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URL: http://users.rcn.com/zap.dnai/laws.txt

LAWS, RULES, PRINCIPLES, EFFECTS, PARADOXES, LIMITS, CONSTANTS, EXPERIMENTS, & THOUGHT-EXPERIMENTS IN PHYSICS

version 1.0
compiled by Erik Max Francis
Please send all comments, additions, corrections, and suggestions to max@west.darkside.com

Ampere's law

(A.M. Ampere)
The line integral of the magnetic flux around a closed curve is proportional to the algebraic sum of electric currents flowing through that closed curve.
This was later modified to add a second term when it was incorporated into Maxwell's equations.

anthropic principle

Weak anthropic principle. The conditions necessary for the development of intelligent life will be met only in certain regions that are limited in space and time. That is, the region of the Universe in which we live is not necessarily representative of a purely random set of initial conditions; develop creatures who wonder what the initial conditions of the Universe were.
Strong anthropic principle. A more forceful argument that the weak principle: It states, rather straightforwardly, that if the laws of the Universe were not conducive to the development of intelligent creatures to ask about the initial conditions of the Universe, intelligent life would never have evolved to ask the question in the first place. In other words, the laws of the Universe are the way they are because if they weren't, you would not be able to ask such a question.

Arago spot

A bright spot that appears in the shadow of a uniform disc being backlit by monochromatic light emanating from a point source.

Archimedes' principle

A body that is submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid that is displaced, and directed upward along a line through the center of gravity of the displaced fluid.

Atwood's machine

   A weight-and-pulley system devised to measure the acceleration due 
   to gravity at Earth's surface by measuring the net acceleration of 
   a set of weights of known mass around a frictionless pulley.

Avogadro constant;L; N_A (Count A. Avogadro; 1811)

   The number of atoms or molecules in a sample of an idea gas which 
   is at standard temperature and pressure.  It is equal to about 
   6.022 52 x 10^23 mol^-1.

Avogadro's hypothesis (Count A. Avogadro; 1811)

   Equal volumes of all gases at the same temperature and pressure 
   contain equal numbers of molecules.  It is, in fact, only true for 
   ideal gases.

Balmer series (J. Balmer; 1885)

   An equation which describes the emission spectrum of hydrogen when 
   an electron is jumping to the second orbital; four of the lines 
   are in the visible spectrum, and the remainder are in the 
   ultraviolet.

baryon decay

   The theory, predicted by several grand-unified theories, that a
   class of subatomic particles called baryons (of which the nucleons
   -- protons and neutrons -- are members) are not ultimately stable
   but indeed decay.  Present theory and experimentation demonstrate
   that if protons are indeed unstable, they decay with a halflife of
   at least 10^34 y.

Bernoulli's equation

   An equation which states that an irrotational fluid flowing
   through a pipe flows at a rate which is inversely proportional to
   the cross-sectional area of the pipe.  That is, if the pipe
   constricts, the fluid flows faster; if it widens, the fluid flows
   slower.

BCS theory (J. Bardeen, L.N. Cooper, J.R. Schrieffer; 1957)

A theory put forth to explain both superconductivity and superfluidity. It suggests that in the superconducting (or superfluid) state electrons form Cooper pairs, where two electrons act as a single unit. It takes a nonzero amount of energy to break such pairs, and the imperfections in the superconducting solid (which would normally lead to resistance) are incapable of breaking the pairs, so no dissipation occurs and there is no resistance.

Biot-Savart law (J.B. Biot, F. Savart)

A law which describes the contributions to a magnetic field by an electric current. It is analogous to Coulomb's law for electrostatics.

blackbody radiation

The radiation -- the radiance at particular frequencies all across the spectrum -- produced by a blackbody -- that is, a perfect radiator (and absorber) of heat. Physicists had difficulty explaining it until Planck introduced his quantum of action.

Bode's law

   A mathematical formula which generates, with a fair amount of 
   accuracy, the semimajor axes of the planets in order out from the 
   Sun.  Write down the sequence 0, 3, 6, 12, 24, . . . and then add 
   4 to each term.  Then divide each term by 10.  This is intended to 
   give you the positions of the planets measured in astronomical 
   units.
       Bode's law had no theoretical justification when it was first 
   introduced; it did, however, agree with the soon-to-be-discovered 
   planet Uranus' orbit (19.2 au actual; 19.7 au predicted).  
   Similarly, it predicted a missing planet betwen Mars and Jupiter,
   and shortly thereafter the asteroids were found in very similar
   orbits (2.8 au actual for Ceres; 2.8 au predicted).  However, the
   series seems to skip over Neptune's orbit.

Bohr's complementarity principle (N. Bohr)

   The principle that a given system cannot exhibit both wave-like
   behavior and particle-like behavior at the same time.  That is,
   certain experiments will reveal the wave-like nature of a system,
   and certain experiments will reveal the particle-like nature of a
   system, but no experiment will reveal both simultaneously.

Bohr magneton (N. Bohr)

   The quantum of magnetic moment.

Bohr radius (N. Bohr)

   The distance corresponding the mean distance of an electron from
   the nucleus in the ground state.

Boltzmann constant; k (L. Boltzmann)

   A constant which describes the relationship between temperature
   and kinetic energy for molecules in an ideal gas.  It is equal to
   1.380 622 x 10^-23 J/K.

Boyle's law (R. Boyle; 1662); Mariotte's law (E. Mariotte; 1676)

   The product of the pressure and the volume of an ideal gas at
   constant temperature is a constant.

