======================SCIENCE_TERMS=======================================
aberration The apparent change in position of a light-emitting object due
to the constancy of the speed of light and the motion of the
observer relative to the emitter. The effect is
nonrelativistic; that is, special relativity is not required
to derive it: all that is needed is Newtonian mechanics and
the assumption of the constancy of the speed of light. The
effect is observable in the apparent change of position of
stars due to Earth's relative motion, and is responsible for
the "tunnel vision" effect of travelling at relativistic
speeds.
ampere; A (after A.M. Ampere, 1775-1836)
The fundamental SI unit of electric current, defined as the
current that, when going through two infinitely-long parallel
conductors of negligible cross-section and placed 1 m apart in
vacuum, results in a force between the two conductors of 2 x
10-7 N/m.
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; or, in differential form,
curl B = J.
This was later modified to add a second term when it was
incorporated into Maxwell's equations.
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, and this process
can only happen at certain times through the evolution of
any given universe.
strong anthropic principle
A more forceful argument than the weak principle: It
implies 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, no intelligent beings would be able to consider
the laws of the Universe at all.
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 NA (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 ideal
gas which is at standard temperature and pressure. It is equal
to about 6.022 52 x 1023 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 in fact
unstable, they decay with a halflife of at least ~1034 y.
beauty criterion (Dirac)
The idea that the more aesthetically pleasing a theory is, the
better it is. Naturally this criterion does not stand up to
the real test -- whether or not predictions of a given theory
agree with observational tests -- but considering that it is a
purely aesthetic quality that is being tested, many of the
most successful theories (special relativity, general
relativity, quantum electrodynamics, etc.) match the criterion
particularly well.
becquerel; Bq (after A.H. Becquerel, 1852-1908)
The derived SI unit of activity, defined as the activity of a
radionuclide decaying at a rate, on the average, of one
nuclear transition every 1 s; it thus has units of s-1.
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.
Bell's inequality (J.S. Bell; 1964)
A quantum mechanical theorem which demonstrates that quantum
mechanics must have nonlocal properties.
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.
Mathematically, it is
dB = (mu0 I)/(4 pi r2) dl cross e
where dl is the infinitesimal directed length of the electric
current causing the magnetic field, I is the current running
through that directed length, r is the distance from that
directed length, and e is the unit vector directed from the
test point to current-producing length.
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.
black-hole dynamic laws; laws of black-hole dynamics
first law of black hole dynamics
For interactions between black holes and normal matter,
the conservation laws of mass-energy, electric charge,
linear momentum, and angular momentum, hold. This is
analogous to the first law of thermodynamics.
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.
This is analogous to the second law of thermodynamics,
with the surface areas of the black holes being a measure
of the entropy of the system.
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 add 4 to each term:
4, 7, 10, 16, 28, ...
Then divide each term by 10. This leaves you with the series
0.4, 0.7, 1.0, 1.6, 2.8, ...
which 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 form of Bode's law (that is, a roughly
geometric series) is not surprising, considering our theories
on the formation of solar systems, but its particular
formulation is thought of as coincidental.
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.
See ideal gas laws.
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.
bradyon See tardon.
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 complement of
the angle of incidence, theta, the wavelength of the x-rays,
lambda, and the distance betwen layers of atoms or ions, d,
are related by the equation
2 d sin theta = n lambda,
where n is an integer.
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
ongoing bombardment by atoms and molecules.
candela; cd The fundamental SI unit of luminous intensity defined as the
luminous intensity in a given direction of a source that emits
monochromatic photons of frequency 540 x 1012 Hz and has a
radiant intensity in that direction of 1/683 W/sr.
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 pair creation in the vicinity of the
plates. Also, the speed of light will be increased in the
region between the two plates, in the direction perpendicular
to them.
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. That is, event
B must occur at a later time t than event A, and further, all
frames must agree upon this ordering.
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 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 [Cerenkov] 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.
Coanda effect The effect that indicates that a fluid tends to flow along a
surface, rather than flow through free space.
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.
conservation laws A law which states that, in a closed system, the total
quantity of something will not increase or decrease, but
remain exactly the same; that is, its rate of change is zero.
For physical quantities, it states that something can neither
be created nor destroyed. Mathematically, if a scalar X is the
quantity considered, then
dX/dt = 0,
or, equivalently,
X = constant.
For a vector field F, the conservation law is written as
div F = 0;
that is, the vector field F is divergence-free everywhere
(i.e., has no sources or sinks).
Some specific examples of conservation laws are:
conservation of mass-energy
The total mass-energy of a closed system remains
constant.
conservation of electric charge
The total electric charge of a closed system remains
constant.
conservation of linear momentum
The total linear momentum of a closed system remains
constant.
conservation of angular momentum
The total angular momentum of a closed system
remains constant.
