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.
particle-wave duality
See wave-particle duality.
Pascal's principle
Pressure applied to an enclosed imcompressible static fluid is transmitted undiminished to all parts of the
fluid.
Paschen series
The series which describes the emission spectrum of hydrogen when the electron is jumping to the third
orbital. All of the lines are in the infrared portion of the spectrum.
Pauli exclusion principle (W. Pauli; 1925)
No two identical fermions in a system, such as electrons in an atom, can have an identical set of quantum
numbers.
Peltier effect (J.C.A. Peltier; 1834)
The change in temperature produced at a junction between two dissimilar metals or semiconductors when
an electric current passes through the junction.
permeability of free space; magnetic constant; mu_0
The ratio of the magnetic flux density in a substance to the external field strength for vacuum. It is equal
to 4 pi x 10-7 H/m.
permittivity of free space; electric constant; epsilon_0
The ratio of the electric displacement to the intensity of the electric field producing it in vacuum. It is
equal to 8.854 x 10-12 F/m.
Pfund series
The series which describes the emission spectrum of hydrogen when the electron is jumping to the fifth
orbital. All of the lines are in the infrared portion of the spectrum.
photoelectric effect
An effect explained by A. Einstein that demonstrate that light seems to be made up of particles, or
photons. Light can excite electrons (called photoelectrons 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.
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.
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.
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.
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.
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.
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.
