Phys TUs LVL 4

This man built a device involving a wire that rotates around a magnet in a pool of mercury, the first homopolar motor, but failed to credit the assistance of his mentor, Humphry Davy. This scientist formulated two laws of electrolysis and demonstrated that an electric charge in a conducting shell induces an equal charge on the shell in his ice pail experiment. His namesake law states that the induced electromotive force in a closed circuit is equal to the negative time rate of change of the magnetic flux in the circuit. That law is the third of Maxwell's equations. He is thr inventor of the dynamo and the namesake of a conductive "cage". For 10 points, name this discoverer of inductance.

Michael Faraday

Verdet’s constant affects the magnitude of an effect named after this man relating the rotation of the plane of polarization of a light wave to an external magnetic field. This scientist discovered that the electric field inside a conductor is zero using an ice pail. (*) Lenz’s law supplements a law named after this scientist that equates the time derivative of the magnetic field flux to the induced electromotive force. This man’s namesake constant is roughly 96 kilocoulombs per mole of electrons, and he names a “cage†used to shield electromagnetic waves. For 10 points, give this British namesake of the SI unit of capacitance.

Michael Faraday

One researcher in this experiment later named cosmic rays and determined that they were indeed originating from outer space. Gerald Horton claimed that this experiment was fraudulent because of unused data points in the published paper. The values determined in this experiment were off by about one percent because of an error in the (*) viscosity of air. This experiment used two electrically charged plates to suspend the namesake material in order to equate the force of gravity with electric force and measure terminal velocity. For 10 points, name this 1909 experiment which determined the elementary charge of an electron.

Millikan Oil Drop Experiment [accept Oil Drop Experiment, Fletcher-Millikan oil drop experiment] <DG>

A quantity denoted by this letter is given by B-field over magnetic permeability minus magnetization. That quantity replaces the B-field in one formulation of Ampère’s law. Loschmidt’s paradox critiqued Boltzmann’s theorem of this letter. In the Schrodinger equation, this letter denotes the energy operator. This letter denotes a quantity given by the sum of potential and kinetic energy and is contrasted with the (*) Lagrangian. A quantity denoted by this letter is a state function by Hess’s law. That quantity minus temperature times entropy gives the Gibbs free energy. For 10 points, give this letter that denotes the Hamiltonian and enthalpy.

H (accept uppercase H; do NOT accept or prompt on “lowercase H†or equivalents) <Yue, Physics; Finals>

The n-vector model generalizes a model of these materials in which their namesake property is given by positive interaction terms “J-sub-i-comma-j.†The flux through these materials increases by sudden jumps as an applied magnetic field is increased. Heisenberg modified a model of these materials whose 2-D form was solved by Lars Onsager. These materials display the (*) Barkhausen effect and are described by the Ising model. These materials exhibit hysteresis and gain their namesake property when their Weiss domains align below the Curie temperature. For 10 points, name these permanent magnets featured in cobalt, nickel, and iron.

ferromagnets (accept ferromagnetism; prompt on just magnets or magnetism) <Yue, Physics; Finals>

This physicist developed an energy distribution that, in the high-frequency range, matches the Wien approximation. One of his concepts was extended by Einstein to explain the photoelectric effect. He resolved the "ultraviolet catastrophe" by showing that the negative fifth power of the wavelength is proportional to (*) blackbody radiation. He also showed that energy is proportional to frequency, with the constant of proportionality equal to six point six times ten to the negative thirty-fourth, so energy can only come in integer multiples of a small unit. For 10 points, name this German theorist who invented quantum mechanics and names the constant "h."

: Max [Karl Ernst Ludwig] Planck [accept Planck's constant]

Two brothers with this last name proposed and solved the St. Petersburg paradox, inventing the theory of logarithmic utility in the process. In 1683, a man of this last name was the first to discover (*) Euler’s constant. Another man of this last name discovered a law in which one half of rho times u squared plus P equals a constant, by applying conservation of energy to fluids. That man of this surname discovered a principle in which increasing the speed of a fluid decreases either its potential energy or pressure. For 10 points, name this family, whose member Daniel names a principle often used to explain lift.

Bernoulli <DM>

This name is given to a sequence of rational numbers whose first few terms are one, one-half, one-sixth, zero, negative one-thirtieth, zero, and one-forty-second. An equation named after Euler and a physicist with this surname can be used to calculate the deflection of a beam given its weight per unit length. A distribution with this name is a (*) binomial distribution with only one trial, and sets a random variable to one with probability p, and to 0 otherwise. A Swiss scientist with this surname names a statement explaining why pressure drops as fluid flow accelerates. For 10 points, give this name of a “principle†often invoked to explain lift.

Bernoulli <Pendyala>

This equation states that in conservative force fields, the sum of kinetic energy per mass, the force potential, and the ratio of pressure to density is constant. It can also be written as the integral of an equation named for Euler. Its application to constricted conditions describes the Venturi effect. Derived from conservation of energy and only applicable to inviscid flow, it is often used incorrectly to explain how airplanes fly or sailboats travel. For 10 points, name this equation inversely relating pressure and velocity, first expounded in Hydrodynamica by a Dutch-Swiss mathematician.

Bernoulli's equation [or Bernoulli's principle, or Bernoulli's theorem]

According to this law, the Euler equations imply a Hamiltonian whose derivative in the direction of the flow is zero. Under the steady flow assumption, this law states that pressure plus one-half density times v-squared plus a potential energy stays constant. The speed of a leak in a (*) tank from a certain height can be determined with Torricelli’s law, a specific case of this principle. This equation results from applying energy conservation to each volume element of a fluid, and it explains why pressure drops as fluid flow accelerates. For 10 points, give this principle named for a Swissman and often used to explain lift on airplane wings.

Bernoulli’s principle (accept “law†or “equation†or any sensible synonym as long as Bernoulli is mentioned)

The narrow escape problem concerns the mean escape time for this phenomenon. Governed by the Langevin equation, its "standard" type is modeled by a Lévy process named for Wiener. It can be described by the Fokker-Planck equation, and an equation stating that this process's mean square displacement is proportional to the product of elapsed time and diffusivity was published in 1905. Its namesake scientist discovered it while watching pollen grains suspended in water, and it was explained by Albert Einstein. For 10 points, name this random movement of particles in a fluid.

Brownian motion

The Fokker-Planck equations for this phenomenon show probability density over time. Another model for this phenomenon is a stochastic differential equation which measures it at long timescales; this is known as the Langevin equation. Through the Stokes-Einstein law, calculations of this phenomenon were used by Jean Baptiste Perrin to determine Avogadro’s number. For 10 points, diffusion is a basic example of what random motion of particles in a fluid, first discovered in grains of pollen by its namesake botanist Robert Brown?

Brownian motion (accept pedesis) <JK>

This man’s namesake gauge sets the divergence of the vector potential equal to zero, and he noted the independence of the sliding velocity in his namesake law on friction. This man’s most famous result can be derived by assuming a spherical surface around a point (*) charge and integrating using Gauss’s Law. This man’s namesake constant is one over 4 pi times the permittivity of free space and appears in his namesake law giving an inverse-squared relationship for the electrostatic force between two charges. For 10 points, give this French physicist who names the SI unit of charge.

Charles-Augustin de Coulomb [accept answers like Coulomb’s Law]

If the pressure gradient is balanced by this phenomenon, a flow is geostrophic. The combined effects of drag and this phenomenon create an Ekman spiral. The ratio of inertial forces to this phenomenon is given by the Rossby number. The strength of this phenomenon is directly proportional to the sine of latitude. This phenomenon results in cyclones spinning counter-clockwise in the Northern Hemisphere but clockwise in the Southern Hemisphere. This “fictitious†force causes flows in a rotating reference frame to be deflected from a straight line. For 10 points, name this effect that results from the Earth’s rotation and which is not actually responsible for the way a toilet flushes.

Coriolis effect or Coriolis force<CV>

The antennae of moths assist them in flying by accounting for this effect, which is also used in mass flow meters. The Rossby number can describe whether this effect is prominent in a system by relating it to inertial forces. When considered on the Earth, the Beta effect leads to its variation with latitude. This effect is caused by a pseudoforce and it was studied by a French scientist interested in water wheels. Leading to deflection of moving objects in rotating reference frames, it drives oceanic and atmospheric currents. For 10 points, name this effect whichcauses cyclones on Earth to rotate counter-clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

Coriolis effect

One person with this surname synthesized radiophosphorus by bombarding aluminum with alpha particles, while another contributed to the artificial synthesis of nitrogen. Another person with this name is the namesake of a law in which the magnetisation of a paramagnetic material is inversely proportional to temperature; that man also names the temperature above which a ferromagnetic material becomes paramagnetic. This name's most famous bearer, who hydrolysed pitchblende to isolate radium, is the namesake of a unit of radioactivity and element number 96. For 10 points, name this surname shared by a husband and wife who discovered polonium, Pierre and Marie.

Curie

Collisions lessen the effect of this phenomenon on spectral lines in the Dicke Effect. Laser vibrometers utilize this phenomenon to measure surfaces without contact, while echocardiograms can determine the speed and direction of blood flow using this effect. Using canal rays, (*) Ives and Stilwell detected the “transverse†type of this effect. It causes redshift and blueshift in astronomical phenomena, and it explains the change in pitch of a passing ambulance’s siren. For 10 points, name this effect in which the frequency of a wave changes for an observer as the source moves.

Doppler effect

This phenomenon is exploited in substances with a closed optical loop, such as rubidium-85, to facilitate laser-cooling into Bose-Einstein condensate. Its transverse and relativistic forms occur due to time dilation when an object approaches the speed of light. For a laterally-moving object, the magnitude of this effect is proportional to the cosine of the angle between it and its viewer. Usually given as a proportion dependent on observer and source velocity, it is the cause of blueshift and redshift. For 10 points, name this effect in which a wave's frequency changes as it moves relative to the observer, often used in weather radar and perceived in passing ambulance sirens.

Doppler-Fizeau effect [accept Doppler shift]

A proof of this law writes an area differential as v times the cross product of time and length differentials and then applies the Lorentz Force Law. One form of this law states that the curl of the electric field is the negative time derivative of the magnetic field, and (*) Lenz’s Law describes the negative sign found in this law. Maxwell generalized this equation and included in his namesake four equations, and it describes the force resulting from a change in magnetic flux. This law forms the basis for transformers since it describes using induction to generate electromotive force. For 10 points, name this law of electromagnetism named for an English physicist.

Faraday’s Law of Electromagnetic Induction Bonuses

This statement generalized for gravity states that the divergence of a gravitational field equals negative 4 pi times big G times density, a law which reduces to Poisson's equation. Using this law on an infinite plane of uniform charge density involves the construction of a namesake "pillbox", an example of a symmetrical surface. This law, which equates the surface integral of E dot dS with Q over the permittivity of free space, is the first of Maxwell's equations. For 10 points, name this law which states that electric flux through a closed surface is proportional to enclosed charge, named for a German physicist and mathematician.

Gauss's Law [or Gauss's flux theorem]

Replacing a vector quantity in this law with the gradient of a scalar gives Poisson’s equation. One formulation of this law gives rho-free in terms of the divergence of the D-field. For a charged cylinder, applying this law involves constructing a larger cylinder. Using this law, one can derive the formula “sigma over epsilon-nought†for an infinite sheet of charge by constructing a (*) “pillbox.†In its integral formulation, this law involves calculating the charge enclosed by an imaginary surface and the electric flux through that surface. For 10 points, give this first of the Maxwell equations, named for the German namesake of the normal distribution.

Gauss’s law for electricity (do NOT accept or prompt on “Gauss’s law for magnetismâ€) <Yue, Physics>

One form of this phenomenon involves tying cyclotron frequencies to degenerate Landau levels, and is performed on gallium arsenide interfaces, although it was recently discovered in room-temperature graphene. A class of low-impulse spacecraft ion thrusters are based on and named for this phenomenon. A filling factor for a type of this phenomenon multiplies a standardized resistance. That factor was found to take on rational values, which earned Klaus von Klitzing the Nobel Prize. The inverse of the carrier density is proportional to this effect's namesake coefficient. For 10 points, name this physical effect, the voltage difference across a conductor in a magnetic field.

Hall effect [accept spin Hall effect; accept quantum Hall effect after "cyclotron"]

One derivation of this relation named for Robertson uses expectation values of Hermitian operators. Mandelshtam and Tamm derived a corollary of this statement which multiplies the variance of time with the variance of energy, a term which is greater than or equal to the reduced Planck constant over 2. According to this law, electrons of known velocity passing through a slit would result in a probability distribution rather than a single position as classical mechanics predicts. For 10 points, name this quantum principle which asserts the impossibility of perfect measurement of both a particle's position and its momentum.

Heisenberg uncertainty principle [prompt on "Heisenberg"]

This statement explains why there is a limit on the line-width of spectral lines, and a generalization of it is given by the Robertson-Schrodinger relation. This statement follows since the commutator of certain conjugate variables is nonzero, and it can be given as an (*) inequality involving h-bar over two. A thought experiment showing this statement describes the trade-offs in measuring a particle with a microscope, and one usage of it states that both position and momentum cannot be known with exact precision. For 10 points, give this “uncertainty†principle named for a German physicist.

Heisenberg’s uncertainty principle (accept either or both underlined part, but accept just Heisenberg after “uncertainty†is read and prompt if they just try giving uncertainty principle again)

This particle is produced along with a muon, and antimuon by the collision of an electron and a positron in the Bjorken process. This particle's decay into two tau leptons has not yet been observed, casting doubt on its postulated spin of zero. This elementary particle was initially hypothesized to explain, through spontaneous symmetry breaking, why the W and Z bosons are massive, and we now know that its namesake field is what imparts mass to matter. It is a target of the Large Hadron Collider. For 10 points, name this no-longer-hypothetical boson discovered in 2012, nicknamed the "God particle".

Higgs boson [prompt on "God particle" before mention]

Extensions of this relation to 3 dimensions involve a fourth-order tensor with 81 coefficients symbolized sigma for stiffness, or Cauchy's 36-entry compliance matrix. Inapplicable to rubber, this relation applies below the yield strength to linear-elastic materials for which Young's modulus is defined. Usable for a parallel or series system of harmonic oscillators, as well as individuals, for 10 points, name this law stating that the restoring force is proportional to displacement, by the formula F equals negative k x, in springs.

Hooke's Law

One expression of this law includes lambda and mu, the Lamé parameters. The compliance tensor appears in its 3-dimensional generalization, formulated by Cauchy. The constant parameter appearing in this law can be approximated using the bulk modulus and Young's modulus. The integral of this equation with respect to displacement gives an expression for elastic potential energy, and it is only applicable up to the elastic limit. It states that the restoring force is proportional to the displacement, or "F equals negative k x." For 10 points, name this law describing the behavior of springs.

Hooke's law

For homogenous and isotropic materials, this relation is defined in 3 dimensions with Lamé’s first and second parameters. Cauchy’s (“co-sheezâ€) generalization of this principle utilizes a 36-entry compliance matrix with Poisson's ratio, Young’s modulus, and the shear modulus. For continuous media, this law relates the second order (*) strain and stress tensors. This law is valid for stresses below the yield strength. Objects that obey this law follow simple harmonic motion and the constant in this law relates to the stiffness of a material. For 10 points, name this principle of physics, denoted “F = -kx†that states the restoring force is proportional to displacement for a spring.

Hooke’s Law <AP>

With Cotes, this man names a set of methods for numerical integration, including the trapezoid rule. One constant sometimes named for him in an equation derived by him was determined using a torsion balance in the Cavendish experiment. For shallow temperature gradients, his law of cooling approximates heat flow between two points as proportional to the temperature difference between them. When the de Broglie wavelength is small, a set of laws named for this man hold; one of those laws states that force is equal to mass times acceleration. For 10 points, name this namesake of the SI unit of force and three laws of motion that underlie classical mechanics.

Isaac Newton <AS>

A conversation with Edmund Halley inspired this scientist to produce the work De Motu, which he expanded into his most famous work. This scientist designed the first realizable reflecting telescope, and was the main developer of the corpuscular theory of light, as laid out in his Opticks. In his most famous work, he demonstrated that the planets were attracted to the Sun by an inverse-square law force. This physicist used prisms to show that white light could be separated into its constituent colors. For 10 points, name this author of the Philosophiae Naturalis Principia Mathematica who proposed the existence of gravity.

Isaac Newton <CV>

This man showed that the viscosity of gases was independent of their pressure, a result first verified by him and his wife Katherine. A set of equations involving the second derivative of each thermodynamic potential with respect to their natural variables is named for this physicist, and he proposed the displacement current as a modification to (*) Ampere’s Law. A thought experiment proposed by this physicist considers a figure that separates gas particles by their speed and apparently decreases entropy; that figure is this man’s namesake “demon.†For 10 points, name this Scottish physicist who described electromagnetism in a set of four namesake equations.

James Clerk Maxwell <Xiong>

A spacecraft named for this person uses a photometer to measure the brightness of stars in the constellations Cygnus, Lyra, and Draco. This man described a model of the universe consisting of nested Platonic solids, one for each planet, in his ​Mysterium Cosmographicum. A spacecraft named for this person has used the "transit method" to discover over 1,000 (*) ​exoplanets since 2009. A set of postulates named for this man includes the "equal areas in equal time" law and the statement that orbits are ellipses with the sun at one focus. For 10 points, name this one-time assistant to Tycho Brahe, a German astronomer who proposed three laws of planetary motion.

Johannes Kepler​ [or Iohannes Keplerus​]

It doesn’t involve a “demon,†but this man proposed a problem involving mixing two chambers of gas that appears to violate the Second Law of Thermodynamics. One quantity named for this man is equal to surface area times surface tension, and he proposed a formula for the degrees of freedom in his (*) namesake phase rule. The change in one quantity named for this man is proportional to the natural log of the equilibrium constant, and is also equal to negative delta H minus T times delta S. A quantity named for this man determines whether a reaction is spontaneous. For 10 points, name this American scientist who names a type of “free energy.â€

Josiah Willard Gibbs (accept Gibbs paradox; accept Gibbs free energy; accept Gibbs phase rule)

This device’s data output, measured in inverse femtobarns, exceeds any other device of its kind. It’s not RHIC, but one substance created by this device is described by QCD at high temperature and density. The final injector for this device is the SPS. This device is believed capable of detecting particles such as neutralinos, which arise in supersymmetric theories. A toroidal apparatus in this device is being used to search for the last unknown Standard Model particle, which gives mass to all the other particles. For 10 points, name this particle accelerator in Switzerland and France built by CERN, which is looking for, among other things, the Higgs boson.

Large Hadron Collider [or LHC] <DStobierski/AS>

A factor named for this scientist is equal to e to the quantity negative beta times the energy of the particle, and the sum of that factor for all energies is the partition function. This physicist is the second in an equation giving the power from a blackbody as proportional to the (*) fourth power of temperature, and he defined entropy as k-sub-b times the natural logarithm of the number of microstates. The constant named after this scientist equals the ideal gas constant divided by Avogadro’s number and is symbolized lowercase k. For 10 points, name this Austrian physicist whose contributions to statistical mechanics include co-naming a distribution with Maxwell.

Ludwig Boltzmann <Jin>

Loschmidt's paradox points out the broken time reversal symmetry caused by this man’s assumption of molecular chaos in this man’s H-theorem. He names a probability distribution proportional to e to the negative state energy over temperature times his namesake constant. The average translational kinetic energy of an ideal gas is equal to three halves temperature times this man’s constant. A law relating a blackbody’s radiative power to the fourth power of temperature is co-named for this man and Stefan. For 10 points, name this Austrian physicist whose namesake constant is equal to the ideal gas constant over Avogadro’s constant.

Ludwig Boltzmann <SH>

This man names a period of time in the history of the universe, during which the four fundamental forces were unified, that period lasted for an amount of time that is one unit in his system of natural called "God's units." This man's introduction of the "action quantum" in his study of heat theory led him to formulate an eponymous law that reduces to Rayleigh-Jeans Law at long wavelengths. That law of blackbody radiation helped to resolve the "ultraviolet catastrophe" and led to the development of quantum theory. For 10 points, name this scientist, whose constant has value 6.626*10^-34 joule-seconds and is symbolized by the letter h.

Max (Karl Ernst Ludwig) Planck

This scientist's namesake "epoch" is the first "10 to the minus 43" seconds of the universe's life, during which quantum gravity was significant. He also names a system of maximally natural units. One quantity named for this man is the quantum of action. That quantity also appears in a law named for this man, which correctly described the blackbody spectrum and solved the "ultraviolet catastrophe". That same quantity is about "6.6 times 10 to the minus 34 Joule-seconds", and is the constant of proportionality relating the energy of a photon to its frequency, and is denoted by the letter h. For 10 points, name this founder of quantum theory.

Max (Karl Ernst Ludwig) Planck [accept Paul (Adrien Maurice) Dirac until "frequency" is read]

With Sommerfeld, this scientist names a procedure to determine the allowed discrete states of a classical trajectory. This scientist names a quantity equal to h-bar over the quantity electron mass times c times alpha, or about 5.3 times 10 to the negative 11 meters. The most probable (*) distance between a proton and electron in a hydrogen atom is this man’s namesake “radius,†and this man’s principle of complementarity was a key component of the Copenhagen interpretation. For 10 points, name this Danish physicist who proposed that electrons travel in quantized orbits around the nucleus in an outdated model of the atom.

Niels (Henrik David) Bohr

The Compton wavelength is equal to the fine-structure constant times a quantity named for this man with a value of about 0.53 angstroms. This man described the imitation of quantum physics to classical mechanics at large numbers as the correspondence principle, and he has a namesake (*) “radius.†The Rydberg formula for spectral lines is successfully explained by a model named for this man using transitions in energy levels, and that model named for this man preceded the quantum model. For 10 points, name this Danish physicist who theorized a model of the atom with positively charged nuclei and concentric rings of orbiting electrons.

Niels (Henrik David) Bohr (accept answers like Bohr radius or Bohr model)

This scientist's last patent concerned an aircraft capable of vertical take-off, and he correctly determined Earth's resonant frequency. He designed the Wardenclyffe Tower, intended for wireless power transmission and worldwide broadcast, but that project never came to fruition, just like a charged-particle beam weapon popularly known as this man's death ray. He is most famous for promoting an energy supply system that could travel farther without losing energy by utilizing a transformer. For 10 points, name this Serbian-American scientist best known for a feud with Edison in which he advocated for alternating current, the namesake of an electrical resonant transformer coil.

Nikola Tesla

For a World’s Exposition, this man constructed a metal Egg of Columbus. This man claimed an electric generator he built had caused an earthquake in New York, and he attempted to send Transatlantic signals by constructing the Wardenclyffe Tower. This scientist theorized a “Teleforce†that was essentially a (*) death ray, and he names the SI unit of magnetic flux density. Visible electric shocks are displayed with this man’s namesake coil, and he used a transformer to utilize the safer and more energy efficient alternating current. For 10 points, name this Serbian-American scientist who feuded with Thomas Edison in the War of the Currents.

Nikola Tesla Bonuses

The proportionality constant in a generalization of this statement is equal to the product of electron density, charge squared, and mean free time divided by mass, and that generalization happens in the Drude model. One form of this statement sets the current density equal to the product of conductivity and the electric field, and it can be used to derive a description of Joule heating where the (*) power dissipated is proportional to the current squared. A term in this law is replaced with impedance in AC circuits, and materials following this law exhibit a linear I-V curve. For 10 points, name this law that states that voltage is equal to current times resistance.