There are several other laws that deal with particle physics,
such as conservation of baryon number, of strangeness, etc.,
which are conserved in some fundamental interactions (such as
the electromagnetic interaction) but not others (such as the
weak interaction).
constancy principle (A. Einstein)
One of the postulates of A. Einstein's special theory of
relativity, which puts forth that the speed of light in vacuum
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.
See tachyons, causality principle.
Cooper pairs (L.N. Cooper; 1957)
See BCS theory.
Copernican principle (N. Copernicus)
The idea, suggested by Copernicus, that the Sun, not the
Earth, is at the center of the Universe. We now know that
neither idea is correct (the Sun is not even located at the
center of our Galaxy, much less the Universe), but it set into
effect a long chain of demotions of Earth's and our place in
the Universe, to where it is now: On an unimpressive planet
orbiting a mediocre star in a corner of a typical galaxy, lost
in the Universe.
Coriolis pseudoforce (G. de Coriolis; 1835)
A pseudoforce 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 "force" is orthogonal to the object's
velocity.
correspondence limit (N. 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.
See correspondence principle.
correspondence principle (N. 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.
See correspondence limit.
cosmic background radiation; primal glow
The background of radiation mostly in the frequency range 3 x
1011 to 3 x 108 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/m3.
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 constant Lambda
The constant introduced to the Einstein field equation,
intended to admit static cosmological solutions. At the time
the current philosophical view was the steady-state model of
the Universe, where the Universe has been around for infinite
time. Early analysis of the field equation indicated that
general relativity allowed dynamic cosmological models only
(ones that are either contracting or expanding), but no static
models. Einstein introduced the most natural abberation to the
field equation that he could think of: the addition of a term
proportional to the spacetime metric tensor, g, with the
constant of proportionality being the cosmological constant:
G + Lambda g = 8 pi T.
Hubble's later discovery of the expansion of the Universe
indicated that the introduction of the cosmological constant
was unnecessary; had Einstein believed what his field equation
was telling him, he could have claimed the expansion of the
Universe as perhaps the greatest and most convincing
prediction of general relativity; he called this the "greatest
blunder of my life."
cosmological redshift An effect where light emitted from a distant source appears
redshifted because of the expansion of spacetime itself.
Compare Doppler effect.
coulomb; C (after C. de Coulomb, 1736-1806)
The derived SI unit of electric charge, defined as the amount
of charge transferred by a current of 1 A in a period of 1 s;
it thus has units of A s.
Coulomb's law (C. de Coulomb)
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; mathematically,
F = 1/(4 pi epsilon0) (q Q/r2) e,
where q and Q are the strengths of the two charges, r is the
distance between the two, and e is a unit vector directed from
the test charge to the second.
Curie constant; C (P. Curie)
A characteristic constant, dependent on the material in
question, which indicates the proportionality between its
susceptibility and its thermodynamic temperature.
Curie's law (P. Curie)
The susceptibility, khi, of an isotropic paramagnetic
substance is related to its thermodynamic temperature T by the
equation
khi = C/T
See Curie-Weiss law.
Curie-Weiss law (P. Curie, P.-E. Weiss)
A more general form of Curie's law, which states that the
susceptibility, khi, of an paramagnetic substance is related
to its thermodynamic temperature T by the equation
khi = C/T - W
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 uncertainty principle implies
that one cannot know both the position and velocity of a particle to
arbitrary precision.
Dirac constant; Planck constant, modified form; hbar
A sometimes more convenient form of the Planck constant, defined as
hbar = h/(2 pi).
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.
Compare cosmological redshift.
Drake equation (F. Drake; 1961)
A method of estimating the number of intelligent, technological species
(i.e., able to communicate with other species) in existence in our
Galaxy.
N = R fp ne fl fi ft L.
N is the number of species described above at any given moment in our
Galaxy. The parameters it is computed from are as follows:
R the rate of star formation in our Galaxy (in stars per
year);
fp the fraction of stars which have planets;
ne the number of habitable planets per system with planets;
fl the fraction of habitable planets upon which life
arises;
fi the fraction of these planets upon which life develops
intelligence;
ft the fraction of these planets where the intelligence
develops into a technological civilization capable of
communication; and
L the mean lifetime of such a technological civilization.
Of these quantities, only the first -- R -- is known with anything like
any reliability; it is on the order of 10 stars per year. The others,
most notably the fractions, are almost entirely pure speculation at
this point. Calculations made by respectable astronomers differ by
something like ten orders of magnitude in the final estimation of the
number of species out there.
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.
Edwards-Casimir quantum vacuum drive
A hypothetical drive exploiting the peculiarities of quantum
mechanics by restricting allowed wavelengths of virtual
photons on one side of the drive (the bow of the ship); the
pressure generated from the unrestricted virtual photons
toward the aft generates a net force and propels the drive.
