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Glossary: Q - Z

Any quantum system in which a physical property can take on only discrete values is said to be quantized. For instance, the energy of a confined particle is quantized. This is in contrast to a situation in which the energy can vary continuously, which is the case for a free particle.
quantum chromodynamics
Quantum chromodynamics, or QCD, is the theory that describes the strong nuclear force. It is a quantum field theory in which quarks interact with one another by exchanging force-carrying particles called "gluons." It has two striking features that distinguish it from the weak and electromagnetic forces. First, the force between two quarks remains constant as the quarks are pulled apart. This explains why single quarks have never been found in nature. Second, quarks and gluons interact very weakly at high energies. QCD is an essential part of the Standard Model and is well tested experimentally; however, calculations in QCD can be very difficult and are often performed using approximations and computer simulations rather than solved directly.
quantum electrodynamics
Quantum electrodynamics, or QED, is the quantum field theory that describes the electromagnetic force. In QED, electromagnetically charged particles interact by exchanging virtual photons, where photons are the force carried of the electromagnetic force. QED is one of the most stringently tested theories in physics, with theory matching experiment to a part in 1012.
quantum field theory (QFT)
Quantum field theory, or QFT, is a generalization of quantum mechanics capable of describing relativistic particles. It is currently the standard mathematical formalism used in particle physics, as well as certain areas of condensed matter and atomic physics. In QFT, fields rather than particles are the fundamental objects. Particles correspond to vibrations of these fields. This formulation puts particles and forces on equal footing, as both are described by fields. An interaction between two particles, which are vibrations in the field that correspond to that type of particle, proceeds through the exchange of the particle that corresponds to a vibration in the field associated with the force. For example, electrons are vibrations of the electron field, and photons are vibrations of the electromagnetic field. When two electrons repel, they exchange photons.
quantum number
A quantum number is a number that characterizes a particular property of a quantum mechanical state. For example, each atomic energy level is assigned a set of integers that is uniquely related to the quantized energy of that level.
The quarks are a family of fundamental particles in the Standard Model. The quark family has three generations, shown in Unit 1, Fig. 1: up and down quarks, the charm and strange quarks, and top and bottom quarks. Individual, isolated quarks are never observed in nature. Instead, we observe bound groups of quarks as baryons and mesons.
Just as particles can be described as waves through the wave-particle duality, waves can be described as particles. Quasiparticles are the quantized particles associated with various types of waves in condensed matter systems. They are similar to particles in that they have a well-defined set of quantum numbers and can be described using the same mathematical formalism as individual particles. They differ in that they are the result of the collective behavior of a physical system.
A qubit is the quantum counterpart to the bit for classical computing. A bit, which is short for binary digit, is the smallest unit of binary information and can assume two values: zero and one. A qubit, or quantum bit, is in a quantum superposition of the values zero and one. Because the qubit is in a superposition and has no definite value until it is measured directly, quantum computers can operate exponentially faster than classical computers.
random walk
The random walk is the trajectory that arises when an object moves in steps that are all the same length, but in random directions. The path of a molecule in a gas follows a random walk, with the step size determined by how far (on average) the molecule can travel before it collides with something and changes direction. The behavior of many diverse systems can be modeled as a random walk, including the path of an animal searching for food, fluctuating stock prices, and the diffusion of a drop of food coloring placed in a bowl of water.
real number
Real numbers are most easily defined by contrast to what they are not: imaginary numbers. The set of real numbers includes counting numbers, integers, rational numbers that can be written as fractions, and irrational numbers such as . They can be thought of as all the points on a number line stretching from negative infinity to infinity.
In the context of cosmology, the term recombination refers to electrons combining with atomic nuclei to form atoms. In our standard model of cosmology, this took place around 390,000 years after the Big Bang. Prior to the time of recombination, the universe was filled with a plasma of electrically charged particles. Afterward, it was full of neutral atoms.
The term redshift is used for a number of different physical effects that lengthen the wavelength of photons, shifting them toward the red end of the spectrum. The Doppler shift of an object moving away from an observer is a redshift, as are the gravitational redshift (Unit 3), and the cosmological redshift due to the expansion of the universe (Unit 11).
