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Anti-de Sitter/Conformal Field Theory (AdS/CFT) is a mathematical relationship between two separate descriptions of the same physics. According to AdS/CFT, a string theory in a region of Anti-de Sitter (AdS) space is equivalent to a conformal field theory (CFT) on the boundary of that region. Anti-de Sitter space has negative curvature (a two-dimensional plane is curved in a saddle shape rather than flat), and is one of the simplest geometries in which the equations of general relativity can be solved. A conformal field theory is the type of field theory used in the Standard Model. Although AdS/CFT describes an artificially simple situation—we appear to live in flat space, not Anti-de Sitter space—the mathematical correspondence between the two descriptions of physics has allowed relatively straightforward field theory calculations to shed light on problems associated with the quantum mechanics of black holes. AdS/CFT has also been used the other way, with black hole calculations providing insight into complicated particle collisions and condensed matter systems that are difficult to understand with the conventional field theory approach.
alkali metals
The alkali metals are the chemical elements in the first column of the periodic table. They all have one valence electron. Alkali metals are commonly used atoms in atomic physics experiments for several reasons. Their structure is relatively simple and provides energy states that are convenient for laser cooling. Many of their transition frequencies match convenient laser sources. Also, the single valence electron's magnetic moment allows the atoms to be easily trapped using magnetic fields, which is convenient for the evaporative cooling process necessary to reach ultracold temperatures.
alpha rays
Alpha particles, also known as alpha rays, consist of two protons and two neutrons bound together into a particle identical to the nucleus of a helium atom. Alpha particles are emitted when certain radioactive atoms decay, and typically have an energy of about 5 MeV.
angular momentum
In classical physics, the angular momentum of a system is the momentum associated with its rotational motion. It is defined as the system's moment of inertia multiplied by its angular velocity. In quantum mechanics, a system's total angular momentum is the sum of the angular momentum from its rotational motion (called orbital angular momentum) and its spin.
antiferromagnetic order
An antiferromagnet is a magnet in which the microscopic magnetic moments inside the material line up in a grid on which neighboring moments point in opposite directions. The interaction energy between two magnetic moments in an antiferromagnet is lower when the two moments point in opposite directions. This can lead to a frustrated system with multiple ground states.
Antimatter is a type of matter predicted by Paul Dirac when he attempted to write down a version of quantum mechanics that incorporated Einstein's theory of special relativity. In the Standard Model, every particle has a corresponding antiparticle that has the same mass but opposite electric charge, baryon number, and strangeness. When a particle meets its antiparticle counterpart, the pair annihilates: they disappear, and their total energy is converted into other particles.
An antiquark is the antimatter counterpart of a quark. See: antimatter, quark.
atomic fountain
An atomic fountain is a cloud of cold atoms that is given a push upward with a laser pulse. The laser is tuned to the right energy to transfer its momentum to the atoms, which fly up until gravity takes over, reversing their motion so they fall back down. The path the atoms take is analogous to the path of water in a fountain.
atomic number
The atomic number of an atom, denoted by Z, is the number of protons in its nucleus. The atomic number of an atom determines its place in the periodic table, and thus which chemical element it is.
The axion is a hypothetical particle that naturally arises in the solution to the strong-CP problem proposed by Peccei and Quinn in 1977. Axions are electrically neutral, and experiments have shown that their mass must be less than 1 eV. While they are relatively light particles, slow-moving axions could be produced in copious amounts in the early universe, and thus could be a significant component of the dark matter.
B factory
A B factory is a particle physics apparatus designed to create B mesons, which are mesons that contain one bottom antiquark and one quark of a different flavor. In a B factory, electrons and positrons from an accelerator collide, producing B mesons and anti-B mesons in equal amounts. The science goal of the B factories is to study CP violation in B meson decay, which may shed light on why the universe contains more matter than antimatter.
