Физические законы, переменные, принципы

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Municipal Liceum ? 57

Laws, rules, principles, effects, paradoxes, limits, constants,
experiments, & thought-experiments in physics.

Pupil : Morozov Michael


1998Ampere’s law (A.M. Ampere)

The line integral of the magnetic flux around a closed curve
isproportional to the algebraic sum of electric currents flowingthrough
that closed curve. This was later modified to add a second term when
it wasincorporated 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; only those favorable to
intelligent life would actually 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 (D.F.J. Arago)

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

Archimedes’ principle

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

Atwood’s machine

A weight-and-pulley system devised to measure the acceleration dueto
gravity at Earth’s surface by measuring the net acceleration ofa 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 whichis
at standard temperature and pressure. It is equal to about6.022 52 x
10^23 mol^-1.

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

Equal volumes of all gases at the same temperature and
pressurecontain equal numbers of molecules. It is, in fact, only true
forideal gases.

Balmer series (J. Balmer; 1885)

An equation which describes the emission spectrum of hydrogen whenan
electron is jumping to the second orbital; four of the linesare in the
visible spectrum, and the remainder are in theultraviolet.

Baryon decay

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

Bernoulli’s equation

An equation which states that an irrotational fluid flowingthrough a
pipe flows at a rate which is inversely proportional tothe
cross-sectional area of the pipe. That is, if the pipeconstricts, the
fluid flows faster; if it widens, the fluid flowsslower.

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

A theory put forth to explain both superconductivity
andsuperfluidity. It suggests that in the superconducting
(orsuperfluid) state electrons form Cooper pairs, where two electronsact
as a single unit. It takes a nonzero amount of energy tobreak such
pairs, and the imperfections in the superconductingsolid (which would
normally lead to resistance) are incapable ofbreaking the pairs, so no
dissipation occurs and there is noresistance.

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

A law which describes the contributions to a magnetic field by
anelectric current. It is analogous to Coulomb’s law forelectrostatics.

Blackbody radiation

The radiation — the radiance at particular frequencies all
acrossthe spectrum — produced by a blackbody — that is, a
perfectradiator (and absorber) of heat. Physicists had
difficultyexplaining it until Planck introduced his quantum of action.

Bode’s law

A mathematical formula which generates, with a fair amount
ofaccuracy, the semimajor axes of the planets in order out from theSun.
Write down the sequence 0, 3, 6, 12, 24, . . . and then add4 to each
term. Then divide each term by 10. This is intended togive you the
positions of the planets measured in astronomicalunits.

Bode’s law had no theoretical justification when it was
firstintroduced; it did, however, agree with the
soon-to-be-discoveredplanet 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
similarorbits (2.8 au actual for Ceres; 2.8 au predicted). However,
theseries seems to skip over Neptune’s orbit.

Bohr magneton (N. Bohr)

The quantum of magnetic moment.

Bohr radius (N. Bohr)

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

Boltzmann constant; k (L. Boltzmann)

A constant which describes the relationship between temperatureand
kinetic energy for molecules in an ideal gas. It is equal to1.380 622 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
atconstant temperature is a constant.

Brackett series (Brackett)

The series which describes the emission spectrum of hydrogen whenthe
electron is jumping to the fourth orbital. All of the linesare 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 thelayers
of atoms or ions are regularly separated, the maximumintensity of the
reflected ray occurs when the sine of thecompliment of the angle of
incidence is equal to an integermultiplied by the wavelength of x-rays
divided by twice thedistance between layers of atoms or ions.

Brewster’s law (D. Brewster)

The extent of the polarization of light reflected from atransparent
surface is a maximum when the reflected ray is atright angles to the
refracted ray.

Brownian motion (R. Brown; 1827)

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

Carnot’s theorem (S. Carnot)

The theorem which states that no engine operating between
twotemperatures 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
inuniform circular motion. One feels a “force” outward from thecenter
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 neutronstar.

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

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

Cherenkov radiation (P.A. Cherenkov)

Radiation emitted by a massive particle which is moving fasterthan
light in the medium through which it is travelling. Noparticle can
travel faster than light in vacuum, but the speed oflight in other
media, such as water, glass, etc., are considerablylower. Cherenkov
radiation is the electromagnetic analogue of thesonic boom, though
Cherenkov radiation is a shockwave set up inthe electromagnetic field.