Ohm’s law <Xiong>

A function named for this scientist is equal to the divergence of r-hat over 4 pi r-squared and scales as a function of one over the scaling factor. This scientist names an equation which uses a basis of matrices with anticommutators proportional to the four-by-four identity matrix that forms a Clifford algebra. Inner products are depicted with (*) bras and kets in this scientist’s namesake notation, and he explained negative energy states using holes in his namesake sea to represent positrons. Everywhere but at the origin, this man’s namesake delta function has a value of zero. For 10 points, name this physicist who predicted the existence of antimatter.

Paul Dirac <Yue>

Because particles like helium-4 do not obey this statement, a large proportion of such particles are able to fall into the ground state at low temperatures. Formally, this statement says the wave functions of fermions are anti-symmetric with respect to exchange, and it explains the (*) electron degeneracy pressure that supports white dwarfs. This statement says two fermions cannot have the same four quantum numbers, which practically means that two electrons in the same energy level and orbital must have opposite spin. For 10 points, give this quantum mechanics “exclusion principle†named for an Austrian physicist.

Pauli exclusion principle <Jin>

He’s not Torricelli, but this man names a point P in acute triangles for which the sum of the distances from P to the vertices is minimized. This man’s namesake numbers have the form “2 to the 2 to n plus 1,†and he names a statement that for a prime p, then [read underlined part slowly] (*) p divides “(a to the p) minus a.†One of this man’s statements was proven using the Taniyama-Shimura conjecture by Andrew Wiles and states that there are no nontrivial integer solutions to the equation “a to the n†plus “b to the n†equals “c to the n†for n greater than two. For 10 points, name this French mathematician with namesake “Little†and “Last†theorems.

Pierre de Fermat (accept answers like Fermat’s Last Theorem)

This scientist names a function that’s the propagator for the Klein-Gordon equation, and he names a notation in which scalar operations written with a “slash†are equal to their namesake vector operators contracted with the vector of gamma matrices. He popularized the “differentiation-under-the-integral sign†trick, and with John Wheeler, this scientist developed the (*) path integral. This man won the Nobel Prize for his work on quantum electrodynamics, and he names a diagram displaying particle interactions. For 10 points, name this American physicist who wrote a book whose title asks him, “Surely You’re Joking!â€

Richard (Phillips) Feynman <Pendyala>

This man suggested writing a book on the head of a pin by directly manipulating individual atoms in his talk "There's Plenty of Room at the Bottom". His eponymous ratchet violates the second law of thermodynamics. He devised the path integral formulation, which he called a "sum over histories," that helped him with Schwinger and Tomonaga renormalize quantum electrodynamics. Using another formalism named for him, one can illustrate the interactions of charged particles using force-carrying photons. For 10 points, name this American physicist known for his lectures on physics and his namesake diagrams.

Richard Feynman

This scientist scored highest in the 1939 Putnam competition. This physicist provided a quantum mechanical explanation for Landau’s theory of superfluidity and worked with Murray Gell-Mann to develop a model of weak decay. With Tomonaga and Schwinger, this man received the (*) 1965 Nobel Prize in Physics for his work on quantum electrodynamics. This physicist was an ardent enthusiast of bongo drums and is known for a famous lecture series compiled from his teaching at the California Institute of Technology. For 10 points, name this physicist and author of There’s Plenty of Room at the Bottom whose namesake diagrams depict the behavior of subatomic particles.

Richard Phillips Feynman <AP>

A tube containing radium and bismuth-214 was a component of this experiment’s setup, which is sometimes also named after Geiger and Marsden. An equation describing one parameter in this experiment relates it to the negative fourth power of the velocity. That parameter is the number of particles (*) scattered through a certain angle. Most particles passed through the namesake material with no deflection, but about 1 in 2000 were deflected more than 90 degrees. For 10 points, name this experiment that verified the existence of the positively charged atomic nucleus.

Rutherford gold foil experiment <SR Chemistry>

Carathéodory introduced the concept of "adiabatic accessibility" to approach this statement, holding that an initial adiabatically isolated state would not be able to approach other states in its neighborhood. This postulate appears to contradict T-symmetry in Loschmidt's paradox, and heat from a reservoir cannot perfectly be converted into work in the Kelvin-Planck formulation of this statement. This postulate states that heat cannot flow from a colder body to a warmer body without doing work, according to Clausius's formulation. Apparently violated by Maxwell's Demon, for 10 points, name this law which states that the entropy of a closed system always increases.

Second Law of Thermodynamics

The Principle of Carathéodory is one formulation of this statement, and Loschmidt’s paradox and Poincare recurrence reveal flaws in Boltzmann’s H-theorem regarding this statement. An expression of this law states that heat cannot move from a cold to hot body by (*) itself; that expression is the Clausius statement. A hypothetical creature capable of separating fast and slow molecules, called Maxwell’s demon, would violate this law. For 10 points, name this law stating that, for a closed system, entropy always increases.

Second Law of Thermodynamics

Mordehai Milgrom modified this man's theories in an attempt to explain the galaxy rotation problem without using dark matter. A law named after this man states that a body's rate of heat loss is proportional to the temperature difference between the body and the environment. He demonstrated that white light is made up of the full spectrum of colors in his treatise Opticks. He gives his name to a kilogram-meter per second squared, the SI unit of force, and he stated that "F equals m a." For 10 points, name this British physicist who names three laws of motion and may have been hit by a falling apple.

Sir Isaac Newton

This man used Divine intervention to explain anomalies that were later accounted for in Laplace's calculus of variations. As part of this man's studies of alchemy, he translated the Emerald tablet, and he thought the world would end after 2060. In his more serious scientific endeavors, he related an object's temperature and the ambient temperature to its rate of (*) cooling. He gave a mathematical basis to Kepler's laws of planetary motion in his Philosophiae Naturalis Principia Mathematica, which also contains his universal law of gravitation. For 10 points, name this English scientist who developed three laws of motion and discovered calculus concurrently with Leibniz.

Sir Isaac Newton

This scientist classified cubic equations into 72 species, but missed six other types. A law named for this man states that the rate of temperature change of a body is proportional to the difference in temperatures between the body and its surroundings. This scientist names a type of (*) fluid where shear stress has a linear relationship with motion. This scientist’s version of Kepler’s 3rd law includes a factor of four pi squared over the universal gravitation constant. This scientist’s second law states force equals mass times acceleration. For 10 points, name this scientist who discovered calculus with Leibniz and developed three laws of motion.

Sir Isaac Newton <BC>

The first steps towards creating this construct were taken by Sheldon Glashow’s 1961 proposal of electroweak interactions, which were later proven during a 1973 experiment at CERN that discovered neutral weak currents caused by Z boson exchange. This theory accurately predicted the ratio of masses between (*) W± and Z0 (“w-plus-minus and zero-naughtâ€) bosons discovered in 1983. This construct groups the four force carriers as gauge bosons but does not yet incorporate dark matter. For 10 points, name this model that, while categorizing the 13 fundamental particles, has been unable to account for all 4 fundamental forces.

Standard Model <AJ>

A 1937 extended version of this experiment revealed that state transitions could be induced using RF fields in a process influential to the development of MRI machines known as a Rabi oscillation. In 1927, Phipps and Taylor reproduced this experiment using hydrogen atoms instead of atoms of (*) silver. A sulfur-containing cigar was used to visualize the two spots on the detector in this experiment which provides the paradigm for understanding quantum observation. In this experiment, beams in an inhomogeneous magnetic field split due to intrinsic angular momentum. For 10 points, name this doubly-eponymous experiment which showed that electrons have quantized spin.

Stern-Gerlach experiment <McMaken>

This man was a member of the Uranium Club during World War II, and a group named for him contains 3 by 3 upper triangular matrices with ones on the diagonal. Equivalent to Schrödinger's wave formulation, a theory he developed along with Max Born and Pascual Jordan represents physical observables by matrices and is called matrix mechanics. Derived from matrix mechanics, a relation named for this physicist implies that his namesake pairs, such as energy and time or position and momentum, do not commute. That relation is one of quantum mechanics' most well-known results. For 10 points, name this German physicist, best known for his Uncertainty Principle.

Werner (Karl) Heisenberg

This physicist’s work with Born and Jordan was able to explain election rules. State-vectors are treated as stationary while operators vary in time in his namesake picture of quantum mechanics. This physicist’s most famous result can be derived from the (*) canonical commutation relation. That result of his states that the product of the standard deviations in position and momentum is greater than h-bar over two, which implies we can’t simultaneously know a particle’s position and speed. For 10 points, give this physicist who developed a namesake “uncertainty†principle.

Werner Heisenberg

One set of mathematical constructs named for this man are Hermitian and unitary, and thus correspond to the observables of the complex Hilbert space with two dimensions. This man used the conservation of energy and momentum in beta decay to theorize the existence of the neutrino. He names a set of three matrices that describe spin, and one of his results explains why neutron stars below the Tolman-Oppenheimer-Volkoff limit don't collapse. That principle concerns the anti-symmetric quantum states of fermions, explaining why electrons with the same spin cannot occupy the same orbital. For 10 points, name this Austrian theoretical physicist with a namesake Exclusion Principle.

Wolfgang Pauli

The characteristic energy of these phenomena is proportional to the square of atomic number according to Moseley’s law. Charles Barkla and Manne Siegbahn both won Nobel Prizes for studying the elemental spectra of these phenomena. “Photo 51†is an image of DNA produced using these phenomena by Rosalind Franklin, who determined crystal structures via the diffraction of these phenomena, as described by (*) Bragg’s law. The discovery of this radiation won the first Nobel Prize in Physics for Wilhelm Röntgen. Ranging in frequency between UV and gamma rays, these areâ€"for 10 pointsâ€"what short-wavelength type of radiation that can be used to image bones?

X-rays [or X-radiation; or Röntgen radiation; prompt on electromagnetic radiation or radiation] <SE>

The principle of complementarity was demonstrated by a version of this experiment, the Afshar experiment. The output is determined by the path of one particle in a variant of this experiment known as the quantum eraser. One phenomenon involved in this experiment results if the difference in path length is an integer multiple of another quantity. That phenomenon is (*) constructive interference. This experiment contradicted the corpuscular theory of light by proving its wave-particle duality. For 10 points, name this experiment where light was shined through two namesake apparatuses, first performed in 1801 by Thomas Young.

Young’s double-slit experiment [accept either until “Youngâ€] <BC>

One scientist found the WKB approximation for this process using the time dependent Schrödinger equation. It’s not fusion, but in this process, certain species penetrate the Coulomb barrier, and it occurs on the upper right of a graph comparing Z and A-minus-Z, named the “belt of stability.†One explanation for this process was the Geiger-Nuttall Law, which was later refuted by George (*) Gamow. One application of this process using americium-241 results in the ionization of air in smoke detectors. This process decreases the atomic number by two. For 10 points, name this form of radioactive decay in which namesake particles, helium nuclei, are emitted.

alpha decay [accept alpha after “decayâ€; prompt on radioactive decay until mention; prompt on radioactivity and word forms until mention] <BC>

Rotational invariance is the associated symmetry of this quantity by Noether’s theorem. The quantum operator for this quantity equals negative i h-bar times the cross product of radius and the gradient. Torque is equal to the time derivative of this quantity which is equal to the (*) cross product of radius with a similarly named quantity. The conservation of this quantity is often demonstrated through a figure skater pulling in her arms. For 10 points, name this quantity equal to moment of inertia times angular velocity, often symbolized L.

angular momentum

In the Laplace-Runge-Lenz vector, this quantity is crossed with linear momentum. J-coupling of this quantity can be used to determine dihedral angles in a form of spectroscopy which can only be used on nuclides with a nonzero value of this quantity. The quantum numbers “m sub L†and “m sub S†correspond to the orbital and spin types of this quantity. Classically, this vector is the time integral of torque and for rigid bodies, it is the product of the moment of inertia and angular velocity. For 10 points, name this quantity, which equals the cross product of position with linear momentum, often symbolized “Lâ€.

angular momentum [accept spin angular momentum; accept orbital angular momentum; prompt on “spin†before it is read; do not accept “momentum†or “linear momentumâ€] <DSteinberg/AS>

A cylindrical mode converter can generate one form of this quantity, which is defined in terms of cylindrical coordinates for light. This quantity is equal to integer multiples of the reduced Planck’s constant in the Bohr model because it is quantized, and this quantity changes direction for a system undergoing precession. An ice skater will spin faster when they pull in their arms due to the conservation of this quantity. Net torque is the time derivative of this quantity, which is equal to moment of inertia times angular velocity. For 10 points, name this quantity symbolized L, the rotational analog of linear momentum.

angular momentum [prompt on momentum, do not accept “linear momentumâ€] <BM>

9. In quantum mechanics, the square of the operator corresponding to this quantity commutes with the Hamiltonian if the potential is central. Kepler’s Second Law arises from the fact that areal velocity is equal to this quantity divided by twice the mass of the orbiting body, and the (*) orbital form of this quantity is quantized in units of the reduced Planck’s constant. Noether’s Theorem applied to rotational invariance yields the conservation of this quantity, and its intrinsic form is called spin. This quantity is equal to the moment of inertia times the angular velocity. For 10 points, name this physical quantity, the rotational counterpart of momentum.

angular momentum(accept spinuntil “Keplerâ€Í¾ prompt on “momentumâ€Í¾ do not accept or prompt on “linear momentumâ€)

On Feynman diagrams, lines denoting particles of this substance bear leftward- or downward-pointing arrows. While baryons typically contain none, all mesons have exactly one particle of this substance. The Sakharov conditions explain the asymmetry that leads to the universe’s deficiency of this substance. In the most common type of pair production, the (*) positive particle is this type of substance. This substance was initially understood as negative energy “holes†in the Dirac sea, since particles of it have the same mass but opposite charge to their counterparts. Positrons are an example ofâ€"for 10 pointsâ€"what stuff that annihilates normal matter when they come into contact?

antimatter [or antiparticles; accept antiquarks until “positiveâ€] <SE>

The Born-Oppenheimer approximation, which allows approximate decomposition of atomic wavefunctions, depends on the relative "slow" motion of these entities. The subclass of mesons known as pions mediates the attractive forces within it, which is sometimes known as the residual strong force. This entity's discovery disproved J.J. Thomson's Plum Pudding model and came about by the unexpected scattering of decaying radium by gold foil in the Rutherford Experiment. For 10 points, name this region of the atom which can split or merge in its fission or fusion, also known as an alpha particle in the context of helium that consists of protons and neutrons.

atomic nucleus

One model for the energy of these objects contains a volume term whose energy arises from the energy of a pion-mediated interaction in these objects; that model treats these objects as incompressible liquid drops. They are found to be particularly stable when they are composed of magic numbers of particles. Its constituents are the two most stable baryons, composed of up and down quarks. The disproof of the plum pudding model by Rutherford’s gold foil experiment led to the conclusion that these structures exist. For 10 points, name this structure, which may undergo beta decay and is composed of protons and neutrons.

atomic nucleus [or atomic nuclei; accept nuclides] <AS>

The square of this value minus one was shown to be proportional to the frequency of a K-alpha X-ray line by Moseley. The screening constant is subtracted from this value in Slater’s rules, and this value squared appears in the numerator of the Rydberg formula for the energy of an electron in a (*) hydrogen-like atom. This quantity increases by 1 in beta-minus decay. This value is symbolized uppercase Z, and the periodic table is ordered by it. The atomic mass is equal to the number of neutrons plus, for 10 points, what number equal to the number of protons in the nucleus of a given atom?

atomic number (accept nuclear charge or Z until read)

Dvyanuka (“div-ya-NOO-kaâ€) and tryanuka (“tri-ya-NOO-kaâ€) were proposed by one philosopher as combinations of these entities. That philosopher, who called these entities “anu,†was Kanada. Crookes tubes can be used to find parts of these entities that were previously called “corpuscles.†Following the development of (*) quantum theory, the main model of this entity involved shells with discrete energy levels. Using cathode rays in a famous experiment, J. J. Thomson compared these entities to plum puddings. For 10 points, name these units of matter usually consisting of neutrons, protons, and electrons.

atoms [accept anu before mention] <DM>

The energy of these particles is displayed on a Kurie-Fermi plot. Cherenkov radiation in spent fuel bays is most commonly caused by these particles. These particles accompany a less massive particle of opposite lepton number during their namesake decay, which is mediated by W bosons. Steps two and three of the main uranium-238 decay series release these particles as thorium decays to protactinium and then to uranium. When one of these particles is released from a nucleus, the atomic number changes, but not the atomic mass. For 10 points, name these particles that consist of high energy electrons or positrons.

beta particles [or beta decay] (prompt on electron or positron before mention) <AG>

In physical theories, large extra dimensions are often invoked to try and explain why this parameter is so small, and the critical density of the universe is equal to three times the Hubble parameter squared divided by eight pi times this parameter. In Planck units, the speed of light, Dirac’s constant, and this constant are set to have a value of (*) 1, and it was first measured using lead balls and a torsion balance. In SI units, this constant has a value of 6.67 times 10 to the minus 11 Newton meters squared per kilogram squared. For 10 points, name this constant that was first measured by Henry Cavendish.

big G (accept universal gravitational constant or Newton’s constant; accept “uppercase G†and prompt on just “G,†but do not accept or prompt on just “lowercase gâ€) <Pendyala>

Lucas’s theorem reduces one of these numbers to a product of them modulo p. Products of these numbers can be summed using Vandermonde’s convolution, and a sum of them can be simplified with the hockey-stick identity. If the row index is fixed, they sum to (*) “2 to the n,†and they’re given by the formula [read underlined part slowly] “n factorial over k factorial times (n minus k) factorial.†The namesake theorem of these numbers describes their generation by expanding “one plus x†to the n, and they make up Pascal’s Triangle. For 10 points, name these “coefficients†that describe the number of ways to choose k things from n possibilities, or n choose k.

binomial coefficients (prompt on descriptive answers like “n choose k†or “members of Pascal’s triangle†or “number of combinationsâ€)

The "fuzzball model" is thought to describe these objects, from which energy can be harvested by means of the Penrose process. Ones described by the Kerr metric cause frame-dragging within their ergospheres. Their only known properties are mass, charge, and angular momentum, due to the no-hair theorem. For a given mass, the Schwarzschild radius gives the surface of their event horizons, which contain a singularity of infinite density. Studied by Stephen Hawking, for 10 points, identify these massive, compact space objects from which not even light can escape.

black holes

Lummer and Kurlbaum modeled these objects as a cavity with a miniscule hole. A law derived by multiplying the Bose-Einstein distribution by the density of states gives these objects' peak energy as roughly 2.8 times the Boltzmann constant times temperature, in accord with Wien's law. A function of the frequency of these objects squared fails at low wavelengths in the ultraviolet catastrophe. That law, the Rayleigh-Jeans law, was improved by Planck. Their emissive power is proportional to temperature to the fourth power. For 10 points, name these theoretical bodies named for their ability to absorb and re-radiate all incident electromagnetic radiation.

blackbodies

High compressibility of objects subject to this phenomenon leads to instability at equilibria. Flows driven by this force can be estimated with the Boussinesq approximation. The Cartesian Devil demonstrates this force, whose ratio to viscosity can be approximated with the Grashof number. This force regulates isostasy, and is responsible for convection. The earliest claim about this force was that an object in a fluid is lifted with force equal to the weight of displaced fluid, this being Archimedes' principle. For 10 points, name this property that allows boats to float.

buoyancy

In the Miller effect, this quantity is increased because of the amplification of its effect at input and output terminals, and complex impedance for the device associated with this quantity can be derived from the Laplace transform of Ohm’s law for this quantity. This quantity’s parasitic form limits the efficiency of circuits at high frequencies. In parallel plates, this value is equal to permittivity times area divided by the amount of separation between the plates. The simplest way to obtain this value is to dividing charge by voltage, and its SI unit of measurement is the farad. For 10 points, name this measure of the ability of a body to store an electrical charge.

capacitance <JK>

A type of the device associated with this quantity is made from aluminum and requires conditioning before use. This quantity may be computed for a configuration by imagining some charges and dividing those charges by the voltage difference they induce. This quantity times the resistance is the time constant. This quantity adds when the namesake devices are placed in (*) parallel, while its reciprocal, the elastance, is added when those devices are connected in series. Its value for parallel plates can be increased by inserting a dielectric. For 10 points, name this quantity describing the strength of devices that store charge, usually measured in farads.

capacitance <SR Physics>

For the characteristic impedance of a lossless transmission line, this value is multiplied by “j omega†in the denominator of the square root. For a circuit, the impedance is equal to the reciprocal of the complex unit times angular frequency times this value. This value is proportional to the reciprocal of the log of the ratio of the (*) shell diameters for a coaxial cable. This value is proportional to plate area and inversely proportional to distance in its namesake parallel-plate device, and its product with voltage is the charge. For 10 points, name this quantity that describes the ability of a namesake circuit element to store charge.

capacitance (accept capacitor; prompt on uppercase C)

This quantity is increased by a factor of one plus the negative gain of the amplifier in the Miller effect. A type of component will have this form of reactance above its resonant frequency when displaying its "parasitic" type. Calculation of it for an arbitrary shape is accomplished by solving Laplace's equation with a constant potential along a conductor's surface. This quantity's inverse is elastance, and it is additive in series. For one type of device, it is inversely related to the distance between two plates, and in general, it equals charge over voltage. For 10 points, name this measure of the ability to store charge, measured in farads.

capacitance [prompt on C]

Condenser microphones use variable versions of this device to transduce sound. “Super†examples of this device use high-surface-area substances like charcoal in a double-layer to achieve better performance than in electrolytic ones. In parallel, its equivalent characteristic parameter is the sum of the individual characteristic parameters. Fringing fields tend to draw dielectric materials into these devices, in which the dielectric separates two conducting plates. Their namesake property is measured by the amount of charge they store per unit voltage. For 10 points, name this device which stores energy in an electric field, whose namesake property is measured in Farads.

capacitors [accept variable capacitors; accept supercapacitors] <DSteinberg/AS>

The presence of this phenomenon is identified by the measurement of exponential divergence, governed by the Lyapunov exponents. In continuous systems, it can only arise if the equations of motion are nonlinear and more than two-dimensional, as in the Sinai billiard. The double pendulum exhibits this phenomenon at intermediate energies. This phenomenon often gives rise to attractors with non-integer dimension known as “strangeâ€, such as the Lorenz attractor. For 10 points, name this deterministic yet unpredictable phenomenon in which systems are highly sensitive to initial conditions, which could result from a butterfly flapping its wings in Brazil.

chaos [or word forms] <AS> Round 10 Bonuses

In systems with this behavior, all open sets of phase space will eventually overlap with one another, due to topological mixing. By the Poincare-Bendixson theorem, this phenomenon is forbidden in systems with fewer than 3 phase-space dimensions, because strange attractors cannot form in those systems. Systems with this property, which requires nonlinear equations of motion, include dynamical billiards, the logistic map, and the double pendulum. Because systems with this property are highly sensitive to initial conditions, they are unpredictable yet deterministic. For 10 points, name this phenomenon in which the butterfly effect might occur.

chaos [or word forms] <BH/AS>

This principle is directly equivalent to the time-invariance of a system's dynamics, which is why it is locally but not globally true on a cosmological level. Early evidence for this principle came from an experiment in which a falling weight was used to heat up a container of water, performed by Joule. This principle proves that so-called "over-unity" devices do not exist. One version of this statement describes the change in internal energy as being the sum of heat input and work done. That version is the first law of thermodynamics. For 10 points, name this fundamental principle of physics, which states that the total amount of energy in a closed system is constant.

conservation of energy [or conservation of mass-energy; accept first law of thermodynamics before it is read]

