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Natural Laws Discovered by Now

Natural Laws Discovered by Now

Rule# Aberration Definition
1 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.
2 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.
3 Ampere’s law, modified form The line integral of the magnetic field 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.
4 Anthropic principle
5 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.
6 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.
7 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.
8 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.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 Bell’s inequality (J.S. Bell; 1964) A quantum mechanical theorem which demonstrates that if quantum mechanics were to rely on hidden variables, it must have nonlocal properties.
16 Bernoulli’s equation In an irrotational fluid, the sum of the static pressure, the weight of the fluid per unit mass times the height, and half the density times the velocity squared is constant throughout the fluid.
17 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.
18 Black-hole dynamic laws; laws of black-hole dynamics
19 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.
20 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.
21 Bohr magneton (N. Bohr) The quantum of magnetic moment.
22 Bohr radius (N. Bohr) The distance corresponding the mean distance of an electron from the nucleus in the ground state of the hydrogen atom.
23 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.
24 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.
25 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.
26 bradyon
27 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.
28 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.
29 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.
30 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.
31 Carnot’s theorem (S. Carnot) The theorem which states that no engine operating between two temperatures can be more efficient than a reversible engine.
32 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.
33 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.
34 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.
35 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.
36 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.
37 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.
38 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.
39 Coanda effect The effect that indicates that a fluid tends to flow along a surface, rather than flow through free space.
40 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.
41 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.
42 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 given below.
43 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).
44 conservation of electric charge The total electric charge of a closed system remains constant.
45 conservation of linear momentum The total linear momentum of a closed system remains constant.
46 conservation of mass-energy The total mass-energy of a closed system remains constant.
47 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.
48 Cooper pairs (L.N. Cooper; 1957)
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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.”
56 Cosmological redshift An effect where light emitted from a distant source appears redshifted because of the expansion of spacetime itself.
57 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.
58 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.
59 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.
60 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
61 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
62 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.
63 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.
64 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.
65 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.
66 Dirac constant; Planck constant, modified form; hbar A sometimes more convenient form of the Planck constant, defined as
hbar = h/(2 pi).
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 Electric constant
76 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.
77 Equation of continuity An equation which states that a 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. It is in essence a restatement of the consevation of mass during constant flow.
78 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.
79 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.
80 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.
81 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.
82 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.
83 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.
84 Faraday’s first law of electrolysis The amount of chemical change during electrolysis is proportional to the charge passed.
85 Faraday’s first law of electromagnetic induction An electromotive force is induced in a conductor when the magnetic field surrounding it changes.
86 Faraday’s law The line integral of the electric field 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.
87 Faraday’s law (M. Faraday) The line integral of the electric field 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.
88 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,
89 Faraday’s second law of electromagnetic induction The magnitude of the electromotive force is proportional to the rate of change of the field.
90 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.
91 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.
92 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.
93 Fictitious force
94 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.
95 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.
96 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.
97 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.
98 Gauss’ law The electric flux through 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.
99 Gauss’ law (K.F. Gauss) The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface; in differential form,
div E = rho,
where rho is the charge density.
100 Gauss’ law for magnetic fields The magnetic flux through a closed surface is zero; no magnetic charges exist. In differential form,
div B = 0.
101 Gauss’ law for magnetic fields (K.F. Gauss) The magnetic flux through a closed surface is zero; no magnetic charges exist; in differential form,
div B = 0.
102 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.
103 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?
104 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.
105 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.
106 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.
107 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.
108 Heisenberg uncertainty principle
109 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.
110 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.
111 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.
112 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.
113 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.
114 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.
115 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.
116 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.
117 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.
118 ideal gas laws Boyle’s law The pressure of an ideal gas is inversely proportional to the volume of the gas at constant temperature.
119 Ideal gas laws Charles’ law The volume of an ideal gas is directly proportional to the thermodynamic temperature at constant pressure.
120 Josephson effects (B.D. Josephson; 1962) Electrical effects observed when two superconducting materials are separated by a thin layer of insulating material.
121 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.
122 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.
123 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
124 Joule’s laws (J.P. Joule)
125 Joule’s second law The internal energy of an ideal gas is independent of its volume and pressure, depending only on its temperature.
126 Kelvin effect
127 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.
128 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.
129 Kepler’s first law A planet orbits the Sun in an ellipse with the Sun at one focus.
130 Kepler’s laws (J. Kepler)
131 Kepler’s second law A ray directed from the Sun to a planet sweeps out equal areas in equal times.
132 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.
133 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.
134 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.
135 Kirchhoff’s first law An incandescent solid or gas under high pressure will produce a continuous spectrum.
136 Kirchhoff’s law of radiation (G.R. Kirchhoff) The emissivity of a body is equal to its absorptance at the same temperature.