Brackett series (Brackett)

   The series which describes the emission spectrum of hydrogen when
   the electron is jumping to the fourth orbital.  All of the lines
   are in the infrared portion of the spectrum.

Bragg's law (Sir W.L. Bragg; 1912)

   When a beam of x-rays strikes a crystal surface in which the
   layers of atoms or ions are regularly separated, the maximum
   intensity of the reflected ray occurs when the sin of the
   compliment of the angle of incidence is equal to an integer
   multiplied by the wavelength of x-rays divided by twice the
   distance between layers of atoms or ions.

Brewster's law (D. Brewster)

   The extent of the polarization of light reflected from a
   transparent surface is a maximum when the reflected ray is at
   right angles to the refracted ray.

Brownian motion (R. Brown; 1827)

   The continuous random motion of solid microscopic particles when
   suspended in a fluid medium due to the consequence of continuous
   bombardment by atoms and molecules.

Carnot's theorem (S. Carnot)

   The theorem which states that no engine operating between two 
   temperatures can be more efficient than a reversible engine.

centrifugal pseudoforce

   A pseudoforce -- a fictitious force resulting from being in a non- 
   inertial frame of reference -- that occurs when one is moving in 
   uniform circular motion.  One feels a "force" outward from the 
   center of motion.

Chandrasekhar limit (S. Chandrasekhar; 1930)

   A limit which mandates that no white dwarf (a collapsed, 
   degenerate star) can be more massive than about 1.2 solar masses.  
   Anything more massive must inevitably collapse into a neutron 
   star.

Charles' law (J.A.C. Charles; c. 1787)

   The volume of an ideal gas at constant pressure is proportional to 
   the thermodynamic temperature of that gas.

Cherenkov radiation (Cherenkov)

   Radiation emitted by a massive particle which is moving faster 
   than light in the medium through which it is travelling.  No 
   particle can travel faster than light in vacuum, but the speed of
   light in other media, such as water, glass, etc., are considerably
   lower.  Cherenkov radiation is the electromagnetic analogue of the
   sonic boom, though Cherenkov radiation is a shockwave set up in
   the electromagnetic field.

Compton effect (A.H. Compton; 1923)

   An effect that demonstrates that photons (the quantum of
   electromagnetic radiation) have momentum.  A photon fired at a
   stationary particle, such as an electron, will impart momentum to
   the electron and, since its energy has been decreased, will
   experience a corresponding decrease in frequency.

Coriolis pseudoforce (G. de Coriolis; 1835)

   A pseudoforce -- a fictitious force, like the centrifugal "force"
   -- which arises because the rotation of the Earth varies at
   different latitutdes (maximum at the equator, zero at the poles).

correspondence principle

   The principle that when a new, more specialized theory is put
   forth, it must reduce to the more general (and usually simpler)
   theory under normal circumstances.  There are correspondence
   principles for general relativity to special relativity and
   special relativity to Newtonian mechanics, but the most widely 
   known correspondence principle (and generally what is meant when 
   one says "correspondence principle") is that of quantum mechanics 
   to classical mechanics.

cosmic background radiation (primal glow)

   The background of radiation mostly in the frequency range 3 x 
   10^11 to 3 x 10^8 Hz discovered in space in 1965.  It is believed 
   to be the cosmologically redshifted radiation released by the Big 
   Bang itself.  Presently it has an energy density in empty space of 
   about 4 x 10^-14 J/m^3.

cosmological redshift

   An effect where light emitted from a distant source appears 
   redshifted because of the expansion of space itself.  Compare with 
   the Doppler effect.

Coulomb's law

   The primary law for electrostatics, analogous to Newton's law of 
   universal gravitation.  It states that the force between two point 
   charges is proportional to the algebraic product of their 
   respective charges as well as proportional to the inverse square 
   of the distance between them.

Curie-Weiss law (P. Curie, P.-E. Weiss)

   A more general form of Curie's law, which states that the
   susceptibility of a paramagnetic substance is inversely
   proportional to the thermodynamic temperature of the substance
   less the Weiss constant, a characteristic of that substance.

Curie's law (P. Curie)

   The susceptibility of a paramagnetic substance is inversely
   proportional to the thermodynamic temperature of the substance.
   The constant of proportionality is called the Curie constant.

Dalton's law of partial pressures (J. Dalton)

   The total pressure of a mixture of ideal gases is equal to the sum
   of the partial pressures of its components; that is, the sum of
   the pressures that each component would exert if it were present
   alone and occuped the same volume as the mixture.

Davisson-Germer experiment (C.J. Davisson, L.H. Germer; 1927)

   An experiment that conclusively confirmed the wave nature of
   electrons; diffraction patterns were observed by an electron beam
   penetrating into a nickel target.

de Broglie wavelength (L. de Broglie; 1924)

   The prediction that particles also have wave characteristics,
   where the effective wavelength of a particle would be inversely 
   proportional to its momentum, where the constant of 
   proportionality is the Planck constant.

Doppler effect (C.J. Doppler)

   Waves emitted by a moving observer will be blueshifted 
   (compressed) if approaching, redshifted (elongated) if receding.  
   It occurs both in sound as well as electromagnetic phenomena, 
   although it takes on different forms in each.

Dulong-Petit law (P. Dulong, A.T. Petit; 1819)

   The molar heat capacity is approximately equal to the three times 
   the gas constant.