Lambert’s law states that the intensity from a diffusely reflecting surface is proportional to this function. The nth term of the Taylor series for this function is negative one to the n, times x to the two n, divided by two n factorial. The Fourier series of an even function only contains terms having this function. The (*) hyperbolic version of this function is equal to e to the x plus e to the negative x divided by two. That function forms the catenary curve. Its namesake law generalizes the Pythagorean theorem. For 10 points, identify this trigonometric function equal to the adjacent leg over the hypotenuse.

cosine <SR Math>

For a droplet on a flat surface in equilibrium, the Young-Laplace equation multiplies the liquid-vapor surface tension by this function of the contact angle. The power factor for an AC circuit can be calculated as this function of the phase angle. For small angles, this function of the angle can be approximated as (*) one. The law named for this function reduces to the Pythagorean theorem for right triangles, and the magnitude of the normal force on an inclined plane is proportional to this function of slope angle. For 10 points, name this trigonometric function commonly defined as adjacent over hypotenuse and contrasted with sine.

cosine <Xiong>

Both the skin effect and the proximity effect reduce the amount of this quantity. The density of this quantity equals conductivity times the electric field. The EMF of self-inductance is proportional to the time-derivative of this quantity. A term with units of this quantity was introduced by Maxwell and is known as its "displacement" type. The magnetic field created by this quantity is given in the (*) Biotâ€"Savart (" bee-OH sah-VAR ") law. This quantity times voltage equals power. This quantity times resistance equals voltage in Ohm's Law. For 10 points, name this speed of the flow of charge, whose SI unit is the ampere.

current

This letter prefixes baryons made up of three up or down quarks, and in mathematics it symbolizes the modular discriminant, symmetric difference, and the Laplace operator. A function described by this letter models the density of a point charge and is named for Paul (*) Dirac. A quadruple bond contains one sigma bond, two pi bonds, and one bond described by this letter. Heat must be added to a reaction if this letter is present in the chemical equation, and this letter denotes a change in a quantity. For 10 points, name this fourth letter of the Greek alphabet whose uppercase form resembles a triangle.

delta <Park>

In one case, this process produces an intensity function that varies as sinc-squared of position. In general, the output of this phenomenon is the Fourier transform of the transmission function in the limit where the parallel rays approximation can be used. This phenomenon has a (*) Fraunhofer type, and it limits image resolution to at most 1.22 times the wavelength. This phenomenon produces an intensity profile when light is shined through two slits, as in an experiment by Thomas Young, and a namesake “grating†using this phenomenon. For 10 points, name this process in which light rays ‘bend’ around obstacles, usually contrasted with reflection or refraction.

diffraction (prompt on “interferenceâ€)

Due to this phenomenon, wavelength over diameter times one point two two equals angular resolution, by Rayleigh's Criterion. This effect can be modelled by considering each point on a wavefront as a source of a spherical wave, by Huygens' principle. This phenomenon creates the Airy Disk and Newton's (*) Rings. When this effect occurs with X-rays in crystals, it's modelled by Bragg's law. It occurs whenever light passes an obstacle, as a result of interference. For 10 points, name this optical phenomenon that can be produced by a double slit, like Thomas Young did, or by its namesake kind of "grating."

diffraction [prompt on "interference" until it's mentioned]

. In kinetic theory, the Einstein relation states that the constant of this phenomenon is equal to the product of the mobility, Boltzmann’s constant, and the absolute temperature. The ambipolar form of this phenomenon occurs due to the interactions of charged species with an electric field. In a gas, the first of (*) Graham’s laws says that the rate of this process is inversely proportional to the square root of density. Fick’s laws describe this process, an example of which is osmosis. For 10 points, name this process where particles move from a region of high concentration to low concentration.

diffusion <AP> Bonuses

The rate at which momentum undergoes this physical process is related to a fluid's kinematic viscosity. In a semiconductor at equilibrium, the current due to charge carrier drift is opposed by the current due to this process. This process is described as a random walk in the Brownian motion model. The flux associated to this stochastic process is proportional to the negative gradient of concentration, according to Fick's law. Unlike convection, this process does not entail bulk motion of substance. When a solvent moves, rather than a solute, this process is called osmosis. For 10 points, name this process in which particles migrate to regions of lower concentration.

diffusion [accept Brownian motion until it is read; prompt on "osmosis"; prompt on "random walk"]

One equation that governs these objects involves the ideality factor, which is multiplied by the thermal voltage. The saturation current is another term in that law, the Shockley equation. These devices typically overheat above the breakdown voltage, although the reverse-biased "avalanche" type will not. These devices, symbolized on circuit diagrams with a triangle and a vertical line, consist of a single P-N junction. With low forward resistances but very high reverse resistances, for 10 points, name these circuit components, designed to allow current to flow in only one direction, which may be "light-emitting".

diodes

D’Alembert’s paradox concerns a set of conditions in which this force is zero. One type of this force arising from the boundary layer around an object is known as skin friction. The magnitude of this force is given by six pi times the product of velocity, radius, and viscosity for small spherical particles. At high (*) Reynolds numbers, this force depends on velocity squared, and at low Reynolds number, this force is proportional to velocity and can be calculated via Stokes’ law. Terminal velocity is reached when this force equals the force of gravity. For 10 points, name this force which opposes the motion of an object in a fluid.

drag <Xiong>

A coefficient associated with this force is equal to one when stagnation pressure builds up over an entire surface. Potential flow solutions to the Euler equation indicate that this force should be zero in direct opposition to observation in a paradox named after Jean d'Alembert. The power needed to overcome this force is proportional to the third power of velocity and at very low Reynolds numbers, this force for spherical objects is proportional to the fluid velocity, according to Stokes' Law. This force leads to an object reaching terminal velocity and counteracts thrust. For 10 points, name this force which opposes an object's motion through fluid, including air.

drag [Accept air drag. Prompt on "air resistance."]

The reciprocal of this value is the limiting probability in the hat-check problem, and this value is taken to the power of “minus x squared†in the standard error function. A function that uses this number has Taylor series entries of the form (*) “x to the n over n factorial,†and according to Euler’s identity, this number raised to “i times pi†plus one equals zero. This number is equal to the nth power of the quantity “One plus one over n†as n goes to infinity, and this number to the power x is the exponential function. For 10 points, give this number roughly equal to 2.718 that forms the base of the natural logarithm.

e (accept Napier’s constant or Euler’s number; do not accept Euler’s constant, as that’s actually something else)

For the recursive function [read slowly] “f of x equals f of (x minus one) plus f of (x minus two),†with bases cases “f of zero equals one†and “f of one equals one,†this is the number of additional times that the function will be called when computing f of four. The n-queens problem is usually stated with n as this value. In the standard RGB color system, this number of (*) bits is used to store each individual color value. In binary, this many consecutive ones are used to write the hexadecimal number FF and the decimal number 255. It’s the number of bits in a byte. For 10 points, name this number expressed 1000 [“one zero zero zeroâ€] in binary, the base of the octal numeral system.

eight <Xiong>

One variety of this property defines eight different types of gluons; hadrons with that type of this property cannot be isolated or directly observed due to confinement. Unlike that "color" type, the more common type of this causes a point to be accelerated in proportion to it by the Lorentz force. Its conservation is assumed by Kirchoff's first circuit rule, and the Millikan oil-drop experiment measured the "elementary" one. For 10 points, name this property measured in coulombs, whose rate of change is current and which can be positive or negative.

electric charge [accept color charge until "color" is read]

The time derivative of this quantity's density equals the negative divergence of current density. The energy stored in a capacitor equals one half times this quantity squared, divided by capacitance. The magnetic force on a moving particle is equal to this quantity times the cross product of (*) velocity and magnetic field by the Lorentz force law. Capacitance is equal to this quantity divided by voltage. The electrostatic force on an object equals this quantity times the external electric field. For 10 points, name this quantity, often symbolized by the letter Q, which is measured in Coulombs.

electric charge [prompt on "Q"]

A "dark" type of this phenomenon manifests in light-sensitive devices like CCDs even when there is no light entering the device. A rectifier is used to force this phenomenon to be unidirectional. The areal density of this quantity equals conductivity times electric field. When these phenomena are "steady", the magnetostatic approximation holds, whence the magnetic field generated by them is described by the Biot-Savart law. Inductors resist changes in this quantity. Per Ohm's law, this is the ratio of voltage to resistance. For 10 points, name this quantity which measures the flow of electric charge in units of amperes.

electric current

The density of this quantity is equal to the time derivative of the D-field. A device that produces a constant amount of this quantity is represented by a diamond with an arrow within it. This quantity is the subject of the skin effect, in which it is preferentially distributed towards the surface of an object due to self-inductance. This quantity, which is measured in an SI base unit, is the subject of Kirchhoff’s node rule, which is an alternate statement of charge conservation. The power dissipated by a wire is proportional to the square of the “direct†type of this quantity. For 10 points, name this quantity that is related to resistance and voltage by Ohm’s law and is measured in amperes.

electric current <AS>

The introduction of a term with units of this quantity allowed Maxwell to formulate the equation for light as an electromagnetic wave. That term was introduced into Ampère's law and is called "displacement [this]." This quantity squared is proportional to the energy stored in inductors. Devices that measure this quantity are hooked up in (*) series, and have very low internal resistance. It times voltage gives power. It only flows in one direction through diodes. For 10 points, name this flow of charge, which comes in "alternating" and "direct" types.

electric current [prompt on "I "; accept direct current; accept alternating current]

This quantity is responsible for changes in refractive indices proportional to the square of this quantity in the Kerr effect. A vector that describes the directional energy flux density is equal to the magnetic field times this quantity and is called the Poynting vector. Drift velocity is equal to this quantity times electron mobility. A dipole experiences a torque equal to charge times separation times this quantity. This quantity is zero within a conductor. The integral of this quantity dotted with area over a closed surface is proportional to the charge enclosed by Gauss' law. For 10 points, name this field that has units of force per unit charge and is symbolized by the letter E.

electric field [accept E before it is read]

This quantity appears in the first row and column of the Faraday tensor. Potential energy due to the presence of this quantity is equal to one-half permittivity times the volume integral of the magnitude of this quantity squared. The Poynting vector is the cross product of the H field and this (*) quantity’s vector. this quantity is constant between parallel plates in a capacitor. If charges are stable, then Coulomb's law can be used to find this quantity which is measured in Newtons per coulomb. For 10 points, name this field symbolized with an E.

electric field [prompt on “Eâ€]

Leon Chua theorized this property's current-dependent analogue in 1971; in 2008, scientists at HP used thin films of titanium dioxide to make a two-terminal device governed by that "memory" variety of it. Devices named for Carey Foster or Kelvin can accurately measure small values of it using a setup like the Wheatstone bridge. This real analogue of reactance and real part of impedance quantifies thermal dissipation of energy, and equals the quotient of voltage and current. For 10 points, identify this quantity in circuit elements governed by Ohm's Law and measured in ohms, the inverse of electrical conductance.

electrical resistance [prompt "R;" prompt "memristance" or "memory resistance" until "memory variety" is read]

The work function measures the binding energy of these things. “Configurations†of them are often abbreviated by writing the symbol of a noble gas in square brackets. Multiplying their charge by one volt gives a unit of energy that is frequently used in particle physics. In an atom, the state of one of these is uniquely defined by four indices, including the spin quantum number, which exists due to the Pauli exclusion principle. In the Bohr model, these things orbit in distinct shells, but modern theories treat them as a cloud of probability surrounding a nucleus. For 10 points, name these negatively-charged subatomic particles.

electrons <AS>

This phenomenon's namesake "darkening" and "brightening" occur when a star rotates at high speeds, and gives stars an oblate spheroid shape. Its carriers are theorized to have coherent states detectable by instruments like LIGO. A research team in China controversially discovered that the speed of this force exceeds the speed of light. Considered the curvature in of spacetime in general relativity, an inverse-square law was proposed for the strength of this force by Isaac Newton. For ten points, name this force, which on Earth yields an acceleration of 9.8 meters per second squared perpendicular to the ground.

gravity

Describing their motion was the original intent of a formula containing Pauli matrices, the Dirac equation. They are discharged en masse in a tube named for William Crookes; in an experiment using a nickel crystal, these particles were shown to diffract like waves by Davisson and Germer. Hertz discovered that they are emitted when matter is hit by sufficiently-energetic light. Emitted in beta-minus decay, they became the first discovered leptons in 1897, when J.J. Thomson determined cathode rays were made of them. For 10 points, name this ubiquitous elementary particle with negative charge.

electrons [prompt "cathode rays" since it's sort of unclear throughout]

One way to define this quantity in terms of other physical constants is the square root of 2hαε0c [“two h alpha epsilon-nought câ€]. The quantum Hall effect states that conductance comes in discrete multiples of this quantity squared divided by Planck's constant, and (*) Faraday’s constant is equal to this quantity times Avogadro’s number. This quantity was inferred using an experiment that observed the terminal velocity of oil droplets and was carried out by Robert Millikan. This constant is about 1.6 times 10 to the negative 16 coulombs, and it’s symbolized lowercase e. For 10 points, give this constant, the charge of a certain subatomic particle.

elementary charge (accept charge of an electron; accept charge of a proton; prompt on lowercase e before mention; prompt on just charge before mention) <Xiong>

This quantity can be written as a differential operator equal to v plus negative h bar squared over two m times the Laplacian. The differential of this quantity is equal to temperature times change in entropy minus pressure times change in volume. Force is the negative derivative of one form of this quantity, the change of which is net work. The impossibility of perpetual motion machines is equivalent to the conservation of this quantity by the first law of thermodynamics. For 10 points, name this quantity with thermal, kinetic, and potential varieties.

energy [accept Hamiltonian before "temperature"] <SH>

Claude Shannon defined this concept for source coding in information theory, and an intensive definition of this property for gases inspired Gibbs's paradox. Defined macroscopically as Boltzmann's constant times the natural log of the microstate number, omega, its change often equals change in heat over temperature, and it represents thermal energy unavailable to perform work. This state function tends only to increase by the Second Law of Thermodynamics. Symbolized S, for 10 points, name this thermodynamic quantity, a system's measurable disorder.

entropy [prompt "S" until read]

On a certain type of thermodynamic diagram, lines along which this quantity is constant are given by an expression in which one quantity is raised to the ratio of specific heats; those lines are called adiabats. The difference between the Gibbs free energy and the enthalpy is equal to this quantity times temperature, to which it is conjugate. This quantity can be measured in units of Boltzmann’s constant, which is the proportionality factor relating it to the logarithm of the number of available microstates. This quantity is non-decreasing, according to the second law of thermodynamics. For 10 points, name this quantity that is a measure of disorder.

entropy [prompt on “Sâ€] <AS>

Kirchoff’s law of radiation only applies to systems in these states, and one type of these states includes the Lagrange point solutions to the three-body problem. Located at the critical points of potential energy graphs, these states can be identified by a second derivative test as neutral, stable, or unstable. These states are “dynamic†when two inverse processes occur at the same rate, or when a body has balanced forces acting on it but a non-zero velocity. The transitivity of this condition is the zeroth law of thermodynamics. For 10 points, name this balanced state, the “thermal†variety of which involves no heat exchange.

equilibrium [accept thermodynamic equilibrium] <SH>

A smoothing technique described by this term is often contrasted with moving average smoothing. The interarrival times in a Poisson process are modeled by a probability distribution described by this term. During bacterial growth, a phase described by this term occurs between the (*) lag phase and stationary phase. Radioactivity is an example of a decay process described by this term, which also describes a function that is the inverse of the logarithmic function. For 10 points, name this adjective that describes functions of the form “f of x equals b raised to the x powerâ€.

exponential <Park>

This function of distance appears in the radial wavefunction for s orbitals. The vapor pressure of a liquid may be approximated by this function of negative one over temperature. When a reaction is said to be “nth-orderâ€, the “n†refers to the argument of this function, and a first-order reaction obeys an integrated rate law that contains it. This function’s inverse is applied to the reaction quotient in the Nernst equation. This operation, followed by division, is performed on individual concentrations to compute the equilibrium constant using the law of mass action. For 10 points, name this operation which may be applied to a pKa to find the Ka, and which is the inverse of the logarithm.

exponentiation [or raising something to a power; or equivalents; do not accept “multiplicationâ€] <AS>

Wilhelm Lenz invented a statistical mechanical model of this phenomenon whose two-dimensional form was solved by Lars Onsager. The double-exchange mechanism results in this property of Heusler alloys. The exchange interactions between (*) electrons is responsible for this phenomenon, which is exhibited by alloys of rare-earth elements. This property, which disappears completely above the Curie temperature, arises from the alignment of electrons in neighbouring atoms. For 10 points, name this type of permanent magnetism exhibited by nickel, cobalt, and iron.

ferromagnetism <AP>

The Stoner criterion must be fulfilled for this property to arise in a simplified model of a solid, and RKKY theory predicts oscillations in objects with this property. The noise in the output of an object with this property is called the Barkhausen effect, and this property arises in an object below the (*) Curie temperature. Objects with this property can induce it in other metals with contact, and alnico, rare earth metals like neodymium, and lodestone exhibit this property. Iron, nickel, and cobalt exhibit, for 10 points, what permanent, strongest kind of magnetism?

ferromagnetism [prompt on “magnetismâ€]

If J is greater than 0 in the energy function negative J times the sum of the quantity S-sub-i S-sub-i-plus-one, these materials follow a model solved by Lars Onsager; those S terms signify spins. They cause a crackling noise when placed near loudspeakers in an effect named for Barkhausen. They are made up of similarly-aligned domains which grow smaller with temperature, losing their namesake property above the Curie point; those domains of dipole moments remain aligned even if the external field is removed. For 10 points, name these strongest and most commonly used metals whose north and south poles attract, exemplified by cobalt, nickel, and iron.

ferromagnets [accept ferromagnetism; accept Ising model until "these materials" is read]

When the Knudsen number in one of these substances is much less than 1, the continuum hypothesis is a valid assumption. MHD is the study of electrically-charged ones. Kolmogorov scales are functions of the rate at which kinetic energy associated with eddies in them is dissipated. Transverse waves cannot propagate through these substances. The Reynolds number describes the ratio of inertial and viscous forces in them, and they are modeled by the Navier-Stokes equations. Inviscid ones move faster when their pressure drops, according to Bernoulli’s principle. For 10 points, name these substances which flow, including plasmas, liquids, and gases.

fluids [prompt on “liquids†or “gases†or “plasmasâ€] <BH/AS>

The value of a specific type of this quantity in a rotating reference frame is equal to the cross product of v and -2m times omega. This quantity's third and fourth derivatives are known as "snatch" and "shake", respectively. This quantity is equal to k times the absolute value of the product of two point charges divided by the square of their distance in a law named for Coulomb. With units of kilogram meters per seconds squared, also known as newtons, for ten points, name these vector quantities which are always found in equal and opposite pairs according to Newton's Third Law.

forces

The regular polyhedron that has this many faces is given the Schlafli symbol “3, 3,†and the Klein group has this order. In evolutionary biology, this number of “Fs†denotes the basic drives needed for human (*) survival. The total power radiated from a surface is proportional to this power of absolute temperature according to the Stefan-Boltzmann Law, and an atom loses this many neutrons and protons total when undergoing alpha decay. There are this many fundamental forces. For 10 points, give this number of hydrogen atoms in methane and the atomic number of beryllium.

four

One form of this quantity equals the square root of mass times g times length divided by moment of inertia for a physical pendulum. For a spring, that same value is the square root of the spring constant over mass. That quantity is symbolized omega and is known as the "angular" type of this value. For an electromagnetic wave, this quantity is equal to cover lambda, making this value inversely proportional to wavelength. This quantity has units of inverse seconds because it is the reciprocal of the period. For 10 points, name this quantity representing the number of cycles per unit time, often measured in hertz.

frequency [or angular frequency; prompt on "f"]

This phenomenon originates from asperities which can be modeled with the Archard equation. On an atomic scale, this is described by the Tomlinson model, including a namesake parameter that, when greater than one, results in the stick-slip variety of this phenomenon. Reye hypothesized that this is proportional to volume of wear debris. Amontons' second law states that it is independent of the area of the contact surface. It is equal to the normal force times mu, its namesake coefficient, which has static and kinetic varieties. For ten points, name this force that acts opposite motion.

friction

The rate at which the properties of one of these substances change can be defined in terms of a lapse rate. The derivation of one law that approximately describes them takes the net impulse due to a collision with a wall to be exactly twice a particle’s normal momentum; that assumption is part of kinetic molecular theory. The Maxwell-Boltzmann distribution describes the speeds of individual particles in these substances. A constant named for these substances is a macroscopic version of Boltzmann’s constant, and takes on a value of 8.31 in standard SI units. Ideal ones are described by the law “P V equals n R Tâ€. For 10 points, name this least-dense state of matter.

gases [accept ideal gases] <AS>

This theory predicts an increase in traveling distance proportional to the negative log of 1 minus R dot x in an effect named for Shapiro. The left side of an equation that governs this theory includes a term named for Ricci as well as a term equal to half the metric tensor times the scalar curvature. That equation is solved for by the Kerr and Schwarzschild metrics. This theory predicts that light will be deflected away from massive matter through gravitational lensing. For 10 points, this theory describing gravity and the curvature of spacetime, posited by Einstein and contrasted with a "special" counterpart.

general relativity [prompt on partial; do not accept "special relativity"]

The proposed experiment STEP is meant to test a theory about this phenomenon. The particles theorized to explain this phenomenon are spin-2 bosons that travel at the speed of light. The first type of a wave based on this phenomenon was observed in (*) 2016 and was caused by the collision of two black holes. Escape velocity equals the square root of the quantity 2 times the constant for this phenomenon times the mass of the body divided by the radius. Earth’s value for acceleration due to this force is 9.8 meters-per-second-squared. For 10 points, name this fundamental force that is described classically by an inverse square law.

gravity [accept word forms such as gravitational force] <BC>

According to one theory of this phenomenon, free particles move along geodesics. That theory also predicts that this phenomenon will cause light to be redshifted. The equivalence principle asserts that this phenomenon and inertia behave identically.This non-thermal phenomenon must be present for convection to occur. This phenomenon, which is not described by GUTs, is treated as a consequence of the curvature of spacetime in general relativity. Newton described this interaction as an inverse-square force. For 10 points, name this weakest of the fundamental forces, which causes an acceleration of 9.8 meters per second squared on Earth.

gravity [or word forms]

This system has one elliptical separatrix. Small oscillations about a stable equilibrium point will produce approximately this type of system; the frequency of those oscillations is the square root of the second derivative of the potential energy at that point divided by the mass. When one of these systems is (*) damped, it can be described by a Q factor, which quantifies how fast this system loses energy. For 10 points, name this system that experiences a restoring force proportional to its displacement, the classic example of which is a mass on a spring.

harmonic oscillator [prompt on “oscillatorâ€; anti-prompt on “simple harmonic oscillatorâ€] <SR Physics>

The 21-centimeter line is cased by hyperfine transitions of this element. Two atoms of this element are involved in a chain reaction releasing neutrinos and gamma rays, and the Teller-Ulam design was for a device using this element. Its antimatter counterpart was created and confined at CERN in November 2010, and the visible spectral line emissions of this element give rise to the Balmer series. The Bohr model was originally conceived to describe an atom of this element, which is converted into helium in stars. For 10 points, name this lightest element with an atomic number of 1.

hydrogen

For a Lorentz oscillator, this quantity is equal to the square root of the real part of the dielectric constant, denoted epsilon. Transverse mode radiation is zero when these quantities are equal to each other, according to Fresnel’s equations. The critical angle equals the arcsine of the ratio of these quantities in two media, and a law named after a Dutch scientist relates these quantities to the sine of the angle of incidence and refraction. For 10 points, give the name for these quantities which most commonly describe how light is transmitted through a medium.