137 Kirchhoff’s laws (G.R. Kirchhoff)
138 Kirchhoff’s rules (G.R. Kirchhoff)
139 Kirchhoff’s second law A low-density gas will radiate an emission-line spectrum with an underlying emission continuum.
140 Kirchhoff’s third law Continuous radiation viewed through a low-density gas will produce an absorption-line spectrum.
141 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.
142 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.
143 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.
144 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.
145 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.
146 Lambert’s third law The luminous intensity of light decreases exponentially with distance as it travels through an absorbing medium.
147 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.
148 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.
149 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.
150 Law of parismony
151 laws of black-hole dynamics
152 Laws of thermodynamics
153 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.
154 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.
155 left-hand rule The opposite-chirality version of the right-hand rule.
156 Lenz’s law (H.F. Lenz; 1835) An induced electric current always flows in such a direction that it opposes the change producing it.
157 loop rule The sum of the potential differences encountered in a round trip around any closed loop in a circuit is zero.
158 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.
159 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.
160 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.
161 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.
162 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.
163 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.
164 Mach number (E. Mach) The ratio of the speed of an object in a given medium to the speed of sound in that medium.
165 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.
166 magnetic constant
167 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.
168 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.
169 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.
170 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.
171 Maxwell’s equations (J.C. Maxwell; 1864) Four elegant equations which describe classical electromagnetism in all its splendor.
172 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.
173 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.
174 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.
175 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.
176 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.
177 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.
178 mu_0
179 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.
180 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.
181 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.
182 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.
183 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.
184 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.
185 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.
186 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.
187 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.
188 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.
189 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.
190 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.
191 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.
192 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.
193 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.
194 particle-wave duality
195 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.
196 Pascal’s principle Pressure applied to an enclosed imcompressible static fluid is transmitted undiminished to all parts of the fluid.
Q = F m z/M.
197 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.
198 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.
199 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.
200 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.
201 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.
202 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.
203 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.
204 Planck constant, reduced; hbar
205 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.
206 Planck equation The quantum mechanical equation relating the energy of a photon E to its frequency nu:
E = h nu.
207 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.
208 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.
209 Poisson equation (S.D. Poisson) The differential form of Gauss’ law, namely,
div E = rho,
210 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.
211 Pressure law The pressure of an ideal gas is directly proportional to the thermodynamic temperature at constant volume.
212 pseudoforce A “force” which arises because an observer is naively treating an accelerating frame as an inertial one.
Examples Coriolis pseudoforce, centrifugal pseudoforce.
213 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.
214 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.
215 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.
216 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.
217 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.
218 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.
219 Resolving power
220 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.
221 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.
222 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.
223 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).
224 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.
225 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.
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.
226 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.
227 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.
228 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.
229 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.
230 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.
231 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.
232 Snell’s law
233 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.
234 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.
235 standard quantum limit The limit imposed on standard methods of measurement by the uncertainty principle within quantum mechanics.
236 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.
237 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.
238 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.
239 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.
240 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.
241 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.
242 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.
243 superfluidity The phenomena by which, at sufficiently low temperatures, a fluid can flow with zero viscosity. Its causes are associated with superconductivity.
244 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:
245 superposition principle of forces The net force on a body is equal to the sum of the forces impressed upon it.
246 superposition principle of states The resultant quantum mechnical wavefunction due to two or more individual wavefunctions is the sum of the individual wavefunctions.
247 superposition principle of waves The resultant wave function due to two or more individual wave functions is the sum of the individual wave functions.
248 Système Internationale d’Unités (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.
249 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.
250 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.
251 tardon A particle which has a positive real mass and travels at a speed less than c in all inertial frames.
Compare tachyon, luxon.
252 tardyon
253 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.
254 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.
255 thermodynamic laws
256 Third law of thermodynamics For changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero.
257 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.
258 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.
259 Titius-Bode law
260 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.
261 Trojan points L4 and L5, the two dynamically stable Lagrange points (under certain conditions).
262 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.
263 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.
264 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.
265 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.
266 uniformity principle (E.P. Hubble) 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).
267 universal age paradox In a more generalized sense, the uncertainty principle tells us that the act of observing changes the observed in fundamental way.
268 universal constant of gravitation; G 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.
269 van der Waals force (J.D. van der Waals) 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.
270 volt; V (after A. Volta, 1745-1827) 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.
271 watt; W (after J. Watt, 1736-1819) 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.
272 wave-particle duality 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.
273 Weak anthropic principle 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.
274 weak equivalence principle; principle of uniqueness of freefall 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.
275 weber; Wb (after W. Weber, 1804-1891) 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.
276 Weiss constant 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.
277 Wiedemann-Franz law 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.
278 Wien displacement law A characteristic constant dependent on the material, used in calculating the susceptibility of paramagnetic materials.