See Casimir effect.
Ehrenfest paradox (Ehernfest, 1909)
The special relativistic "paradox" involving a rapidly
rotating disc. Since any radial segment of the disc is
perpendicular to the direction of motion, there should be no
length contraction of the radius; however, since the
circumference of the disc is parallel to the direction of
motion, it should contract.
Einstein field equation
The cornerstone of Einstein's general theory of relativity,
relating the gravitational tensor G to the stress-energy
tensor T by the simple equation
G = 8 pi T.
Einstein-Podolsky- Rosen effect; EPR 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 or travel possible.
electric constant See permeability of free space.
Eotvos law of capillarity (Baron L. von Eotvos; c. 1870)
The surface tension gamma of a liquid is related to its
temperature T, the liquid's critical temperature, T*, and its
density rho by
gamma ~= 2.12 (T* - T)/rho3/2.
EPR effect See Einstein-Podolsky-Rosen effect.
epsilon_0 See permittivity of free space.
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."
Although that in practical situations -- say, sitting in a
closed room -- it would be possible to determine whether the
acceleration felt was due to uniform thrust or due to
gravitation (say, by measuring the gradient of the field; if
nonzero, it would indicate a gravitational field rather than
thrust); however, such differences could be made arbitrarily
small. The idea behind the equivalence principle is that it
acts around the vicinity of a point, rather than over
macroscopic distances. It would be impossible to say whether
or not a given (arbitrary) acceleration field was caused by
thrust or gravitation by the use of physics alone.
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 -- any effect that takes place when an observer is
accelerating should also take place in a gravitational field,
and vice versa.
See weak equivalence principle.
ergosphere
The region around a rotating black hole, between the event
horizon and the static limit, where rotational energy can be
extracted from the black hole.
event horizon
The radius that a spherical mass must be compressed to in
order to transform it into a black hole, or the radius at
which time and space switch responsibilities. Once inside the
event horizon, 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 horizon. In this sense, the event
horizon is a "point of no return."
The radius of the event horizon, r, for generalized black
holes (in geometrized units) is
r = m + (m2 - q2 - s/m2)1/2,
where m is the mass of the hole, q is its electric charge, and
s is its angular momentum.
See Schwarzschild radius.
faint, young sun paradox
Theories of stellar evolution indicate that as stars mature
on the main sequence, they grow steadily hotter and brighter;
calculations suggest that at about the time of the formation
of Earth, the Sun was roughly two-thirds the brightness that
it is now. However, there is no geological evidence on Earth
(or on Mars) for the Sun being fainter in the past. At
present there is no clear resolution for this paradox.
farad; F (after M. Faraday, 1791-1867)
The derived SI unit of capacitance, defined as the
capacitance in a capacitor that, if charged to 1 C, has a
potential difference of 1 V; thus, it has units of C/V.
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 104 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; in differential form,
curl E = -dB/dt,
where here d/dt represents partial differentiation.
Faraday's laws of electrolysis (M. Faraday)
Faraday's first law of electrolysis
The amount of chemical change during electrolysis is
proportional to the charge passed.
Faraday's second law of electrolysis
The charge Q equired to deposit or liberate a mass m is
proportional to the charge z of the ion, the mass, and
inversely proprtional to the relative ionic mass M;
mathematically,
Q = F m z/M.
Faraday's laws of electromagnetic induction (M. Faraday)
Faraday's first law of electromagnetic induction
An electromotive force is induced in a conductor when
the magnetic field surrounding it changes.
Faraday's second law of electromagnetic induction
The magnitude of the electromotive force is proportional
to the rate of change of the field.
Faraday's third law of electromagnetic induction
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, that states 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.
fictitious force See pseudoforce.
Fizeau method (A. Fizeau, 1851)
One of the first truly relativistic experiments, intended to
measure the speed of light. Light is passed through a
spinning cogwheel driven by running water, is reflected off a
distant mirror, and then passed back through the spinning
cogwheel. When the rate of running water (and thus the
spinning of the cogwheel) is synchronized so that the
returning pulses are eclipsed, c can be calculated.
Gaia hypothesis (J. Lovelock, 1969)
The idea that the Earth as a whole should be regarded as a
living organism and that biological processes stabilize the
environment.
Gauss' law (K.F. Gauss)
The electric flux normal to a closed surface is proportional
to the algebraic sum of electric charges contained within
that closed surface; in differential form,
div E = rho,
where rho is the charge density.