index of refraction <JK>

Imaginary values of this quantity correspond to a phase shift between applied and resultant electric field in a material. This quantity is related to a material’s density and polarizability in the Lorentz-Lorenz equation, and the OPL is equal to this quantity times the distance travelled by light. At (*) angles greater than the arcsine of the ratio of two of these quantities, light experiences total internal reflection. Snell’s law equates the ratio of this value for two substances to the ratio of the sines of the angles of incidence and refraction. For 10 points, name this quantity equal to the speed of light in a vacuum over its speed in a given material.

index of refraction (accept refractive index or n)

Electromagnetic metamaterials with a negative value for this property have been constructed, which may see use in optically imaging things that are smaller than the diffraction limit. One is subtracted from this quantity in the Lensmaker's equation. When this quantity is polarization-dependent, as in calcite, a "double" type of this phenomenon may occur, called birefringence. This quantity measures how much slower light becomes in a medium. At an interface, Snell's law relates the angles of incidence to these quantities. For 10 points, name this dimensionless property of a medium that measures how much a ray of light is bent when it enters that medium.

index of refraction [or refractive index]

A generalization of a law describing this effect states that the curl of the electric field equals the negative partial time derivative of the magnetic field. Eddy currents, which dissipate heat, are generated by this effect, and the direction of the result of this effect is given by (*) Lenz’s law. This effect is described by an equation which states that the time derivative of magnetic flux equals EMF; that law is named for Faraday. Generators and transformers rely on this effect. For 10 points, name this effect in which a changing magnetic field produces a current.

induction

This effect can be used to produce drag or heating by creating eddy currents. A quantity related to this phenomenon equals voltage over the time-derivative of current. A law about this phenomenon can be written "curl E equals negative partial B partial t." This phenomenon opposes the original change in flux by Lenz's Law. One equation about it states that the negative time-derivative of magnetic flux is the (*) EMF. A circuit part that relies on this phenomenon resists changing electric current. This phenomenon makes transformers, generators, and motors possible. For 10 points, name this electromagnetic effect modelled by Faraday's law, in which a changing magnetic field creates an electric current.

induction [accept inductance]

Navigation systems described by this word use gyroscopes to independently dead-reckon their own trajectories. In all reference frames described by this word, Lorentz scalars are measured to have the same length, and Newton’s laws are true without fictitious forces. A rotational quantity described by this word is related along three different axes in plane figures, according to the perpendicular-axis theorem. Eotvos was the first to prove a result underlying general relativity: that the gravitational form of mass was equal to this form of mass. For 10 points, name this tendency of a body at rest to remain at rest, the subject of Newton’s first law of motion, which is measured by mass.

inertia [or word forms; or inertial navigation systems; or inertial reference frames; or moment of inertia; or inertial mass; do not accept anything containing “non-inertialâ€] <AS>

The sum of squares of visibility of this effect and definiteness of a photon’s path are less than or equal to one in the Englertâ€"Greenberger equation. This effect is destroyed when a “which way†marker observes a quantum system. This effect was measured after two light beams combine in the (*) Michelsonâ€"Morley experiment. A resulting pattern from this effect is seen in Young’s double slit experiment. For 10 points, name this effect occurring when two or more waves superimpose that has “constructive†or “destructive†types.

interference <SY Physics>

The differential of this quantity is equal to T times dS minus p times dV, implying it is minimized at constant entropy and volume. Using the free expansion of gas into vacuum, Joule’s experiment kept this quantity and gravity constant. The temperature derivative of this quantity is the constant-volume heat capacity, and this (*) state function is equal to the enthalpy minus the product of P and V. By the first law of thermodynamics, the change in this quantity is the heat supplied plus the work done, and it is symbolized by uppercase U. For 10 points, name this measure of the total energy inside a system given by the sum of the potential and kinetic energy.

internal energy (accept just energy before “uppercase U†is read, and accept just internal after “energy†is first read; prompt on “uppercase U†before read)

A polypeptide chain named for this letter is a linker-component of antibodies IgA and IgM. In NMR spectroscopy, this letter is used to denote the value of spin-spin couplings and encodes information about bond geometry. In electromagnetism, this letter symbolizes the current density field, and it’s the first letter of a SI unit equivalent to a (*) newton-meter. The “hat†form of this letter usually denotes the unit vector pointing in the y-direction, in contrast with the x-vector symbolized as i-hat. For 10 points, give this letter whose capital form stands for the SI unit for energy, the Joule.

j (accept either lowercase j or uppercase J, should they specify) <Pendyala>

In quantum position space, the operator corresponding to this quantity equals negative h-bar squared over two times the mass, all times the Laplacian. For a relativistic particle, this quantity is equal to: the Lorentz factor minus 1, times mass times the speed of light squared. This quantity is equal to the average of the Hamiltonian and the Lagrangian. It can be defined as one-half (*) momentum squared over mass. The rotational kind of it is given by one-half moment of inertia, times angular velocity squared, while its translational kind is one-half mass times velocity squared. For 10 points, potential energy is often converted to what type of energy possessed by moving objects?

kinetic energy

Von Weizsäcker names a functional for this quantity, whose average value is given by the virial theorem. Symbolized by a capital T in the Lagrangian and Hamiltonian formulas, it can be calculated as "p squared over 2 m." The change in this quantity equals the work done by the net force. It is conserved in elastic, but not inelastic, collisions. For rotational motion, it equals "one-half I omega squared," while for a non-rotating object it equals "one-half m v squared." For 10 points, name this type of energy often contrasted with potential energy.

kinetic energy

In the photoelectric effect, the maximum value of this quantity for the released particles is proportional to frequency of the incoming particles, provided that the frequency is above the threshold frequency. Usually symbolized T in the Lagrangian and Hamiltonian formulas, its average value for a mole of ideal gas is three-halves the constant R times temperature. Work done by a net force is equal to change in this quantity, whose rotational form is moment of inertia times angular velocity over two. For 10 points, name this quantity classically equal to one-half mass times velocity squared, which is measured in joules and contrasted with potential energy in moving objects.

kinetic energy [prompt "T" until read; prompt "E sub K;" prompt "energy of motion"]

The value of this for particles equals the quantity the Lorentz factor minus one, times mass times the speed of light. In the absence of outside forces, the value of this for superfluids remains constant. The value of this for a photon is given by multiplying (*) Planck’s constant by frequency. The rotational form of this quantity is given by one half the moment of inertia times the angular velocity squared while for non-relativistic velocities, the translational form is equal to one half of the mass times velocity squared. For 10 points, name this type of energy that is caused by the motion of an object, in contrast with potential energy.

kinetic energy [prompt on energy] <BC>

The fact that the operator for this and position do not commute, called the canonical commutation relation, underlies much of the weirdness of quantum mechanics. This quantity is proportional to wavenumber. A term containing this variable must be added to Einstein's "E equals m c squared" equivalence to make it exactly correct. Planck's constant divided by this quantity equals a particle's de Broglie wavelength. The square of this quantity divided by twice an object's mass equals kinetic energy. Force is the time derivative of this quantity, and a change in this quantity is called an impulse. For 10 points, name this kinematic quantity equal to mass times velocity.

linear momentum [or translational momentum]

In particle accelerators, a magnetic analogue of these devices consists of a series of quadrupole magnets. When these devices are dispersive, they are said to suffer from a chromatic defect. In one phenomenon named for these objects, geodesics are bent around a massive object, yielding results like a four-pointed Einstein cross surrounding a massive galaxy. The power of these devices is measured in units of inverse length and is conventionally given in diopters. An approximation named for a “thin†one can be used to compute their focal lengths. Non-ideal ones suffer from coma and other optical aberrations. For 10 points, name these objects that refract light.

lens [prompt on “focuser†or “collimatorâ€] <AS>

This quantity's operator equals "negative i h-bar del," and it equals Planck's constant divided by the de Broglie wavelength. The translational invariance of the Lagrangian gives rise to one property of this quantity, which is the canonical conjugate of position. Euler's first law gives this quantity in terms of the velocity of the center of mass, and it equals zero in the center-of-mass frame of reference. The original statement of Newton's second law was that force equals this quantity's derivative. This quantity is conserved in collisions within closed systems. For 10 points, name this quantity equal to mass times velocity.

linear momentum [do not accept "angular momentum"]

A system's Hamiltonian differentiated with respect to a generalized version of this quantity is equal to the time derivative of position. It is described in quantum mechanics by i times h-bar times the gradient operator, and its Planck unit is equal to h bar over the Planck length, and it is equal to Planck's constant divided by a particle's de Broglie wavelength. Via Noether's theorem, it results from translational invariance of laws of motion. Impulse describes its change in time, and force is its derivative. For 10 points, name this quantity conserved in elastic and inelastic collisions, the product of mass and velocity.

linear momentum [or translational momentum; do not accept "angular momentum"]

In a vacuum, the curl of this quantity is "1 over c-squared, partial-E partial-t." A differential bit of it is proportional to "I, d-l cross r, all over r cubed." A constant that determines it has numerical value "4-pi times 10 to the negative 7." The line integral of this quantity equals "mu-nought times I-enclosed." Its divergence, or its integral around a closed surface, is (*) zero, by Gauss's law, which states the impossibility of this kind of monopole. One of these things exerts a force proportional to the sine of the angle between it and a current-carrying wire. One of these generated by a current is modelled by the Biot-Savart ["BEE-oh sa-VAR"] and Ampère's laws. For 10 points, name this counterpart to the electric field.

magnetic field [or B-field; accept H-field; prompt on any answer just about "magnets" in general]

A beam of light interacting with one of these entities has its plane of polarization rotated in an effect named after Faraday. The strength of this entity produced by a steady current can be calculated using the Biotâ€"Savart Law. This quantity is crossed with velocity to find the (*) Lorentz force, and the electric field divided by the permeability of free space crossed with this quantity is the Poynting vector. A current flowing perpendicular to one of these results in a voltage difference in the Hall effect. For 10 points, name this field denoted by a capital B, the counterpart of the electric field.

magnetic field [prompt on “B fieldâ€] <SR Physics>

Birefringence results from these entities in the Voigt effect, while light is polarized with a rotation linearly dependent one of their components in the Faraday effect. The force exerted by them is proportional to the cross product of these entities with the velocity of a nearby charged particle, and they are expulsed by superconductors in a phenomenon discovered by Meissner. One differential equation stating that they have a divergence equal to zero, named after Gauss, is the second of Maxwell's equations. Their strength is measured in teslas and they are denoted by the letter B. For 10 points, name these entities that often surround a material that has north and south poles.

magnetic fields

An "effective" form of this quantity used to calculate conductivity in the Drude model is equal to three times the harmonic mean of three similarly-named values specific to each dimension. Its invariant form is proportional to the square root of the difference of the squares of energy and momentum times the speed of light. Some of this quantity is lost when atoms bond, this value's defect. Black holes are completely categorized by charge, angular momentum, and this quantity. Given by force divided by acceleration, for 10 points, name this measure of an object's inertia, measured in kilograms.

mass [accept effective mass before "this value"]

Normal modes may be identified by computing the determinant of the K-matrix minus angular frequency squared times the matrix named for this quantity. According to the no-hair theorem, a black hole can be characterized entirely by charge, angular momentum, and this property. In special relativity, the first law of thermodynamics describes the conservation of this quantity. The equivalence principle states that the gravitational and inertial forms of it are the same. The motion of gravitating bodies is most easily described in barycentric coordinates, also known as “center-of-this†coordinates. For 10 points, force is equal to acceleration times what quantity?

mass [accept mass-energy; prompt on “energyâ€] <BH/AS>

Waves of this quantity are responsible for maintaining the structure of spiral galaxies, according to the theory of Lin and Shu. The critical version of this property for the universe is used in computing a parameter also named for this property, denoted omega, which is approximately equal to one. In one formulation of Bernoulli’s principle, the dynamic pressure is given as one-half this times fluid velocity squared. This intensive property is constant in an isochoric process. A hydrometer can determine the specific gravity, and thus, this quantity, which determines whether or not an object will float in a fluid. For 10 points, what quantity is given as mass divided by volume?

mass density <AS> Bonuses

This physical quantity is unchanged in certain situations, according to the Stretch Rule. This quantity for a uniform rod is four times as large when measured from the end instead of from the center. When measured through the center of a uniform sphere, this quantity is equal to two fifths times the (*) total mass times the radius squared. The parallel axis theorem can be useful for determining this quantity. It is equal to angular momentum over angular velocity or torque over angular acceleration. For 10 points, name this quantity equal to mass times distance squared, the rotational analog of mass.

mass moment of inertia [or angular mass; or rotational inertia; or second moment of the area; prompt on "I"]

A process for which this condition holds at all times is termed a quasistatic process. In thermodynamics, state functions are only defined in systems with this property. Under the IAU definition, if a body is subjected to gravitational and pressure gradient forces, then it must attain the hydrostatic type of this condition to be a planet. The (*) ​thermal type of this condition holds transitively, according to the zeroth law of thermodynamics. This condition arises at an extremum of potential energy, with maxima and minima corresponding to its stable and unstable types, respectively. For 10 points, name this motionless condition in which all the forces on an object sum to zero.

mechanical equilibrium

These devices are particularly useful when shaped like a paraboloid because a source at the parabola’s focus will produce a collimated beam. These devices are popular for use in telescopes because they intrinsically do not suffer from chromatic aberrations. A convex one of these devices always forms a virtual image. The equation of image formation for these devices differs from a similar “thin†device in swapping the one over focal length and one over image distance terms. For 10 points, name these optical devices that reflect light instead of refracting light like lenses do.

mirrors <CV>

These particles were postulated by Wolfgang Pauli in 1930 to explain the conservation of energy, momentum, and spin during beta decay. The proton-proton chain produces two of these particles, which take 8 minutes to travel from the (*) Sun’s core to Earth. One method of detecting these particles relies on radiation produced when they travel through tanks of water and these particles are known to oscillate between different flavors during flight. A deficiency in the solar form of these particles was determined by both the Homestake and Super Kamiokande detectors. For 10 points, name this group of neutral leptons that come in electron, muon, and tau varieties.

neutrinos <AP>

Bonner spheres are used to determine their energy spectra, and high energy resolution can be achieved by a type of spin echo spectroscopy involving these particles. The R-process and S-process are two ways in which they can be captured. These particles are produced in spallation, and their speed is moderated by heavy water or graphite. Three of them are produced in the fission of uranium-236, and they are composed of two down quarks and one up quark. The number of these particles equals the mass number minus the atomic number. For 10 points, name these subatomic particles with zero charge.

neutrons

The "cold" varieties of these particles can be produced using liquid deuterium, and are used for measuring their scattering. They can be detected by gas proportional detectors filled with helium-3. They are used in NAA and PGAA to determine the elemental composition of a sample. PT symmetry would be violated by the existence of a dipole moment for these particles that are produced in spallation. One of their down quarks changes to an up quark in beta minus decay. Isotopes have the same number of protons but different numbers of, for 10 points, these particles with no electric charge.

neutrons

An upper value of 10 to the -28 was set for the EDM of this particle, though a non-zero electric dipole moment for it would violate PT-symmetry. The “fast†forms of these particles are converted into their “thermal†forms by a namesake moderator. (*) Spallation usually refers to the production of these particles, and they have a lifetime of approximately 15 minutes. Two down quarks and one up quark compose this baryon that was discovered by James Chadwick in 1932. Isotopes differ in their number of these particles. For 10 points, name these chargeless particles found in atomic nuclei along with protons.

neutrons (do not accept “neutrinosâ€)

Material buckling must be equal to geometric buckling for this process to occur at a steady state. The product of thermal utilization factor and three other factors gives K, the effective neutron multiplication factor, which must be greater than one for this process to occur. This process may be halted by iodine pits or poisoning with xenon. More material is produced than consumed by this process in breeder reactors. It is sustained when a material has a supercritical mass, and it can occur when a neutron is absorbed by plutonium-239 or uranium-235. For 10 points, name this energy-releasing reaction in which the nucleus of a particle is split into smaller parts, used in atom bombs.

nuclear fission [do not accept "fusion"]

In one device in which this process occurs, lasers are fired at both apertures of a hohlraum. This process is employed in the secondary in the Teller-Ulam device. Another device in which it occurs is covered in a lithium blanket, which breeds tritium from fast neutrons; that device is a tokamak, in which a plasma is magnetically confined. Muon catalysis lowers the activation energy for this process over a million-fold. Astrophysically, this occurs in the proton-proton chain, which culminates in the formation of helium and is the primary source of energy in the sun. For 10 points, name this process in which lighter elements are combined to form heavier elements.

nuclear fusion [prompt on “nuclear reactionsâ€; do not accept “fissionâ€] <AS>

Attaching two of these devices end to end creates a chaotic device whose trajectories trace out part of a topological torus. The generic equation of motion for these devices is "theta-double-dot equals negative k times sine theta", assuming there are no extended masses present, as in the "compound" type of this device. One type of these devices picks up a geometric phase as the Earth rotates, causing it to precess; that type is named for Foucault. The period of these devices equals "2 pi times root (length over small g)". For 10 points, name this simple device consisting of a weight suspended from a string, which exhibit approximate simple harmonic motion.

pendulum [accept simple pendulum; accept Foucault's pendulum; accept double pendulum]

The Blackburn variety of these objects can be represented with the Lissajous curve, and their Q factors include a gamma factor in the denominator due to Archimedes's principle and air resistance. Though it breaks down at high amplitudes, the small angle approximation allows the period of these systems to be represented as 2 pi times the square root of L over the acceleration due to gravity. A common use of these objects is to knock over dominoes or to trace lines in the sand to demonstrate the rotation of the earth. For 10 points, name these systems which feature a suspended weight swinging freely from a fixed point, including a variety named for Leon Foucault.

pendulums [Accept pendula. Prompt on simple harmonic oscillator before mention.]

For many materials, these phenomena are accompanied by a divergence in the length scale on which molecular motion is correlated. Paul Ehrenfest classified these phenomena using order parameters, and the Curie point is a (*) second-order example of them. The coexistence curve represents the parameters along which these occur, and they can no longer occur at the critical point. These occurrences are represented by the crossing of pressure-temperature boundary lines on their namesake diagrams. These occurrences are exemplified by deposition and sublimation. For 10 points, name these occurrences in which one state of matter becomes another.

phase transitions (accept phase change or phase transformations or any logical synonym of “transitionâ€; prompt on partial answer, especially just phases)

It’s not superconductivity, but Landau formulated a theory of these phenomena divided into universality classes by their critical exponents. This non-magnetic phenomenon occurs in the 2-dimensional Ising model when aligned magnetic moments become disordered at the Curie temperature. Second-order ones are continuous and first-order ones involve latent heat. A diagram of these for water is shaped like a Y and plots pressure against temperature. They occur at critical points, when several forms of a substance can coexist. For 10 points, name these transformations which include melting and boiling.

phase transitions [accept phase changes; accept critical transitions before “critical pointsâ€] <SH>

The 1923 Nobel Prize in Physics was awarded for work on the elementary electric charge and this phenomenon. The kinetic energy of particles undergoing this effect is given by Planck’s constant times the frequency minus the work function. For a given surface, this effect does not occur below a certain frequency, called the (*) threshold frequency. In 1887, an apparatus consisting of a coil with a spark gap was used by Heinrich Hertz to observe this phenomenon. A 1905 paper by Albert Einstein used the idea of discrete quanta of light to explain this effect. For 10 points, name this effect in which electrons are ejected from a metal due to incident light.

photoelectric effect <AP>

One of these objects can couple with a quasiparticle of plasma oscillation known as a plasmon to form a polariton. Low-energy annihilation produces at least two of these particles, which are represented by wavy lines in Feynman diagrams. The momenta of these particles may be calculated by multiplying the reduced Planck constant by the wave vector. Besides the gluon, this boson is the only massless particle in the Standard Model, and it mediates the electromagnetic force. This particle's speed in a vacuum, c, cannot be exceeded by any matter. For 10 points, name this elementary particle, the quantum of light.

photons [prompt on "gamma"]

Six times this quantity times the dynamic viscosity times the radius times the velocity gives the force exerted on a spherical object in Stokes’ law. Eight times this value times the universal gravitational constant times the stress-energy tensor appears in the numerator of Einstein’s field equation. Dividing (*) Planck’s constant by two times this number gives the reduced Planck constant, which appears in the Heisenberg uncertainty equation. Raising e to the power i times this number equals negative one. For 10 points, identify this constant, the ratio of a circle’s circumference to its diameter.

pi <SR Physics>

The Berlincourt meter measures this effect's namesake coefficient, symbolized D33, which is used in the constitutive equations that describe both its direct and converse varieties. An analogue of this phenomenon caused by applying a magnetic field to a ferromagnetic material is known as magnetostriction. Barium titanate and Rochelle salts can exhibit this effect because they lack a center of symmetry, and this phenomenon is also observed in crystals that accumulate charge due to deformation, like quartz. For 10 points, name this effect in which an applied mechanical strain generates voltage in a material.

piezoelectricity

If an electrode is inserted into one of these substances, its potential is constrained by a Debye sheath. The Z and theta forms of the Bennett pinch can be used to constrain these substances. They’re not superconductors, but the conductivity of these substances can be considered infinite. In some (*) fusion reactors, these substances are constrained into loops using particle beams or magnetic fields. Other forms of constraining these substances include the tokamak. These substances only naturally occur on earth during lightning strikes. For 10 points, name this fourth state of matter with a higher energy than a gas.

plasma <AJ>

This property determines which formulas to use for R and T in the Fresnel equations. The Jones vector describes this property, as does a quantity computed using Mueller calculus, the Stokes vector. The Faraday effect is a change in this property caused by a magnetic field, and a ray with this property is transmitted perfectly at Brewster's angle. It can be elliptical, circular, or linear, and only transverse waves can have this property. Glare-reducing sunglasses take advantage of this property, which can be achieved using certain camera lenses. For 10 points, name this property of a wave that oscillates in a single plane.

polarization [accept word forms such as polarized]

These particles are found in cosmic rays, where the anomalously large fraction observed by PAMELA in 2008 has led scientists to speculate a primary source other than the interstellar medium. Applications of these particles include a namesake emission tomography that detects the gamma rays they emit upon annihilation. Discovered by Anderson in 1932, one of these particles and a neutrino are among the products of beta positive decay and Dirac theorized their existence as negative energy solutions to his namesake equation. For 10 points, name these positively-charged fermions, antiparticles of electrons.

positron [Accept beta plus until beta is mentioned.]