279 Wien’s displacement law constant, b 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.
280 Woodward-Hoffmann rules 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.
281 Young’s experiment; double-slit experiment (T. Young; 1801) The constant of the Wien displacement law. It has the value 2.897 756 x 10-3 m K.
282 Zeeman effect; Zeeman line splitting (P. Zeeman; 1896) Rules governing the formation of products during certain types of organic reactions.
283 Zeroth law of thermodynamics 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 diffracted through these slits and develops an interference pattern on the other side of the screen.

 

Rule# Aberration Definition
1 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.
2 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.
3 Ampere’s law, modified form The line integral of the magnetic field 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.
4 Anthropic principle
5 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.
6 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.
7 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.
8 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.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 Bell’s inequality (J.S. Bell; 1964) A quantum mechanical theorem which demonstrates that if quantum mechanics were to rely on hidden variables, it must have nonlocal properties.
16 Bernoulli’s equation In an irrotational fluid, the sum of the static pressure, the weight of the fluid per unit mass times the height, and half the density times the velocity squared is constant throughout the fluid.
17 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.
18 Black-hole dynamic laws; laws of black-hole dynamics
19 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.
20 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.
21 Bohr magneton (N. Bohr) The quantum of magnetic moment.
22 Bohr radius (N. Bohr) The distance corresponding the mean distance of an electron from the nucleus in the ground state of the hydrogen atom.
23 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.
24 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.
25 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.
26 bradyon
27 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.
28 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.
29 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.
30 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.
31 Carnot’s theorem (S. Carnot) The theorem which states that no engine operating between two temperatures can be more efficient than a reversible engine.
32 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.
33 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.
34 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.
35 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.
36 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.
37 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.
38 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.
39 Coanda effect The effect that indicates that a fluid tends to flow along a surface, rather than flow through free space.
40 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.
41 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.
42 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 given below.
43 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).
44 conservation of electric charge The total electric charge of a closed system remains constant.
45 conservation of linear momentum The total linear momentum of a closed system remains constant.
46 conservation of mass-energy The total mass-energy of a closed system remains constant.
47 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.
48 Cooper pairs (L.N. Cooper; 1957)
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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.”
56 Cosmological redshift An effect where light emitted from a distant source appears redshifted because of the expansion of spacetime itself.
57 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.
58 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.
59 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.
60 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
61 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
62 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.
63 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.
64 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.
65 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.
66 Dirac constant; Planck constant, modified form; hbar A sometimes more convenient form of the Planck constant, defined as
hbar = h/(2 pi).
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 Electric constant
76 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.
77 EPR effect epsilon_0
78 Equation of continuity An equation which states that a 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. It is in essence a restatement of the consevation of mass during constant flow.
79 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.
80 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.
81 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.
82 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.
83 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.
84 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.
85 Faraday’s first law of electrolysis The amount of chemical change during electrolysis is proportional to the charge passed.
86 Faraday’s first law of electromagnetic induction An electromotive force is induced in a conductor when the magnetic field surrounding it changes.
87 Faraday’s law The line integral of the electric field 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.
88 Faraday’s law (M. Faraday) The line integral of the electric field 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.
89 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,
90 Faraday’s second law of electromagnetic induction The magnitude of the electromotive force is proportional to the rate of change of the field.
91 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.
92 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.
93 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.
94 Fictitious force
95 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.
96 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.
97 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.
98 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.
99 Gauss’ law The electric flux through 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.
100 Gauss’ law (K.F. Gauss) The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface; in differential form,
div E = rho,
where rho is the charge density.
101 Gauss’ law for magnetic fields The magnetic flux through a closed surface is zero; no magnetic charges exist. In differential form,
div B = 0.
102 Gauss’ law for magnetic fields (K.F. Gauss) The magnetic flux through a closed surface is zero; no magnetic charges exist; in differential form,
div B = 0.
103 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.
104 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?
105 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.
106 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.
107 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.
108 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.
109 Heisenberg uncertainty principle
110 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.
111 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.
112 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.
113 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.
114 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.
115 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.
116 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.
117 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.
118 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.
119 ideal gas laws Boyle’s law The pressure of an ideal gas is inversely proportional to the volume of the gas at constant temperature.
120 Ideal gas laws Charles’ law The volume of an ideal gas is directly proportional to the thermodynamic temperature at constant pressure.
121 Josephson effects (B.D. Josephson; 1962) Electrical effects observed when two superconducting materials are separated by a thin layer of insulating material.
122 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.
123 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.
124 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
125 Joule’s laws (J.P. Joule)
126 Joule’s second law The internal energy of an ideal gas is independent of its volume and pressure, depending only on its temperature.
127 Kelvin effect
128 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.
129 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.
130 Kepler’s first law A planet orbits the Sun in an ellipse with the Sun at one focus.
131 Kepler’s laws (J. Kepler)
132 Kepler’s second law A ray directed from the Sun to a planet sweeps out equal areas in equal times.
133 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.
