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;
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 than 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 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 items in a sample of a substance which is equal to
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 idea, 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, Titius-Bode 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 semimajor axes 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 between Mars and Jupiter,
and shortly thereafter the asteroids were found in very similar
orbits (2.77 au actual for Ceres; 2.8 au predicted). The series,
however, seems to skip over Neptune's orbit. The series is
presently thought of as a coincidence; the only simple types of
sequence would be either arithmetic or geometric, whereas the
series indicated by Bode's law is neither.
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 of the hydrogen atom.
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 sine 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.
Casimir effect (Casimir)
A quantum mechanical effect, where two very large plates placed
close to each other will experience an attractive force, in the
absence of other forces. The cause is virtual particle-
antiparticle creation in the vicinity of the plates.
causality principle
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.
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" directed 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 1.4 masses solar.
Any degenerate mass 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 (P.A. 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.
chronology protection conjecture (S.W. Hawking)
The concept that the formation of any closed timelike curve will
automatically be destroyed by quantum fluctuations as soon as it
is formed. In other words, quantum fluctuations prevent time
machines from being created.
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.
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.
constancy principle (Einstein)
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 (collectively called luxons, including photons,
gravitons, and possibly neutrinos, should they prove to indeed be
massless) travel at lightspeed, and all other particles must
travel at slower speeds.
Coriolis pseudoforce (G. de Coriolis; 1835)
A pseudoforce -- a fictitious force, like the centrifugal "force"
-- which arises because of motion relative to a frame which is
itself rotating relative to second, inertial frame. The magnitude
of the Coriolis "force" is dependent on the speed of the object
relative to the noninertial frame, and the direction of the
Coriolis force is orthogonal to the object's velocity.
correspondence limit (Bohr)
The limit at which a more general theory reduces to a more
specialized theory when the conditions that the specialized theory
requires are taken away.
correspondence principle (Bohr)
The principle that when a new, more general theory is put forth,
it must reduce to the more specialized (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.
cosmic censorship conjecture (R. Penrose, 1979)
The conjecture, so far totally undemonstrated within the context
of general relativity, that all singularities (with the possible
exception of the Big Bang singularity) are accompanied by event
horizons which completely surround them at all points in time.
That is, problematic issues with the singularity are rendered
irrelevant, since no information can ever escape from a black
hole's event horizon.
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.
determinism principle
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.
Doppler effect (C.J. Doppler)
Waves emitted by a moving object as received by an 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.
Eddington limit (Sir A. Eddington)
The theoretical limit at which the photon pressure would exceed
the gravitational attraction of a light-emitting body. That is, a
body emitting radiation at greater than the Eddington limit would
break up from its own photon pressure.
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 point-of-no-return around a black hole, where no particle
entering can ever escape. Inside the horizon, time and space
switch responsibilities, and to move forward in time is to move
closer to the singularity. In this way, once entering the event
horizon, no force of will or nature can prevent you from hitting
the singularity in a finite (and very short) amount of proper
time.
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.
Fermi paradox (E. Fermi)
E. Fermi's conjecture, simplified with the phrase, "Where are
they?" questioning that if the Galaxy is filled with intelligent
and technological civilizations, why haven't they come to us yet?
There are several possible answers to this question, but since we
only have the vaguest idea what the right conditions for life and
intelligence in our Galaxy, it and Fermi's paradox are no more
than speculation.
Fizeau experiment (A. Fizeau, 1851)
One of the first truly relativistic experiments, which involved
measuring interference patterns of light beams moving through
water which was in turn moving.
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?
gravitational radius
See Schwarzschild radius.
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.
hoop conjecture (K.S. Thorne, 1972)
The conjecture (as yet unproven, though there is substantial
evidence to support it) that a nonspherical object, nonspherically
compressed, will only form a black hole when all parts of the
object lie within the gravitational radius; that is, when a "hoop"
of the gravitational circumference can be rotated in all
directions and completely encloses the object in question.
Hubble constant; H_0 (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 constant of proportionality is
Hubble's constant, H_0. 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
distribution 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.
law of reflection
For a wavefront intersecting a reflecting surface, the angle of
incidence is equal to the angle of reflection, in the same plane
defined by the ray of incidence and the normal.
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.
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.
law of parismony
See Occam's razor.
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 energy
confinement 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; c. 1870)
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.
magnetic monopole
A hypothetical particle which constitutes sources and sinks of the
magnetic field. Magnetic monopoles have never been found, but
would only cause fairly minor modifications to current theories.
They also seem to be predicted by some grand-unified theories. If
magnetic monopoles do exist, they do not seem to be very common in
our Universe.
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 net 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 idea that one measures the
velocity of light as being added vectorially to the velocity of
the emitter.
