B- E Gas Laws & Magnetics

See ideal gas laws.

Brackett series (Brackett)

The series which describes the emission spectrum of hydrogen when the electron is jumping to the fourth orbital. All of the lines are in the infrared portion of the spectrum.

bradyon

See tardon.

Bragg’s law (Sir W.L. Bragg; 1912)

When a beam of x-rays strikes a crystal surface in which the layers of atoms or ions are regularly separated, the maximum intensity of the reflected ray occurs when the complement of the angle of incidence, theta, the wavelength of the x-rays, lambda, and the distance betwen layers of atoms or ions, d, are related by the equation

2 d sin theta = n lambda,

where n is an integer.

Brewster’s law (D. Brewster)

The extent of the polarization of light reflected from a transparent surface is a maximum when the reflected ray is at right angles to the refracted ray.
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Brownian motion (R. Brown; 1827)

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The fundamental SI unit of luminous intensity defined as the luminous intensity in a given direction of a source that emits monochromatic photons of frequency 540 x 1012 Hz and has a radiant intensity in that direction of 1/683 W/sr.

Carnot’s theorem (S. Carnot)giant magnets for sale
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The theorem which states that no engine operating between two temperatures can be more efficient than a reversible engine.

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A quantum mechanical effect, where two very large plates placed close to each other will experience an attractive force, in the absence of other forces. The cause is virtual particle-antiparticle pair creation in the vicinity of the plates. Also, the speed of light will be increased in the region between the two plates, in the direction perpendicular to them.

causality principle

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The principle that cause must always preceed effect. More formally, if an event A (“the cause”) somehow influences an event B (“the effect”) which occurs later in time, then event B cannot in turn have an influence on event A. That is, event B must occur at a later time t than event A, and further, all frames must agree upon this ordering.

The principle is best illustrated with an example. Say that event A constitutes a murderer making the decision to kill his victim, and that event B is the murderer actually committing the act. The principle of causality puts forth that the act of murder cannot have an influence on the murderer’s decision to commit it. If the murderer were to somehow see himself committing the act and change his mind, then a murder would have been committed in the future without a prior cause (he changed his mind). This represents a causality violation. Both time travel and faster-than-light travel both imply violations of causality, which is why most physicists think they are impossible, or at least impossible in the general sense.

centrifugal pseudoforce

A pseudoforce that occurs when one is moving in uniform circular motion. One feels a “force” directed outward from the center of motion.

Chandrasekhar limit (S. Chandrasekhar; 1930)

A limit which mandates that no white dwarf (a collapsed, degenerate star) can be more massive than about 1.4 masses solar. Any degenerate mass more massive must inevitably collapse into a neutron star.

Charles’ law (J.A.C. Charles; c. 1787)

The volume of an ideal gas at constant pressure is proportional to the thermodynamic temperature of that gas.

Cherenkov [Cerenkov] radiation (P.A. Cherenkov)

Radiation emitted by a massive particle which is moving faster than light in the medium through which it is travelling. No particle can travel faster than light in vacuum, but the speed of light in other media, such as water, glass, etc., are considerably lower. Cherenkov radiation is the electromagnetic analogue of the sonic boom, though Cherenkov radiation is a shockwave set up in the electromagnetic field.

chronology protection conjecture (S.W. Hawking)

The concept that the formation of any closed timelike curve will automatically be destroyed by quantum fluctuations as soon as it is formed. In other words, quantum fluctuations prevent time machines from being created.

Coanda effect

The effect that indicates that a fluid tends to flow along a surface, rather than flow through free space.

complementarity principle (N. Bohr)

The principle that a given system cannot exhibit both wave-like behavior and particle-like behavior at the same time. That is, certain experiments will reveal the wave-like nature of a system, and certain experiments will reveal the particle-like nature of a system, but no experiment will reveal both simultaneously.

Compton effect (A.H. Compton; 1923)

An effect that demonstrates that photons (the quantum of electromagnetic radiation) have momentum. A photon fired at a stationary particle, such as an electron, will impart momentum to the electron and, since its energy has been decreased, will experience a corresponding decrease in frequency.

conservation laws

A law which states that, in a closed system, the total quantity of something will not increase or decrease, but remain exactly the same; that is, its rate of change is zero. For physical quantities, it states that something can neither be created nor destroyed. Mathematically, if a scalar X is the quantity considered, then

dX/dt = 0,

or, equivalently,

X = constant.

For a vector field F, the conservation law is written as

div F = 0;

that is, the vector field F is divergence-free everywhere (i.e., has no sources or sinks).

Some specific examples of conservation laws are:

conservation of mass-energy

The total mass-energy of a closed system remains constant.

conservation of electric charge

The total electric charge of a closed system remains constant.

conservation of linear momentum

The total linear momentum of a closed system remains constant.

conservation of angular momentum

The total angular momentum of a closed system remains constant.

There are several other laws that deal with particle physics, such as conservation of baryon number, of strangeness, etc., which are conserved in some fundamental interactions (such as the electromagnetic interaction) but not others (such as the weak interaction).

constancy principle (A. Einstein)

One of the postulates of A. Einstein’s special theory of relativity, which puts forth that the speed of light in vacuum is measured as the same speed to all observers, regardless of their relative motion. That is, if I’m travelling at 0.9 c away from you, and fire a beam of light in that direction, both you and I will independently measure the speed of that beam as c.