Einstein-Podolsky-Rosen effect

   Consider the following quantum mechanical thought-experiment:  
   Take a particle which is at rest and has spin zero.  It 
   spontaneously decays into two fermions (spin 1/2 particles), which 
   stream away in opposite directions at high speed.  Due to the law 
   of conservation of spin, we know that one is a spin +1/2 and the 
   other is spin -1/2.  Which one is which?  According to quantum 
   mechanics, neither takes on a definite state until it is observed 
   (the wavefunction is collapsed).
       The EPR effect demonstrates that if one of the particles is
   detected, and its spin is then measured, then the other particle
   -- no matter where it is in the Universe -- instantaneously is
   forced to choose as well and take on the role of the other
   particle.  This illustrates that certain kinds of quantum
   information travel instantaneously; not everything is limited by
   the speed of light.
       However, it can be easily demonstrated that this effect does
   not make faster-than-light communication possible.

equivalence principle

   The basic postulate of A. Einstein's general theory of relativity,
   which posits that an acceleration is fundamentally
   indistinguishable from a gravitational field.  In other words, if
   you are in an elevator which is utterly sealed and protected from
   the outside, so that you cannot "peek outside," then if you feel a
   force (weight), it is fundamentally impossible for you to say
   whether the elevator is present in a gravitational field, or
   whether the elevator has rockets attached to it and is
   accelerating "upward."
       The equivalence principle predicts interesting general
   relativistic effects because not only are the two
   indistinguishable to human observers, but also to the Universe as
   well, in a way -- any effect that takes place when an observer is
   accelerating should also take place in a gravitational field, and
   vice versa.

ergosphere

   The region around a rotating black hole, between the event horizon
   and the static limit, where rotational energy can be extracted
   from the black hole.

event horizon

   The radius of surrounding a black hole at which a particle would
   need an escape velocity of lightspeed to escape; that is, the
   point of no return for a black hole.

Faraday constant; F (M. Faraday)

   The electric charge carried by one mole of electrons (or singly-
   ionized ions).  It is equal to the product of the Avogadro
   constant and the (absolute value of the) charge on an electron; it
   is 9.648 670 x 10^4 C/mol.

Faraday's law (M. Faraday)

   The line integral of the electric flux around a closed curve is
   proportional to the instantaneous time rate of change of the 
   magnetic flux through a surface bounded by that closed curve.

Faraday's laws of electrolysis (M. Faraday)

   1.  The amount of chemical change during electrolysis is 
       proportional to the charge passed.
   2.  The charge required to deposit or liberate a mass is 
       proportional to the charge of the ion, the mass, and 
       inversely proprtional to the relative ionic mass.  The 
       constant of proportionality is the Faraday constant.

Faraday's laws of electromagnetic induction (M. Faraday)

   1.  An electromotive force is induced in a conductor when the 
       magnetic field surrounding it changes.
   2.  The magnitude of the electromotive force is proportional to 
       the rate of change of the field.
   3.  The sense of the induced electromotive force depends on the 
       direction of the rate of the change of the field.

Fermat's principle; principle of least time (P. de Fermat)

   The principle, put forth by P. de Fermat, states that the path 
   taken by a ray of light between any two points in a system is 
   always the path that takes the least time.

Gauss' law (K.F. Gauss)

   The electric flux through a closed surface is proportional to the
   algebraic sum of electric charges contained within that closed
   surface.

Gauss' law for magnetic fields (K.F. Gauss)

   The magnetic flux through a closed surface is zero; no magnetic
   charges exist.

grandfather paradox

   A paradox proposed to discount time travel and show why it
   violates causality.  Say that your grandfather builds a time
   machine.  In the present, you use his time machine to go back in
   time a few decades to a point before he married his wife (your
   grandmother).  You meet him to talk about things, and an argument
   ensues (presumably he doesn't believe that you're his
   grandson/granddaughter), and you accidentally kill him.
       If he died before he met your grandmother and never had
   children, then your parents could certainly never have met (one of
   them didn't exist!) and could never have given birth to you.  In
   addition, if he didn't live to build his time machine, what are
   you doing here in the past alive and with a time machine, if you
   were never born and it was never built?

Hall effect

   When charged particles flow through a tube which has both an 
   electric field and a magnetic field (perpendicular to the electric 
   field) present in it, only certain velocities of the charged 
   particles are preferred, and will make it undeviated through the 
   tube; the rest will be deflected into the sides.  This effect is 
   exploited in such devices as the mass spectrometer and in the 
   Thompson experiment.  This is called the Hall effect.

Hawking radiation (S.W. Hawking; 1973)

   The theory that black holes emit radiation like any other hot 
   body.  Virtual particle-antiparticle pairs are constantly being 
   created in supposedly empty space.  Every once in a while, one 
   will be created in the vicinity of a black hole's event horizon.  
   One of these particles might be catpured by the black hole, 
   forever trapped, while the other might escape the black hole's 
   gravity.  The trapped particle, which would have negative energy 
   (by definition), would reduce the mass of the black hole, and the 
   particle which escaped would have positive energy.  Thus, from a 
   distant, one would see the black hole's mass decrease and a 
   particle escape the vicinity; it would appear as if the black hole
   were emitting radiation.  The rate of emission has a negative
   relationship with the mass of the black hole; massive black holes
   emit radiation relatively slowly, while smaller black holes emit
   radiation -- and thus decrease their mass -- more rapidly.