Complementarity principle (N. Bohr)

The principle that a given system cannot exhibit both
wave-likebehavior 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 asystem, but
no experiment will reveal both simultaneously.

Compton effect (A.H. Compton; 1923)

An effect that demonstrates that photons (the quantum
ofelectromagnetic radiation) have momentum. A photon fired at
astationary particle, such as an electron, will impart momentum tothe
electron and, since its energy has been decreased, willexperience 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 atdifferent
latitutdes (maximum at the equator, zero at the poles).

correspondence principle.

The principle that when a new, more specialized theory is putforth,
it must reduce to the more general (and usually simpler)theory under
normal circumstances. There are correspondenceprinciples for general
relativity to special relativity andspecial relativity to Newtonian
mechanics, but the most widelyknown correspondence principle (and
generally what is meant whenone says “correspondence principle”) is that
of quantum mechanicsto classical mechanics.

Cosmic background radiation; primal glow

The background of radiation mostly in the frequency range 3 x10^11
to 3 x 10^8 Hz discovered in space in 1965. It is believedto be the
cosmologically redshifted radiation released by the BigBang itself.
Presently it has an energy density in empty space ofabout 4 x 10^-14

cosmological redshift

An effect where light emitted from a distant source
appearsredshifted because of the expansion of space itself. Compare
withthe Doppler effect.

Coulomb’s law

The primary law for electrostatics, analogous to Newton’s law
ofuniversal gravitation. It states that the force between two
pointcharges is proportional to the algebraic product of theirrespective
charges as well as proportional to the inverse squareof the distance
between them.

CPT theorem

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

A more general form of Curie’s law, which states that
thesusceptibility of a paramagnetic substance is inverselyproportional
to the thermodynamic temperature of the substanceless the Weiss
constant, a characteristic of that substance.

Curie’s law (P. Curie)

The susceptibility of a paramagnetic substance is
inverselyproportional 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 sumof
the partial pressures of its components; that is, the sum ofthe
pressures that each component would exert if it were presentalone 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
ofelectrons; diffraction patterns were observed by an electron
beampenetrating 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 inverselyproportional to
its momentum, where the constant ofproportionality is the Planck

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 timesthe
gas constant.

Einstein-Podolsky-Rosen effect

Consider the following quantum mechanical thought-experiment:Take a
particle which is at rest and has spin zero. Itspontaneously decays
into two fermions (spin 1/2 particles), whichstream away in opposite
directions at high speed. Due to the lawof conservation of spin, we
know that one is a spin +1/2 and theother is spin -1/2. Which one is
which? According to quantummechanics, neither takes on a definite state
until it is observed(the wavefunction is collapsed).

The EPR effect demonstrates that if one of the particles isdetected,
and its spin is then measured, then the other particle– no matter where
it is in the Universe — instantaneously isforced to choose as well and
take on the role of the otherparticle. This illustrates that certain
kinds of quantuminformation travel instantaneously; not everything is
limited bythe speed of light.

However, it can be easily demonstrated that this effect doesnot 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
fundamentallyindistinguishable from a gravitational field. In other
words, ifyou are in an elevator which is utterly sealed and protected
fromthe outside, so that you cannot “peek outside,” then if you feel
aforce (weight), it is fundamentally impossible for you to saywhether
the elevator is present in a gravitational field, orwhether the elevator
has rockets attached to it and isaccelerating “upward.”

The equivalence principle predicts interesting generalrelativistic
effects because not only are the twoindistinguishable to human
observers, but also to the Universe aswell, in a way — any effect that
takes place when an observer isaccelerating should also take place in a
gravitational field, andvice versa.


The region around a rotating black hole, between the event
horizonand the static limit, where rotational energy can be
extractedfrom the black hole.

Event horizon

The radius of surrounding a black hole at which a particle wouldneed
an escape velocity of lightspeed to escape; that is, thepoint 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
Avogadroconstant and the (absolute value of the) charge on an electron;
itis 9.648 670 x 10^4 C/mol.

Faraday’s law (M. Faraday)

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

Faraday’s laws of electrolysis (M. Faraday)

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

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

An electromotive force is induced in a conductor when the magnetic
field surrounding it changes.