Gauss' law for magnetic fields (K.F. Gauss)
The magnetic flux normal to a closed surface is zero; no
magnetic charges exist; in differential form,
div B = 0.
geometrized units A system of units whereby certain fundamental constants (G,
c, k, and h) are set to unity. This makes calculations in
certain theories, such as general relativity, much easier to
deal with, since these constants appear frequently.
As a result of converting to geometrized units, all
quantities are expressed in terms of a unit of distance,
traditionally the cm.
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?
gray; Gy (after L.H. Gray, 1905-1965)
The derived SI unit of absorbed dose, defined as the absorbed
dose in which the energy per unit mass imparted to the matter
by ionizing radiation is 1 J/kg; it thus has units of J/kg.
gravitational radius See event horizon.
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. Occasionally, a pair will
be created just outside the event horizon of a black hole.
There are three possibilities:
1. both particles are captured by the hole;
2. both particles escape the hole;
3. one particle escapes while the other is captured.
The first two cases are straightforward; the virtual
particle-antiparticle pair recombine and return their energy
back to the void via the uncertainty principle.
It is the third case that interests us. In this case, one of
the particles has escaped (and is speeding away to infinity),
while the other has been captured by the hole. The escapee
becomes real and can now be detected by distant observers. But
the captured particle is still virtual; because of this, it
has to restore conservation of energy by assigning itself a
negative mass-energy. Since the hole has absorbed it, the hole
loses mass and thus appears to shrink. From a distance, it
appears as if the hole has emitted a particle and reduced in
mass.
The rate of power emission is proportional to the inverse
square of the hole's mass; thus, the smaller a hole gets, the
faster and faster it emits Hawking radiation. This leads to a
runaway process; what happens when the hole gets very small is
unclear; quantum theory seems to indicate that some kind of
"remnant" might be left behind after the hole has emitted away
all its mass-energy.
Hawking temperature The temperature of a black hole caused by the emission of
Hawking radiation. For a black hole with mass m, it is
T = (hbar c3)/(8 pi G k m).
Since blackbody power emission is proportional to the area of
the hole and the fourth power of its thermodynamic
temperature, the emitted power scales as m-2 -- that is, as
the inverse square of the mass.
hbar See Dirac constant.
Heisenberg uncertainty principle
See uncertainty principle.
henry; H (after W. Henry, 1775-1836)
The derived SI unit of inductance, defined as the inductance
of a closed circuit in which an electromotive force of 1 V is
produced when the electric current varies uniformly at a rate
of 1 A/s; it thus has units of V s/A.
hertz; Hz (after H. Hertz, 1857-1894)
The derived SI unit of frequency, defined as a frequency of 1
cycle per s; it thus has units of s-1.
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 its event horizon; that is,
when a "hoop" of the event horizon circumference can be
rotated in all directions and will completely enclose the
object in question.
Hubble constant; H0 (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. Since the Universe is
self-gravitating, it is not truly constant. In cosmology, it
is defined as
H = (da/dt)/a,
where a is the 4-radius of the Universe. When evaluated for
the present, it is written
H0 == H(t = now).
The Hubble constant is not known to great accuracy (only
within about a factor of 2), but is believed to lie somewhere
between 50 and 100 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 the Hubble constant, H0. The cause is
interpreted as the expansion of spacetime itself.
Huygens'construction; Huygens' principle (C. Huygens)
The mechanical propagation of a wave (specifically, 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,
P V = n R T,
where P is the pressure, V is the volume, n is the number of
moles present, and T is the temperature of the sample.
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.
pressure law
The pressure of an ideal gas is directly proportional
to the thermodynamic temperature at constant volume.
joule; J (after J.P. Joule, 1818-1889)
The derived SI unit of energy defined as the amount of work
done by moving an object through a distance of 1 m by
applying a force of 1 N; it thus has units of N m.
Joule-Thomson effect; Joule-Kelvin effect (J.P. Joule, W. Thomson [later Lord Kelvin])
The change in temperature that occurs when a gas expands
into a region of lower pressure.
Joule's laws (J.P. Joule)
Joule's first law
The heat Q produced when a current I flows through a
resistance R for a specified time t is given by
Q = I2 R t
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.
kelvin; K (after Lord Kelvin, 1824-1907)
The fundamental SI unit of thermodynamic temperature defined
as 1/273.16 of the thermodynamic temperature of the triple
point of water.
Kelvin effect See Thomson experiment.
Kepler's 1-2-3 law Another formulation of Kepler's third law, which relates the
mass m of the primary to a secondary's angular velocity
omega and semimajor axis a:
m o= omega2 a3.
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.
kilogram; kg The fundamental SI unit of mass, which is the only SI unit
still maintained by a physical artifact: a platinum-iridium
bar kept in the International Bureau of Weights and Measures
at Sevres, France.
Kirchhoff's law of radiation (G.R. Kirchhoff)
The emissivity of a body is equal to its absorptance at the
same temperature.