Heisenberg uncertainty principle (W. Heisenberg; 1927)

   A principle, central to quantum mechanics, which states that the
   momentum (mass times velocity) and the position of a particle
   cannot both be known to infinite accuracy; the more you know about
   one, the lest you know about the other.
       It can be illustrated in a fairly clear way as follows:  To
   see something (let's say an electron), we have to fire photons at
   it, so they bounce off and come back to us, so we can "see" it.
   If you choose low-frequency photons, with a low energy, they do
   not impart much momentum to the electron, but they give you a very
   fuzzy picture, so you have a higher uncertainty in position so
   that you can have a higher certainty in momentum.  On the other
   hand, if you were to fire very high-energy photons (x-rays or
   gammas) at the electron, they would give you a very clear picture
   of where the electron is (high certainty in position), but would
   impart a great deal of momentum to the electron (higher 
   uncertainty in momentum).
       In a more generalized sense, the uncertainty principle tells 
   us that the act of observing changes the observed in fundamental 
   way.

Hooke's law (R. Hooke)

   The stress applied to any solid is proportional to the strain it 
   produces within the elastic limit for that solid.  The constant of 
   that proportionality is the Young modulus of elasticity for that 
   substance.

Hubble constant; H` (E.P. Hubble; 1925)

   The constant which determines the relationship between the 
   distance to a galaxy and its velocity of recession due to the 
   expansion of the Universe.  It is not known to great accuracy, but 
   is believed to lie between 49 and 95 km/s/Mpc.

Hubble's law (E.P. Hubble; 1925)

   A relationship discovered between distance and radial velocity.  
   The further away a galaxy is away from is, the faster it is 
   receding away from us.  The cause is interpreted as the expansion 
   of space itself.

Huygens' construction; Huygens' principle (C. Huygens)

   The mechanics propagation of a wave of light is equivalent to
   assuming that every point on the wavefront acts as point source of
   wave emission.

ideal gas constant; universal molar gas constant; R

   The constant that appears in the ideal gas equation.  It is equal
   to 8.314 34 J/K/mol.

ideal gas equation

   An equation which sums up the ideal gas laws in one simple
   equation.  It states that the product of the pressure and the
   volume of a sample of ideal gas is equal to the product of the
   amount of gas present, the temperature of the sample, and the
   ideal gas constant.

ideal gas laws

   Boyle's law.  The pressure of an ideal gas is inversely
       proportional to the volume of the gas at constant temperature.
   Charles' law.  The volume of an ideal gas is directly proportional
       to the thermodynamic temperature at constant pressure.
   The pressure law.  The pressure of an ideal gas is directly
       proportional to the thermodynamic temperature at constant
       volume.

Joule-Thomson effect; Joule-Kelvin effect (J. Joule, W. Thomson)

   The change in temperature that occurs when a gas expands into a
   region of lower pressure.

Joule's laws

   Joule's first law.  The heat produced when an electric current
       flows through a resistance for a specified time is equal to
       the square of the current multiplied by the resistivity
       multiplied by the time.
   Joule's second law.  The internal energy of an ideal gas is
       independent of its volume and pressure, depending only on its
       temperature.

Josephson effects (B.D. Josephson; 1962)

   Electrical effects observed when two superconducting materials are
   separated by a thin layer of insulating material.

Kepler's laws (J. Kepler)

   Kepler's first law.  A planet orbits the Sun in an ellipse with
       the Sun at one focus.
   Kepler's second law.  A ray directed from the Sun to a planet
       sweeps out equal areas in equal times.
   Kepler's third law.  The square of the period of a planet's orbit 
       is proportional to the cube of that planet's semimajor axis; 
       the constant of proportionality is the same for all planets.

Kerr effect (J. Kerr; 1875)

   The ability of certain substances to differently refract light 
   waves whose vibrations are in different directions when the 
   substance is placed in an electric field.

Kirchhoff's law of radiation (G.R. Kirchhoff)

   The emissivity of a body is equal to its absorptance at the same 
   temperature.

Kirchhoff's rules (G.R. Kirchhoff)

   The loop rule.  The sum of the potential differences encountered 
       in a round trip around any closed loop in a circuit is zero.
   The point rule.  The sum of the currents toward a branch point is 
       equal to the sum of the currents away from the same branch 
       point.

Kohlrausch's law (F. Kohlrausch)

   If a salt is dissolved in water, the conductivity of the solution 
   is the sum of two values -- one depending on the positive ions and 
   the other on the negative ions.

Lambert's laws (J.H. Lambert)

   Lambert's first law.  The illuminance on a surface illuminated by
       light falling on it perpendicularly from a point source is
       proportional to the inverse square of the distance between the
       surface and the source.
   Lambert's second law.  If the rays meet the surface at an angle,
       then the illuminance is also proportional to the cosine of the
       angle with the normal.
   Lambert's third law.  The luminous intensity of light decreases
       exponentially with the distance that it travels through an
       absorbing medium.

Landauer's principle

   A principle which states that it doesn't explicitly take energy to
   compute data, but rather it takes energy to _erase_ any data,
   since erasure is an important step in computation.

Laplace's equation (P. Laplace)

   For steady-state heat conduction in one dimension, the temperature
   distrubtion is the solution to Laplace's equation, which states
   that the second derivative of temperature with respect to
   displacement is zero.