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 pathtaken
by a ray of light between any two points in a system isalways the path
that takes the least time.

Fermi paradox

E. Fermi’s conjecture, simplified with the phrase, “Where arethey?”
questioning that if the Galaxy is filled with intelligentand
technological civilizations, why haven’t they come to us yet?There are
several possible answers to this question, but since weonly have the
vaguest idea what the right conditions for life andintelligence in our
Galaxy, it and Fermi’s paradox are no morethan speculation.

Gauss’ law (K.F. Gauss)

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

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

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

Grandfather paradox

A paradox proposed to discount time travel and show why itviolates
causality. Say that your grandfather builds a timemachine. In the
present, you use his time machine to go back intime a few decades to a
point before he married his wife (yourgrandmother). You meet him to
talk about things, and an argumentensues (presumably he doesn’t believe
that you’re hisgrandson/granddaughter), and you accidentally kill him.

If he died before he met your grandmother and never hadchildren,
then your parents could certainly never have met (one ofthem didn’t
exist!) and could never have given birth to you. Inaddition, if he
didn’t live to build his time machine, what areyou doing here in the
past alive and with a time machine, if youwere never born and it was
never built?

Hall effect

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

Hawking radiation (S.W. Hawking; 1973)

The theory that black holes emit radiation like any other hotbody.
Virtual particle-antiparticle pairs are constantly beingcreated in
supposedly empty space. Every once in a while, onewill 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’sgravity. The trapped particle, which would
have negative energy(by definition), would reduce the mass of the black
hole, and theparticle which escaped would have positive energy. Thus,
from adistant, one would see the black hole’s mass decrease and
aparticle escape the vicinity; it would appear as if the black holewere
emitting radiation. The rate of emission has a negativerelationship
with the mass of the black hole; massive black holesemit radiation
relatively slowly, while smaller black holes emitradiation — and thus
decrease their mass — more rapidly.

Heisenberg uncertainty principle (W. Heisenberg; 1927)

A principle, central to quantum mechanics, which states that
themomentum (mass times velocity) and the position of a particlecannot
both be known to infinite accuracy; the more you know aboutone, the lest
you know about the other.

It can be illustrated in a fairly clear way as follows: Tosee
something (let’s say an electron), we have to fire photons atit, 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 donot impart much
momentum to the electron, but they give you a veryfuzzy picture, so you
have a higher uncertainty in position sothat you can have a higher
certainty in momentum. On the otherhand, if you were to fire very
high-energy photons (x-rays orgammas) at the electron, they would give
you a very clear pictureof where the electron is (high certainty in
position), but wouldimpart a great deal of momentum to the electron
(higheruncertainty in momentum). In a more generalized sense, the
uncertainty principle tellsus that the act of observing changes the
observed in fundamentalway.

Hooke’s law (R. Hooke)

The stress applied to any solid is proportional to the strain
itproduces within the elastic limit for that solid. The constant ofthat
proportionality is the Young modulus of elasticity for thatsubstance.

Hubble constant; H_0 (E.P. Hubble; 1925)

The constant which determines the relationship between thedistance
to a galaxy and its velocity of recession due to theexpansion of the
Universe. It is not known to great accuracy, butis 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 isreceding away
from us. The constant of proportionality isHubble’s constant, H_0. The
cause is interpreted as the expansionof space itself.

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

The mechanics propagation of a wave of light is equivalent
toassuming that every point on the wavefront acts as point source ofwave

Ideal gas constant; universal molar gas constant; R

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

Ideal gas equation

An equation which sums up the ideal gas laws in one simpleequation.
It states that the product of the pressure and thevolume of a sample of
ideal gas is equal to the product of theamount of gas present, the
temperature of the sample, and theideal 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
aregion 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

Josephson effects (B.D. Josephson; 1962)

Electrical effects observed when two superconducting materials
areseparated 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 lightwaves
whose vibrations are in different directions when thesubstance 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

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 solutionis
the sum of two values — one depending on the positive ions andthe 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

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

Landauer’s principle

A principle which states that it doesn’t explicitly take energy
tocompute 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
temperaturedistribution is the solution to Laplace’s equation, which
statesthat the second derivative of temperature with respect
todisplacement is zero.