Kirchhoff's laws (G.R. Kirchhoff)
Kirchhoff's first law
An incandescent solid or gas under high prssure will
produce a continuous spectrum.
Kirchhoff's second law
A low-density gas will radiate an emission-line
spectrum with an underlying emission continuum.
Kirchhoff's third law
Continuous radiation viewed through a low-density gas
will produce an absorption-line spectrum.
Kirchhoff's rules (G.R. Kirchhoff)
loop rule
The sum of the potential differences encountered in a
round trip around any closed loop in a circuit is zero.
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.
Kirkwood gaps (Kirkwood)
Gaps in the asteroid belt, caused by resonance effects from
Jupiter. Similar gaps exist in Saturn's rings, due to the
resonance effects of shepherd moons.
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 proportional to the cosine of the angle
with the normal.
Lambert's third law
The luminous intensity of light decreases exponentially
with distance as it travels through an absorbing medium.
Lagrange points Points in the vicinity of two massive bodies (such as the
Earth and the Moon) where each others' respective gravities
balance. There are five, labelled L1 through L5. L1, L2, and
L3 lie along the centerline between the centers of mass
between the two masses; L1 is on the inward side of the
secondary, L2 is on the outward side of the secondary; and L3
is on the outward side of the primary. L4 and L5, the
so-called Trojan points, lie along the orbit of the secondary
around the primary, sixty degrees ahead and behind of the
secondary.
L1 through L3 are points of unstable equilibrium; any
disturbance will move a test particle there out of the
Lagrange point. L4 and L5 are points of stable equilibrium,
provided that the mass of the secondary is less than about
1/24.96 the mass of the primary. These points are stable
because centrifugal pseudoforces work against gravity to
cancel it out.
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 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;
mathematically,
d2 T/dr2 = 0.
Laue pattern (M. von Laue)
The pattern produced on a photographic film when
high-frequency electromagnetic waves (such as x-rays) are
fired at a crystalline solid.
laws of black-hole dynamics
See black-hole dynamic laws.
law of parismony See Occam's razor.
laws thermodynamics See thermodynamic laws.
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, nG
tau is between 1014 and 1015 s/cm3.
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.
left-hand rule The opposite-chirality version of the right-hand rule.
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; NL
The number of particles per unit volume of an ideal gas at
standard temperature and pressure. It has the value 2.687 19
x 1025 m-3.
lumen; lm The derived SI unit of luminous flux, defined as the luminous
flux emitted by a uniform point source of 1 cd emitting its
luminous energy over a solid angle of 1 sr; it thus has units
of cd sr.
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.
lux; lx The derived SI unit of illuminance equal to the illuminance
produced by a luminous flux of 1 lm distributed uniformly
over an area of 1 m2; it thus has units of lm/m2.
luxon A particle which travels solely at c (the speed of light in
vacuum). All luxons have a rest mass of exactly zero. Though
they are massless, luxons do carry momentum. Photons are the
prime example of luxons (the name itself is derived from the
Latin word for light).
Compare tardon, tachyon.
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 number (E. Mach)
The ratio of the speed of an object in a given medium to the
speed of sound in that medium.
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 constant See permeability of free space.
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
Maxwell's equations. 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' law (E.L. Malus)
The light intensity I of a ray with initial intensity I0
travelling through a polarizer at an angle theta between the
polarization of the light ray and the polarization axis of
the polarizer is given by
I = I0 cos2 theta.
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 perfect
insulators.
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 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 normal to a closed surface is
proportional to the algebraic sum of electric
charges contained within that closed surface; in
differential form,
div E = rho,
where rho is the charge density.
Gauss' law for magnetic fields
The magnetic flux normal to a closed surface is
zero; no magnetic charges exist. In differential
form,
div B = 0.
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; in
differential form,
curl E = -dB/dt,
where d/dt here represents partial differentation.
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 differential form,
curl H = J + dD/dt,
where d/dt here represents partial differentiation.
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; the speed can be
found by computing (epsilon0 mu0)-1/2, which is c, the speed
of light in vacuum.
mediocrity principle The principle that there is nothing particularly interesting
about our place in space or time, or about ourselves. This
principle probably first made its real appearance in the
scientific community when Shapley discovered that the
globular clusters center around the center of the Galaxy, not
around the solar system. The principle can be considered a
stronger form of the uniformity principle; instead of no
place being significantly different than any other, the
mediocrity principle indicates that, indeed, where you are is
not any more special than any other.
Meissner effect (W. Meissner; 1933)
The decrease of the magnetic flux within a superconducting
metal when it is cooled below the transition temperature.
That is, superconducting materials reflect magnetic fields.
metre; meter; m The fundamental SI unit of length, defined as the length of
the path traveled by light in vacuum during a period of 1/299
792 458 s.