Laue pattern (M. von Laue)

   The pattern produced on a photographic film when high-frequency 
   electromagnetic waves (such as x-rays) are fired at a crystalline 
   solid.

laws of conservation

   A law which states that, in a closed system, the total quantity of 
   something will not increase or decrease, but remain exactly the 
   same.  For physical quantities, it states that something can 
   neither be created nor destroyed.
       The most commonly seen are the laws of conservation of mass- 
   energy (formerly two conservation laws before A. Einstein), of 
   electric charge, of linear momentum, and of angular momentum.  
   There are several others that deal more with particle physics, 
   such as conservation of baryon number, of strangeness, etc., which 
   are conserved in some fundamental interactions but not others.

law of reflection

   For a wavefront intersecting a reflecting surface, the angle of 
   incidence is equal to the angle of reflection.

laws of black hole dynamics

   First law of black hole dynamics.  For interactions between black 
       holes and normal matter, the conservation laws of total
       energy, total momentum, angular momentum, and electric charge,
       hold.
   Second law of black hole dynamics.  With black hole interactions,
       or interactions between black holes and normal matter, the sum
       of the surface areas of all black holes involved can never
       decrease.

laws of thermodynamics

   First law of thermodynamics.  The change in internal energy of a
       system is the sum of the heat transferred to or from the
       system and the work done on or by the system.
   Second law of thermodynamics.  The entropy -- a measure of the
       unavailability of a system's energy to do useful work -- of a
       closed system tends to increase with time.
   Third law of thermodynamics.  For changes involving only perfect
       crystalline solids at absolute zero, the change of the total
       entropy is zero.
   Zeroth law of thermodynamics.  If two bodies are each in thermal
       equilibrium with a third body, then all three bodies are in
       thermal equilibrium with each other.

Lawson criterion (J.D. Lawson)

   A condition for the release of energy from a thermonuclear 
   reactor.  It is usually stated as the minimum value for the 
   product of the density of the fuel particles and the containment 
   time for energy breakeven.  For a half-and-half mixture of 
   deuterium and tritium at ignition temperature, n_G tau is between 
   10^14 and 10^15 s/cm^3.

Le Chatelier's principle (H. Le Chatelier; 1888)

   If a system is in equilibrium, then any change imposed on the 
   system tends to shift the equilibrium to reduce the effect of that 
   applied change.

Lenz's law (H.F. Lenz; 1835)

   An induced electric current always flows in such a direction that 
   it opposes the change producing it.

Loschmidt constant; Loschmidt number; N_L

   The number of particles per unit volume of an ideal gas at 
   standard temperature and pressure.  It has the value 2.687 19 x 
   10^25 m^-3.

lumeniferous aether

   A substance, which filled all the empty spaces between matter, 
   which was used to explain what medium light was "waving" in.  Now
   it has been discredited, as Maxwell's equations imply that
   electromagnetic radiation can propagate in a vacuum, since they
   are disturbances in the electromagnetic field rather than
   traditional waves in some substance, such as water waves.

Lyman series

   The series which describes the emission spectrum of hydrogen when
   electrons are jumping to the ground state.  All of the lines are
   in the ultraviolet.

Mach's principle (E. Mach; 1870s)

   The inertia of any particular particle or particles of matter is
   attributable to the interaction between that piece of matter and
   the rest of the Universe.  Thus, a body in isolation would have no
   inertia.

Magnus effect

   A rotating cylinder in a moving fluid drags some of the fluid
   around with it, in its direction of rotation.  This increases the
   speed in that region, and thus the pressure is lower.
   Consequently, there is a net force on the cylinder in that
   direction, perpendicular to the flow of the fluid.  This is called
   the Magnus effect.

Malus's law (E.L. Malus)

   The light intensity travelling through a polarizer is proportional
   to the initial intensity of the light and the square of the cosine
   of the angle between the polarization of the light ray and the
   polarization axis of the polarizer.

Maxwell's demon (J.C. Maxwell)

   A thought experiment illustrating the concepts of entropy.  We
   have a container of gas which is partitioned into two equal sides;
   each side is in thermal equilibrium with the other.  The walls
   (and the partition) of the container are a perfect insulator.
       Now imagine there is a very small demon who is waiting at the
   partition next to a small trap door.  He can open and close the
   door with negligible work.  Let's say he opens the door to allow a
   fast-moving molecule to travel from the left side to the right, or
   for a slow-moving molecule to travel from the right side to the
   left, and keeps it closed for all other molecules.  The next
   effect would be a flow of heat -- from the left side to the right
   -- even though the container was in thermal equilibrium.  This is
   clearly a violation of the second law of thermodynamics.
       So where did we go wrong?  It turns out that information has 
   to do with entropy as well.  In order to sort out the molecules 
   according to speeds, the demon would be having to keep a memory of 
   them -- and it turns out that increase in entropy of the simple 
   maintenance of this simple memory would more than make up for the 
   decrease in entropy due to the heat flow.

Maxwell's equations (J.C. Maxwell; 1864)

   Four elegant equations which describe classical electromagnetism 
   in all its splendor.  They are:
       Gauss' law.  The electric flux through a closed surface is 
           proportional to the algebraic sum of electric charges 
           contained within that closed surface.
       Gauss' law for magnetic fields.  The magnetic flux through a 
           closed surface is zero; no magnetic charges exist.
       Faraday's law.  The line integral of the electric flux around 
           a closed curve is proportional to the instantaneous time 
           rate of change of the magnetic flux through a surface 
           bounded by that closed curve.
       Ampere's law, modified form.  The line integral of the 
           magnetic flux around a closed curve is proportional to the 
           sum of two terms:  first, the algebraic sum of electric
           currents flowing through that closed curve; and second,
           the instantaneous time rate of change of the electric flux
           through a surface bounded by that closed curve.
   In addition to describing electromagnetism, his equations also
   predict that waves can propagate through the electromagnetic
   field, and would always propagate at the same speed -- these are
   electromagnetic waves.