A relativistic particle is traveling close enough to the speed of light that classical physics does not provide a good description of its motion, and the effects described by Einstein's theories of special and general relativity must be taken into account.
relativistic limit
In general, the energy of an individual particle is related to the sum of its mass energy and its kinetic energy by Einstein's equation E2 = p2c2 + m2c4, where p is the particle's momentum, m is its mass, and c is the speed of light. When a particle is moving very close to the speed of light, the first term (p2c2) is much larger than the second (m2c4), and for all practical purposes the second term can be ignored. This approximation—ignoring the mass contribution to the energy of a particle—is called the "relativistic limit."
The results of particle physics experiments are often expressed as the probability of particles interacting in the detector depending on how much energy the particles have. As the particle energy increases, the interaction probability changes slowly and smoothly, except at certain special energies called "resonances," which appear as bumps on the graph of probability versus energy. At a resonance, the probability of the particles interacting increases significantly. For example, the J/psi meson was discovered when the electron-positron collision energy just equaled the mass of the charm quark and anti-charm quark, creating a huge spike in particle production. Finding resonances is the primary way new particles are discovered in particle accelerator experiments. The mass of the new particle is the resonance energy.
resonance curve
A resonance curve is a graph of the response of an atomic system to electromagnetic radiation as a function of the frequency of the radiation. The simplest example of a resonance curve is the single peak that appears as a laser's frequency is scanned through the difference between two energy levels in the atoms.
Rutherford scattering
The term Rutherford scattering comes from Ernest Rutherford's experiments that led to the discovery of the atomic nucleus. Rutherford directed a beam of alpha particles (which are equivalent to helium nuclei) at a gold foil and observed that most of the alpha particles passed through the foil with minimal deflection, but that occasionally one bounced back as if it had struck something solid.
scalar field
A scalar field is a smoothly varying mathematical function that assigns a value to every point in space. An example of a scalar field in classical physics is the gravitational field that describes the gravitational potential of a massive object. In meteorology, the temperature and pressure distributions are scalar fields. In quantum field theory, scalar fields are associated with spin-zero particles. All of the force-carrying particles as well as the Higgs boson are generated by scalar fields.
Second Law of Thermodynamics
The second law of thermodynamics states that the entropy of an isolated system will either increase or remain the same over time. This is why heat flows from a hot object to a cold object, but not the other way; and why it's easy to dissolve salt in water, but not so easy to get the salt back out again.
shell model
The shell model of atomic structure is based on the notion that electrons in an atom occupy "shells" that can fill up, so only a certain number of electrons will fit in a given shell. G. N. Lewis found this idea useful in explaining the chemical properties of different elements. Lewis's shell model is consistent with the Bohr model of the atom in which electrons are thought of as orbiting the nucleus. The "shells" are three-dimensional counterparts of two-dimensional circular orbits with different radii. Although we now know that the Bohr model of the atom is not correct, the concept of shells is still sometimes used to describe the arrangement of electrons in atoms according to the Pauli exclusion principle.
Singularity is a mathematical term that refers to a point at which a mathematical object is undefined, either because it is infinite or degenerate. A simple example is the function 1/x. This function has a singularity at x = 0 because the fraction 1/0 is undefined. Another example is the center of a black hole, which has infinite density. In our standard model of cosmology, the universe we live in began as a spacetime singularity with infinite temperature and density.
The Stanford Linear Accelerator Center (SLAC) is a linear particle accelerator (linac) operated by Stanford University. SLAC is the longest linear accelerator in the world, accelerating electrons or positrons for two miles. The collision energy when the accelerated particles hit a fixed target is 50 GeV. Since the SLAC began operation in 1966, its results have led to Nobel Prizes for the discovery of the J/Psi particle, which provided evidence for the existence of the charm quark, the discovery of structure inside protons and neutrons indicating that they are made of quarks, and the discovery of the tau lepton. SLAC is now used in a wide variety of projects that range from astrophysics to biology, chemistry, and materials science.