The term "baryon" refers to any particle in the Standard Model that is made of three quarks. Murray Gell-Mann arranged the baryons into a periodic table-like structure according to their baryon number and strangeness (see Unit 1, Fig. 1). Protons and neutrons are the most familiar baryons.
baryon number
Every particle composed of quarks is assigned a baryon number. A particle's baryon number is one-third the number of quarks minus the number of antiquarks in the particle. Baryon number is conserved in collisions, which means that the total baryon number of incoming particles is the same as the total baryon number of the particles produced in the collision.
baryonic matter
In the context of cosmology, including discussions of dark matter and the evolution of the universe, the term "baryonic matter" refers to the so-called ordinary matter described by the Standard Model. The atoms and molecules we are made of are considered baryonic matter. Axions and WIMPs are examples of nonbaryonic matter. Most of the dark matter is presumed to be nonbaryonic; however, no nonbaryonic matter has been directly detected in experiments.
BCS theory
BCS theory is the theory of superconductivity put forward in 1957 by John Bardeen, Leon Cooper, and John Schreiffer, who received the 1972 Nobel Prize for their effort. The basic premise of BCS theory is that under the right conditions inside a conductor, electrons can form weakly bound pairs called "Cooper pairs" that form a condensate. Pairs in the condensate experience no resistance as they travel through the conductor.
beta decay
Beta decay is a type of radioactive decay in which a beta particle (electron or positron) is emitted together with a neutrino. Beta decay experiments provided the first evidence that neutrinos exist, which was unexpected theoretically at the time. Beta decay proceeds via the weak interaction.
beta rays
Beta particles, also known as beta rays, are the electrons emitted when a neutron in the nucleus of a radioactive atom decays into a proton. Beta particles typically have an energy of up to 2.5 MeV, sharing the total energy released in the radioactive decay with a neutrino that is produced at the same time.
The Bevatron is a particle accelerator operated at the Lawrence Berkeley National Laboratory from 1954 to 1993. It was designed to test the hypothesis that every particle has a corresponding antiparticle, and accelerated protons to high enough energies (6.2 GeV) that antiprotons might be produced in a collision with a fixed target. The Bevatron successfully produced antiprotons, and remained a productive research facility through several upgrades until its decommissioning in 1993.
black hole
A black hole is a region of space where gravity is so strong that nothing can escape its pull. Black holes have been detected through their gravitational influence on nearby stars and through observations of hot gas from surrounding regions accelerating toward them. These black holes are thought to have formed when massive stars reached the end of their cycle of evolution and collapsed under the influence of gravity. If a small volume of space contains enough mass, general relativity predicts that spacetime will become so highly curved that a black hole will form.
A blackbody is an object that absorbs all incident electromagnetic radiation and re-radiates it after reaching thermal equilibrium. The spectrum of light emitted by a blackbody is smooth and continuous, and depends on the blackbody's temperature. The peak of the spectrum is higher and at a shorter wavelength as the temperature increases.
Bohr Correspondence Principle
The Bohr Correspondence Principle states that the predictions of quantum mechanics must match the predictions of classical physics in the physical situations that classical physics is intended to describe, and does describe very accurately. Mathematically, this means that the equations of quantum mechanics must smoothly turn into the equations of classical mechanics as the de Broglie wavelength of particles becomes very small, and the energy state quantum number gets very large.
Bose-Einstein condensate
A Bose-Einstein condensate, or BEC, is a special phase of matter in which the quantum mechanical wavefunctions of a collection of particles line up and overlap in a manner that allows the particles to act as a single quantum object. The electrons in a superconductor form a BEC; superfluid helium is an example of a liquid BEC. BECs can also be created from dilute gases of ultracold atoms and molecules.
A boson is a particle with integer, rather than half-integer, spin. In the Standard Model, the force-carrying particles such as photons are bosons. Composite particles can also be bosons. Mesons such as pions are bosons, as are 4He atoms. See: fermion, meson, spin.
brane, p-brane
In string theory, branes are fundamental objects that exist in a specific number of spatial dimensions. The "p" in p-brane stands for the number of dimensions that brane has. For example, a string is a 0-brane, a membrane is a 2-brane, and we could live on a 3-brane.
