum of the electron field, and so on. This is sometimes referred to as second quantization.
quantum chromodynamics (QCD) The quantum field theory of the colour force between quarks carried by a system of eight coloured gluons.
quantum electrodynamics (QED) The quantum field theory of the electromagnetic force between electrically charged particles, carried by photons.
quantum entanglement A term coined by Erwin Schrödinger in 1935. Refers to a specific set of circumstances or physical processes in which the properties and behaviour of two or more quantum wave-particles are governed by a single wavefunction. Experiments on entangled particles (especially entangled photons) have been used to provide practical tests of local and crypto-non-local hidden variable extensions of quantum theory based on Bell’s and Leggett’s inequalities.
quantum field In classical field theory a ‘force field’ is ascribed a value at every point in spacetime and can be scalar (magnitude but no direction) or vector (magnitude and direction). The ‘lines of force’ made visible by sprinkling iron filings on a piece of paper held above a bar magnetic provides a visual representation of such a field. In a quantum field theory, forces are conveyed by ripples in the field which form waves and—because waves can also be interpreted as particles—as quantum particles of the field. This idea can be extended beyond the carriers of forces (bosons) to include matter particles (fermions). Thus, the electron is the quantum of the electron field, and so on.
quantum number The description of the physical state of a quantum system requires the specification of its properties in terms of total energy, linear and angular momentum, electric charge, etc. One consequence of the quantization of such properties is the appearance in this description of regular multiples of the associated quanta. The recurring integral or half-integral numbers which multiply the sizes of the quanta are called quantum numbers. When placed in a magnetic field, the electron spin may be oriented along or against the field lines of force, giving rise to ‘spin-up’ and ‘spin-down’ orientations characterized by the quantum numbers +½ and –½. Other examples include the principal number, n, which characterizes the energy levels of electrons in atoms, electric charge, quark colour charge, etc.
quantum probability The wavefunctions of quantum wave-particles such as electrons are necessarily extended and delocalized through a region of space, for example in an orbital around the central proton in a hydrogen atom. The square of the amplitude of the wavefunction at some specific location is then related to the probability of ‘finding’ the electron at this point. The same principle applies to wavefunctions formed from superpositions. For example, if we form a wavefunction which is a mixture of spin-up and spin-down functions, then the probability that we will observe spin-up is given by the square of the amplitude of this component in the superposition. If spin-up is actually observed, the spin-down component ‘disappears’. See Collapse of the wavefunction.
quark The elementary constituents of hadrons. Hadrons are composed of triplets of spin ½ quarks (baryons) or combinations of quarks and anti-quarks (mesons). The quarks form three generations, each with different flavours. The up and down quarks, with electric charges +2⁄3 and –1⁄3 and masses of 1.8–3.0 MeV/c2 and 4.5−5.3 MeV/c2 respectively, form the first generation. Protons and neutrons are composed of up and down quarks. The second generation consists of the charm and strange quarks, with electric charges +2⁄3 and –1⁄3 and masses of 1.28 GeV/c2 and 95 MeV/c2, respectively. The third generation consists of bottom and top quarks, with electric charges +2⁄3 and –1⁄3 and masses of 4.18 GeV/c2 and 173 GeV/c2, respectively. Quarks also carry colour charge, with each flavour of quark possessing red, green, or blue charges.
redshift In the rainbow spectrum of colours, the energy of the light radiation increases from red through to violet. This means that red light has a lower frequency (and longer wavelength) compared with other colours. When the wavelength of radiation is increased as a result of the Doppler Effect or the cosmological expansion of spacetime, the result is referred to as a ‘redshift’. This doesn’t mean that the radiation becomes ‘redder’, just that its wavelength is increased. For example, red light may be redshifted into invisible infrared wavelengths.
renormalization One consequence of introducing particles as the quanta of fields is that they may undergo self-interaction, i.e. they can interact with their own fields. This means that techniques, such as perturbation theory, used to solve the field equations tend to break down, as the self-interaction terms appear as infinite corrections. Renormalization was developed as a mathematical device used to eliminate these self-interaction terms, by redefining the parameters (such as mass and charge) of the field particles themselves. See also Self-energy.
Schwarzschild solution/radius German physicist Karl Schwarzchild was the first to provide exact solutions of Einstein’s gravitational field equations, whilst serving in the German Army in 1916. The Schwarzschild solutions establish a fundamental boundary, called the Schwarzschild radius. A spherical mass, m, compressed to a radius less than the Schwarzschild radius (given by Gm/c2, where c is the speed of light and G is the gravitational constant) will become a black hole—its escape velocity exceeds the speed of light.
secondary quality A concept developed by the classical modern and mechanical philosophers in the seventeenth century, most closely associated with English philosopher John Locke. The secondary qualities of an object result from the sensations that it produces in the mind of an observer, and include things like colour, taste, touch, sound, and smell. See also Primary quality.