Laue pattern (M. von Laue)

The pattern produced on a photographic film when
high-frequencyelectromagnetic waves (such as x-rays) are fired at a

Laws of conservation

A law which states that, in a closed system, the total quantity
ofsomething will not increase or decrease, but remain exactly thesame.
For physical quantities, it states that something canneither be created
nor destroyed.

The most commonly seen are the laws of conservation of mass-energy
(formerly two conservation laws before A. Einstein), ofelectric 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., whichare conserved in some fundamental
interactions but not others.

Law of reflection

For a wavefront intersecting a reflecting surface, the angle
ofincidence 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

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 thermonuclearreactor.
It is usually stated as the minimum value for theproduct of the density
of the fuel particles and the containmenttime for energy breakeven. For
a half-and-half mixture ofdeuterium and tritium at ignition temperature,
n_G tau is between10^14 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 thesystem
tends to shift the equilibrium to reduce the effect of thatapplied

Lenz’s law (H.F. Lenz; 1835)

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

Loschmidt constant; Loschmidt number; N_L

The number of particles per unit volume of an ideal gas atstandard
temperature and pressure. It has the value 2.687 19 x10^25 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. Nowit has been
discredited, as Maxwell’s equations imply thatelectromagnetic radiation
can propagate in a vacuum, since theyare disturbances in the
electromagnetic field rather thantraditional waves in some substance,
such as water waves.

Lyman series

The series which describes the emission spectrum of hydrogen
whenelectrons are jumping to the ground state. All of the lines arein
the ultraviolet.

Mach’s principle (E. Mach; 1870s)

The inertia of any particular particle or particles of matter
isattributable to the interaction between that piece of matter andthe
rest of the Universe. Thus, a body in isolation would have noinertia.

Magnus effect

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

Malus’s law (E.L. Malus)

The light intensity travelling through a polarizer is proportionalto
the initial intensity of the light and the square of the cosineof the
angle between the polarization of the light ray and thepolarization axis
of the polarizer.

Maxwell’s demon (J.C. Maxwell)

A thought experiment illustrating the concepts of entropy. Wehave 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 thepartition next to a small trap door.
He can open and close thedoor with negligible work. Let’s say he opens
the door to allow afast-moving molecule to travel from the left side to
the right, orfor a slow-moving molecule to travel from the right side to
theleft, and keeps it closed for all other molecules. The net
effectwould be a flow of heat — from the left side to the right —
eventhough the container was in thermal equilibrium. This is clearlya
violation of the second law of thermodynamics. So where did we go
wrong? It turns out that information hasto do with entropy as well. In
order to sort out the moleculesaccording to speeds, the demon would be
having to keep a memory ofthem — and it turns out that increase in
entropy of the simplemaintenance of this simple memory would more than
make up for thedecrease in entropy due to the heat flow.

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

Four elegant equations which describe classical electromagnetismin
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
alsopredict that waves can propagate through the electromagneticfield,
and would always propagate at the same speed — these areelectromagnetic

Meissner effect (W. Meissner; 1933)

The decrease of the magnetic flux within a superconducting metalwhen
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
toverify the existence of the proposed “lumeniferous aether”
throughwhich light waves were thought to propagate. Since the
Earthmoves through this aether, a lightbeam fired in the
Earth’sdirection of motion would lag behind one fired sideways, where
noaether effect would be present. This difference could be detectedwith
the use of an interferometer.

The experiment showed absolutely no aether shift whatsoever,where
one should have been quite detectable. Thus the aetherconcept was
discredited as was the constancy of the speed oflight.

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 betweencharged plates.
After charging the drop with x-rays, he adjustedthe electric field
between the plates so that the oil drop wasexactly balanced against the
force of gravity. Then the charge onthe drop would be known. Millikan
did this repeatedly and foundthat all the charges he measured came in
integer multiples only ofa 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;
themagnitude of this force is proportional to the product of the
twomasses and is also proportional to the inverse square of thedistance
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

Ohm’s law (G. Ohm; 1827)

The ratio of the potential difference between the ends of aconductor
to the current flowing through it is constant; theconstant of
proportionality is called the resistance, and isdifferent for different

Olbers’ paradox (H. Olbers; 1826)

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

Pascal’s principle

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

Paschen series

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

Pauli exclusion principle (W. Pauli; 1925)