Brownian motion
Brownian motion is the seemingly random motion that a small particle (say, a grain of pollen) undergoes when it is suspended in a liquid. First documented by Scottish botanist Robert Brown, it was explained by Einstein as the result of the pollen grain being buffeted by the random motion of molecules in the liquid. Brownian motion is similar to the random walk, and the equations governing Brownian motion can be derived from the random walk equations by making the step size infinitely small along with a few other mathematical assumptions.
bubble chamber
Bubble chambers were the primary detectors used to study particles produced in particle accelerator collisions throughout the 1960s and 1970s. A bubble chamber is a vessel filled with superheated liquid, usually hydrogen, which will immediately boil when disturbed. When a charged particle passes through a bubble chamber, a trail of bubbles traces out its path through the liquid. Photographs of these trails allowed particle physicists to figure out what particles were produced in high energy collisions. Bubble chambers supplanted cloud chambers because they are easier to build in large sizes and the higher density in the liquid gave better resolution in the detector.
Some chemical reactions proceed much more quickly in the presence of a particular molecule than they do when that molecule is absent. The molecule, called a "catalyst," is said to catalyze the reaction.
Cepheid variable stars
Cepheid variable stars are high-luminosity stars that undergo very regular variations in brightness. A typical Cepheid will dim to a fraction of its maximum brightness and then grow brighter again with a period ranging from a few days to several months. During this cycle, the star is moving between two different states. At maximum brightness, the star is more compact and hotter, and pressure within the star causes it to expand. As the star expands, the pressure is released and the star cools. Eventually, the force of gravity is stronger than the outward pressure on within the star, and it collapses in on itself, heating, becoming brighter, and starting the cycle over again. The absolute luminosity of Cepheids, which are 5 to 20 times more massive than the Sun, is related in a precise way to the period of the brightness oscillation, which allows them to be used as standard candles. See: luminosity, standard candle.
charge conjugation
Charge conjugation is an operation that changes a particle into its antiparticle.
chiral symmetry
A physical theory has chiral symmetry if it treats left-handed and right-handed particles on equal footing. Chiral symmetry is spontaneously broken in QCD.
closed string
In string theory, a closed string forms a loop. Unlike open strings, closed strings are not attached to other objects; however, a closed string can be broken apart to form an open string. Open strings and closed strings have different properties, and give rise to different sets of fundamental particles.
cloud chamber
Cloud chambers are one of the earliest types of detectors used to study particles in cosmic rays and those produced in particle accelerator collisions. A cloud chamber is an airtight box filled with supersaturated water vapor. When a charged particle passes through a cloud chamber, liquid water droplets condense out of the vapor along the particle's path, leaving a visible trail.
In QCD, color is the name given to the charge associated with the strong force. While the electromagnetic force has positive and negative charges that cancel one another out, the strong force has three types of color, red, green, and blue, that are canceled out by anti-red, anti-green, and anti-blue.
In string theory, the term compactification refers to how an extra dimension is made small enough that we cannot perceive it. The three spatial dimensions we are familiar with from daily life are essentially infinite, while compactified dimensions are curled up, and have a finite size that ranges from a few microns (10-6 m) down to the Planck length.
In the context of physics and math, the term complex refers to the presence of complex numbers and is not a synonym of complicated. Thus, a "complex wave" is a mathematical function that describes a wave that can take on complex number values.
complex adaptive system (CAM)
A complex adaptive system, or CAM, is a population of individual components that react to both their environments and to one another. The state of the population is constantly evolving, and emergent behavior often appears. Biological and ecological systems are examples of complex adaptive systems, as are the Internet, human society, and the power grid.
complex number
A complex number is a composite of a real number and an imaginary number, and can be written in the form a+bi where a and b are real numbers and i is the square root of -1.