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.
muon experiment
An experiment which demonstrates verifies the prediction of time
dilation by special relativity. Muons, which are short-lived
subatomic particles, are created with enormous energy in the upper
atmosphere by the interaction of energetic cosmic rays. Muons
have a very short halflife in their own reference frame, about 2.2
us. Since they are travelling very close to c, however, time
dilation effects should become important. A naive calculation
would indicate that, without special relativistic effects, the
muons would travel on the average only about 700 m before
decaying, never reaching the surface of the Earth. Observations
reveal, however, that significant numbers of muons _do_ reach the
Earth. The explanation is that muon is in a moving frame of
reference, and thus time is slowed down for the muons relative to
the Earth, effectively extending the halflife of the muons
relative to the Earth, allowing some of them to reach the surface.
negative feedback principle
The idea that in a system where there are self-propagating
circumstances, those new circumstances tend to act against
previously existing circumstances. Such a principle is really a
restatement of a conservation law. For instance, Lenz's law (see)
is an example of the principle of negative feedback.
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
constant velocity (which may be zero) 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 force is always opposed by an
equal and opposite reaction force.
no-hair conjecture (1960s)
The conjecture (proved in the 1970s and 1980s) within general
relativity that a black hole has only three salient external
characteristics: mass, angular momentum, and electric charge.
All other properties (including baryon number, lepton number,
strangeness, etc.) are destroyed as matter falls into the horizon.
Note that there is some indication that quantum mechanical
considerations in quantum gravity will result in a "quantum hair"
coming into play. However, that 1. would constitute a prediction
of a theory which does not yet formally exist, and 2. is utterly
insignificant for solar-massed black holes, the only types that
can be formed today.
Occam's [or Ockham's] razor (William of Occam [or Ockham]; c. 1340)
The suggestion that the simpler a theory is, the better. If two
theories predict phenomena to the same accuracy, then the one
which is simpler is the better one. Moreover, additional aspects
of a theory which do not lend it more powerful predicting ability
are unnecessary and should be stripped away.
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.
particle-wave duality
See wave-particle duality.
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.
Poisson spot (S.D. Poisson)
See Arago spot. Poisson originally predicted the existence of
such a spot, and used the prediction to demonstrate how the wave
theory of light must be in error to produce such a
counterintuitive result. Subsequent observation of the Arago spot
provided a decisive confirmation of the wave nature of light.
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.
Schwarzschild radius (K. Schwarzschild, 1915)
The radius that a spherical mass must be compressed to in order to
transform it into a black hole; more generally, in the
Schwarzschild metric, the radius at which the time and space
switch responsibilities. Once inside the Schwarzschild radius, it
is fundamentally impossible to escape to the outside.
Furthermore, nothing can prevent a particle from hitting the
singularity in a very short amount of proper time once it has
entered the Scwarzschild radius. In this sense, the Schwarzschild
radius is a "point of no return."
simultaneity principle
The principle that all frames of reference will have invariant
simultaneity; that is, two events perceived as simultaneous (i.e.,
having the same time coordinate) in one frame will be perceived as
simultaneous in all other frames. According to special
relativity, however, this is not the case; in special relativity,
simultaneity is frame-dependent.
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
The speed at which electromagnetic radiation propagates in a
vacuum; it is defined as 299 792 458 m/s.
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.
standard quantum limit
The limit imposed on standard methods of measurement by the
uncertainty principle within quantum mechanics.
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 mechnical 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.
tachyon
A purely speculative particle, which is presumed to travel faster
than light. According to Einstein's equations of special
relativity, a particle with an imaginary rest mass and a velocity
greater than c would have a real momentum and energy. Ironically,
the greater the kinetic energy of a tachyon, the slower it
travels, approaching c asymptotically (from above) as its energy
approaches infinity. Alternatively, a tachyon losing kinetic
energy travels faster and faster, until as the kinetic energy
approaches zero, the speed of the tachyon approaches infinity;
such a tachyon with zero energy and infinite speed is called
transcendent.
Special relativity does not seem to specifically exclude
tachyons, so long as they do not cross the lightspeed barrier and
do not interact with other particles to cause causality
violations. Quantum mechanical analyses of tachyons indicate that
even though they travel faster than light they would not be able
to carry information faster than light, thus failing to violate
causality.
tau-theta paradox (1950s)
When two different types of kaons, tau and theta (today tau refers
to a completely different particle), tau decays into three
particles, while the theta decays into two. The tau and theta
differ only in parity; and at the time, it was thought that parity
was strictly conserved, and that particles differing only in
parity should behave exactly the same. Since the tau and theta
differed only in parity, a paradox ensued. The paradox was
resolved when experiments carried out accord to F. Yang and T.D.
Lee's theoretical calculations indeed indicate that parity is not
conserved in weak interactions.
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.
Tipler machine
A solution to Einstein's equation of general relativity that
allows time travel. An extremely dense (on the order of the
density of neutron star matter), infinitely long cylinder which
rotates very rapidly can form closed timelike curves in its
vicinity, which will allow time travel and possible subsequent
violations of causality.
Titius-Bode law
See Bode's law.
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 Henrik.
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.
uniformity principle (Hubble, E.P.)
The principle that the laws of physics here and now are not
significantly different from the laws of physics in previous or
future epochs of time, or elsewhere in the Universe.
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.
Home
Previous Page
Club Information
Observing Sessions
Calendar of Events
Current attractions
Newsletter
FAQ
Whats
New
Astro
Photos
Other
Links
Web Site Updated:
April 28, 2007 18:12
Maintained by Doug Bock