Sloan Digital Sky Survey
The Sloan Digital Sky Survey (SDSS) is one of the most extensive and ambitious astronomical surveys undertaken by modern astronomers. In its first two stages, lasting from 2000 to 2008, SDSS mapped almost 30 percent of the northern sky using a dedicated 2.5 meter telescope at the Apache Point Observatory in New Mexico. The survey used a 120-megapixel camera to image over 350 million objects, and collected the spectra of hundreds of thousands of galaxies, quasars, and stars. Notable SDSS discoveries include some of the oldest known quasars and stars moving fast enough to escape from our galaxy. SDSS data has also been used to map the distribution of dark matter around galaxies through observations of weak gravitational lensing and to study the evolution of structure in the universe through observations of how both galaxies and quasars are distributed at different redshifts. The third phase of the survey is scheduled to end in 2014, and is expected to yield many exciting scientific discoveries.
Snell's Law
Snell's law describes how the path of a light ray changes when it moves into a material with a different index of refraction. According to Snell's law, if a light ray traveling through a medium with index of refraction n1 hits the boundary of a material with index n2 at angle , the light path is bent and enters the new material at an angle given by the relation n1sin = n2 sin.
A soliton is a stable, isolated wave that travels at a constant speed. As a soliton travels, its shape does not change and it does not dissipate. If it collides with another wave, it emerges from the collision unscathed. In a sense, it is a wave that behaves like a particle. Solitons have been predicted and observed in nearly every medium in which waves propagate, including fluids such as water, transparent solids such as optical fibers, and magnets.
In classical physics, space and time are considered separate things. Space is three-dimensional, and can be divided into a three-dimensional grid of cubes that describes the Euclidean geometry familiar from high-school math class. Time is one-dimensional in classical physics. Einstein's theory of special relativity combines the three dimensions of space and one dimension of time into a four-dimensional grid called "spacetime." Spacetime may be flat, in which case Euclidean geometry describes the three space dimensions, or curved. In Einstein's theory of general relativity, the distribution of matter and energy in the universe determines the curvature of spacetime.
special relativity
Einstein developed his theory of special relativity in 1905, 10 years before general relativity. Special relativity is predicated on two postulates. First, the speed of light is assumed to be constant in all inertial frames. Second, the laws of physics are assumed to be the same in all inertial frames. An inertial frame, in this context, is defined as a reference frame that is not accelerating or in a gravitational field. Starting from these two postulates, Einstein derived a number of counterintuitive consequences that were later verified by experiment. Among them are time dilation (a moving clock will run slower than a stationary clock), length contraction (a moving ruler will be shorter than a stationary ruler), the equivalence of mass and energy, and that nothing can move faster than the speed of light. See: general relativity, spacetime.
spontaneous emission
An atom in an excited state can decay down to a lower state by emitting a photon with an energy equal to the difference between the initial, higher energy level and the final, lower energy level. When this process takes place naturally, rather than being initiated by disturbing the atom somehow, it is called spontaneous emission.
spontaneous symmetry breaking
Spontaneous symmetry breaking is said to occur when the theory that describes a system contains a symmetry that is not manifest in the ground state. A simple everyday example is a pencil balanced on its tip. The pencil, which is symmetric about its long axis and equally likely to fall in any direction, is in an unstable equilibrium. If anything (spontaneously) disturbs the pencil, it will fall over in a particular direction and the symmetry will no longer be manifest.
A superconducting quantum interference device, or SQUID, is a tool used in laboratories to measure extremely small magnetic fields. It consists of two half-circles of a superconducting material separated by a small gap. The quantum mechanical properties of the superconductor make this arrangement exquisitely sensitive to tiny changes in the local magnetic field. A typical SQUID is sensitive to magnetic fields hundreds of trillions of times weaker than that of a simple refrigerator magnet.
standard candle
In astronomy, a standard candle is a class of objects whose distances can be computed by comparing their observed brightness with their known luminosity. Cepheid variable stars are useful as standard candles because their pulsation period is related to their luminosity in a known way. To use a Cepheid variable star to make a distance measurement, an astronomer would measure the apparent brightness of the star and its pulsation period, then calculate the luminosity of the star from its period, and finally compute the distance by comparing the apparent brightness to the calculated luminosity.