Compton scattering
Compton scattering is the scattering of photons from electrons. When Arthur Compton first explored this type of scattering experimentally by directing a beam of electrons onto a target crystal, he found that the wavelength of the scattered photons was longer than the wavelength of the photons incident on the target, and that larger scattering angles were associated with longer wavelengths. Compton explained this result by applying conservation of energy and momentum to the photon-electron collisions.
conformation distribution
The internal potential energy that a molecule has depends on its physical structure, or conformation. Molecules tend toward structures that minimize their potential energy. Sometimes there is not a single, unique minimum energy conformation. In this case, the conformation distribution is the set of lowest energy states that a molecule can occupy.
cosmic microwave background
The cosmic microwave background (CMB) radiation is electromagnetic radiation left over from when atoms first formed in the early universe, according to our standard model of cosmology. Prior to that time, photons and the fundamental building blocks of matter formed a hot, dense soup, constantly interacting with one another. As the universe expanded and cooled, protons and neutrons formed atomic nuclei, which then combined with electrons to form neutral atoms. At this point, the photons effectively stopped interacting with them. These photons, which have stretched as the universe expanded, form the CMB. First observed by Penzias and Wilson in 1965, the CMB remains the focus of increasingly precise observations intended to provide insight into the composition and evolution of the universe.
cosmic string
A cosmic string is a one-dimensional topological defect stretching across the universe, essentially an extremely thin, extremely dense line in space that would deform spacetime around it according to general relativity. Cosmic strings have been predicted by various theories, but never detected. It is possible that if the period of inflation in the early universe ended in a collision between a brane and an anti-brane, cosmic strings were produced in the process.
cosmological constant
The cosmological constant is a constant term that Einstein originally included in his formulation of general relativity. It has the physical effect of pushing the universe apart. Einstein's intent was to make his equations describe a static universe. After astronomical evidence clearly indicated that the size of the universe is changing, Einstein abandoned the cosmological constant though other astrophysicists, such as Georges Lemaître and Sir Arthur Stanley Eddington, thought it might be the source of cosmic expansion. The cosmological constant is a simple explanation of dark energy consistent with the observations; however, it is not the only possible explanation, and the value of the cosmological constant consistent with observation is over 60 orders of magnitude different from what theory predicts.
Coulomb's Law
Coulomb's Law states that the electric force between two charged particles is proportional to the product of the two charges divided by the square of the distance between the particles.
counting number
The counting numbers are the integers greater than zero: 1, 2, 3 … .
CP violation
The CP operation is a combination of charge conjugation (C) and parity (P). In most interactions, CP is conserved, which means that the interaction proceeds exactly the same way if the CP operation is performed on the interacting particles. If CP is conserved, particles with opposite charge and parity will interact in the same way as the original particles. CP violation occurs when an interaction proceeds differently when the CP operation is performed—particles with opposite charge and parity interact differently than the original particles. CP violation was first observed in neutral kaon systems.
critical density
In cosmology, the critical density is the density of matter and energy that corresponds to a flat geometry in general relativity. The critical density is given by 8H0/3G, where G is the gravitational constant. For a Hubble constant of 70 km/sec/Mpc, = 9 x 10-27 kg/m3.
cross section
A cross section, or scattering cross section, is a measure of the probability of two particles interacting. It has units of area, and depends on the initial energies and trajectories of the interacting particles as well as the details of the force that causes the particles to interact.