self-energy In a quantum field theory, particles are envisaged as fundamental fluctuations or vibrations of the field. One consequence is that particles may undergo self-interaction—they interact with their own fields. Such interactions increase the energy of the particle by an amount called self-energy. In early versions of the quantum field theory of electrons, the self-energy was found to be infinite. This problem was resolved by applying the techniques of renormalization.
spacetime and spacetime metric The distance between one position in a co-ordinate system and another can be determined from the values of the co-ordinates at these two positions. So, in a three-dimensional Euclidean space, if the positions are l1 = x1y1z1 and l2 = x2y2z2, the distance Δl = l2 – l1 can be found by applying Pythagoras’ theorem: Δl2 = Δx2 + Δy2 + Δz2. This ‘distance function’ is often referred to as a metric. It has an important property: no matter how we define the co-ordinate system (no matter how we define x, y, and z), the metric will always be the same (mathematicians say that it is ‘invariant’). We can extend Euclidean space to include a fourth dimension of time. To ensure that the resulting spacetime metric is invariant we need a structure such as Δs2 = Δ(ct)2 – Δx2 – Δy2 – Δz2, where s is a generalized spacetime interval, t is time, and c is the speed of light. We could swop these around and define Δs2 such that the time interval is negative and the spatial intervals positive—so long as these are of opposite sign, Δs2 is invariant. The choice of signs is a simply a matter of convention.
special relativity Developed by Einstein in 1905, the special theory of relativity asserts that all motion is relative, and there is no unique or privileged frame of reference against which motion can be measured. All inertial frames of reference are equivalent—an observer stationary on Earth should obtain the same results from the same set of physical measurements as an observer moving with uniform velocity in a spaceship. Out go classical notions of absolute space, time, absolute rest, and simultaneity. In formulating the theory, Einstein assumed that the speed of light in a vacuum represents an ultimate speed, which cannot be exceeded. The theory is ‘special’ only in the sense that it does not account for accelerated motion or gravity; this is covered in Einstein’s general theory of relativity.
spectrum Any physical property which has a range of possible values may be said to have a ‘spectrum’. The most obvious example is the range of colours produced when light is passed through a prism or a collection of raindrops to produce a rainbow. The resulting spectrum may appear continuous (as in a rainbow) or it may be discrete, consisting of a set of specific values. The absorption or emission spectrum of hydrogen atoms exhibits a series of ‘lines’ corresponding to radiation frequencies that are absorbed or emitted by the atoms. The positions (frequencies) of these lines in the spectrum relate to the energies of the electron orbitals involved.
spin All elementary particles exhibit a type of angular momentum called spin. Although the spin of the electron was initially interpreted in terms of ‘self-rotation’ (the electron spinning on its own axis, like a spinning top), spin is a relativistic phenomenon and has no counterpart in classical physics. Particles are characterized by their spin quantum numbers. Particles with half-integral spin quantum numbers are called fermions. Particles with integral spin quantum numbers are called bosons. Matter particles are fermions. Force particles are bosons.
standard model, of big bang cosmology See Λ-CDM.
standard model, of particle physics The currently-accepted theoretical model describing matter particles and the forces between them, with the exception of gravity. The standard model consists of a collection of quantum field theories which describes three generations of quarks and leptons, the photon, W, and Z particles, colour force gluons, and the Higgs boson.
standing wave Waves confined to oscillate between fixed points will interfere and may settle into a series of standing or stationary wave patterns. This is the basis for the production of musical notes in string or wind instruments, and there are many examples of naturally occurring standing waves in the atmosphere close to mountains and in river rapids. A condition for establishing standing waves in a stationary medium is that the waves must contain an integral number of half-wavelengths.
strange quark A second-generation quark with charge –1⁄3, spin ½ (fermion), and a mass of 95 MeV/c2. The property of ‘strangeness’ was identified as a characteristic of a series of relatively low energy (low mass) particles discovered in the 1940s and 1950s by Murray Gell-Mann and independently by Kazuhiko Nishijima and Tadao Nakano. This property was subsequently traced by Gell-Mann and George Zweig to the presence in these composite particles of the strange quark.
strangeness Identified as a characteristic property of particles such as the neutral lambda, neutral and charged sigma and xi particles, and the kaons. Strangeness was used together with electric charge and isospin to classify particles according to the ‘Eightfold Way’ by Murray Gell-Mann and Yuval Ne’eman. This property was subsequently traced to the presence in these composite particles of the strange quark.
strong force The strong nuclear force, or colour force, binds quarks and gluons together inside hadrons and is described by quantum chromodynamics. The force that binds protons and neutrons together inside atomic nuclei (also referred to as the strong nuclear force) is thought to be the result of a ‘leakage’ of the colour force binding quarks inside the nucleons. See Colour force.
SU(2) symmetry group The special unitary group of transformations of two complex variables. Identified by Chen Ning Yang and Robert Mills as the symmetry group on which a quantum field theory of the strong nuclear force should be based, SU(2) was subsequently identified with the weak force and can also be used to describe the residual strong force acting between protons and neutrons, carried by pions.