Standard Model
The Standard Model is the name given to the current theory of fundamental particles and how they interact. It includes three generations of quarks and leptons interacting via the strong, weak, and electromagnetic forces. The Standard Model does not include gravity.
standard model of cosmology
Our best model for how the universe began and evolved into what we observe now is called the "standard model of cosmology." It contends that the universe began in a Big Bang around 14 billion years ago, which was followed by a short period of exponential inflation. At the end of inflation, quarks, photons, and other fundamental particles formed a hot, dense soup that cooled as the universe continued to expand. Roughly 390,000 years after the end of inflation, the first atoms formed and the cosmic microwave background photons decoupled. Over the course of billions of years, the large structures and astronomical objects we observe throughout the cosmos formed as the universe continued to expand. Eventually the expansion rate of the universe started to increase under the influence of dark energy.
standing wave
A standing wave is a wave that does not travel or propagate: The troughs and crests of the wave are always in the same place. A familiar example of a standing wave is the motion of a plucked guitar string.
stationary states
In quantum mechanics, a stationary state is a state of a system that will always yield the same result when observed in an experiment. The allowed energy states of a harmonic oscillator (Unit 5, section 5) are an example, as are the allowed energy levels of an atom. Stationary states correspond to quantum wavefunctions that describe standing waves.
Strangeness is a number assigned to Standard Model particles made of quarks. It is defined as the number of strange quarks minus the number of anti-strange quarks in the particle. Strangeness is useful in arranging baryons into a "periodic table," and is conserved in strong and electromagnetic interactions, but not in weak interactions.
strong interaction
The strong interaction, or strong nuclear force, is one of the four fundamental forces of nature. It acts on quarks, binding them together into mesons. Unlike the other forces, the strong force between two particles remains constant as the distance between them grows, but actually gets weaker when the particles get close enough together. This unique feature ensures that single quarks are not found in nature. True to its name, the strong force is a few orders of magnitude stronger than the electromagnetic and weak interactions, and many orders of magnitude stronger than gravity.
strong-CP problem
The strong-CP problem is a particular inconsistency between experimental observations of strong interactions and the theory that describes them. Unlike in weak interactions, CP violation has never been observed in strong interactions. However, the theory that describes strong interactions allows CP violation to occur. So why is it not observed? That is the strong-CP problem. Various attempts to resolve the strong-CP problem have been proposed, but none have been experimentally verified. See: axion, charge, CP violation, parity.
Sunyaev-Zel'dovich Effect
The Sunyaev-Zel'dovich, or S-Z, effect creates a distinctive pattern of temperature variation in the cosmic microwave background as CMB photons pass through galaxy clusters. Between the galaxies in a cluster, there is a gas containing energetic electrons that scatter about 1 percent of the CMB photons. The scattered photons gain energy from the electrons, leaving a cold spot in the CMB when observed at the original photon energy. The more energetic scattered photons appear as a hot spot when the CMB is observed with a receiver tuned to a slightly higher radio frequency. The S-Z effect allows astronomers to identify galaxy clusters across the entire sky in a manner that is independent of redshift. See: cosmic microwave background, galaxy cluster.
A supernova is an exploding star that can reach a luminosity of well over 100 million times that of the Sun. A supernova's brightness rises and falls rapidly over the course of about a month, then fades slowly over months and years. There are two broad classes of supernovae: those that get their energy from a sudden burst of fusion energy and those whose energy comes from gravitational collapse. In practice, these are distinguished on the basis of their different light curves and spectral characteristics. The type Ia supernovae used as standard candles in measurements of the expansion rate of the universe are thought to arise from the explosion of white dwarf stars in a binary system. As the white dwarf draws matter from its companion star, its carbon core reaches the temperature and density at which it can ignite and fuse explosively in a nuclear flame to iron. This violent explosion destroys the star, and creates about half a solar mass of radioactive isotopes that power the bright peak of the light curve.
In the theory of supersymmetry, every Standard Model particle has a corresponding "sparticle" partner with a spin that differs by 1/2. Superpartner is the general term for these partner particles. The superpartner of a boson is always a fermion, and the superpartner of a fermion is always a boson. The superpartners have the same mass, charge, and other internal properties as their Standard Model counterparts. See: supersymmetry.