Meissner effect (W. Meissner; 1933)

   The decrease of the magnetic flux within a superconducting metal
   when it is cooled below the critical temperature.  That is,
   superconducting materials reflect magnetic fields.

Michelson-Morley experiment (A.A. Michelson, E.W. Morley; 1887)

   Possibly the most famous null-experiment of all time, designed to
   verify the existence of the proposed "lumeniferous aether" through
   which light waves were thought to propagate.  Since the Earth
   moves through this aether, a lightbeam fired in the Earth's
   direction of motion would lag behind one fired sideways, where no
   aether effect would be present.  This difference could be detected
   with the use of an interferometer.
       The experiment showed absolutely no aether shift whatsoever, 
   where one should have been quite detectable.  Thus the aether 
   concept was discredited as was the constancy of the speed of 
   light.

Millikan oil drop experiment (R.A. Millikan)

   A famous experiment designed to measure the electronic charge.  
   Drops of oil were carried past a uniform electric field between 
   charged plates.  After charging the drop with x-rays, he adjusted 
   the electric field between the plates so that the oil drop was 
   exactly balanced against the force of gravity.  Then the charge on 
   the drop would be known.  Millikan did this repeatedly and found 
   that all the charges he measured came in integer multiples only of 
   a certain smallest value, which is the charge on the electron.

Newton's law of universal gravitation (Sir I. Newton)

   Two bodies attract each other with equal and opposite forces; the 
   magnitude of this force is proportional to the product of the two 
   masses and is also proportional to the inverse square of the 
   distance between the centers of mass of the two bodies.

Newton's laws of motion (Sir I. Newton)

   Newton's first law of motion.  A body continues in its state of 
       rest or of uniform motion unless it is acted upon by an
       external force.
   Newton's second law of motion.  For an unbalanced force acting on
       a body, the acceleration produces is proportional to the force
       impressed; the constant of proportionality is the inertial
       mass of the body.
   Newton's third law of motion.  In a system where no external
       forces are present, every action is always opposed by an equal
       and opposite reaction.

Ohm's law (G. Ohm; 1827)

   The ratio of the potential difference between the ends of a
   conductor to the current flowing through it is constant; the
   constant of proportionality is called the resistance, and is
   different for different materials.

Olbers' paradox (H. Olbers; 1826)

   If the Universe is infinite, uniform, and unchanging then the
   entire sky at night would be bright -- about as bright as the Sun.
   The further you looked out into space, the more stars there would
   be, and thus in any direction in which you looked your line-of-
   sight would eventually impinge upon a star.  The paradox is
   resolved by the Big Bang theory, which puts forth that the 
   Universe is not infinite, non-uniform, and changing.

Pascal's principle

   Pressure applied to an enclosed imcompressible static fluid is 
   transmitted undiminished to all parts of the fluid.

Paschen series

   The series which describes the emission spectrum of hydrogen when 
   the electron is jumping to the third orbital.  All of the lines 
   are in the infrared portion of the spectrum.

Pauli exclusion principle (W. Pauli; 1925)

   No two identical fermions in a system, such as electrons in an 
   atom, can have an identical set of quantum numbers.

Peltier effect (J.C.A. Peltier; 1834)

   The change in temperature produced at a junction between two 
   dissimilar metals or semiconductors when an electric current 
   passes through the junction.

permeability of free space; magnetic constant; mu_0

   The ratio of the magnetic flux density in a substance to the 
   external field strength for vacuum.  It is equal to 4 pi x 10^-7 
   H/m.

permittivity of free space; electric constant; epsilon_0

   The ratio of the electric displacement to the intensity of the
   electric field producing it in vacuum.  It is equal to 8.854 x
   10^-12 F/m.

Pfund series

   The series which describes the emission spectrum of hydrogen when
   the electron is jumping to the fifth orbital.  All of the lines
   are in the infrared portion of the spectrum.

photoelectric effect

   An effect explained by A. Einstein that demonstrate that light
   seems to be made up of particles, or photons.  Light can excite
   electrons (called photoelectrons) to be ejected from a metal.
   Light with a frequency below a certain threshold, at any
   intensity, will not cause any photoelectrons to be emitted from
   the metal.  Above that frequency, photoelectrons are emitted in
   proportion to the intensity of incident light.
       The reason is that a photon has energy in proportion to its
   wavelength, and the constant of proportionality is Planck's
   constant.  Below a certain frequency -- and thus below a certain
   energy -- the incident photons do not have enough energy to knock
   the photoelectrons out of the metal.  Above that threshold energy,
   called the workfunction, photons will knock the photoelectrons out
   of the metal, in proportion to the number of photons (the
   intensity of the light).  At higher frequencies and energies, the
   photoelectrons ejected obtain a kinetic energy corresponding to
   the difference between the photon's energy and the workfunction.

Planck constant; h

   The fundamental constant equal to the ratio of the energy of a
   quantum of energy to its frequency.  It is the quantum of action.
   It has the value 6.626 196 x 10^-34 J s.