SU(3) symmetry group The special unitary group of transformation of three complex variables. Used by Gell-Mann, Harald Fritzsch, and Heinrich Leutwyler as a local symmetry on which to base a quantum field theory of the colour force between quarks and gluons.
substantial form The theory of forms originated with the ancient Greek philosopher Plato but it was his student, Aristotle, who most clearly distinguished between matter (the undifferentiated ‘stuff’ of material substance) and form (which differentiates and organizes matter and gives an object its essential characteristics). In medieval philosophy, the notion of substantial forms was used to rationalize many aspects of Christian doctrine, such as transubstantiation.
superconductivity Discovered by Heike Kamerlingh Onnes in 1911. When cooled below a certain critical temperature, certain crystalline materials lose all electrical resistance and become superconductors. An electric current will flow indefinitely in a superconducting wire flowing with no energy input. Superconductivity is a quantum mechanical phenomenon explained using the BCS mechanism, named for John Bardeen, Leon Copper, and John Schrieffer.
superposition In quantum mechanics, quantum entities can behave like particles and they can also behave like waves. But waves can be combined—they can be added together in a ‘superposition’. Such combinations describe diffraction and interference effects. In a quantum measurement, it is necessary to form a superposition which contains contributions from the wavefunctions describing all the different possible outcomes. The square of the amplitude of each wavefunction in the superposition relates to the probability that the corresponding outcome will be observed. When the measurement is made, the wavefunction ‘collapses’ and all the other possible outcomes disappear.
symmetry-breaking Spontaneous symmetry-breaking occurs whenever the lowest energy state of a physical system has lower symmetry than higher-energy states. As the system loses energy and settles to its lowest energy state, the symmetry spontaneously reduces, or ‘breaks’. For example, a pencil perfectly balanced on its tip is symmetrical, but under the influence of the background environment (such as small currents or air) it will topple over to give a more stable, lower-energy, less symmetrical state, with the pencil lying along one specific direction.
tera A prefix denoting trillion. A tera electron volts (TeV) is a trillion electron volts, 1012 eV, or 1,000 GeV.
top quark Also sometimes referred to as the ‘truth’ quark. A third-generation quark with charge +2⁄3, spin ½ (fermion), and a mass of 173 GeV/c2. It was discovered at Fermilab in 1995.
trillion A thousand billion or a million million, 1012, or 1,000,000,000,000.
U(1) symmetry group The unitary group of transformations of one complex variable. It is equivalent (the technical term is ‘isomorphic’) with the circle group, the multiplicative group of all complex numbers with absolute value of unity (in other words, the unit circle in the complex plane). It is also isomorphic with SO(2), a special orthogonal group which describes the symmetry transformation involved in rotating an object in two dimensions. In quantum electrodynamics, U(1) is identified with the phase symmetry of the electron wavefunction.
uncertainty principle Discovered by Werner Heisenberg in 1927. The uncertainty principle states that there is a fundamental limit to the precision with which it is possible to measure pairs of ‘conjugate’ observables, such as position and momentum and energy and the rate of change of energy with time. The principle can be traced to the fundamental duality of wave and particle behaviour in quantum objects.
void In the atomic theory of the ancient Greek philosophers, matter was thought to consist of tiny, indivisible atoms moving restlessly in empty space, which was called the void. In this context, void simply means space empty or devoid of any matter, and which today we tend to call a vacuum.
W, Z particles Elementary particles which carry the weak nuclear force. The W particles are spin-1 bosons with unit positive and negative electrical charge (W+, W–) and masses of 80.4 GeV/c2. The Z0 is an electrically neutral spin-1 boson with mass 91.2 GeV/c2. The W and Z particles gain mass through the Higgs mechanism.
wave–particle duality A fundamental property of all quantum particles, which exhibit both delocalized wave behaviour (such as diffraction and interference) and localized particle behaviour, depending on the type of apparatus used to make measurements on them. First suggested as a property of matter particles such as electrons by Louis de Broglie in 1923.
wavefunction The mathematical description of matter particles such as electrons as ‘matter waves’ leads to equations characteristic of wave motion. Such wave equations feature a wavefunction whose amplitude and phase evolves in space and time. The wavefunctions of the electron in a hydrogen atom form characteristic three-dimensional patterns around the nucleus called orbitals. Wave mechanics—an expression of quantum mechanics in terms of matter waves—was first elucidated by Erwin Schrödinger in 1926.
wavefunction collapse See Collapse of the wavefunction.
weak force The weak force is so called because it is considerably weaker than both the strong and electromagnetic forces, in strength and range. The weak force affects both quarks and leptons and weak force interactions can change quark and lepton flavour: for example, turning an up quark into a down quark and an electron into an electron neutrino. The weak force was originally identified as a fundamental force from studies of beta radioactive decay. Carriers of the weak force are the W and Z particles. The weak force was combined with electromagnetism in the quantum field theory of the electro-weak force by Steven Weinberg and Abdus Salam in 1967–1968.
Yang–Mills field theory A form of quantum field theory developed in 1954 by Chen Ning Yang and Robert Mills. Yang–Mills field theories underpin all the components of the current standard model of particle physics.