The average value of this quantity is related to twice the average value of a related quantity by the Virial theorem. This quantity is subtracted in the definition of the Lagrangian. Force is equal to the negative (*) gradient of this quantity. It equals one-half k displacement squared for a simple harmonic oscillator. The “gravitational†form of this quantity is often symbolized “U†and on earth is defined as mass times little g times the height of an object. For 10 points, name this type of stored energy often contrasted with kinetic.

potential energy

In Newtonian gravity, this quantity satisfies Poisson’s equation. This quantity is equal to half the difference between the Hamiltonian and Lagrangian, and the operator for it is symbolized with a capital V. For a dipole, this quantity is given by negative the dipole moment (*) dotted with the electric field. In one form, this quantity is one-half charge times capacitance squared, and it is one-half k times the displacement squared in a spring. This quantity is mass times little g times height in its gravitational form. For 10 points, name this form of energy contrasted with kinetic.

potential energy (prompt on energy; accept specific types like electrical potential energy or gravitational potential energy; do not accept or prompt on just “potentialâ€)

This quantity cannot be defined for force fields which are functions of odd powers of velocity or for rotational fields. The shapes of this function’s minima determine the stability of equilibria. The derivative of this function with respect to position is proportional to force. One type of this quantity is defined as zero at infinity and is described by a “one-over-R†term times the product of the participating masses. The negative change in this quantity equals work performed. It comes from the arrangement of particles in a system, and one type equals mass times height above Earth times gravitation. For 10 points, name this type of energy which is added to kinetic energy to yield total energy.

potential energy [accept potential after “type of energy†is read; do not accept or prompt on “potential†before “type of energy†is read] <AS>

For AC circuits, the expression for the average of this quantity includes a namesake factor which accounts for differences in this quantity between DC and AC currents. In fluid systems, this quantity is equal to pressure times volumetric flow rate. In a rotational system, this quantity equals torque times angular velocity, while its electrical type can be expressed as both current times voltage and as voltage squared divided by resistance. Its integral with respect to time gives the work done on a system, and its instantaneous form equals force dotted with velocity. For 10 points, name this quantity measuring the rate at which energy is transferred, which is measured in watts.

power

This quantity is proportional to charge squared times acceleration squared according to the Larmor formula, and it equals the surface integral of intensity. The optical type of this quantity is the reciprocal of focal length, and in fluid systems, it equals flow rate times pressure. In electrical systems, it equals current squared times resistance, or simply current times voltage. For rotational systems, it equals torque times angular velocity. Calculated as force times velocity, it is the rate at which energy is transferred. For 10 points, name this quantity measured in watts.

power

For a periodic signal, the average of this quantity over the peak value is equal to pulse length over period, the duty cycles. In chain and belt drives, friction and wear in the chains and belts reduce the output for this quantity, resulting in a decreased mechanical advantage. In fluid systems, this quantity can be expressed as pressure times volumetric flow rate. It is equal to current squared times resistance, current times voltage, or work over time. For 10 points, name this quantity measured in watts.

power [prompt on P]

A special relativistic correction to one form of this phenomenon was made by Llewellyn Thomas, and the geodetic effect is a form of it named for Willem de Sitter. A variety of this phenomenon involving magnetic moments in external magnetic fields is named for Joseph (*) Larmor. A wobbling along the path of this phenomenon is called nutation, and a spinning bike wheel can hang from one string at the end of a horizontal axis using it. This phenomenon classical form has angular velocity directly proportional to torque. For 10 points, name this phenomenon in which the axis of rotation shifts, an effect usually demonstrated with gyroscopes.

precession (accept word forms)

A substance's bulk modulus has the same units as this quantity, and is equal to "negative volume times the derivative of ​this value with respect to volume." A reference value of 20 millionths of this quantity's SI unit is used to define the decibel in acoustics. This value is equalized in all directions and at all points in a fluid according to (*) ​Pascal's principle. This value is added to kinetic and potential terms to give a constant in Bernoulli's equation, which implies that this value decreases if a fluid's velocity increases. For 10 points, name this quantity equal to force divided by the area over which it is applied, which is measured in the atmosphere with a barometer.

pressure

For a photon, this quantity equals power flux density over the speed of light. The hypsometric equation relates thickness to the natural log of a ratio of two values of this quantity. The change in this quantity is proportional to density times head loss, and is inversely proportional to the fourth power of pipe radius. An incompressible fluid transmits this quantity equally in all directions, and an increase in fluid velocity decreases this quantity. It is inversely proportional to volume, and directly proportional to temperature. For 10 points, name this quantity measured in pascals, the amount of force per unit area.

pressure

This quantity has a namesake head that represents the internal energy due to a type of this quantity. The Clausius-Clapeyron equation states that the slope of a coexistence curve equals the derivative of this quantity over the derivative of temperature. Evangelista (*) Torricelli invented a device for measuring this quantity, and the first part of his last name is the origin of a unit for measuring this. For an ideal gas at constant temperature, Boyle’s law states that the absolute form of this quantity is inversely proportional to volume. For 10 points, name this property of gases equal to force over unit area that measured in Pascals.

pressure <AP>

The Poiseuille equation describes a drop in this quantity. This quantity, plus: density times gravitational acceleration times height, plus: one half density times velocity squared is usually constant. Change in this quantity is distributed evenly in all directions, by (*) Pascal's law. An increase in velocity causes a decrease in this quantity, by Bernoulli's principle. The difference in this quantity between the top and bottom of an object yields the buoyant force on an object. This quantity increases with depth. For 10 points, name this physical quantity equal to force over area.

pressure [prompt on "P"]

. A model named for Georgi and Glashow predict the decay of this particle into a positron and neutral pion, although this particle’s half-life may be on the order of 10 to the 33 years. This most-stable baryon is also the chief constituent of cosmic rays. In stellar cores, a “chain†named for this particle is the primary mechanism for nucleosynthesis and fusion. Containing two up quarks and one down quark, this particle is responsible for determining an element's atomic number. For 10 points, name this positively-charged subatomic particle which is in the nucleus along with neutrons.

proton <BM> Bonuses

This particle’s “radius puzzle†deals with its size, and its “spin crisis†dealt with its unexplained spin. Segre and Chamberlain won the 1959 Nobel Prize in Physics for discovering its antiparticle. This particle may decay into a pion and a positron, and its hypothetical half-life is 10 to the (*) 36th years. A chain reaction named for two of these particles occurs in small stars, and they were discovered by Ernest Rutherford. The number of them in an atom, denoted Z, is called the atomic number. Composed of two up quarks and one down quark, for 10 points, name these positively charged baryons found in nuclei.

protons

On a standard nuclide chart, the drip line for these objects is the closest drip line to the "A equals Z" line. This thing combined with a lighter thing during cosmological recombination. Most cosmic rays are these things, which are the stablest baryons, and which are about 1836 times heavier than the heaviest first-generation lepton. Unsuccessful experimental efforts to observe the decay of this particle have included Super-Kamiokande. A "chain" reaction named for these particles generates most of the sun's energy. The number of these in an atom is typically denoted "Z" and is called the atomic number. For 10 points, name this positively-charged nuclear particle.

protons [or hydrogen-1 nuclei; or protium nuclei; prompt on "hydrogen"]

A system of a spring, a mass, and one of these devices oscillates with an angular frequency of two time the spring constant over the sum of the mass and the mass of this device. One of these devices with two masses attached has an acceleration proportional to the difference of the masses over the sum of the masses and is called an (*) Atwood machine. Mechanical advantage increases directly with the number of these devices in a block and tackle system. For 10 points, name this simple machine made of cable attached to a wheel on an axle.

pulley <SY Physics>

Drag modeled by this function of velocity arises from the energy need to move the medium, and is not analytically solvable in general. Potential energy extrema are all locally approximated by this type of function. The power dissipated by a resistor equals resistance times this function of current. This type of function is the potential of a system which is used to model diatomic molecules as harmonic oscillators. The denominator of the expression for gravitational force contains this function of distance. An object moving in uniform gravity follows this type of trajectory. For 10 points, identify this function, which is applied to velocity in the expression for kinetic energy.

quadratic [or word forms; or parabolic or word forms; accept x squared; accept x to the second power (or “n†or anything instead of “x†in that answer); prompt on “polynomialâ€] <AS>

These particles interact by an effective potential that is about constant at short distances but linear at large distances, explaining why particle collisions result in their pair production. Regularities in the SU(3) classification scheme led to their proposal, and these charged particles cannot exist in (*) isolation due to color confinement. A combination of this particle and its antiparticle make up a meson, and three of them form a baryon. Gluons mediate the strong interaction between two of these particles. For 10 points, name this particle that comes in “flavors†such as up, top, charm, and strange.

quark <Xiong>

The existence of these particles disproved a model proposed by Shoichi Sakata. The Upsilon Particle, discovered at Fermilab in 1977, provided experimental data for one of these particles and its antiparticle. (*) Deep inelastic scattering provided the first evidence for the existence of these particles, and they have color charge, according to QCD. Mesons are composed of one of these particles and its antiparticle, and baryons contain three of them. Making up hadrons like protons and neutrons, for 10 points, name these elementary particles that exist in six flavors, including charm and strange.

quarks

The parton model was introduced by Feynman to describe certain scattering experiments before the discovery of these particles. The Eightfold Way describes symmetries between these particles, and a quantum number possessed by these particles has the symmetry group SU(3). In (*) quantum chromodynamics, confinement prevents these particles from being observed in isolation. These particles have a spin of one-half and a baryon number of one-third. Protons and neutrons are composed of three of these particles. For 10 points, name these elementary particles that come in varieties like up, down, and strange.

quarks <SR Physics>

The G-I-M mechanism led to the prediction of one type of these particles, and these particles were first directly confirmed by deep inelastic scattering at SLAC in 1968. These particles were proposed to explain flavor SU(3), and a 2015 experiment found bound states of (*) five of these particles. These particles were proposed by George Zweig and Murray Gell-Mann. and they combine in twos and threes to form mesons or baryons. These particles are subject to color confinement, and they have strange, charm, top, bottom, up, and down varieties. For 10 points, name these fermions that are found within protons and neutrons.

quarks (do not accept or prompt on larger groupings like “fermions†or “hadrons†or “mesons†or “baryonsâ€)

The radiation per unit solid angle of a wave undergoing this process varies with the cosine of the angle between the line of sight and the perpendicular. Lambert's emission law applies to the directionally independent form of this process, in which a microscopically rough interface causes it to occur in many different angles in the "diffuse" type of this phenomenon. The "specular" variety of this process is modeled by a law which states that the angle of incidence equals this process's namesake angle. For 10 points, name this optical phenomenon in which a wavefront rebounds off of a surface, often facilitated by mirrors.

reflection

A catoptric system contains devices that only perform this phenomenon to produce images. This phenomenon in solids increases as conductivity increases according to the Hagenâ€"Rubens relation, which makes metals and plasmas good at this phenomenon. The appearance of an evanescent wave indicates the (*) total internal type of this phenomenon, which occurs in fiber optic cables. This phenomenon can either be specular or diffuse. The angle at which this phenomenon occurs is equal to the angle of incidence. For 10 points, name this phenomenon in which light bounces off a surface, occurring in mirrors.

reflection <SY Physics>

This scientific phenomenon helps explain Fata Morgana. The Fresnel equations describe this phenomenon's relationship to reflectance and polarization. Certain classes of metamaterials can have a negative value for a number associated with this phenomenon. A law describing this phenomenon was derived by Fermat from his principle of least time, and that law indicates that the ratio of phase velocities in two media are proportional to the sine of the angle of incidence to this phenomenon's namesake angle. For 10 points, name this optics phenomenon described by Snell's Law, in which light bends because of a change in medium.

refraction

The haloalkane R134A is a common substance used in these devices. Their namesake substances evaporate adiabatically in the vapor-compression type of these devices. A primitive example of one of these used for liquefaction relies on the Linde cycle. The efficiency of these devices is described by the coefficient of performance. They may operate by reversing the (*) Carnot cycle, or by expanding pressurized gas, and their efficiency is the amount of cooling divided by the work input. For 10 points, name these devices used to keep food cold.

refrigerators <SR Chemistry>

For an electrical component envisioned by Leon Chua, this quantity depends on previous values, indicating that electrical components can have a memory for this quantity. Predictions for this quantity are too low in AC circuits because of the Skin Effect. In AC circuits, this is the real quantity added to the reactance to calculate the impedance. This quantity is equal to a material-dependent constant times length divided by cross-sectional area and by Ohm's law, it is equal to voltage over current. For 10 points, name this quantity whose SI unit is the ohm, which measures a circuit element's opposition to the passage of current.

resistance

Norton and Thévenin name equivalent, reducible forms of this quantity, while darker-colored bands represent higher percent tolerances related to this quantity. In Joule heating, this quantity allows for power loss, which can be calculated by current squared times this quantity. This quantity for a wire is proportional to its length over its cross-sectional area. The complex form of it is expressed as Z and is called impedance. Generally expressed as voltage over current via Ohm’s Law, this quantity is high for insulators and low for conductors. For 10 points, name this electrical quantity measured in ohms which is a material’s opposition to the flow of current.

resistance <BM>

Hard-drives rely on the ‘giant’ form of a phenomenon where this quantity changes depending on the orientation of adjacent ferromagnetic layers. In a series AC circuit, this quantity has no effect on the resonant frequency but instead determines the current at resonance. The differential form of this value is the slope of an (*) IV-curve. This quantity in a parallel circuit can be calculated as the reciprocal of the sum of reciprocals of this quantity for each branch, and in linear materials it is proportional to length over cross-sectional area. In ideal materials, voltage is equal to current times, for 10 points, what quantity measured in Ohms?

resistance (accept resistivity until “IV-curveâ€)

This term can refer to a matching between the kinetic energies of two particles and those two particles' bound-state energy. That type, used to study Bose-Einstein condensates, is named for Feshbach. Another type formed the Huygens and Kirkwood gaps, and the Laplacian type refers to the integer ratios between the orbital periods of Io, Europa, and Ganymede. In chemistry, it can be depicted by a double arrow between contributing forms, and the delocalized electrons that form its eponymous structures stabilize benzene. For 10 points, give this scientific term, which in physics refers to a system's tendency to oscillate more strongly when driven at certain frequencies.

resonance [accept Feshbach resonance; accept orbital resonance]

A diagnostic technique that employs this phenomenon measures relaxation times following the application of 90-degree and 180-degree RF pulses. In a half-open cylinder, this phenomenon arises at characteristic values twice those in a half-open cone, explaining why the clarinet overblows at the twelfth. In an RLC circuit, the frequency described by this term is given by the negative one half power of L times C. In chemistry, this term refers to a way of representing the contribution of delocalized electrons via multiple Lewis structures. For 10 points, give this term which describes systems which oscillate more strongly at some frequencies than others, which is employed in MRI.

resonance [accept word forms; accept resonance structures; accept resonant frequency; accept magnetic resonance] <AS>

The space of all operations that correspond to these motions is called SO(3). Phasors can be interpreted as vectors undergoing this motion. Gradients of scalar fields do not do this, as evidenced by the vanishment of the curl operator on those vector fields. Any motion of this type can be decomposed into three orthogonal uniaxial motions, perhaps using Euler angles, or by specifying the yaw, pitch, and roll. In spherical coordinates, these motions correspond to those in which the radius coordinate is unchanged. Where this motion exists, angular momentum is nonzero. For 10 points, name this type of motion in which a body moves about an axis but not along it.

rotation [accept circulation; or word forms; do not accept “circular motionâ€] <AS>

Multiple instances of this phenomenon cause Kikuchi lines to appear in TEM. Interactions with phonons cause the Brillouin form of this phenomenon, which is described by Mie theory. The Klein-Nishina formula governs this phenomenon, one type of which has Stokes and anti-Stokes forms and is named for Raman. Another elastic type named for Thomson is the low-energy version of the Compton form of this phenomenon. The color of the sky is a result of the Rayleigh form of this phenomenon. For 10 points, name this phenomenon in which particles are deflected from originally straight paths.

scattering

Electrons in these materials can acquire an effective mass much larger than their actual mass. A member of the III-V [“three-fiveâ€] class of these materials is gallium arsenide. The physicist Walter Schottky discovered that a junction between a metal and one of these materials can be used as a rectifier, and they have a small but finite (*) band gap of only a few eV. They can be classified as “n-type†or “p-type†based on the presence of electrons or holes, and introducing small impurities to them can be used to “dope†them. For 10 points, name these materials with an electrical conductivity between that of metals and insulators.

semiconductors <Pendyala>

Whether crystal momenta in certain energy states are identical makes a certain property of these materials either direct or indirect. Quantum dots are nano-sized crystals of these materials. Regions in these materials in which mobile charge carriers have been diffused away are termed (*) depletion zones, and the degree of holes and electrons differentiates the p-type and n-type of these materials. Adding impurities to strengthen these materials is termed doping, and examples of them include germanium and silicon. For 10 points, name these materials with resistances between those of conductors and insulators.

semiconductors (anti-prompt [ask for less specific] on band gaps; anti-prompt on specific semiconductors like silicon)

A modified type of this phenomenon stops as quickly as possible when its characteristic equation only involves one double root, a "critical" situation. In another situation, this phenomenon can be easily modelled by setting "I alpha" equal to "negative m-g-l-theta" using the small-angle approximation. Modelling it involves solving a second-order differential equation with no first-derivative termÂâ€"like (*) "m d-squared-x d-t-squared equals negative k-x." It occurs when the displacement is proportional to the restoring force, as in Hooke's law. For 10 points, name this oscillation demonstrated by springs and pendula.

simple harmonic motion [accept simple harmonic oscillation; accept harmonic oscillator; prompt on "oscillation"]

Bertrand’s theorem for a radial one of these objects states that it is one of two force potentials with bound orbits for which a closed orbit also exists. An equation for resonant frequency of these objects is one half pi times angular frequency and is represented by a sinusoidal graph. When these objects are “damped,†a frictional force opposes the velocity of those objects, and Hooke’s law is an equation for this type of system because the restoring elastic force F is directly proportional to displacement. For 10 points, name this type of system exemplified by springs and pendulums.

simple harmonic oscillator [accept SHO] <JK>

With Gordon, this function names a partial differential equation with soliton solutions. Euler solved the Basel problem using its series expansion, which only has odd powers. For small angles, this function can be approximated by y = x. Its namesake law equates the ratios between this function of an angle and the length of the opposite side in a triangle. This function is positive in the first and second quadrants, and corresponds to the y-coordinate on a unit circle. This reciprocal of cosecant is defined in a right triangle as "opposite over hypotenuse." For 10 points, name this trigonometric function often paired with cosine.

sine [accept sine of x, sine of theta, etc.]

The Hafele-Keating experiment and its follow-ups supported this theory while spending less than $8,000, and the Mossbauer rotor experiment shows an effect this theory implies at a higher precision than the Ives-Stillwell experiment. It can be accounted for mathematically using the Lorentz Transformation, and can lead to a paradox involving aging and space travel, the Twin Paradox. This theory reconciled Newton's Laws and Maxwell's equations by stating that there is no absolute frame of reference and that the speed of light is constant. For 10 points, name this theory developed by Einstein which shows the relationship between space and time and which preceded general relativity.

special relativity [Prompt on "relativity." Do not accept "general relativity."]

The width of these phenomena can be minimized with a tunable dye laser. Their displacement equals magnetic quantum number times Bohr magneton times magnetic field in the Zeeman effect. Two of these denoted D2 are also called the sodium doublet. Their wavelengths are proportional to the difference of inverse squares of principal quantum numbers by the Rydberg formula, and they include hydrogen's visible Balmer series and the sun's Fraunhofer lines. Caused by absorption and emission of photons, for 10 points, name these bright or dark bands on a continuous spectrum.

spectral lines [accept emission lines or absorption lines before mention]

This quantity is cubed in the denominator of the formula for the Abraham-Lorentz force, and the time-averaged Poynting vector divided by this quantity gives radiation pressure. Beta is equal to velocity divided by this quantity. (*) Cherenkov radiation occurs when this quantity is exceeded in a medium, and vacuum permittivity times permeability gives this quantity squared. This quantity is constant in all reference frames, and a 2013 experiment apparently showed this value being exceeded, though special relativity basically says that that’s impossible. For 10 points, name this “universal speed limit,†a value symbolized by lowercase c.

speed of light (accept obvious equivalents but prompt on “lowercase câ€; Ed’s note: if anyone’s wondering why Cherenkov radiation says this quantity is exceeded, and then we say it’s impossible, it’s because it’s exceeded in a medium)

This quantity equals one over the square root of mu naught times epsilon naught. In one formulation of Planck’s Law, spectral radiance is proportional to the cube of frequency divided by the square of this property. In particle physics, mass is measured as (*) electron volts divided by the square of this quantity and Cherenkov radiation is emitted when a particle’s velocity exceeds this constant for a medium. In September 2011, the OPERA project erroneously claimed that they had measured tau neutrinos moving faster than this constant. For 10 points, name this constant often symbolized as “c,†the maximum speed at which all matter in the universe can travel.

speed of light [accept c before read] <AP>

The Fizeau experiment measured this quantity in moving water. Though it's not the age of the universe, this quantity's finitude can resolve Olbers's paradox. It's equal to the reciprocal of the square root of the product of permittivity and permeability of free space. Cerenkov radiation occurs when particles exceed the local value of this in a transparent medium, emitting a largely ultraviolet bluish glow. The interferometer used by Michelson and Morley failed to find any "ether" that would cause this quantity to vary. For 10 points, name this constant symbolized in E equals m c squared by c, which is the fastest possible speed.

speed of light [accept c]

The Einstein tensor contains this quantity to the fourth power in its denominator. Maxwell discovered that this quantity is equal to one over the square root of the product of the vacuum permittivity and permeability. Cherenkov radiation occurs when this quantity is (*) exceeded in its local frame. Length contraction occurs as objects approach this constant. The equivalence of mass to energy depends on this constant squared, according to Einstein’s famous equation. For 10 points, name this constant, the rate at which a photon travels in a vacuum, denoted by the letter “c.â€

speed of light [prompt on “câ€] <SY Physics>

The interaction represented by "[this quantity] dot L" gives rise to the "2 J plus 1" degeneracy. Potts and Ising modeled ferromagnetism using a lattice of variables representing this quantity. It produces a magnetic dipole moment that gives rise to the Zeeman effect. An experiment in which silver atoms were fired through a magnetic field, performed by Stern and Gerlach, showed that this quantity is quantized. Its value is the fourth quantum number, which equals plus or minus one-half for an electron. For 10 points, name this quantity, the intrinsic angular momentum of a subatomic particle.

spin angular momentum [prompt on "angular momentum" before it is mentioned; prompt on "S"]

A collection of objects with this property on a lattice makes up the Ising model, which models ferromagnetism. Applying a correction based on Thomas precession gives the correct gyromagnetic ratio that relates this quantity to the magnetic dipole moment. The operators representing this property are multiples of the Pauli matrices. The coupling of this intrinsic property to another, similar property gives rise to fine structure in atoms. It is conventionally measured in units of h-bar, and in that system, fermions have half-integer values of it. For 10 points, name this intrinsic property of subatomic particles which is distinguished from orbital angular momentum.

spin angular momentum [prompt on “angular momentumâ€; do not prompt on or accept “momentumâ€; do not accept “orbital angular momentumâ€] <BH>

In IR spec, the spacing between the rightmost P-branch line and leftmost R-branch line is proportional to the square root of this value over the reduced mass. This quantity can be generalized to a fourth-order tensor called the elasticity tensor, and in the isotropic case, it is the cross-sectional area of a material times (*) Young’s modulus over the equilibrium length. The frequency of an oscillator is the square root of this quantity over mass. It is proportional to the stiffness for its namesake device, and force is equal to negative this constant times displacement. For 10 points, name this constant symbolized k that appears in Hooke’s law.

spring constant (accept k until read, accept force constant, prompt on “Young’s modulus†until read)

In the fine structure constant, the charge of an electron is raised to this power. By the divergence theorem, any law in one over this many degrees can be written in Gaussian form. Kepler's Third Law establishes a proportional relationship between the cube of the semimajor axis of an orbit and this power of its period. The force between two electric charges and the intensity of light emanating from a source both vary inversely with this power of the distance. In the formula for the area of a circle this power is assigned to the radius. For 10 points, give this name for when a term is raised to a power of two.

square [accept 2 or second power before "two"]

For a parabolic dispersion relation in three-dimensions, the resulting density of states is proportional to this nonlinear function of the energy. For sodium chloride, the molar solubility is equal to this function of the solubility product constant. Graham’s law gives the rate of (*) effusion as proportional to the reciprocal of this function of the molar mass. The length of a vector is this function of the sum of the squares of each coordinate point, and Pythagoras discovered that this function applied to two is irrational. This function is equivalent to the one-half power. For 10 points, name this function that is the inverse of the square.