In quantum mechanics, it is possible for a particle or system of particles to be in a superposition state in which the outcome of a measurement is unknown until the measurement is actually made. For example, neutrinos can exist in a superposition of electron, muon, and tau flavors (Units 1 and 2). The outcome of a measurement of the neutrino's flavor will yield a definite result—electron, muon, or tau—but it is impossible to predict the outcome of an individual measurement. Quantum mechanics tells us only the probability of each outcome. Before the measurement is made, the neutrino's flavor is indeterminate, and the neutrino can be thought of as being all three flavors at once.
superposition principle
Both quantum and classical waves obey the superposition principle, which states that when two waves overlap, the resulting wave is the sum of the two individual waves.
Supersymmetry, or SUSY, is a proposed extension to the Standard Model that arose in the context of the search for a viable theory of quantum gravity. SUSY requires that every particle have a corresponding superpartner with a spin that differs by 1/2. While no superpartner particles have yet been detected, SUSY is favored by many theorists because it is required by string theory and addresses other outstanding problems in physics. For example, the lightest superpartner particle could comprise a significant portion of the dark matter.
symmetry transformation
A symmetry transformation is a transformation of a physical system that leaves it in an indistinguishable state from its starting state. For example, rotating a square by 90 degrees is a symmetry transformation because the square looks exactly the same afterward.
A synchrotron is a type of circular particle accelerator similar to the cyclotron, but capable of accelerating particles to much higher energies. It consists of a toroidal tube in a magnetic field. Charged particles are injected into the synchrotron's beam tube from a preliminary accelerator, usually a linac. Once in the synchrotron, the magnetic field directs the particles in a circular path. A voltage is placed across short sections of the beam tube along the path the particles follow. The particles are accelerated each time they pass through one of these voltages. As the particles speed up, the strength of the magnetic field is increased to keep the particles traveling in the same circular path. After circling through the accelerator many times, the particles are traveling at nearly the speed of light. The Bevatron, Tevatron, and LHC are all synchrotron accelerators.
The tau, also called the tauon, is a fundamental particle in the Standard Model. It is a member of the third generation of leptons. The tau is negatively charged, and is heavier than the electron and muon.
The Tevatron is a particle accelerator operated at the Fermi National Accelerator Laboratory in Batavia, Illinois. Since the completion of construction in 1983, the Tevatron has accelerated counterpropagating beams of protons and antiprotons in a 6.28 kN diameter synchrotron ring. Many important aspects of the Standard Model were supported by Tevatron experiments. Notably, the top quark was first discovered in Tevatron collisions. The Tevatron is the most powerful proton-antiproton collider in the world, with collision energies of up to 2 TeV. Only the LHC, a proton-proton collider, is capable of creating higher energy collisions.
Topology is the mathematical study of what happens to objects when they are stretched, twisted, or deformed. Objects that have the same topology can be morphed into one another smoothly, without any tearing. For example, a donut and a coffee cup have the same topology, while a beach ball is in a different topological category.
torsion pendulum
A conventional pendulum is a mass suspended on a string that swings periodically. A torsion pendulum is a mass suspended on a string (or torsion fiber) that rotates periodically. When the mass of a torsion pendulum is rotated from its equilibrium position, the fiber resists the rotation and provides a restoring force that causes the mass to rotate back to its original equilibrium position. When the mass reaches its equilibrium position, it is moving quickly and overshoots. The fiber's restoring force, which is proportional to the rotation angle of the mass, eventually causes the mass to slow down and rotate back the other way. Because the restoring force of the torsion fiber is very small, a torsion pendulum can be used to measure extremely small forces affecting the test mass.
Tunneling, or quantum tunneling, takes place when a particle travels through a region that would be forbidden according to the laws of classical physics. Tunneling occurs because quantum wavefunctions extend slightly past the boundaries that define where a particle is allowed to be. For example, in classical physics, an electron is allowed to move through a conductor but not through an insulator. However, if a thin layer of insulator is placed between two conductors, the electron can tunnel through from one conductor to the other because its wavefunction extends into the insulating layer.