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

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

The change in temperature produced at a junction between
twodissimilar metals or semiconductors when an electric currentpasses
through the junction.

permeability of free space; magnetic constant; mu_0

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

permittivity of free space; electric constant; epsilon_0

The ratio of the electric displacement to the intensity of
theelectric field producing it in vacuum. It is equal to 8.854 x10^-12

Pfund series

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

Photoelectric effect

An effect explained by A. Einstein that demonstrate that lightseems
to be made up of particles, or photons. Light can exciteelectrons
(called photoelectrons) to be ejected from a metal.Light with a
frequency below a certain threshold, at anyintensity, will not cause any
photoelectrons to be emitted fromthe metal. Above that frequency,
photoelectrons are emitted inproportion to the intensity of incident
light. The reason is that a photon has energy in proportion to
itswavelength, and the constant of proportionality is Planck’sconstant.
Below a certain frequency — and thus below a certainenergy — the
incident photons do not have enough energy to knockthe photoelectrons
out of the metal. Above that threshold energy,called the workfunction,
photons will knock the photoelectrons outof the metal, in proportion to
the number of photons (theintensity of the light). At higher
frequencies and energies, thephotoelectrons ejected obtain a kinetic
energy corresponding tothe difference between the photon’s energy and
the workfunction.

Planck constant; h

The fundamental constant equal to the ratio of the energy of
aquantum 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 becauseit
assumed that electromagnetic radiation is quantized.

Poisson spot (S.D. Poisson)

See Arago spot. Poisson predicted the existence of such a spot,and
actually used it to demonstrate that the wave theory of lightmust be in

Principle of causality

The principle that cause must always preceed effect. Moreformally,
if an event A (“the cause”) somehow influences an eventB (“the effect”)
which occurs later in time, then event B cannotin turn have an influence
on event A. The principle is best illustrated with an example. Say
thatevent A constitutes a murderer making the decision to kill
hisvictim, and that event B is the murderer actually committing theact.
The principle of causality puts forth that the act ofmurder cannot have
an influence on the murderer’s decision tocommit it. If the murderer
were to somehow see himself committingthe act and change his mind, then
a murder would have beencommitted in the future without a prior cause
(he changed hismind). This represents a causality violation. Both time
traveland faster-than-light travel both imply violations of
causality,which is why most physicists think they are impossible, or
atleast impossible in the general sense.

Principle of determinism

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

Rayleigh criterion; resolving power

A criterion for the how finely a set of optics may be able
todistinguish. It begins with the assumption that central ring ofone
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’sspectrum, including the Balmer, Lyman, Paschen, Brackett,
andPfund series.

Schroedinger’s cat (E. Schroedinger; 1935)

A thought experiment designed to illustrate the counterintuitiveand
strange notions of reality that come along with quantummechanics.

A cat is sealed inside a closed box; the cat has ample air,food, and
water to survive an extended period. This box isdesigned so that no
information (i.e., sight, sound, etc.) canpass into or out of the box —
the cat is totally cut off fromyour observations. Also inside the box
with the poor kitty(apparently Schroedinger was not too fond of felines)
is a phialof a gaseous poison, and an automatic hammer to break it,
floodingthe box and killing the cat. The hammer is hooked up to a
Geigercounter; this counter is monitoring a radioactive sample and
isdesigned to trigger the hammer — killing the cat — should
aradioactive decay be detected. The sample is chosen so thatafter, say,
one hour, there stands a fifty-fifty chance of a decayoccurring.

The question is, what is the state of the cat after that onehour has
elapsed? The intuitive answer is that the cat is eitheralive or dead,
but you don’t know which until you look. But it_is_ one of them.
Quantum mechanics, on the other hands, saysthat the wavefunction
describing the cat is in a superposition ofstates: the cat is, in fact,
fifty per cent alive and fifty percent dead; it is both. Not until one
looks and “collapses thewavefunction” is the Universe forced to choose
either a live cator a dead cat and not something in between.

This indicates that observation also seems to be an importantpart of
the scientific process — quite a departure from theabsolutely
objective, deterministic way things used to be withNewton.