square root function (accept one-half power before read)

This value can be displayed graphically using a quadric named for Cauchy, and the ‘diagonal’ values of this quantity’s matrix form simplify to the pressure gradient in incompressible liquids. When a force is applied to an object, the normal form of this quantity occurs perpendicular to the object’s cross-section, in contrast to this quantity’s (*) shear form. This quantity is usually plotted on the y-axis of a curve that is straight for elastic materials due to Hooke’s Law. The tensile form of this quantity appears as the numerator in Young’s modulus. Pressure is a specific type of, for 10 points, what measure of the force per area, usually contrasted with strain?

stress (accept stress vector; accept specific kinds of stress like shear stress or tensile stress)

A tensor which contains terms for this quantity, energy, and momentum is related to the Ricci tensor and the metric tensor by the Einstein field equations. For a fluid, the only term describing its response to this quantity is the bulk modulus, which describes the compressional form of this quantity. The shear form of this quantity is related by an expression involving Poisson’s ratio and Young’s modulus to the shear deformation. Plastic deformation begins when this quantity exceeds an object’s yield point. For 10 points, name this quantity, a measure of the force per unit area that deforms a body, which is related in simple materials to strain by Hooke’s law.

stress [accept compressional stress; accept shear stress; prompt on “strengthâ€; prompt on “pressureâ€] <BH/AS>

Delta baryons turn into nucleons and pions due to this phenomenon. The residual form of this phenomenon is described by the Yukawa interaction, and a theory of this phenomenon involves a non-Abelian gauge theory based on the SU(3) symmetry group. The eight independent (*) carriers of this force are explained by Quantum Chromodynamics. This force involves a color charge and is responsible for the interactions between quarks through the exchange of gluons. This force is merged with electromagnetic interactions and the weak force in a Grand Unified Theory. For 10 points, name this fundamental force that holds neutrons and protons together in a nucleus.

strong nuclear force <AP>

Hideki Yukawa estimated the range of this phenomenon to be about one fermi by modeling it as an exchange of neutral pions. It imparts over 99% of the mass of a certain 938-MeV particle. It is described by the gauge group SU(3). Since the theory describing it has running coupling constants, it cannot be solved perturbatively at low energy, giving rise to asymptotic freedom. At high energies, it exhibits confinement. Its bosons carry color charge and might couple to one another, forming glueballs. For 10 points, name this fundamental force described by quantum chromodynamics, which is mediated by gluons and holds protons and neutrons together in the nucleus.

strong nuclear force [or strong interaction; or quantum chromodynamics or QCD until “force†is read] <BH>

Transition to this phenomenon is marked by a discontinuous jump in electric heat capacity. One theory about this phenomenon introduced the concepts of coherence length and penetration depth, explaining small perturbations in density and the decay of external magnetic fields. That theory is named for Ginzburg and Landau. Explained bythe condensation of electrons into phonon-exchanging Cooper Pairs, materials exhibiting this phenomenon expel magnetic fields in an effect named for Meissner. For 10 points, name this phenomenon which occurs at very low temperatures and is defined as the absence of electrical resistance.

superconductivity

These entities' free energy is minimized when "del squared of B equals B over lambda squared," according to the London equation. They are characterized by the coherence length and penetration depth in Ginzburg-Landau theory, and they are classified as Type I or Type II. These substances' properties arise from phonon exchanges between Cooper pairs of electrons, and they become perfectly diamagnetic by expelling magnetic fields from their interior. Governed by BCS theory and exhibiting the Meissner effect, they typically exist at low temperatures. For 10 points, name these materials with zero electrical resistance.

superconductors

In RTGs, the generation of a gradient of this quantity by radioactive decay is converted to a voltage via the Seebeck effect. This quantity can become negative in quantized spin systems. One scale for it is defined by the triple point of water. An ideal gas particle’s kinetic energy is three-halves Boltzmann’s constant times this quantity. Heat capacity is the ratio of heat added to the change in it. The third law of thermodynamics predicts a lower limit on this quantity, which is known as absolute zero. For 10 points, name this quantity, which is identical for any two bodies in thermal equilibrium, and which may be measured in degrees Kelvin.

temperature [or absolute temperature; do not accept “heat†or “energyâ€] <SL>

These materials are characterized by an equation that includes a hopping integral, the t-J model, itself derived from the Hubbard model. By comparing the coherence length to the London penetration depth, one can determine if these materials are Type I or Type II. A critical temperature above the boiling point of nitrogen characterizes the high-temperature type of these materials, which include cuprate perovskites like YBCO. These materials expel interior magnetic fields through the Meissner Effect, a phenomenon explained by Cooper pairs in the BCS theory. For 10 points, name these materials which exhibit zero electrical resistance.

superconductors [or word forms]

The landscape described by this formalism consists of roughly “ten to the five-hundred†metastable vacua. The spacetime geometry described by it incorporates worldsheets bound to D-branes, as well as compactified spaces. Criticism of it often focuses on the large number of free parameters in the theory, making it practically untestable; however, this formalism also provides a basis for the anthropic principle. In the mid-90s, Ed Witten revolutionized this field when he united all types of them into M-theory, which describes an 11-dimensional universe. For 10 points, name this theory of everything in which all matter is composed of namesake tiny loops of energy.

superstring theory <BH>

A form of this quantity described by the word “brightness†is used to approximate a grey body by a black body. A particular wavelength is related to this quantity by Wien’s displacement law. This variable is inversely proportional to thermodynamic beta. It is formally defined as the derivative of internal energy with respect to entropy. An equivalence relation involving it is established by the zeroth law of thermodynamics. The efficiency of the Carnot cycle is a function of this property of the reservoirs. Specific heat is the energy required to cause a given amount of change in this quantity. For 10 points, name this property of a material that can be measured in kelvins.

temperature <AS>

The number of photons in a photon gas is proportional to the third power of this quantity, and it’s the partial derivative of internal energy with respect to entropy at constant volume. Lasers triggering a population inversion can curiously produce a negative value for this quantity, and the efficiency of a (*) Carnot engine is one minus the ratio of this quantity in the cold and hot reservoirs. According to the Third Law of Thermodynamics, entropy is zero when this quantity is zero, which occurs at about negative 273 on a certain scale. For 10 points, name this quantity measured on scales like Kelvin or Celsius.

temperature (prompt on uppercase T) <Jin>

This quantity’s square is in the denominator of the “B nu†formulation of the Rayleigh-Jeans law. In a medium, this quantity is scaled by the square root of the product of the relative permeability and permittivity. In Planck units, this electromagnetic quantity is normalized to one. This physical constant is used to define the meter. This quantity is the only one of its type to be constant in all inertial reference frames. The Michelson-Morley experiment demonstrated its constancy by showing that luminiferous ether did not exist. If tachyons exist, they travel faster than this speed. For 10 points, what is the maximum speed at which anything can travel, often denoted “c�

the speed of light (in vacuum) [accept c until it is read] <AS>

Events in this paradigm are mathematically described by a manifold whose symmetry is the Poincaré group, called the Minkowski space; that space's "light cone" and "world line" constructs can be used to understand questions of causality. This theory uses a factor symbolized gamma in Lorentz transforms; its consequences include time dilation and length contraction. Postulating that there is no privileged inertial reference frame, and that there is a constant speed of light, for 10 points, identify this theory of Albert Einstein's which is not as applicable as its later, "general" counterpart.

theory of special relativity [prompt on "relativity"; do not prompt on or accept "general relativity"]

The root-mean-square speed for particles in an ideal gas is equal to the square root of this number times R T over M. The electric field strength due to an electric dipole decays at this power of distance, and this constant is in the denominator of the moment of inertia of (*) a rod rotated about one end. The semi-major axis is raised to this power in one of Kepler’s laws, and jerk is this derivative of position with respective to time. A “law†states that as the surface area grows by the second power, the volume instead grows by this power. For 10 points, give this number, the number of spatial dimensions.

three (accept third or cube)

This is the number of possible arrangements of a pair of identical bosons in a two-level system. A DC circuit that exhibits damped harmonic oscillation must contain at least this many passive elements. This is the smallest nonexistent multipole moment. Any gravitating system with at least this many bodies is not analytically integrable. The electron’s charge is this number times the down quark charge. The thermodynamic law of this number isn’t really a law, and describes the entropy of ideal crystals in a certain limit. There are this many generations of quarks. For 10 points, give this number that is also the number of observable spatial dimensions in the universe.

three [accept tripole] <AS>

The integral with respect to this quantity of a Lagrangian yields an action. The principle of detailed balance requires that dynamics be symmetric under the reversal of this variable, which is conjugate to energy. If a quantity's value is independent of this variable, the quantity is conserved. The SI unit of this variable is defined by a device that employs cesium. This quantity experiences "dilation" at relativistic speeds. The derivative of momentum with respect to this quantity is force. Entropy may explain why the so-called "arrow" of this phenomenon is unidirectional. For 10 points, name this dimension that is used to describe which things happen before or after other things.

time

This quantity is the only physically-meaningful axis of a Feynman diagram. Detailed balance describes conditions under which systems are reversible in this variable. All physical laws are believed to be invariant under charge conjugation, parity inversion, and reversal of this variable. Loosely speaking, virtual particles are permitted by the form of the Heisenberg uncertainty principle that relates energy to this quantity. Hyperfine transitions in cesium are used to define the SI unit for this quantity, which undergoes dilation at relativistic speeds. The change in position per unit change in this is velocity. For 10 points, name this dimension which is not space.

time <AS>

For a deformable beam, this quantity has a value at each point equal to the negative flexural rigidity of the beam times its curvature. For a dipole in an electric field, this quantity is equal to the cross product of the field strength and the dipole vector, and it’s zero for gravitational interactions because the force always points in the direction of the (*) radial vector. This value is the rate of change of a system’s angular momentum. This value is equal to “uppercase I times alpha,†or the moment of inertia times the angular acceleration. For 10 points, name this rotational analogue to force.

torque (accept moment of force, prompt on “tauâ€) <Pendyala>

This quantity is equal to the cross product of dipole moment and electric field, and an epicyclic mechanism including "sun" and "planet" gears "multiply" it. Varignon proved that this is additive when applied at the same point. Power is the scalar product of this quantity and omega, or angular velocity. Work is the integral of this quantity with respect to theta, and a lever in rotational equilibrium has a net value of zero for this quantity. This quantity can be measured by newton-meters or joules per radian, and is denoted by the letter tau. For 10 points, name this time derivative of angular momentum and rotational analogue of force, which is the cross product of lever arm and force.

torque [also accept moment]

One form of this quantity is represented as the cross product of lambda times magnetization and the derivative of magnetization in the Landau-Lifshitz-Gilbert equation. For an electric dipole, this quantity with a "spin-transfer" variety is equal to the cross product of the dipole moment and the electric field, while for a rigid body, this quantity can be maximized by increasing the distance from the pivot point or increasing the tangential component of force. With units of newton-meters, it is the time derivative of angular momentum. For 10 points, name this quantity, the rotational analogue of force.

torque [or moment]

Darlington pairs consist of two of these devices, which are described by the Ebers-Moll model. The first one ever created was of the point-contact variety, made by Brattain, Shockley, and Bardeen. These devices either have base, emitter, and collector pins, or gate, source and drain pins. The field-effect type have mostly replaced the bipolar junction type of these devices, which are made of sandwiched p and n type semiconductors. The density of these devices on computer chips doubles every 18-24 months, according to Moore's law. For 10 points, name these devices used as amplifiers and switches.

transistors [accept bipolar junction transistors until "point-contact" is read]

This number is the dimension of the phase space of a free particle confined to a plane. For the Earth-Sun system, the Lagrange point of this number is the furthest from the Sun. One statement given this number describes the areal velocity of a certain system as constant. The spin projection quantum number has this many possible values. Systems with more than this number of gravitating bodies are non-integrable. The moment of inertia is proportional to mass times this power of linear dimension. This number of parallel lines represents a capacitor in a circuit diagram. For 10 points, which numbered law of Newton states that "F equals m a"?

two [or L2; or Kepler's second law; or two-body problem; or squared; or second power; or Newton's second law]

Physical laws obeying a power law with a scaling exponent equal to negative one times this constant arise from the divergence theorem and can also be written in a Gauss’ law form. Terminal and escape velocity both have a dimensionless prefactor equal to the square root of this number. The final velocity of an object dropped from a height h is equal to the square root of g h times this number, the reciprocal of which is multiplied by m v squared to give kinetic energy. For 10 points, acceleration is what derivative of position with respect to time?

two or second <SH>

Strange measurements of this quantity in an Australian mineshaft led to speculation about a fifth fundamental force in the 1980s. This quantity has a power of negative one-half in the Planck mass, and it is multiplied by eight pi in the numerator of a fraction in the tensor form of (*) the Einstein field equations. This fundamental constant was measured using balls of lead and a torsion balance in an experiment by Henry Cavendish. This constant is about 6.67 times 10 to the negative 11 Newton meters squared over kilograms squared. For 10 points, name this physical constant that appears in an equation giving the force of attraction between two masses.

universal gravitational constant (accept word forms; accept Newton’s constant before “Newton†is read; accept big G or uppercase G; prompt on G; do not accept “little gâ€; do not accept anything with “accelerationâ€)

Materials are prepared for use in this medium by "baking them out" to remove volatiles. The technique of sputtering is used to deposit coatings and films in the presence of this medium. A medium that is similar to this one is said to be "rarefied". This medium has zero electromagnetic susceptibility, and hence a refractive index of precisely 1, not accounting for its polarization by virtual pair production. The beam lines of particle accelerators are filled with this medium, as are cathode ray tubes. This medium is ideally characterized by having zero pressure. For 10 points, name this medium that is characterized by the absence of matter, found in outer space.

vacuum [or free space; accept partial vacuum]

The replacement theorem shows that every basis of a space named for this word has the same size. Some of these structures are linearly dependent if one of them can be written as a combination of the others. Calculus on [this]-valued functions uses the operators "div" and "curl." A type of graphics named for this word can be (*) scaled indefinitely, unlike raster graphics. In epidemiology, this is the term for pathogen-carrying organism, such as a mosquito. They can be multiplied by scalars, and the parallelogram law governs their addition. For 10 points, name these structures which are often depicted on the Cartesian plane as an arrow with magnitude and direction.

vectors

This description is applied to bosons with a spin of 1, since their spin states transform like one of these things. One class of these objects is classified as either spacelike, timelike, or null. One operation on one of these things is set equal to zero in Gauss's law for magnetism; that operation is called "divergence", or "del dot". A basis for these things is typically denoted "i hat, j hat, k hat" in rectangular coordinates. The cross product of two of these things yields another one of these things, and addition on them is performed "tip to tail". For 10 points, give this name for a mathematical object with a magnitude and a direction, often expressed as tuples of scalars.

vectors [or vector fields; or three-vectors; accept four-vectors; accept unit vectors]

Dividing a wave's angular frequency with its angular wavenumber yields this quantity's "group" form. The square root of 3 times the gas constant times temperature divided by the molar mass of a gas describes the "root mean square" measure of this quantity. Integrating this function of a particle from T1 to T2 yields the displacement. When the force of gravity on an object in free fall equals the drag force, the object has reached the "terminal" form of this value, which is constant because acceleration equals zero. For 10 points, name this vector quantity with units of meters per second and a magnitude equal to speed.

velocity

Combining two of these quantities requires adding the quantities and dividing by one plus the product of the normalized form of these quantities, which is known as Einstein’s addition formula. Relativistic beta is given by a normalized form of this quantity, and inertial (*) reference frames are characterized by a possibly non-zero constant value for it. One-half the mass times this quantity squared gives the kinetic energy, and this quantity is the time derivative of an object’s position. For 10 points, give this vector quantity that gives both the speed and direction of an object.

velocity (prompt on speed; prompt on relativistic beta) <Xiong>

The relativistic version of this quantity is tangent to the world line. For a modulated wave, "omega over k" and "d omega dk" give its phase and group forms, respectively. The magnetic force on a charged particle is proportional to "[this quantity] cross B." "Square root of 2 g R" is the minimum magnitude of this quantity needed to escape Earth's orbit, and its vertical component is zero at the highest point of projectile motion. Its rate of change is acceleration, and it is defined as the derivative of position. For 10 points, name this vector quantity whose magnitude is speed.

velocity [prompt on "v"; do not accept "speed"]

Op-amps convert a small amount of this quantity into a larger amount of it. In an inductor, it equals the inductance times the time derivative of current. In circuit diagrams, sources of one form of this quantity are represented by a short line adjacent and parallel to a longer line. The integral form of Faraday’s law determines the amount of this quantity generated by changing magnetic flux. When the E-field is irrotational, or conservative, its negative gradient is the electric field. For 10 points, name this quantity which measures electric potential energy per unit charge, and which is related to current and resistance by Ohm’s law.

voltage [or scalar potential; or electric potential or electrostatic potential before “electric potential energy†is read; accept emf or electromotive force; prompt on “potential†or “potential difference†before “electric potential energy†is read] <AS>

This quantity in the Josephson effect is proportional to the time derivative of the phase difference. This quantity is defined as the line integral of "E dot ds," and the electric field is perpendicular to this quantity's contour lines. The sum of this quantity around a closed loop equals zero, according to Kirchhoff's loop rule. This quantity is equal for any two components connected in parallel. Capacitance equals charge divided by this quantity, which equals current times resistance, according to Ohm's law. For 10 points, name this quantity that equals 1.5 for a double-A battery.

voltage or electrical potential difference [do not accept "electrical potential"]

A fluid flow is non-divergent if and only if the time derivative of this property for a small fluid element is zero. The dynamic pressure is equal to half this property times the square of the velocity of an incompressible fluid. This property for an ideal gas is found by dividing (*) pressure by the product of the ideal gas constant and temperature. The buoyant force acting on an object of given volume is directly proportional to this property of the fluid. The specific gravity of an object is this property for that object divided by this property for water. For 10 points, name this fluid property that determines whether an object floats or sinks.

volumetric mass density (accept rho)

This quantity times the derivative of pressure with respect to this quantity is equal to a substance's bulk modulus. The degeneracy pressure of matter is a function only of this intensive property of the matter. Surfaces along which this property is constant are called "isopycnic". The specific volume is the reciprocal of this quantity. This property is constant through the entirety of a homogeneous substance. Little g times the volume of a submerged object times this property of the displaced fluid equals the buoyant force, according to Archimedes's principle. For 10 points, name this quantity that equals mass per unit volume.

volumetric mass density [accept number density]

This quantity, raised to the fifth power, appears in the denominator of Planck’s law. The sine of the angle of minimal resolvable detail for a circular aperture equals 1.22 times this quantity over d. This quantity equals 2d sine theta divided by n according to (*) Bragg’s law. This quantity is equal to Planck’s constant divided by the product of mass and velocity by de Broglie’s equation. In general, it is equal to velocity divided by frequency. For 10 points, name this quantity that is the distance between peaks of a wave.

wavelength

In field theory, the 'range' of a force is approximately equal to the reduced form of this quantity for its corresponding gauge boson. The energy levels of the particle-in-a-box are derived by assuming that a half-integer multiple of this property of the particle is equal to box length. The fundamental of an open pipe is given when this value is twice the (*) length of the pipe, and two pi divided by this value gives lowercase k, or the wavenumber. The phase speed is given by this property times the frequency, and visible light occurs when this property has values from about 400 to 750 nanometers. For 10 points, give this distance between consecutive troughs or peaks for a wave.

wavelength (accept lambda before read and Compton wavelength at any point in the question; do not accept or prompt on just “length†at any point, even at end of question) Bonuses

One experiment that seeks to detect one form of these uses two observatories spaced 3000 kilometers apart to detect motion in an interferometer. That experiment is LIGO. An experiment that scattered electrons off a nickel crystal showed that electrons exhibit some properties of these phenomena. That experiment was the Davisson-Germer experiment, which confirmed an idea first put forth by de Broglie that matter has properties of particles and these. Young’s double-slit experiment produced an interference pattern, demonstrating that light is one of these. For 10 points, name these periodic disturbances that can be transverse, like light, or longitudinal, like sound.

waves [accept gravitational waves; accept matter waves; accept de Broglie waves] <AD>

The defining equation named for these things is conventionally written "u sub tt equals c times u sub xx". These things can be bounded by envelopes and may have distinct group and phase velocities. The behavior of these things at a barrier is characterized by transmission and reflection coefficients. When these things are spatially localized, they are called "packets". Those that propagate transversely may possess polarization. De Broglie showed that particles have properties of these things. For 10 points, name these things that are generically oscillatory motions, typically characterized by an amplitude and a frequency.

waves [or waveforms; prompt on "oscillations" or word forms]

Some fermions have different eigenstates for this force than for mass, causing their oscillations. This force may be mediated by charge-current and neutral-current interactions. This interaction may change the flavor of quarks in a process described by a 3-by-3 matrix named for Kobayashi and Maskawa. An experiment by Chien-Shiung Wu showed that this interaction violates parity symmetry. This force was (*) unified with the electromagnetic force by Glashow, Weinberg, and Salam and it is carried by W and Z bosons. For 10 points, name this force, which is stronger than gravity but less powerful than the strong force.

weak force <SR Physics> Bonuses

It's not change in volume, but this quantity is zero for an isochoric process because there is no area under its P-V curve, while in an isobaric process, this measurement is equal to P times delta V. For an object in circular motion, this quantity is also zero, because the line integral of the tangential component of the centripetal force along its path is zero. Because this quantity is equal to change in kinetic energy, it has units of joules, and it is path-independent for conservative forces. Equal to the dot product of force and displacement, for 10 points, name this scalar quantity calculated by multiplying force and distance, symbolized W.

work

The Hamiltonâ€"Jacobi equation states that the Hamiltonian operator plus the time derivative of action is equal to this value. The Laplace equation sets divergence of the gradient of a function equal to this number. The Dirac delta function is infinite at this value. Kirchhoff’s (*) loop law states that this value is the voltage of a circuit loop. The electric field of a conductor equals this value. This number is equal to the acceleration of an object with constant velocity. For 10 points, name this number of dimensions of a point, the lowest non-negative number.

zero <SY Physics>

In Euler's buckling formula, the critical buckling load is equal to this number squared times Young's modulus times area moment of inertia over length squared. Coulomb's constant equals the reciprocal of 4 times this value times the permittivity of free space. The reduced Planck constant, defined as Planck's constant divided by two times this quantity, is useful when dealing with radians, because two times this quantity of radians measures the angle of a full circle. It is equal to a circle's circumference divided by its diameter. For 10 points, name this mathematical constant which is represented to three significant figures as 3.14.

Ï€ (pi)

This scientist’s fluctuationâ€"dissipation relation considers the ratio between absolute temperature and drag coefficient and was co-discovered by William Sutherland. This man modeled the heat capacity of a solid by considering a lattice of quantum harmonic oscillators, and the four-by-four Ricci [“REE-cheeâ€] tensor and a factor of 8 pi (*) big-G over speed of light to the fourth power feature in a tensor equation by him. This scientist developed a theory with ten field equations as well as a theory implying mass-energy equivalence. For 10 points, name this physicist behind the theories of general and special relativity as well as the equation E equals m c squared.

Albert Einstein <Yue>

This man names a system of non-SI units in which the constant in Coulomb’s law is exactly 1, and electric and magnetic fields have the same dimension. That system includes a unit equal to 10,000 teslas that is named for this man, which measures the strength of magnetic fields. A law sometimes named for him states that the divergence of the (*) magnetic field is zero, forbidding the existence of magnetic monopoles. That law is one of two named for him that are paired with Ampère’s and Faraday’s laws to form Maxwell’s equations. For 10 points, identify this German mathematician who names an improvement to Coulomb’s law for calculating electric fields.