A cyclotron is a type of particle accelerator, first developed in the 1930s, consisting of two D-shaped cavities in a constant magnetic field. There is a gap between the cavities, so they form a circle with a missing stripe in the middle. A radioactive source placed in the center of the cyclotron—in the gap between the cavities—provides particles that will be accelerated. When a charged particle is emitted by the radioactive source, it is accelerated by a voltage placed across the gap. The magnetic field bends the particle's path so it travels in a circle. When the particle circles back to the gap, it is traveling in the opposite direction. At that point, the voltage across the gap is reversed so the particle is accelerated further. The voltage is alternated so that the particle is accelerated each time it crosses the gap. As the particle speeds up, its path is bent less by the magnetic field and it travels in an increasingly larger circle. Eventually, it spirals out of the cyclotron moving at a high speed. The largest cyclotron currently in use is TRIUMF at the University of British Columbia in Vancouver, Canada.
dark energy
Dark energy is the general term for the substance that causes the universe to expand at an accelerated rate. Although dark energy is believed to be 74 percent of the total energy in the universe, we know very few of its properties. One active area of research is to determine whether dark energy behaves like the cosmological constant or changes over time.
dark forces
Dark forces arise in a 2009 theory to explain various experimental results in high-energy astrophysics. The theory proposes that dark matter WIMPs can decay into force-carrying particles, denoted by the Greek letter phi (). The particles would be associated with a new force of nature, distinct from the strong force, weak force, electromagnetism, and gravity.
dark matter
Dark matter is a form of matter unlike the ordinary matter that is described by the Standard Model. It accounts for most of the mass in the universe, but only has been observed indirectly through its gravitational influence on ordinary matter. Dark matter is believed to account for 23 percent of the total energy in the universe.
de Broglie wavelength
A particle's de Broglie wavelength, , is defined as Planck's constant divided by the particle's momentum, p: = h/p. The de Broglie wavelength is named after Louis de Broglie, the French physicist who first suggested that it might be useful to describe particles as waves. A relativistic electron has a de Broglie wavelength of around a nanometer, while a car driving down the highway has a de Broglie wavelength of around 10-38 meters. Quantum mechanical effects tend to be important at the scale of an object's de Broglie wavelength; thus we need to describe electrons quantum mechanically, but classical physics is adequate for cars and most other macroscopic objects.
Diffraction is the spreading of a wave after it encounters an obstacle, a sharp corner, or emerges from a slit. If the slit is small, the spreading is large and is accompanied by an interference pattern with a central peak surrounded by weaker side lobes. In this context, "small" means comparable to the wavelength of the diffracting wave. The fact that light diffracts when passed through a small slit is evidence of its wave nature.
In condensed matter physics, doping refers to the deliberate introduction of impurities into an extremely pure crystal. For example, a crystal of pure silicon might be doped with boron atoms that change the material's electrical properties, making it a more effective semiconductor.
Doppler cooling
Doppler cooling is a technique that uses laser light to slow, and thus cool, moving atoms. An atom will absorb a photon that has an energy equal to the difference between two energy levels in the atom. When the atom absorbs a photon, it also absorbs the photon's momentum and gets a push in the direction that the photon was traveling. If the photon and atoms were traveling in opposite directions, the atom slows down. However, when the atom is moving relative to the laser, the laser light is Doppler shifted in the atom's reference frame. To cool moving atoms, the laser must be tuned slightly to the red to account for the Doppler shift of atoms moving toward the light source.
Doppler shift (Doppler effect)
The Doppler shift is a shift in the wavelength of light or sound that depends on the relative motion of the source and the observer. A familiar example of a Doppler shift is the apparent change in pitch of an ambulance siren as it passes a stationary observer. When the ambulance is moving toward the observer, the observer hears a higher pitch because the wavelength of the sound waves is shortened. As the ambulance moves away from the observer, the wavelength is lengthened and the observer hears a lower pitch. Likewise, the wavelength of light emitted by an object moving toward an observer is shortened, and the observer will see a shift to blue. If the light-emitting object is moving away from the observer, the light will have a longer wavelength and the observer will see a shift to red. By observing this shift to red or blue, astronomers can determine the velocity of distant stars and galaxies relative to the Earth. Atoms moving relative to a laser also experience a Doppler shift, which must be taken into account in atomic physics experiments that make use of laser cooling and trapping.