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.
See constancy principle.
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.
mole; mol The fundamental SI unit of substance, defined as the amount
of substance that contains as many elementary units (atoms,
molecules, ions, etc.) as there are atoms in 0.012 kg of
carbon-12.
mu_0 See permeability of free space.
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.
NA See Avogadro constant.
NL See Loschmidt constant.
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.
Example Lenz's law.
newton; N (after Sir I. Newton, 1642-1727)
The derived SI unit of force, defined as the force required
to give a mass of 1 kg an acceleration of 1 m/s2; it thus
has units of kg m/s2.
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; mathematically,
F = (G m M/r2) e,
where m and M are the masses of the two bodies, r is the
distance between. the two, and e is a unit vector directed
from the test mass to the second.
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 produced 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.
Noether theorem (Noether)
A theorem which demonstrates that symmetries are what gives
rise to conserved quantities. For instance, translational
symmetry (the fact that the laws of physics work the same in
all places) gives rise to conservation of momentum, since
position and momentum are complementary. Additionally,
conservation of energy is indicated by time symmetry, and
conservation of angular momentum is indicated by isotropy.
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.
null experiment An experiment which, after being executed, yields no result.
Null experiments are just as meaningful as non-null
experiments; if current theory predicts an observable effect
(or predicts there should be no observable effect), and
experimentation (within the required accuracy) does not
yield said effect, then the null experiment has told us
something about our theory.
See Michelson-Morley experiment.
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; Omega; O (after G. Ohm, 1787-1854)
The derived SI unit of electric resistance, defined as the
resistance between two points on a conductor when a constant
potential difference of 1 V produces a current of 1 A in the
conductor; it thus has units of V/A.
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 non-uniform, dynamic, and
(probably) finite.
parsec The unit of distance defined as the distance indicated by an
Earth-orbit parallax of 1 arcsec. It equals about 206 264 au,
or about 3.086 x 1016 m.
particle-wave duality See wave-particle duality.
pascal; Pa The derived SI unit of pressure defined as 1 N acting over an
area of 1 m2; it thus has units of N/m2.
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 in this context) 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 the Planck
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 constant, reduced; hbar
See Dirac constant.
Planck equation The quantum mechanical equation relating the energy of a
photon E to its frequency nu:
E = h nu.
Planck radiation law A law which described blackbody radiation better than its
predecessor, thus resolving the ultraviolet catastrophe. It
is based on the assumption that electromagnetic radiation is
quantized.
For a blackbody at thermodynamic temperature T, the radiancy
R over a range of frequencies between nu and nu + dnu is
given by
R = 2 pi h nu3/[c3 [exp (h nu/k T) - 1]].
Compare Rayleigh-Jeans law.
Poisson equation (S.D. Poisson)
The differential form of Gauss' law, namely,
div E = rho,
Poisson spot (S.D. Poisson)
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.
pseudoforce A "force" which arises because an observer is naively
treating an accelerating frame as an inertial one.
Examples Coriolis pseudoforce, centrifugal pseudoforce.
See ideal gas constant.
radian; rad The supplementary SI unit of angular measure, defined as the
central angle of a circle whose subtended arc is equal to the
radius of the circle.
Rayleigh-Jeans law For a blackbody at thermodynamic temperature T, the radiancy
R over a range of frequencies between nu and nu + dnu is
given by
R = 2 pi nu2 k T/c2.
Compare Planck radiation law; see ultraviolet catastrophe.
Rayleigh criterion; resolving power
A criterion for determining 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; for an objective lens with diameter d and
employing light with a wavelength lambda (usually taken to be
560 nm), the resolving power is approximately given by
1.22 lambda/d.
reflection law 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.
refraction law For a wavefront travelling through a boundary between two
media, the first with a refractive index of n1, and the other
with one of n2, the angle of incidence theta is related to
the angle of refraction phi by
n1 sin theta = n2 sin phi.
relativity principle The principle, employed by Einstein's relativity theories,
that the laws of physics are the same, at least
qualitatively, in all frames. That is, there is no frame that
is better (or qualitatively any different) from any other.
This principle, along with the constancy principle,
constitute the founding principles of special relativity.
resolving power See Rayleigh criterion.
right-hand rule A trick for right-handed coordinate systems to determine
which way the cross product of two 3-vectors will be
directed. There are a few forms of this rule, and it can be
applied in many ways. If u and v are two vectors which are
not parallel, then u cross v is a vector which is directed in
the following manner: Orient your right hand so that your
thumb is perpendicular to the plane defined by the vectors u
and v. If you can curl your fingers in the direction from
vector u to vector v, your thumb will point in the direction
of u cross v. (If it doesn't, the vector is directed in the
opposite direction.) This has immediate application for
determining the orientation of the z-axis basis unit vector,
k, in terms of the x- and y-axes' basis unit vectors; curl
your right hand in the direction of i to j, and your thumb
will point in the direction of i cross j = k.