Carl Friedrich Gauss [rhymes with “houseâ€] <SE>

This scientist used a radon-beryllium neutron source to induce radioactivity in one experiment, and pressure is exerted at absolute zero by his namesake gas. This scientist names the space between occupied and unoccupied electron states, which is his namesake “surface.†With (*) Dirac, this scientist names a distribution of energy states. This scientist’s paradox concerns the high probability but low evidence for aliens. A particle with half-integer spin that obeys the Pauli exclusion principle is named for this scientist who created a self-sustaining fission in Chicago Pile-1, which went critical in December 1942. For 10 points, name this Italian-born physicist who created the first nuclear reactor.

Enrico Fermi <BC>

This scientist discovered alpha and beta radiation and coined the term gamma radiation. When this scientist irradiated nitrogen gas and observed the resulting emissions, he discovered that all atomic nuclei contain the hydrogen nucleus. This scientist names the diffraction of (*) alpha particles by an electric potential. That type of scattering, named after this scientist, was discovered in the same experiment which first showed that the nucleus was positively charged. This scientist’s most famous experiment involved the detection of alpha particles which scattered off heavy atomic nuclei. For 10 points, name this man who supervised the gold foil experiment.

Ernest Rutherford <K. Li, Chemistry>

Dielectric objects in optical tweezers can be modeled by this law, which was extended by models developed by Ronald Rivlin. A generalized version of this law involves lambda and mu [“mewâ€] terms in a compliance tensor for isotropic materials. The Lamé [“lah-MAYâ€] parameters feature in a formulation of this law, and sums of (*) normal modes are solutions to coupled systems obeying this law. This law predicts that potential energy is quadratic in position and involves a constant with units of Newtons per meter. This law describes a linear restoring force that models simple harmonic motion. For 10 points, name this law describing the behavior of springs.

Hooke’s law <Yue>

An interference pattern created by the reflection of light between two surfaces is called this physicist’s “rings.†His 1704 book Opticks demonstrates how color arises from the reflection of components of white light. He names a law relating the rate of (*) heat loss to the surrounding temperature, called his law of cooling. Another law named for this man is an inverse-square law describing a force between two masses; that is his law of universal gravitation. His second law states that F=ma, for 10 points, name this English scientist who names three laws of motion.

Isaac Newton

He’s not Faraday, but this scientist names an electromagnetic field’s stress tensor. Formulas named for this man result from swapping partial derivatives in a thermodynamic quantity’s second derivative. This man considered the changing electric field in a capacitor when he invented the concept of displacement current. This namesake of several thermodynamic (*) “relations†proposed a thought experiment regarding a violation of the second law of thermodynamics. This man corrected Ampère’s law and included it in his four equations of electromagnetism. For 10 points, name this physicist who theorized a namesake “demon.â€

James Clerk Maxwell <Yue, Physics>

This man’s namesake conjecture posits that hexagonal close packing is the most efficient sphere packing arrangement, and a telescope named for this man finds exoplanets in the habitable region of their stars. The conservation of (*) angular momentum can be used to derive one of his laws, and that law states that a line connecting a planet to the Sun sweeps out “equal areas in equal timesâ€. Using Tycho Brahe’s data, he derived a law stating that the orbit of every planet is an ellipse with the Sun at a focus. For 10 points, name this German astronomer who names three laws of planetary motion.

Johannes Kepler

A coordinate specification named for this scientist has the origin centered on a fluid parcel as it moves through space and time. This man was the first to write the variational form of an equation he often co-names describing the fundamental classical laws of motion known as D'Alembert's principle. A set of (*) points named for this scientist expand on the three discovered by Euler and give special solutions to the three-body problem. This scientist also reformulated classical mechanics using his namesake multipliers. For 10 points, identify this Italian-French scientist who names a quantity given by the kinetic energy minus the potential energy as well as the points L1 through L5.

Joseph-Louis Lagrange <McMaken>

Hamilton’s equations are equivalent to this law but contain only first-order derivatives. The Eulerâ€"Lagrange equations are second-order, like this law, and can be used to derive it from the principle of least action. For a rocket, this law contains a term equal to the relative exhaust velocity times the time derivative of the (*) mass. Integrating this law over time gives the impulse delivered by a force, since the right-hand side contains the time derivative of momentum. The English inventor of calculus discoveredâ€"for 10 pointsâ€"what law, which states that the force on a body equals its mass times its acceleration?

Newton’s second law of motion [accept Eulerâ€"Lagrange equations before “Eulerâ€"Lagrange equationsâ€; prompt on Newton’s law(s) or Newton’s law(s) of motion] <SE>

One rule formulated by this scientist relates causes and effects to dissymmetry. This scientist is the first namesake of a law stating that a constant named for this scientist over the difference between a material-dependent temperature and the absolute temperature equals a material’s magnetic susceptibility. This person, who names that law with Pierre (*) Weiss, demonstrated piezoelectricity. At this scientist’s namesake point, materials lose their ferromagnetism. While investigating pitchblende radioactivity, this scientist and his partner isolated polonium and radium. For 10 points, name this French scientist who shared a Nobel prize for his work on radioactivity with his wife, Marie.

Pierre Curie [prompt on Curie; do not accept or prompt on “Marie Curieâ€] <BC>

In statistical mechanics, this constant to the 3-Nth power is frequently featured in the denominator of quantities as a normalization. This quantity is the numerator of the Compton wavelength. This quantity scales all eigenvalues of spin operators since it has units of angular momentum. This quantity divided by 2 pi gives a related quantity often denoted with a (*) bar. Dividing this quantity by momentum yields wavelength in the de Broglie [“de BROYâ€] relation. This constant is multiplied by frequency to give the energy of a photon. For 10 points, give this constant named for the German physicist who discovered quanta.

Planck’s constant (prompt on h or h-bar before mention; accept reduced Planck’s constant) <Yue, Physics>

Dividing this quantity by the momentum of a massive particle yields the de Broglie wavelength. The change in position of a particle times its change in momentum is greater than or equal to one over four pi times this quantity. (*) Heisenberg’s Uncertainty Principle includes a quantity equal to this quantity divided by two pi, its “reduced†form. This quantity’s namesake was responsible for proving that the negative fifth power of wavelength is proportional to blackbody radiation. For 10 points, name this quantity symbolized h, which is named for the German father of quantum theory.

Planck’s constant [prompt on h until mention; do not accept or prompt on “h bar†or “reduced Planck’s constantâ€; do not accept or prompt on “Planck†alone as this is a unit] <AJ>

In a unique proof of Kepler’s first law, this man constructed an ellipse inside a circle in velocity space. This man invented a framework of quantum mechanics that involves propagators and sums over trajectories. This scientist’s namesake “trick†involves moving a derivative inside an integral. This physicist challenged scientists to build nanoscale motors in his talk (*) “There’s Plenty of Room at the Bottom.†This inventor of the path integral formalism gave a famous set of lectures at Caltech, and used wavy lines to indicate photons in his namesake “diagrams.†For 10 points, name this American physicist who is “surely joking†in the title of his autobiography.

Richard Feynman <Yue, Physics>

A consequence of this law is that the phase velocity of a photon can be less than the speed of light. In many anisotropic materials, the extraordinary photons do not follow this law. When the light being observed is monochromatic, this law can be expressed with ratios of wavelengths. Fermat derived this law using his (*) principle of least time, and a typical method for finding Brewster’s angle applies this law. By substituting a value of 90, this law can be used to find the critical angle for total internal reflection. For 10 points, name this law which equates the ratio of sines of the angles of incidence and refraction to the ratio of the indices of refraction.

Snell’s law (accept Snellius’ law) <K. Li>

One observation predicted by this theory results from the spontaneous symmetry breaking of an SU(2) doublet in a “Mexican hat†potential. Improvements to this theory try to address its CP violation and the fine-tuning of its 19 free parameters. In this theory, local symmetries give rise to gauge bosons that mediate interactions. A single treatment of all the interactions in this theory is the goal of (*) Grand Unified Theories, while “theories of everything†combine it with gravity. The last particle in this theory, the Higgs boson, was discovered in 2012. The electromagnetic, weak, and strong forces are all described byâ€"for 10 pointsâ€"what basic framework of modern particle physics?

Standard Model <SE>

The curl theorem in vector calculus is named after George Stokes and this scientist. This man made one of the first predictions of the age of the Earth by calculating the time it would take the surface of a molten ball to cool down to room temperature. With Joule, this scientist describes the relationship between (*) temperature and pressure during adiabatic [“AD-ea-BAD-ikâ€] expansion of a gas, an effect used in refrigerators. A unit named after this scientist is defined using a fractional value of the triple point of water, and indicates total lack of vibrational energy at zero. For 10 points, name this scientist who names an absolute temperature scale.

William Thomson, 1st Baron Kelvin (accept either underlined part) <K. Li>

The magnetic moment of a loop of wire is equal to the current times a type of this quantity. Since this property of a black hole does not decrease with time, it is analogous to entropy in black hole thermodynamics. A measure of the rate of scattering events that has units of this quantity is often reported in barns. According to Amontons’ second law, frictional force is (*) independent of this property of the contact interface. Orbits sweep out equal amounts of this quantity in equal time according to Kepler’s second law. Pressure, which is often given in units of PSI, is defined as force per unit of this quantity. For 10 points, name this quantity that is measured in square meters.

area [accept cross-sectional area or surface area or contact area; prompt on cross-section; accept specific units of area such as square meters, square centimeters, or square feet; do not accept or prompt on units of length such as “meters,†“centimeters,†or “feetâ€] <SE> Tiebreaker

The geometry of these entities can be approximated by Flamm’s paraboloid. One quantity related to these entities is equal to two times mass times “big G†divided by another constant squared. Under certain circumstances, these entities exhibit the Lense-Thirring effect, according to the Kerr metric. The (*) Penrose process transfers momentum from these entities to objects passing through their ergosphere. These entities can be characterized by three externally observable properties, and they are surrounded by an event horizon inside which the escape velocity is greater than the speed of light. For 10 points, name these massive objects from which light cannot escape.

black holes <BC>

If luminiferous ether existed, one of these devices would orient itself perpendicular to its direction of motion. The reactance of these devices is inversely proportional to the AC frequency. The current leaving these devices is proportional to the time derivative of voltage. In a tank circuit, energy oscillates between the electric field of these devices and the magnetic field of an (*) inductor. When these devices are in parallel, their namesake quantity is summed. That namesake quantity is proportional to both the dielectric constant and the area in the parallel-plate variety of these devices. For 10 points, name these circuit elements which store electric charge.

capacitors (accept parallelâ€"plate capacitors) [Writer’s note: The first clue refers to the Troutonâ€"Noble experiment.] <K. Li, Physics>

In computational physics, this type of principle is explicitly respected by finite volume methods, but not usually by finite element methods. By taking the divergence of both sides of Ampere’s law, one can prove this principle for electric charge. These principles are illustrated locally by continuity equations. Continuous symmetries correspond to statements of this type according to (*) Noether’s theorem. The fact that an ice skater speeds up by pulling in their arms illustrates this principle for angular momentum. Mass, energy, and momentum all haveâ€"for 10 pointsâ€"what property indicating that their amount does not change in time?

conservation laws [accept anything indicating that a quantity is conserved; accept more specific answers like conservation of mass] <SE>

Description acceptable. Inside a dielectric sphere in a uniform electric field, the polarization depends on this function of angular position. In an ideal LC circuit, the sum of the energy stored in the inductor and the capacitor changes with this function of time. Near an infinite uniform plane of charge, the electric field varies with the distance from the plane in (*) this way. While the kinetic and potential energies of an undamped harmonic oscillator vary sinusoidally, the total energy depends on time in this way. The voltage delivered by a DC power source varies with time in this way. For 10 points, how does the total amount of a conserved quantity change in time?

constant [or fixed; accept answers indicating that the quantity does not change] <SE>

The rate of this process appears in the numerator of the Nusselt number, which compares it to a competing process that is described by Fourier’s law. The “natural†type of this phenomenon is due to differences in density, while its “forced†type is due to an external force. The grainy appearance of the Sun’s photosphere is due to the occurrence of this process in the layer below. This process combines (*) advection and diffusion to create vertically-rotating cells in fluids that are heated from below, as hot fluid rises and cold fluid falls. For 10 points, name this mode of heat transfer by bulk motion, which is contrasted with conduction.

convection <SE>

When the Lagrangian is independent of one of these quantities, that one of them is called “cyclic.†In advanced formulations of mechanics, the “generalized†type of these quantities are usually denoted by the letter Q. Transformations in which these quantities change are called “passive,†while those that change a physical system are called “active.†In general, they are the coefficients of a (*) vector’s decomposition in terms of basis vectors. In two dimensions, a radial distance r and an angle “theta†comprise a “polar†set of these numbers. Three numbers x, y, and z comprise the “Cartesian†system ofâ€"for 10 pointsâ€"what numbers used to describe an object’s position?

coordinates [accept coordinate system] <SE>

Solving Laplace’s equation for this geometry often requires Bessel functions. A Gaussian surface of this shape is used to derive the electric field for an infinite line of charge, and the capacitance per length for a system with this geometry has an inverse logarithmic dependence on radii [“RAY-dee-eyeâ€]. It’s not a disk, but this shape with a (*) one-half m r-squared moment of inertia always achieves a higher velocity down an incline than a thin hoop. The coordinate system named for this geometry has r, theta, and z axes, and a solenoid has this shape. For 10 points, name this geometry, named for a shape with volume formula pi r-squared h.

cylindrical (accept word forms; accept cylindrical shell) <Yue>

A photomultiplier tube that registers a signal without actually detecting a photon records this kind of “count.†This adjective describes a substance whose constant energy density leads to an exponentially growing cosmic scale factor. The cosmological constant describes one substance known by this adjective, while (*) MACHOs and WIMPs are proposed examples of another. A form of energy driving the accelerating expansion of the universe is described by this adjective, as is a substance forming 27% of the observable universe. For 10 points, give this adjective describing exotic matter that does not interact with radiation, and hence does not emit detectable light.

dark [accept dark count or dark energy or dark matter] <SE>

A measure of displacement due to this process scales with the square root of six times a namesake quantity times time. In semiconductors, this process’s “current†is contrasted with drift current. A quantity named for this process is given in terms of mobility and temperature by the Einsteinâ€"Smoluchowski relation. That quantity multiplies negative (*) concentration gradient to give flux in Fick’s first law. This process is modeled as a random walk in Brownian motion. When water undergoes this process, it is known as osmosis. For 10 points, name this movement of particles from areas of high concentration to low concentration.

diffusion (prompt on osmosis until mention; prompt on Brownian motion until mention) <Yue, Physics>

The global minimum of the function “x to the x†occurs at the reciprocal of this number. The reciprocals of the factorials of the natural numbers add up to this value. The error function is proportional to the antiderivative of this number to the negative x squared. The integral of “1-over-x, dx†from 1 to this number is equal to 1. This number is the limit, as n approaches infinity, of the quantity “1 plus 1-over-n,†all to the nth power. According to (*) Euler’s formula, “cosine-x plus i sine-x†equals “this number to the i x.†“This number to the x†is the only function that equals its own derivative. For 10 points, name this number roughly equal to 2.718, the base of the natural logarithm.

e <JW> Bonuses

The opposite of this word describes a “deep scattering†technique that was used to prove the existence of quarks. This word describes the linear portion of a stressâ€"strain curve lying below the yield strength. Young’s modulus, which gives the ratio of stress to strain in solid materials, is sometimes called this type of modulus. The kinetic theory of gases assumes that all (*) collisions of particles are of this type, meaning that they conserve kinetic energy as well as momentum. Hooke’s law describes deformation in materials of this type. For 10 points, what word describes materials like rubber bands that return to their original shape after a force is removed?

elastic [or elasticity; accept elastic modulus or perfectly elastic] <SE>

A type of this quantity denoted by the letter X relates the baryon number and lepton number to the weak hyper-[this quantity], denoted Y-sub-w. Integrating the current with respect to time yields this quantity (*) contained within a surface. The derivative of it with respect to a surface element is its “densityâ€. The triboelectric effect gives it to materials when they are rubbed together, and Leyden jars store this quantity. It equals energy transferred over voltage and also equals current times time. For 10 points, name this quantity, symbolized Q and measured in coulombs.

electric charge [accept X-charge before “hyperâ€]

An accelerating particle with a nonzero value for this quantity feels the radiation reaction force, which is proportional to the jerk times the square of this quantity. In a dielectric material, the negative divergence of polarization equals the “bound†density of this quantity. The amount of this quantity enclosed by a “pillbox†equals “electric (*) flux times epsilon-nought,†by Gauss’s law. According to Coulomb’s law, the electrostatic force between two particles is proportional to the product of their values for this quantity. For 10 points, name this quantity measured in coulombs, which is positive for a proton and negative for an electron.

electric charge [prompt on “qâ€] <SE>

A capacitor bank increases this quantity in a process performed in a z-pinch apparatus. A photomultiplier tube amplifies this quantity via secondary emission, and the “dark†form of this quantity can cause interference in photodiodes. The square of this quantity is proportional to the energy stored in inductors. When it is stationary, this quantity produces a (*) magnetic field described by the Biot-Savart Law. This quantity’s density is proportional to charge density and drift velocity. The square of this quantity is equal to power divided by resistance, and diodes only permit the flow of this quantity in one direction. For 10 points, name this quantity whose SI unit is the ampere.

electric current [accept I] <AJ>

The Drude model concerns these particles, and a model by Arnold Sommerfeld gives the zero-temperature pressure of a gas of them. Excitons form from these particles, which were fired at a nickel target in the Davisson-Germer experiment. The Stern-Gerlach experiment demonstrated these particles’ spin angular momentum, and the work function gives their binding energies. Because they are (*) fermions, these particles obey the Pauli exclusion principle. These particles are ejected in the photoelectric effect, and their antiparticle is the positron. For 10 points, name these negatively charged particles.

electrons <Yue>

For the quantum harmonic oscillator, this quantity’s discrete possible values are evenly spaced and start at a value of “one-half h-bar omega.†Leonid Mandelstam and Igor Tamm showed how this quantity and time are paired in a version of Heisenberg’s uncertainty principle. In quantum physics, the (*) Hamiltonian operator computes this quantity for a particular state. When photons shine on a metal, their value for this quantity must exceed the work function for the photoelectric effect to occur. This value for a photon equals Planck’s constant times frequency. For 10 points, name this quantity, whose relativistic “equivalence†with mass sets it equal to “m c-squared.â€

energy [accept total energy; prompt on E] <SE>

Note to moderator: please read all of the phrases in “quotation marks†slowly. “This quantity of X, divided by a positive number a†gives an upper bound on the probability that X is less than a, according to Markov’s inequality. For a CDF “f-of-x,†this value equals the integral of “x f-of-x.†“This function of X-squared, minus the square of this function of X†is equal to this function of the square of quantity: “X minus this function of X,†which gives the (*) variance of X. In the discrete case, this value equals the sum of all outcomes times their probabilities. By the law of large numbers, the sample mean converges to this value. For 10 points, name this value that, for a uniform distribution, equals the sum of the data divided by the number of datapoints.

expected value [or expectation; or EV; accept mean until it’s mentioned] <JR>

Given a prime p and positive integer n, Legendre’s [“luh-jondsâ€] formula yields the largest exponent of p that divides this operation applied to n. The natural log of this function applied to n can be approximated as “n times natural log of n, minus n,†using Stirling’s formula, and it can be analytically extended by the (*) gamma function. Reciprocals of this function can be found in the coefficients of a Taylor polynomial, and this function applied to n yields the number of permutations for n distinct entities. For 10 points, name this function giving the product of a number and all its integer predecessors, denoted by an exclamation point.

factorial <R. Li>

This statement’s inventor was inspired by Benjamin Thompson, Count Rumford’s cannon-boring experiments, which led to the idea of the mechanical equivalent of heat. Max Born’s version of this statement uses the work done by an adiabatic process as a reference. Symbolically, this law adds up two inexact differentials to obtain the change in a state function. For a Bornâ€"Haber cycle, (*) Hess’s law states this more general law in terms of enthalpy. In its basic form, this law states that any change in internal energy equals work done on a system plus heat. For 10 points, name this law of thermodynamics holding that the total energy of a system is conserved.

first law of thermodynamics [prompt on conservation of energy; prompt on first law until “law of thermodynamicsâ€; accept first law after “law of thermodynamicsâ€] <SE>

Molybdenum disulfide can be used to reduce this force. It’s not electrostatics, but Coulomb names a law of this force which states that it is independent of relative velocity. The Stribeck curve quantifies how this force changes non-linearly with contact load. Tribology, which is the study of this force, was pioneered by Guillaume (*) Amontons. The dry variety of this force is proportional to the normal force multiplied by its namesake coefficient. This force comes in both static and kinetic varieties. The work done by this force is dissipated as heat. For 10 points, name this non-conservative force which is reduced by ball bearings and lubricants.

friction <K. Li, Physics> Bonuses

The Larmor frequency is proportional to a constant given by this Greek letter, and a factor with this letter is applied to all components of an energyâ€"momentum four-vector. Oxygen has a value of 7/5 for a constant with this Greek letter, the adiabatic index. This letter denoting particles produced by an electronâ€"positron collision also denotes a factor multiplied by the proper time in time dilation, the (*) Lorentz factor. The brightest events in the universe are named for “bursts†of rays named with this Greek letter. For 10 points, give this Greek letter naming a type of penetrating radiation where photons are emitted, higher in energy than beta or alpha radiation.

gamma (accept specification of lower or upper cases) <Yue>

The Eightfold Way was proposed independently by Yuval Ne'eman and Murray Gell-Mann to organize these things by their strangeness into octets and decuplets. Jets of this class of particles can be observed after collisions of high energy particles in a process known by their name followed by (*) “-ization,†since their constituents spontaneously combine due to color confinement. These composite particles are divided into two families based on whether they are composed of two or three valence quarks. The world’s most powerful particle collider is named after these things, since it collides the only stable, free type of them, the proton. For 10 points, give this name for the general class of particles that includes baryons and mesons and are tested at the LHC.

hadrons [accept mesons before “decuplets,†anti-prompt on baryons, mesons, or quarks] <McMaken>

At the point when the Sackur-Tetrode equation begins to break down, this medium begins to behave into a quantized manner and can take on a Boltzmann form when the constant phi is proportional to capital T to the three-halfs. This medium exists over a wide range of pressures when the temperature reaches the Boyle temperature, and the speed of sound in this medium is given by the square root of (*) gamma R T over M. The internal energy of this medium satisfies Joule’s Law, and an equation of state governing the thermodynamic properties of this medium can be derived from a set of laws by Avogadro, Charles, and Boyle. For 10 points, name this medium that satisfies P V equals n R T and consists of point particles undergoing perfectly elastic collisions.

ideal gas <McMaken>

The ratio of the impedance of free space to this value gives the wave impedance of a medium. For the case of normal incidence, the reflection and transmission coefficients depend only on these values. This value can be used to determine both the reflectance at an interface and (*) Brewster’s angle. The critical angle is equal to the inverse sine of the ratio of these values for two media. Above that angle, a ray of light will undergo total internal reflection. This value quantifies the amount that a ray of light is bent when entering a different medium. For 10 points, name this value which multiplies sine of theta in Snell’s law.