electric dipole moment
The electric dipole moment of a system with two electric charges is defined as the product of the two charges divided by the distance between them. It is a vector quantity, with the positive direction defined as pointing from the (more) negative charge toward the (more) positive charge. The electric dipole moment of a more complicated system of charges is simply the sum of the moments of each pair of charges.
electromagnetic interaction
The electromagnetic interaction, or electromagnetic force, is one of the four fundamental forces of nature. Maxwell first understood at the end of the 19th century that the electric and magnetic forces we experience in daily life are different manifestations of the same fundamental interaction. In modern physics, based on quantum field theory, electromagnetic interactions are described by quantum electrodynamics or QED. The force-carrier particle associated with electromagnetic interactions is the photon.
electron accelerator
An electron accelerator is a particle accelerator designed to accelerate electrons. See: particle accelerator, SLAC.
emergent behavior
Emergent behavior is behavior of a complex system that is not easily predicted from a microscopic description of the system's constituent parts and the rules that govern them.
energy landscape
The energy of a physical system can be represented by a mathematical function that depends on several variables. The energy landscape that the system occupies is this function plotted as a hypersurface in space that is one dimension higher than the relevant number of variables. If the energy depends on one variable, then the energy landscape is a line drawn in a two-dimensional plane. If the energy depends on two variables, the energy landscape is a two-dimensional surface embedded in three-dimensional space that can look like mountains and valleys in a real landscape that one might encounter on the Earth's surface. The ground state of a system is the lowest point on the energy landscape.
In quantum mechanics, entanglement occurs when the quantum states of two particles that may be spatially separated are linked together. A measurement of one of the entangled particles implies the result of the same measurement made on the other entangled particle.
Entropy is a quantitative measure of the amount of order in a system. In statistical mechanics, a system's entropy is proportional to the logarithm of the number of states available to the system. If we consider a collection of water molecules, its entropy is greater at room temperature, when the molecules are bouncing around in a gaseous phase, than at very low temperatures, when the molecules are lined up in a rigid crystal structure.
Enzymes are proteins that catalyze chemical reactions in biological systems.
equivalence principle
The equivalence principle is a basic premise that is essential to every experimentally verified physical theory, including General Relativity and the Standard Model. It states that an object's inertial mass is equivalent to its gravitational mass. The inertial mass of an object appears in Newton's second law: the force applied to the object is equal to its mass times its acceleration. The gravitational mass of an object is the gravitational equivalent of electric charge: the physical property of an object that causes it to interact with other objects through the gravitational force. There is no a priori reason to assume that these two types of "mass" are the same, but experiments have verified that the equivalence principle holds to a part in 1013.
In the late nineteenth century, physicists were putting what they thought were the finishing touches on their theoretical description of electricity and magnetism. In the theory, electromagnetic waves traveled through a medium called "luminiferous ether" just as sound waves travel through the air, or the seismic waves that we experience as earthquakes travel through the Earth. The last remaining detail was to detect the ether and understand its properties. In 1887, Albert Michelson and Edward Morley performed an experiment, verified by many others, that demonstrated that light does not travel through ether. The lack of ether was one of many factors leading Einstein to develop special relativity.
evaporative cooling
Evaporative cooling is a process used in atomic physics experiments to cool atoms down to a few billionths of a degree above absolute zero. The way it works is similar to how a cup of hot coffee cools through evaporation. Atoms are pre-cooled, usually with some kind of laser cooling, and trapped in a manner that imparts no additional energy to the atoms. The warmest atoms are removed from the trap, and the remaining atoms reach a new, lower equilibrium temperature. This process is typically repeated many times, creating small clouds of very cold atoms.
event horizon
A black hole's event horizon is the point of no return for matter falling toward the black hole. Once matter enters the event horizon, it is gravitationally bound to the black hole and cannot escape. However, an external observer will not see the matter enter the black hole. Instead, the gravitational redshift due to the black hole's strong gravitational field causes the object to appear to approach the horizon increasingly slowly without ever going beyond it. Within the event horizon, the black hole's gravitational field warps spacetime so much that even light cannot escape.

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