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
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.
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.
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
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.
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
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.
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
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.
The radiation -- the radiance at particular frequencies all across the spectrum -- produced by a
blackbody -- that is, a perfect radiator (and absorber) of heat. physicsists 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
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
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.
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.
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.
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 physicsists think they are impossible, or at least impossible in the general sense.
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
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
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
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.
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 physicsal quantities, it states that
something can neither be created nor destroyed. Mathematically, if a scalar X is the quantity considered,
dX/dt = 0,
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.
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
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."
An effect where light emitted from a distant source appears redshifted because of the expansion of
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