Planck's radiation law

   A law which more accurately described blackbody radiation because
   it assumed that electromagnetic radiation is quantized.

principle of causality

   The principle that cause must always preceed effect.  More
   formally, if an event A ("the cause") somehow influences an event
   B ("the effect") which occurs later in time, then event B cannot
   in turn have an influence on event A.
       The principle is best illustrated with an example.  Say that
   event A constitutes a murderer making the decision to kill his
   victim, and that event B is the murderer actually committing the 
   act.  The principle of causality puts forth that the act of 
   murder cannot have an influence on the murderer's decision to 
   commit it.  If the murderer were to somehow see himself committing 
   the act and change his mind, then a murder would have been 
   committed in the future without a prior cause (he changed his 
   mind).  This represents a causality violation.  Both time travel 
   and faster-than-light travel both imply violations of causality, 
   which is why most physicists think they are impossible, or at 
   least impossible in the general sense.

principle of determinism

   The principle that if one knows the state to an infinite accuracy 
   of a system at one point in time, one would be able to predict the 
   state of that system with infinite accuracy at any other time, 
   past or future.  For example, if one were to know all of the 
   positions and velocities of all the particles in a closed system, 
   then determinism would imply that one could then predict the 
   positions and velocities of those particles at any other time.  
   This principle has been disfavored due to the advent of quantum 
   mechanics, where probabilities take an important part in the 
   actions of the subatomic world, and the Heisenberg uncertainty
   principle implies that one cannot know both the position and
   velocity of a particle to arbitrary precision.

Rayleigh criterion; resolving power

   A criterion for the how finely a set of optics may be able to
   distinguish.  It begins with the assumption that central ring of
   one image should fall on the first dark ring of the other.
   relativity principle; principle of relativity

Rydberg formula

   A formula which describes all of the characteristics of hydrogen's
   spectrum, including the Balmer, Lyman, Paschen, Brackett, and
   Pfund series.

Schroedinger's cat (E. Schroedinger; 1935)

   A thought experiment designed to illustrate the counterintuitive
   and strange notions of reality that come along with quantum
   mechanics.
       A cat is sealed inside a closed box; the cat has ample air,
   food, and water to survive an extended period.  This box is
   designed so that no information (i.e., sight, sound, etc.) can
   pass into or out of the box -- the cat is totally cut off from
   your observations.  Also inside the box with the poor kitty 
   (apparently Schroedinger was not too fond of felines) is a phial 
   of a gaseous poison, and an automatic hammer to break it, flooding 
   the box and killing the cat.  The hammer is hooked up to a Geiger 
   counter; this counter is monitoring a radioactive sample and is 
   designed to trigger the hammer -- killing the cat -- should a 
   radioactive decay be detected.  The sample is chosen so that 
   after, say, one hour, there stands a fifty-fifty chance of a decay 
   occurring.
       The question is, what is the state of the cat after that one 
   hour has elapsed?  The intuitive answer is that the cat is either 
   alive or dead, but you don't know which until you look.  But it 
   _is_ one of them.  Quantum mechanics, on the other hands, says 
   that the wavefunction describing the cat is in a superposition of 
   states:  the cat is, in fact, fifty per cent alive and fifty per 
   cent dead; it is both.  Not until one looks and "collapses the 
   wavefunction" is the Universe forced to choose either a live cat 
   or a dead cat and not something in between.
       This indicates that observation also seems to be an important 
   part of the scientific process -- quite a departure from the 
   absolutely objective, deterministic way things used to be with
   Newton.

Schwarzchild radius

   The radius that a spherical mass must be compressed to in order to
   transform it into a black hole; that is, the radius of compression
   where the escape velocity at the surface would reach lightspeed.

Snell's law; law of refraction

   A relation which relates the change in incidence angle of a
   wavefront due to refraction between two different media.

speed of light _in vacuo_; c

   One of the postulates of A. Einstein's special theory of
   relativity, which puts forth that the speed of light in vacuum --
   often written c, and which has the value 299 792 458 m/s -- is
   measured as the same speed to all observers, regardless of their
   relative motion.  That is, if I'm travelling at 0.9 c away from
   you, and fire a beam of light in that direction, both you and I
   will independently measure the speed of that beam as c.
       One of the results of this postulate (one of the predictions
   of special relativity is that no massive particle can be
   accelerated to (or beyond) lightspeed, and thus the speed of light
   also represents the ultimate cosmic speed limit.  Only massless 
   particles (photons, gravitons, and possibly neutrinos, should they 
   indeed prove to be massless) travel at lightspeed, and all other 
   particles must travel at slower speeds.

spin-orbit effect

   An effect that causes atomic energy levels to be split because 
   electrons have intrinsic angular momentum (spin) in addition to 
   their extrinsic orbital angular momentum.

static limit

   The distance from a rotating black hole where no observer can 
   possibly remain at rest (with respect to the distant stars) 
   because of inertial frame dragging.

Stefan-Boltzmann constant; sigma (Stefan, L. Boltzmann)

   The constant of proportionality present in the Stefan-Boltzmann 
   law.  It is equal to 5.6697 x 10^-8 W/m^2/K^4.

Stefan-Boltzmann law (Stefan, L. Boltzmann)

   The radiated power (rate of emission of electromagnetic energy) of 
   a hot body is proportional to the emissivity, an efficiency 
   rating, the radiating surface area, and the fourth power of the 
   thermodynamic temperature.  The constant of proportionality is the 
   Stefan-Boltzmann constant.