Schwarzchild radius

The radius that a spherical mass must be compressed to in order
totransform it into a black hole; that is, the radius of
compressionwhere the escape velocity at the surface would reach

Snell’s law; law of refraction

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

speed of light _in vacuo_; cOne of the postulates of A. Einstein’s
special theory ofrelativity, which puts forth that the speed of light in
vacuum –often written c, and which has the value 299 792 458 m/s —
ismeasured as the same speed to all observers, regardless of
theirrelative motion. That is, if I’m travelling at 0.9 c away fromyou,
and fire a beam of light in that direction, both you and Iwill
independently measure the speed of that beam as c. One of the results
of this postulate (one of the predictionsof special relativity is that
no massive particle can beaccelerated to (or beyond) lightspeed, and
thus the speed of lightalso represents the ultimate cosmic speed limit.
Only masslessparticles (photons, gravitons, and possibly neutrinos,
should theyindeed prove to be massless) travel at lightspeed, and all
otherparticles must travel at slower speeds.

Spin-orbit effect

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

Static limit

The distance from a rotating black hole where no observer
canpossibly 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-Boltzmannlaw.
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) ofa
hot body is proportional to the emissivity, an efficiencyrating, the
radiating surface area, and the fourth power of thethermodynamic
temperature. The constant of proportionality is theStefan-Boltzmann

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

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


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


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

Superposition principle of forces

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

Superposition principle of states

The resultant quantum mechnical wavefunction due to two or
moreindividual wavefunctions is the sum of the individualwavefunctions.

Superposition principle of waves

The resultant wave function due to two or more individual
wavefunctions 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
aremaintained at different temperatures, heat is released at a
rateapproximately proportional to the product of the current and
thetemperature gradient.

Twin paradox

One of the most famous “paradoxes” in history, predicted by
A.Einstein’s special theory of relativity. Take two twins, born onthe
same date on Earth. One, Albert, leaves home for a triparound the
Universe at very high speeds (very close to that oflight), while the
other, Henrik, stays at home at rests. Specialrelativity predicts that
when Albert returns, he will find himselfmuch younger than Henrik.
That is actually not the paradox. The paradox stems fromattempting 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 thenreturn. 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
specialrelativity, if Henrik is moving relative to Albert, then
Albertshould measure his clock as ticking slower — and thus Henrik
isthe one who should be younger. But this is not what happens.

So what’s wrong with our analysis? The key point here is thatthe
symmetry was broken. Albert did something that Henrik didnot — Albert
accelerated in turning around. Henrik did noaccelerating, as he and all
the other people on the Earth canattest to (neglecting gravity). So
Albert broke the symmetry, andwhen he returns, he is the younger one.

Ultraviolet catastrophe

A shortcoming of the Rayleigh-Jeans formula, which attempted
todescribe the radiancy of a blackbody at various frequencies of
theelectromagnetic spectrum. It was clearly wrong because as
thefrequency increased, the radiancy increased without bound;something
quite not observed; this was dubbed the “ultravioletcatastrophe.” It
was later reconciled and explained by theintroduction of Planck’s
radiation law.

Universal constant of gravitation; G

The constant of proportionality in Newton’s law of
universalgravitation and which plays an analogous role in A.
Einstein’sgeneral 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 forthe
lattice energy of molecular crystals. There are three
causes:dipole-dipole interaction; dipole-induced dipole moments;
anddispersion forces arising because of small instantaneous dipolesin

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
youare performing. For instance, low frequency electromagneticradiation
tends to act more like a wave than a particle; highfrequency
electromagnetic radiation tends to act more like aparticle than a wave.

Widenmann-Franz law

The ratio of the thermal conductivity of any pure metal to
itselectrical conductivity is approximately constant for any
giventemperature. This law holds fairly well except at lowtemperatures.

Wien’s displacement law

For a blackbody, the product of the wavelength corresponding tothe
maximum radiancy and the thermodynamic temperature is aconstant. As a
result, as the temperature rises, the maximum ofthe radiant energy
shifts toward the shorter wavelength (higherfrequency and energy) end of
the spectrum.

Woodward-Hoffmann rules

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

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

A famous experiment which shows the wave nature of light (andindeed
of other particles). Light is passed from a small sourceonto an opaque
screen with two thin slits. The light is refractedthrough these slits
and develops an interference pattern on theother 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.

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