134 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.
135 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.
136 Kirchhoff’s first law An incandescent solid or gas under high pressure will produce a continuous spectrum.
137 Kirchhoff’s law of radiation (G.R. Kirchhoff) The emissivity of a body is equal to its absorptance at the same temperature.
138 Kirchhoff’s laws (G.R. Kirchhoff)
139 Kirchhoff’s rules (G.R. Kirchhoff)
140 Kirchhoff’s second law A low-density gas will radiate an emission-line spectrum with an underlying emission continuum.
141 Kirchhoff’s third law Continuous radiation viewed through a low-density gas will produce an absorption-line spectrum.
142 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.
143 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.
144 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.
145 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.
146 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.
147 Lambert’s third law The luminous intensity of light decreases exponentially with distance as it travels through an absorbing medium.
148 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.
149 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.
150 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.
151 Law of parismony
152 laws of black-hole dynamics
153 Laws of thermodynamics
154 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.
155 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.
156 left-hand rule The opposite-chirality version of the right-hand rule.
157 Lenz’s law (H.F. Lenz; 1835) An induced electric current always flows in such a direction that it opposes the change producing it.
158 loop rule The sum of the potential differences encountered in a round trip around any closed loop in a circuit is zero.
159 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.
160 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.
161 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.
162 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.
163 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.
164 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.
165 Mach number (E. Mach) The ratio of the speed of an object in a given medium to the speed of sound in that medium.
166 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.
167 magnetic constant
168 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.
169 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.
170 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.
171 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.
172 Maxwell’s equations (J.C. Maxwell; 1864) Four elegant equations which describe classical electromagnetism in all its splendor.
173 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.
174 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.
175 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.
176 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.
177 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.
178 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.
179 mu_0
180 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.
181 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.
182 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.
183 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.
184 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.
185 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.
186 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.
187 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.
188 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.
189 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.
190 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.
191 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.
192 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.
193 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.
194 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.
195 particle-wave duality
196 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.
197 Pascal’s principle Pressure applied to an enclosed imcompressible static fluid is transmitted undiminished to all parts of the fluid.
Q = F m z/M.
198 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.
199 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.
200 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.
201 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.
202 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.
203 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.
204 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.
205 Planck constant, reduced; hbar
206 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.
207 Planck equation The quantum mechanical equation relating the energy of a photon E to its frequency nu:
E = h nu.
208 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.
209 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.
210 Poisson equation (S.D. Poisson) The differential form of Gauss’ law, namely,
div E = rho,
211 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.
212 Pressure law The pressure of an ideal gas is directly proportional to the thermodynamic temperature at constant volume.
213 pseudoforce A “force” which arises because an observer is naively treating an accelerating frame as an inertial one.
Examples Coriolis pseudoforce, centrifugal pseudoforce.
214 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.
215 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.
216 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.
217 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.
218 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.
219 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.
220 Resolving power
221 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.
222 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.
223 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.
224 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).
225 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.
226 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.
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.
227 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.
228 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.
229 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.
230 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.
231 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.
232 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.
233 Snell’s law
234 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.
235 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.
236 standard quantum limit The limit imposed on standard methods of measurement by the uncertainty principle within quantum mechanics.
237 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.
238 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.
239 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.
240 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.
241 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.
242 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.
243 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.
244 superfluidity The phenomena by which, at sufficiently low temperatures, a fluid can flow with zero viscosity. Its causes are associated with superconductivity.
245 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:
246 superposition principle of forces The net force on a body is equal to the sum of the forces impressed upon it.
247 superposition principle of states The resultant quantum mechnical wavefunction due to two or more individual wavefunctions is the sum of the individual wavefunctions.
248 superposition principle of waves The resultant wave function due to two or more individual wave functions is the sum of the individual wave functions.
249 Système Internationale d’Unités (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.
250 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.
251 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.
252 tardon A particle which has a positive real mass and travels at a speed less than c in all inertial frames.
Compare tachyon, luxon.
253 tardyon
254 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.
255 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.
256 thermodynamic laws
257 Third law of thermodynamics For changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero.
258 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.
259 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.
260 Titius-Bode law
261 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.
262 Trojan points L4 and L5, the two dynamically stable Lagrange points (under certain conditions).
263 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.
264 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.
265 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.
266 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.
267 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.
268 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.
269 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.
270 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.
271 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.
272 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.
273 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.
274 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.
275 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.
276 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.
277 Weiss constant A characteristic constant dependent on the material, used in calculating the susceptibility of paramagnetic materials.
278 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.
279 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.
280 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.
281 Woodward-Hoffmann rules Rules governing the formation of products during certain types of organic reactions.
282 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 diffracted through these slits and develops an interference pattern on the other side of the screen.
283 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.
284 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.

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