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.
Dulong-Petit law (P. Dulong, A.T. Petit; 1819)
The molar heat capacity is approximately equal to the three times the ideal gas constant:
C = 3 R.
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.
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.
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.
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.
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.
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.
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.