Stern-Gerlach experiment (O. Stern, W. Gerlach; 1922)

   An experiment that demonstrates the features of spin (intrinsic
   angular momentum) as a distinct entity apart from orbital angular
   momentum.

superconductivity

   The phenomena by which, at sufficiently low temperatures, a
   conductor can conduct charge with zero resistance.

superfluidity

   The phenomena by which, at sufficiently low temperatures, a fluid
   can flow with zero viscosity.

superposition principle of forces

   The net force on a body is equal to the sum of the forces
   impressed upon it.

superposition principle of states

   The resultant quantum mechnaical wavefunction due to two or more
   individual wavefunctions is the sum of the individual
   wavefunctions.

superposition principle of waves

   The resultant wave function due to two or more individual wave
   functions is the sum of the individual wave functions.

Thomson experiment; Kelvin effect (Sir W. Thomson [later Lord Kelvin])

   When an electric current flows through a conductor whose ends are
   maintained at different temperatures, heat is released at a rate
   approximately proportional to the product of the current and the
   temperature gradient.

twin paradox

   One of the most famous "paradoxes" in history, predicted by A.
   Einstein's special theory of relativity.  Take two twins, born on
   the same date on Earth.  One, Albert, leaves home for a trip
   around the Universe at very high speeds (very close to that of
   light), while the other, Henrik, stays at home at rests.  Special
   relativity predicts that when Albert returns, he will find himself
   much younger than Albert.
       That is actually not the paradox.  The paradox stems from
   attempting to naively analyze the situation to figure out why.
   From Henrik's point of view (and from everyone else on Earth),
   Albert seems to speed off for a long time, linger around, and then
   return.  Thus he should be the younger one, which is what we see.
   But from Albert's point of view, it's Henrik (and the whole of the
   Earth) that are travelling, not he.  According to special 
   relativity, if Henrik is moving relative to Albert, then Albert 
   should measure his clock as ticking slower -- and thus Henrik is 
   the one who should be younger.  But this is not what happens.
       So what's wrong with our analysis?  The key point here is that 
   the symmetry was broken.  Albert did something that Henrik did 
   not -- Albert accelerated in turning around.  Henrik did no 
   accelerating, as he and all the other people on the Earth can 
   attest to (neglecting gravity).  So Albert broke the symmetry, and 
   when he returns, _he_ is the younger one.

ultraviolet catastrophe

   A shortcoming of the Rayleigh-Jeans formula, which attempted to 
   describe the radiancy of a blackbody at various frequencies of the 
   electromagnetic spectrum.  It was clearly wrong because as the 
   frequency increased, the radiancy increased without bound; 
   something quite not observed; this was dubbed the "ultraviolet 
   catastrophe."  It was later reconciled and explained by the 
   introduction of Planck's radiation law.

universal constant of gravitation; G

   The constant of proportionality in Newton's law of universal 
   gravitation and which plays an analogous role in A. Einstein's
   general relativity.  It is equal to 6.664 x 10^-11 N m^2/kg^2.

van der Waals force (J.D. van der Waals)

   Forces responsible for the non-ideal behavior of gases, and for
   the lattice energy of molecular crystals.  There are three causes:
   dipole-dipole interaction; dipole-induced dipole moments; and
   dispersion forces arising because of small instantaneous dipoles
   in atoms.

wave-particle duality

   The principle of quantum mechanics which implies that light (and,
   indeed, all other subatomic particles) sometimes act like a wave,
   and sometime act like a particle, depending on the experiment you
   are performing.  For instance, low frequency electromagnetic
   radiation tends to act more like a wave than a particle; high
   frequency electromagnetic radiation tends to act more like a
   particle than a wave.

Widenmann-Franz law

   The ratio of the thermal conductivity of any pure metal to its
   electrical conductivity is approximately constant for any given
   temperature.  This law holds fairly well except at low
   temperatures.

Wien's displacement law

   For a blackbody, the product of the wavelength corresponding to 
   the maximum radiancy and the thermodynamic temperature is a 
   constant.  As a result, as the temperature rises, the maximum of 
   the radiant energy shifts toward the shorter wavelength (higher 
   frequency and energy) end of the spectrum.

Woodward-Hoffmann rules

   Rules governing the formation of products during certain types of 
   organic reactions.

Young's experiment; double-slit experiment (T. Young; 1801)

   A famous experiment which shows the wave nature of light (and 
   indeed of other particles).  Light is passed from a small source 
   onto an opaque screen with two thin slits.  The light is refracted 
   through these slits and develops an interference pattern on the 
   other side of the screen.

Zeeman effect; Zeeman line splitting (P. Zeeman; 1896)

   The splitting of the lines in a spectrum when the source is 
   exposed to a magnetic field.

maximum radiancy and the thermodynamic temperature is a

   constant.  As a result, as the temperature rises, the maximum of 
   the radiant energy shifts toward the shorter wavelength (higher 
   frequency and energy) end of the spectrum.

Woodward-Hoffmann rules Rules governing the formation of products during certain types of organic reactions.

Young's experiment; double-slit experiment (T. Young; 1801)

A famous experiment which shows the wave nature of light (and indeed of other particles). Light is passed from a small source onto an opaque screen with two thin slits. The light is refracted through these slits and develops an interference pattern on the other side of the screen.

Zeeman effect; Zeeman line splitting (P. Zeeman; 1896)

The splitting of the lines in a spectrum when the source is exposed to a magnetic field.