The rule is also applicable in several practical
applications, such as determining which way to turn a screw,
etc. There is also a left-hand rule, which exhibits opposite
chirality.
Roche limit The position around a massive body where the tidal forces due
to the gravity of the primary equal or exceed the surface
gravity of a given satellite. Inside the Roche limit, such a
satellite will be disrupted by tides.
Rydberg constant (Rydberg)
A constant which governs the relationship of the spectral
line features of an atom through the Rydberg formula. For
hydrogen, it is approximately 1.097 x 107 m-1.
Rydberg formula (Rydberg)
A formula which describes all of the characteristics of
hydrogen's spectrum, including the Balmer, Lyman, Paschen,
Brackett, and Pfund series.
For the transition between an electron in orbital m to one in
orbital n (or the reverse), the wavelength lambda involved is
given by
1/lambda = R (1/m2 - 1/n2).
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 The radius r of the event horizon for a Schwarzschild black
hole of mass m is given by (in geometrized units) r = 2 m. In
conventional units,
r = 2 G m/c2.
second; s The fundamental SI unit of time, defined as the period of
time equal to the duration of 9 192 631 770 periods of the
radiation corresponding to the transition between two
hyperfine levels of the ground state of the cesium-133 atom.
siemens; S (after E.W. von Siemens, 1816-1892)
The derived SI unit of electrical conductance equal to the
conductance of an element that has a resistance of 1 O [ohm];
it has units of O-1.
sievert; Sv The derived SI unit of dose equivalent, defined as the
absorbed dose of ionizing radiation multiplied by
internationally-agreed-upon dimensionless weights, since
different types of ionizing radiation cause different types
of damage in living tissue. The Sv, like the Gy, has units of
J/kg.
sigma See Stefan-Boltzmann constant.
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; simultaneity is frame-dependent.
singularity The center of a black hole, where the curvature of spacetime
is maximal. At the singularity, the gravitational tides
diverge; no solid object can even theoretically survive
hitting the singularity. Although singularities generally
predict inconsistencies in theory, singularities within black
holes do not necessarily imply that general relativity is
incomplete so long as singularities are always surrounded by
event horizons.
A proper formulation of quantum gravity may well avoid the
classical singularity at the centers of black holes.
See consmic censorship conjecture.
Snell's law See refraction law.
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; this region is outside of
the event horizon, except at the poles where it meets the
horizon at a point. The region between the event horizon and
the static limit is called the ergosphere.
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/m2/K4.
Stefan-Boltzmann law (Stefan, L. Boltzmann)
The radiated power P (rate of emission of electromagnetic
energy) of a hot body is proportional to the radiating
surface area, A, and the fourth power of the thermodynamic
temperature, T. The constant of proportionality is the
Stefan-Boltzmann constant. Mathematically,
P = e sigma A T4,
where the efficiency rating e is called the emissivity of the
object.
steradian; sr The supplementary SI unit of solid angle defined as the solid
central angle of a sphere that encloses a surface on the
sphere equal to the square of the sphere's radius.
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. The
current theory for explaining superconductivity is the BCS
theory.
superfluidity The phenomena by which, at sufficiently low temperatures, a
fluid can flow with zero viscosity. Its causes are associated
with superconductivity.
superposition principle
The general idea that, when a number of influences are acting
on a system, the total influence on that system is merely the
sum of the individual influences; that is, influences
governed by the superposition principle add linearly. Some
specific examples are:
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.
Syst¸me Internationale d'Unitˇs (SI)
The coherent and rationalized system of units, derived from
the m.k.s. system (which itself is derived from the metric
system) in common use in physics today.
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. But in this case, if tachyons are by
their very nature indetectable, it brings into question how
real they might be.
See Occam's razor; compare tardon, luxon.
tachyon paradox The argument demonstrating that tachyons (should they exist,
of course) cannot carry an electric charge. For a
(imaginary-massed) particle travelling faster than c, the
less energy the tachyon has, the faster it travels, until at
zero energy the tachyon is travelling with infinite velocity,
or is transcendent. Now a charged tachyon at a given
(non-infinite) speed will be travelling faster than light in
its own medium, and should emit Cherenkov radiation. The loss
of this energy will naturally reduce the energy of the
tachyon, which will make it go faster, resulting in a runaway
reaction where any charged tachyon will promptly race off to
transcendence.