index of refraction (or refractive index) <K. Li, Physics>

The Legendre transform of this quantity is Helmholtz free energy, which equals this quantity minus the product of temperature and entropy. Pressure equals the negative partial derivative of this quantity with respect to volume, and temperature is the partial derivative of it with respect to (*) entropy. An increase in this quantity is heat added plus work done on the system, according to the first law of thermodynamics. For 10 points, name this quantity that gives the total amount of potential and kinetic energy in a system, symbolized U.

internal energy [accept U before mentioned, do not prompt on “energyâ€]

A set of possible values represented by this letter appear in the diagonal of the Jordan matrix, and Lagrange multipliers are often denoted by it. Einstein referred to a value denoted by this letter as “his biggest blunder,†and this letter names a helium superfluid transition temperature around 2 kelvin. Two twelve-base pair sticky ends appear in a Esther-Lederberg-discovered (*) phage [“fayjâ€] termed with this Greek letter also used to denote eigenvalues. This Greek letter denotes a quantity equal to the velocity over the frequency of a wave; that quantity with this symbol is the wavelength. For 10 points, give this Greek letter transliterated as “L.â€

lambda <Magee>

Lockheed Martin recently received a contract from the U.S. government to build a system based on these devices. These devices will have jumps in their mode spectrum if their temperature is not kept stable. A type of these devices dimerizes halides using an electrical current, while other types may use mixtures of (*) noble gases. These devices can be used to cool individual atoms by minimizing their vibrations. These devices tend to produce low frequencies because higher frequencies require higher rates of electron pumping. For 10 points, name these devices which produce a coherent stream of photons.

lasers [accept light amplification by stimulated emission of radiation] <AJ>

This quantity’s operator is the generator of translations, and the derivative of energy with respect to it is the group velocity. This quantity is the generalized velocity derivative of the Lagrangian, and its space is also called k-space as it is proportional to inverse wavelength by the de Broglie [“broyâ€] relation. By Noether’s [“NURH-thursâ€] theorem, translational invariance implies its conservation, and its conjugate variable is (*) position. This quantity squared over twice the mass is the kinetic energy, and its time derivative is the force. Impulse gives the change in this quantity, which is conserved in inelastic collisions. For 10 points, name this vector quantity equal to mass times velocity.

linear momentum (do NOT accept or prompt on “angular momentumâ€) <Yue>

Increasing this quantity reduces light polarization in the Hanle [“HAHN-luhâ€] effect, and it is given by values not in the first row or column of the Faraday tensor. This vector’s magnitude is directly proportional to the cyclotron frequency, and its line integral is given by an equation to which a displacement current term was later added. This vector is crossed with velocity in the (*) Lorentz force law. This quantity can be found via Amperian loops or the Biotâ€"Savart law. The flux of this quantity is zero by a law named for Gauss, illustrating that a certain monopole cannot exist. For 10 points, name this vector field that couples to the electric field.

magnetic field (accept H-field or B-field) <Yue>

Electrons in graphene behave as if they have a value of zero for this quantity, and neutrinos oscillate due to their nonzero value of it. The cyclotron frequency is inversely proportional to this quantity. The rocket equation features the logarithm of a ratio between two of these quantities. This quantity’s “reduced†form, used in two-body problems, is symbolized mu. This quantity’s (*) inertial form is equal to its gravitational form according to the equivalence principle. The Higgs boson gives particles a nonzero value of this quantity. This quantity multiplies acceleration to give force. For 10 points, name this quantity measured in kilograms.

mass <Yue, Physics>

For electrons in solids, the second derivative of the dispersion relation is used to define an “effective†value for this quantity. Neutrinos can change flavor because they have a nonzero value for this quantity. In the two-body problem, one uses a harmonic mean to compute a “reduced†version of this quantity denoted with the letter mu. The binding energy of a nucleus can be expressed as a (*) “defect†of this quantity. Particles that interact with the Higgs boson acquire some amount of this quantity; particles that do not, and thus have a zero value for it, include photons. The proton exceeds the electron by a factor of 1,800 inâ€"for 10 pointsâ€"what quantity measured in kilograms?

mass [accept effective mass or reduced mass or mass defect] <SE> Tiebreaker

The WATCHMAN detector will monitor illicit nuclear enrichment by detecting these particles using gadolinium doped water. Detection of this particle relies on observing Cherenkov radiation produced from its interaction with water, and gadolinium amplifies the light by capturing the free neutron created from the inverse (*) beta decay between this particle and a proton. It is unclear whether these fermions are their own antiparticle or not. It is also unclear if a sterile variety of this particle exists in addition to their tau, muon, and electron varieties. For 10 points, name these nearly massless particles.

neutrino (accept specific varieties; do NOT accept “neutronâ€) <K. Li>

Carlo Rubbia pioneered the use of liquid argon time projection chambers to detect these particles with the ICARUS detector, which moved to Fermilab in 2017 to join the MiniBooNE detector for these particles. The fact that the flux of these particles is three times lower than expected is their namesake “problem.†Takaaki Kajita confirmed that these particles have mass by observing their flavor oscillations at Super-Kamiokande. Wolfgang (*) Pauli proposed the existence of these uncharged leptons to explain beta decay. For 10 points, name these neutral, nearly massless particles that move near the speed of light and are produced in huge numbers by the Sun.

neutrinos <SE>

These particles stopped reacting with positrons and electron neutrinos one second after the Big Bang. Following Big Bang nucleosynthesis, almost all of these particles were bound in helium-4 nuclei. The only allowed decay for this particle, beta-minus decay, emits an electron and electron antineutrino. That decay converts one of these particles’ (*) down quarks into an up quark. The fast variety of these particles can be moderated by water, and their controlled release drives nuclear fission. These particles were discovered by James Chadwick. For 10 points, name these neutral particles found with protons in the nucleus.

neutrons <K. Li, Physics>

In 2016, four of these things were first observed connected to each other, and GISANS is a scattering technique used to detect these things. Bertram Brockhouse and Clifford Shull won a Nobel Prize for their work with these things, which can be organized into categories like “epithermal†and (*) “fast.†These things are captured in the r-process and they were discovered by observing how boron interacted with alpha radiation in an experiment by James Chadwick. These things are composed of two down quarks and one up quark, and isotopes are differentiated by their numbers of these particles. For 10 points, name these particles found in the nucleus with no charge.

neutrons [prompt on n0] <BC>

Because the safety factor was less than one in Z-pinch machines, Kruskalâ€"Shafranov kink instabilities resulted in the retraction of this kind of result at ZETA in England. Because of the increase in density, the muon-catalyzed type of this process allows for the reduction of temperature to reach ignition according to the (*) Lawson Criterion. Bremsstrahlung losses can limit efficiency of this process. Graphite electrodes are used in Langmuir probes to measure plasmas that participate in this process and a magnetic field holds plasmas in a torus shape to achieve this in a tokamak. For 10 points, name this process that combines the nuclei of atoms together.

nuclear fusion (prompt on just fusion; do NOT accept or prompt on “nuclear fission†or “fissionâ€) <Owen> Bonuses

Second harmonic generation is studied in the “nonlinear†branch of this field of study, which concerns materials in which polarization is not proportional to the electric field. Components in this area of study can be represented as 2-by-2 transfer matrices in the limit of the paraxial approximation. The principle of least (*) time is useful for plotting trajectories in the “geometric†form of this field. The name of this field is spelled with a “k†in the title of a 1704 treatise that presents the prism experiments performed by its author, Isaac Newton. Diffraction, refraction, and reflection are important topics inâ€"for 10 pointsâ€"what field that studies properties of light?

optics [accept specific nonlinear optics or geometric optics; accept light before “lightâ€; prompt on physics] <SE>

In these systems, the classical Laplaceâ€"Runge [“RUNâ€"guhâ€]â€"Lenz vector is conserved. Bertrand’s theorem gives two possible conditions in which these systems are closed. A “halo†one of these systems can be unstable. A Hohmann [“HOEâ€"manâ€] transfer moves between two of these systems, which often feature a central inverse-square force. These (*) paths, which have mean and true anomalies, are characterized by eccentricity. In these systems, the semi-major axis cubed is proportional to the period squared. These elliptical paths are described by Kepler’s laws. For 10 points, name these paths exemplified by the motion of the Earth around the Sun.

orbits (accept orbital motion; accept two-body problems; prompt on planetary motion or elliptical motion or word forms of these answers; prompt on inverse-square problems) <Yue, Physics>

Pyotr Kapitsa proposed an unusual type of this object that can be held in an unstable equilibrium using a driving force. The moon’s interference supposedly causes these objects to move strangely during solar eclipses in the Allais effect. An enormous one of these objects inside Taipei 101 acts as a tuned mass damper. These objects are described by the equation (*) “theta-double-prime plus g over L times theta equals zero†after applying the small-angle approximation. Their period is independent of mass and oscillation amplitude. A bob on a massless string describesâ€"for 10 pointsâ€"what example of a harmonic oscillator found in grandfather clocks?

pendulums [or pendula; prompt on simple harmonic oscillators] <SE>

The set of these entities over a ring is denoted with an “x†in square brackets. These entities can arbitrarily approximate any continuous function according to the Weierstrass [VYE-ur-strahss] theorem. One of these objects is produced by taking the determinant of “lambda times the identity matrix, minus another matrix.†Most of these functions can’t be solved by (*) radicals, according to the Abelâ€"Ruffini theorem. Factoring these functions can make finding their roots easier, and second-degree examples of them can be solved with the quadratic formula. For 10 points, name these functions of integer powers of a variable, such as “x squared plus five.â€

polynomials [prompt on equations or functions] <AF>

For an ideal dipole antenna, dividing this quantity by current-squared gives the radiation resistance. For an electromagnetic wave, the amount of this quantity per unit area is given by the Poynting vector, and in general its amount per unit area is given by intensity. For a purely resistive load, this quantity’s RMS value is exactly half its peak value. For a resistor, this quantity is equal to “I (*) squared times R†according to Joule’s heating law. This quantity equals current times voltage for electrical systems. In general, it is the time derivative of work. The amount of energy consumed per unit time isâ€"for 10 pointsâ€"what quantity measured in watts?

power [prompt on flux, but do not accept or prompt on “electric flux†or “magnetic fluxâ€] <SE>

One variety of this phenomenon can be related to the ratio of the cosmological scale factor between the two times in question. This phenomenon is commonly calculated by observing how much spectral lines such as the Lyman-alpha line have moved. The (*) Doppler effect can explain this phenomenon, represented by the letter “z,†at small distances. This phenomenon is caused by objects receding along the line of sight and comes in gravitational, cosmological, and relativistic Doppler varieties. For 10 points, name this phenomenon which describes an increase in wavelength named for the first color in the rainbow.

redshift (accept specific varieties; ONLY accept blueshift until “receding†is read, do NOT prompt afterwards; do NOT accept or prompt on “Doppler effectâ€) <K. Li>

Description acceptable. The discovery of a binary system consisting of two neutron stars, one of which had this property, was awarded the 1993 Nobel in Physics. Black holes with this property are described by the Kerr metric. Black holes can be described completely by their mass, charge, and this other property, by the (*) no-hair theorem. Uranus is unusual in that it has this property parallel to the plane of the ecliptic. For a satellite, the rate of this process becomes matched to the orbital period in tidal locking. Pulsars are neutron stars with this property. It maintains the shape of spiral galaxies. For 10 points, name this property that makes planets and stars stars bulge out due to centrifugal force.

rotation [accept word forms like rotating; accept descriptive answers like spinning, having nonzero angular momentum; prompt on pulsars] <HK>

Charles Bennett upheld this law using an information argument, and applying Jensen’s inequality to the Jarzynski equality derives this law. Adiabatic [“AD-ea-BAD-ikâ€] accessibility is defined in Caratheodory’s purely axiomatic formulation of this law, which says in another formulation that the integral of dQ [“d-Qâ€] over T is greater than zero. Clausius’ formulation of this law is that (*) heat cannot move spontaneously from colder to hotter locations. This law was challenged by a thought experiment where particles are sorted based on temperature by Maxwell’s Demon. For 10 points, name this law which states that the entropy of the universe increases over time.

second law of thermodynamics (prompt on partial answer; do NOT accept or prompt on any other law of thermodynamics) <Huang/Yue>

The intrinsic type of these materials have energy levels determined by Fermi-Dirac statistics which can easily induce partially-filled states at room temperature. The Schottky barrier is a potential energy barrier formed at the junction of metals and these materials. The extrinsic type of these materials is formed through the addition of (*) impurities in a process known as “doping,†which can be used to create “p†and “n†types of these materials based on their affinity for electrons or electron holes. For 10 points, identify these materials, examples of which include gallium arsenide and silicon, which have properties between those of an insulator and a conductor.

semiconductors <McMaken>

An analogy that compares these phenomena to electrical signals defines their impedance as the ratio of pressure to flow rate. Hermann von Helmholtz names a kind of cavity that amplifies these phenomena at a particular frequency. A parameter governing these phenomena marks the onset of choked flow in compressible fluids. These phenomena travel at a (*) speed proportional to the square root of air pressure over air density, which works out to about 343 meters per second in room-temperature air. Objects moving faster than these phenomena have a Mach number greater than 1. For 10 points, name these longitudinal waves whose intensity is measured in decibels.

sound waves [accept frequency before “frequencyâ€; prompt on waves before “longitudinal wavesâ€] <SE>

An experiment confirming this theory measured the wavelength of light emitted by a canal ray and found that the redshift of the reflected beam was not equal to the blueshift of the original beam. This theory can be used to show that a magnetic field is produced by viewing an electric field through a moving coordinate system. In this theory, light cones are depicted using (*) Minkowski diagrams, which can also be used to explain length contraction. This theory states that the speed of light is constant regardless of the motion of the source or observer. For 10 points, name this theory describing fast-moving objects that has a more expansive “general†version.

special relativity (prompt on just relativity) [Writer’s note: The second clue refers to the Ivesâ€"Stilwell experiment.] <K. Li, Physics>

The Frisch-Smith experiment confirmed some elements of this theory by observing the lifetime of muons, and the Hafele-Keating experiment helped confirm this theory. In a coordinate transformation related to this theory, a quantity symbolized gamma equals the reciprocal of the square root of one minus v squared over (*) c squared. That quantity is the Lorentz factor. This theory holds the invariance of mass across reference frames, and it predicts time dilation and length contraction near the speed of light. For 10 points, name this theory postulated in 1905 by Albert Einstein that E=mc2, which preceded a related “general†theory.

special relativity [or SR; prompt on relativity, do not accept or prompt on “general relativityâ€] <BC>

The Rayleighâ€"Jeans law in terms of frequency has this constant squared in the denominator, and it is cubed in the denominator of the Larmor formula. This constant squared is one over the vacuum permeability times permittivity as well as the ratio between a nucleus’ binding energy and its mass defect. A “failed†experiment to measure (*) differences in this constant based on orientation led Michelson and Morley to disprove the existence of the luminiferous ether. This constant is the same in all reference frames by special relativity, and it is about three times ten to the eight meters per second. For 10 points, name this maximum speed at which mass can travel.

speed of light (accept c) <K. Li/Yue>

The energy-momentum tensor is divided by this quantity raised to the fourth power in Einstein’s field equations. The Lorentz factor equals one over the square root of one minus velocity squared over this quantity squared. The refractive index of a material is the ratio of this (*) constant to speed, and it is the conversion factor between frequency and wavelength of an electromagnetic wave. This quantity is constant regardless of the observer’s inertial reference frame, and it is equal to approximately three times ten to the eighth meters per second. According to Einstein, for 10 points, energy is equal to mass times what constant squared?

speed of light [accept c]

For fluids, this quantity is given by the Newtonâ€"Laplace equation, which states that this quantity is equal to the square root of the adiabatic index times pressure divided by density. This value is at a minimum in the SOFAR channel. The Prandtlâ€"Glauert singularity occurs at this value. When an object’s velocity exceeds this quantity, a (*) shockwave will form. The Mach number is defined as the ratio of the speed of an object to this quantity for the medium. In dry air at 20 degrees Celsius, this quantity is approximately 343 meters per second. For 10 points, name this quantity which is the speed at which acoustic waves travel.

speed of sound <K. Li, Physics> Bonuses

A concept named for Dirac and this thing consists of the region of space outside of a magnetic monopole in which the vector potential is not defined. The QCD type of this is a color-confining degree of freedom that is classified as a noncritical, and in general, that thing with this name is predicted to be about 10-35 meters long and can be (*) “open†or “closed.†Excitations of this type of medium can be seen with a strobe light, and those oscillations travel with a speed equal to the square root of the tension divided by mu, the mass per unit length. For 10 points, name this thing which lends its name to a theory under the eleven-dimensional M-theory as well as a massless, one-dimensional object that can attach to masses on a pulley.

string <McMaken>

Gravity Probe B relied on the fact that spinning examples of these materials produce a magnetic field in line with their spin axis. In lanthanum barium copper oxide, replacing the lanthanum with the yttrium increases the temperature at which these materials are formed. That substance, (*) YBCO, is described by the Ginzburg-Landau theory and phonons in these materials allow Cooper pairs to form. The Meissner effect leads to these materials expelling a magnetic field, thus allowing these materials to levitate. For 10 points, name materials usually found at low temperatures which do not have electrical resistance.

superconductors [accept word forms; do not accept or prompt on “conductorsâ€] <BC>

This quantity is determined to be non-zero by an accelerating reference frame through a vacuum in the Unruh effect. This quantity for electrons following a certain probability distribution is multiplied by the number density and the Boltzmann constant to find the plasma pressure. This quantity can be measured on the (*) Rankine scale, and changes in it for air cause mirages. This quantity for an enclosed gas is directly proportional to pressure, according to Gay-Lussac’s law, and it is multiplied by the number of moles and a constant symbolized R on one side of the ideal gas law. For 10 points, name this quantity that can be measured on the Kelvin scale.

temperature [prompt on T; do not accept or prompt on “heatâ€] <AJ>

A state is evolved with respect to this quantity by the most commonly used unitary operator in quantum physics. By Noether’s [“NURHâ€"thur’sâ€] theorem, this quantity’s symmetry implies energy conservation. This quantity remains fixed during a Galilean transformation. A constant named for this quantity is the product of resistance and capacitance in an RC circuit. This quantity experiences a namesake (*) “dilation†in special relativity. The change in velocity with respect to this quantity gives acceleration. Entropy could explain why the “arrow†of this quantity points in one direction. For 10 points, name this quantity commonly measured in seconds.

time <Yue, Physics>

This quantity varies along the vertical axis of a Penrose diagram. This quantity corresponds to the first entry in a metric signature. Intervals that lie within the light cone are “like†this quantity, which remains fixed during a Galilean transformation. Muons can be detected on Earth because this quantity’s “coordinate†value is greater than its (*) “proper†value by the Lorentz factor. In Minkowski space, this quantity adds on to 3-D space to become a fourth dimension. Starting from rest with constant acceleration, displacement equals one-half acceleration times this quantity squared. For 10 points, what quantity multiplies a constant acceleration to give the change in velocity?

time [accept time-like interval; prompt on T] <SE>

In 2019, light beams were generated possessing the “self†form of this quantity. It’s not voltage, but motors have “pull-in†and “breakdown†values of this quantity, which is symbolized “M†in Euler’s [“OY-lursâ€] equations for rigid bodies. This quantity is the product of current, area, and magnetic field for a current-carrying loop. Work is given by this quantity integrated over theta. This quantity acts perpendicular to (*) angular momentum when it causes precession. This quantity is the product of moment of inertia and angular acceleration, or the cross product of lever arm and force. For 10 points, name this rotational analogue of force symbolized tau.

torque <Yue, Physics>

The ratio of this quantity to the maximum shear stress on a beam is equal to the polar version of an another quantity. In a magnetic dipole, this quantity is equal to the cross product of the dipole with the magnetic field, and in a loop of wire this quantity equals the product of current, magnetic field, and the area of the loop. In a (*) lever in equilibrium, this quantity has a net value of zero. This quantity is equal to moment of inertia times angular acceleration and is also the time derivative of angular momentum. In a pulley, this quantity is equal to the tension of the rope times the radius of the disk. For 10 points, name this quantity that is the rotational analog of force.

torque [accept tau; accept moment of force] <AJ>

Julius Edgar Lilienfeld invented an early type of these devices in 1930 but failed to widely publicize it. That type of these devices switches from the cutoff regime to the linear regime at the threshold voltage. These devices are produced in complementary pairs in CMOS [see-moss] technology. An applied voltage controls the carrier concentration in the (*) “field effect†class of these devices, whose three terminals are the source, gate, and drain. Two pâ€"n junctions sit back-to-back in their “bipolar junction†type. MOSFETs are the most common type ofâ€"for 10 pointsâ€"what semiconductor devices that amplify electrical signals, which are found by the millions on computer chips?

transistors [accept MOSFETs or FETs before “bipolar junctionâ€] <SE> Tiebreaker

This is the number of degrees of freedom of the Wilberforce pendulum, and Planck’s constant is raised to this power in the Bohr radius. Potentials to this power receive ½ k-b T in average energy by the equipartition theorem, and the spin quantum number has this many possible values. This is the number of connected pendulums needed for a (*) chaotic system and the maximum number of gravitating bodies whose motion can be generally solved. This is the number of masses in a simple Atwood machine, and acceleration is this numbered time derivative of position. For 10 points, give this power to which velocity is raised in the formula for kinetic energy.

two (accept word forms like second) <Yue>

Operations on these objects that always have the same sign are called positive or negative definite. Quadratic forms are usually written as acting on these objects. A norm is defined on these objects. The volume of a parallelepiped can be expressed as a “triple†operation on three of these objects. If no member of a set of them can be written as a sum of multiples, or (*) “combination,†of the others, they’re linearly independent. Pairs of these objects are operated on by the dot product and cross product. They’re often represented as matrix-like “rows†or “columns.†For 10 points, name these mathematical objects that have a magnitude and direction, unlike scalars.

vectors <JW>

One type of this quantity is equal to the product of electron mobility and the applied electric field. That type of this quantity, which is multiplied by number density and charge to give the current density, is its “drift†type. A particle’s cyclotron radius is proportional to the perpendicular component of this quantity. For a wave, one can define both a “phase†and a “group†type of this quantity. Magnetic fields only act on charged particles with a (*) nonzero value for this quantity, since the cross product of this quantity with the magnetic field appears in the Lorentz force law. For 10 points, name this vector quantity equal to the rate of change of position.

velocity [prompt on speed] <SE>

Stationary states of the Morse potential exhibit this kind of motion. Non-linear molecules have “3-N minus 6†modes of this kind of motion, while linear molecules have “3-N minus 5â€. The energy of this kind motion is measured with a wavenumber that falls between 500 and 4000 inverse centimeters. Types of this process include rocking, wagging, and asymmetric stretching. This process is observed for molecules in (*) infrared spectroscopy. Degrees of freedom are composed of translation, rotation, and this type of motion. Objects undergo this type of motion to produce uniform sound waves. For 10 points, name this type of motion in which atoms oscillate with high frequency.

vibrations [or vibrational modes; prompt on oscillations; prompt on normal modes] <CK/AF>

This variable and two physical constants are used to compute the Fresnel number. Planck’s constant over “m times c†gives a value for this quantity used in Compton scattering, a process during which this quantity increases. As this quantity decreases, Mie [mee] scattering is replaced by Rayleigh scattering, whose intensity is inversely proportional to the (*) fourth power of this quantity. Either this quantity or frequency determines the refractive index in dispersion. Frequency can be multiplied by this quantity to give the speed of light. Color is determined byâ€"for 10 pointsâ€"what property that falls between 400 and 700 nanometers for visible light?

wavelength [prompt on lambda] <SE>