Turing machine
In 1937, Alan Turing outlined the details of the Turing machine in a paper investigating the possibilities and limits of machine computation. The machine is an idealized computing device that consists, in its simplest form, of a tape divided up into cells that are processed by an active element called a "head." The cells can be in one of two states. The head moves along the tape, changing the cells from one state to the other and moving either forward or backward according to a set of predetermined instructions. Turing machines can be described with a set of simple mathematical equations that allowed scientists to understand many of the basic properties of digital computing long before the first modern computer was built.
universal gravitational constant
The universal gravitational constant, denoted by G, is the proportionality constant in Newton's law of universal gravitation. The currently accepted value for G is 6.67428±0.00067 x 10-11 N-m2/kg2.
universality of free fall
The universality of free fall, sometimes abbreviated UFF, is the idea that all materials fall at the same rate in a uniform gravitational field. This is equivalent to stating that inertial and gravitational mass are the same. See: equivalence principle, gravitational mass, inertial mass.
valence electron
A valence electron is an electron in the outermost shell of an atom in the Lewis model, or in the orbital with the highest value of the principal quantum number, n, in the quantum mechanical description of an atom. The valence electrons determine most of the chemical and physical properties of the atom. It is the valence electrons that participate in ionic and covalent chemical bonds, and that make the primary contributions to an atom's magnetic moment.
virtual particle
A virtual particle is a particle that appears spontaneously and exists only for the amount of time allowed by the Heisenberg uncertainty principle. According to the uncertainty principle, the product of the uncertainty of a measured energy and the uncertainty in the measurement time must be greater than Planck's constant divided by 4. This means that a particle with a certain energy can spontaneously appear out of the vacuum and live for an amount of time inversely proportional to its energy. The force carriers exchanged in an interaction are virtual particles. Virtual particles cannot be observed directly, but their consequences can be calculated using Feynman diagrams and are verified experimentally.
A vortex is a region in which a fluid or gas flows in a spiral toward the vortex center. The speed of fluid flow is fastest at the center of the vortex, and decreases with distance from the vortex center. Tornados and whirlpools are examples of vortices. Quantized vortices will appear in a superfluid when it is rotated fast enough, and quantized vortices will form in the electron gas inside a type-II superconductor when it is placed in a strong enough magnetic field.
wave mechanics
Wave mechanics is the version of quantum mechanics formulated primarily by Erwin Schrödinger in the 1920s. Following de Broglie's hypothesis that particles can equally well be described as waves, Schrödinger set out to write down a wave equation for quantum systems and proceeded to solve it in many interesting examples. Wave mechanics is mathematically equivalent to Heisenberg's matrix mechanics.
weak interaction
The weak interaction, or weak force, is one of the four fundamental forces of nature. It is called "weak" because it is significantly weaker than both the strong force and the electromagnetic force; however, it is still much stronger than gravity. The weak changes one flavor of quark into another, and is responsible for radioactive decay.
The WIMP, or weakly interacting massive particle, is a candidate for what may comprise the dark matter. WIMPs interact with other forms of matter through gravity and the weak nuclear force, but not through the electromagnetic force or the strong nuclear force. The lack of electromagnetic interactions means that WIMPs are nonluminous and therefore dark. They are assumed to be much heavier than the known Standard Model particles, with a mass greater than a few GeV. WIMP is a general term that can be applied to any particle fitting the above criteria. The neutralino, the supersymmetric partner of the neutrino, is an example of a WIMP candidate.
winding mode
In string theory, a winding mode is a distinct way in which a string can wrap around a compactified extra dimension. If we imagine a single extra dimension compactified into a circle, the simplest winding mode is for the string to wind once around the circle.
Z boson
Z bosons are electrically neutral particles in the Standard Model that, along with the electrically charged W+ and W bosons, mediate weak interactions.
Zeeman effect
Each atomic energy level in which an atom has a non-zero spin splits into two or more separate levels when the atom is placed in an external magnetic field. The splitting grows with the strength of the external field. This effect is named the Zeeman effect after the experimentalist who first studied it in the laboratory, Pieter Zeeman. He received the 1902 Nobel Prize for this work, along with Hendrik Lorentz, the theorist who explained the effect.
zero point energy
The zero point energy is the minimum energy a system can have based on the Heisenberg uncertainty principle.

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