Although the above argument results in a curious conclusion,
the meat of the tachyon paradox is this: In relativity, the
transcendence of a tachyon is frame-dependent. That is, while
a tachyon might appear to be transcendent in one frame, it
would appear to others to still have a nonzero energy. But in
this case we have a situation where in one frame it would
have come to zero energy and would stop emitting Cherenov
radiation, but in another frame it would still have energy
left and should be emitting Cherenkov radiation on its way to
transcendence. Since they cannot both be true, by
relativistic arguments, tachyons cannot be charged.
This argument naturally does not make any account of quantum
mechanical treatments of tachyons, which complicate the
situation a great deal.
tardon A particle which has a positive real mass and travels at a
speed less than c in all inertial frames.
Compare tachyon, luxon.
tardyon See tardon.
tau-theta paradox (1950s)
When two different types of kaons, tau and theta (today tau
refers to a completely different particle) decay, 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 two decay differently, a paradox ensued. The
paradox was resolved when experiments carried out according
to F. Yang and T.D. Lee's theoretical calculations indeed
indicate that parity is not conserved in weak interactions.
tesla; T (after N. Tesla, 1870-1943)
The derived SI unit of magnetic flux density, defined the
magnetic flux density of a magnetic flux of 1 Wb through an
area of 1 m2; it thus has units of Wb/m2.
thermodynamic laws 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.
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 equations 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.
transition temperature
The temperature (dependant on the substance involved) below
which a superconducting substance conducts electricity with
zero resistance; consequently, the temperature above which a
superconductor loses its superconductive properties.
Trojan points L4 and L5, the two dynamically stable Lagrange points (under
certain conditions).
Trojan satellites Satellites which orbit a body at one or the other Trojan
points relative to a secondary body. There are several
examples of this in our own solar system: a group of
asteroids which orbit in the the Trojan points of Jupiter;
daughter satellites which orbit in the Trojan points of the
Saturn-Tethys system, and an additional satellite (Helene)
which orbits in the forward Trojan point of Saturn and Dione.
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 the Planck
radiation law.
uncertainty principle (W. Heisenberg; 1927)
A principle, central to quantum mechanics, which states that
two complementary parameters (such as position and momentum,
energy and time, or angular momentum and angular
displacement) cannot both be known to infinite accuracy; the
more you know about one, the less you know about the other.
It can be illustrated in a fairly clear way as it relates to
position vs. momentum: To see something (let's say an
electron), we have to fire photons at it; 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 (higher 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.
uniformity principle (E.P. Hubble)
The principle that the laws of physics here and now are not
different, at least qualitatively, from the laws of physics
in previous or future epochs of time, or elsewhere in the
Universe. This principle was scoffed at by the ancients who
believed that the laws that governed the Earth and those that
governed the heavens were completely divorced; now it is used
routinely in cosmology to describe the structure and
evolution of the Universe.
universal age paradox Two of the most straightforward methods of calculating the
age of the Universe -- through redshift measurements, and
through stellar evolution -- yield incompatible results.
Recent (mid 1990s) measurements of the distances of distant
galaxies through the use of the Hubble Space Telescope
indicate an age much less than the ages of the oldest stars
that we calculate through stellar evolution theory. At
present there is no conclusion to this paradox; a
cosmological constant would rectify the situation, but it's
possible that the discrepancy will disappear with more
accurate measurements of the age of the Universe using both
methods.
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 6.672 x 10-11 N
m2/kg2.
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.
volt; V (after A. Volta, 1745-1827)
The derived SI unit of electric potential, defined as the
difference of potential between two points on a conductor
carrying a constant current of 1 A when the power dissipated
between the points is 1 W; it thus has units of W/A.
watt; W (after J. Watt, 1736-1819)
The derived SI unit of power, defined as a power of 1 J
acting over a period of 1 s; it thus has units of J/s.
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.
weak equivalence principle; principle of uniqueness of freefall
The idea within general relativity that the worldline of a
freefalling body is independent of its composition,
structure, or state. This principle, embraced by Newtonian
mechanics and gravitation when Newton set the inertial and
gravitational masses equal to each other. This principle is
incorporated into a stronger version with the equivalence
principle.
weber; Wb (after W. Weber, 1804-1891)
The derived SI unit of magnetic flux equal to the flux that,
linking a circuit of one turn, produces in it an
electromotive force of 1 V as it is reduced to zero at a
uniform rate in a period of 1 s; it thus has units of V s.
Weiss constant A characteristic constant dependent on the material, used in
calculating the susceptibility of paramagnetic materials.
See Curie-Weiss law.
Wiedemann-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 displacement law For a blackbody, the product of the wavelength corresponding
to the maximum radiancy and the thermodynamic temperature is
a constant, the Wien displacement law 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.
Wien's displacement law constant, b
The constant of the Wien displacement law. It has the value
2.897 756 x 10-3 m K.
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.