One of the results of this postulate (one of the predictions of special relativity) is that no massive particle can be accelerated to (or beyond) lightspeed, and thus the speed of light also represents the ultimate cosmic speed limit. Only massless particles (collectively called luxons, including photons, gravitons, and possibly neutrinos, should they prove to indeed be massless) travel at lightspeed, and all other particles must travel at slower speeds.

See tachyons, causality principle.

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.

Cooper pairs (L.N. Cooper; 1957)

See BCS theory.

Copernican principle (N. Copernicus)

The idea, suggested by Copernicus, that the Sun, not the Earth, is at the center of the Universe. We now know that neither idea is correct (the Sun is not even located at the center of our Galaxy, much less the Universe), but it set into effect a long chain of demotions of Earth’s and our place in the Universe, to where it is now: On an unimpressive planet orbiting a mediocre star in a corner of a typical galaxy, lost in the Universe.

Coriolis pseudoforce (G. de Coriolis; 1835)

A pseudoforce which arises because of motion relative to a frame which is itself rotating relative to second, inertial frame. The magnitude of the Coriolis “force” is dependent on the speed of the object relative to the noninertial frame, and the direction of the “force” is orthogonal to the object’s velocity.

correspondence limit (N. Bohr)

The limit at which a more general theory reduces to a more specialized theory when the conditions that the specialized theory requires are taken away.

See correspondence principle.

correspondence principle (N. Bohr)

The principle that when a new, more general theory is put forth, it must reduce to the more specialized (and usually simpler) theory under normal circumstances. There are correspondence principles for general relativity to special relativity and special relativity to Newtonian mechanics, but the most widely known correspondence principle (and generally what is meant when one says “correspondence principle”) is that of quantum mechanics to classical mechanics.

See correspondence limit.

cosmic background radiation; primal glow

The background of radiation mostly in the frequency range 3 x 1011 to 3 x 108 Hz discovered in space in 1965. It is believed to be the cosmologically redshifted radiation released by the big bang itself. Presently it has an energy density in empty space of about 4 x 10-14 J/m3.

cosmic censorship conjecture (R. Penrose, 1979)

The conjecture, so far totally undemonstrated within the context of general relativity, that all singularities (with the possible exception of the big bang singularity) are accompanied by event horizons which completely surround them at all points in time. That is, problematic issues with the singularity are rendered irrelevant, since no information can ever escape from a black hole’s event horizon.

cosmological constant; Lambda

The constant introduced to the Einstein field equation, intended to admit static cosmological solutions. At the time the current philosophical view was the steady-state model of the Universe, where the Universe has been around for infinite time. Early analysis of the field equation indicated that general relativity allowed dynamic cosmological models only (ones that are either contracting or expanding), but no static models. Einstein introduced the most natural abberation to the field equation that he could think of: the addition of a term proportional to the spacetime metric tensor, g, with the constant of proportionality being the cosmological constant:

G + Lambda g = 8 pi T.

Hubble’s later discovery of the expansion of the Universe indicated that the introduction of the cosmological constant was unnecessary; had Einstein believed what his field equation was telling him, he could have claimed the expansion of the Universe as perhaps the greatest and most convincing prediction of general relativity; he called this the “greatest blunder of my life.”

cosmological redshift

An effect where light emitted from a distant source appears redshifted because of the expansion of spacetime itself.

Compare Doppler effect.

coulomb; C (after C. de Coulomb, 1736-1806)

The derived SI unit of electric charge, defined as the amount of charge transferred by a current of 1 A in a period of 1 s; it thus has units of A s.

Coulomb’s law (C. de Coulomb)

The primary law for electrostatics, analogous to Newton’s law of universal gravitation. It states that the force between two point charges is proportional to the algebraic product of their respective charges as well as proportional to the inverse square of the distance between them; mathematically,

F = 1/(4 pi epsilon0) (q Q/r2) e,

where q and Q are the strengths of the two charges, r is the distance between the two, and e is a unit vector directed from the test charge to the second.

Curie constant; C (P. Curie)

A characteristic constant, dependent on the material in question, which indicates the proportionality between its susceptibility and its thermodynamic temperature.

Curie’s law (P. Curie)

The susceptibility, khi, of an isotropic paramagnetic substance is related to its thermodynamic temperature T by the equation

khi = C/T

See Curie-Weiss law.

Curie-Weiss law (P. Curie, P.-E. Weiss)

A more general form of Curie’s law, which states that the susceptibility, khi, of an paramagnetic substance is related to its thermodynamic temperature T by the equation

khi = C/T – W

Navigation.

Dalton’s law of partial pressures (J. Dalton)

The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of its components; that is, the sum of the pressures that each component would exert if it were present alone and occuped the same volume as the mixture.

Davisson-Germer experiment (C.J. Davisson, L.H. Germer; 1927)

An experiment that conclusively confirmed the wave nature of electrons; diffraction patterns were observed by an electron beam penetrating into a nickel target.

de Broglie wavelength (L. de Broglie; 1924)

The prediction that particles also have wave characteristics, where the effective wavelength of a particle would be inversely proportional to its momentum, where the constant of proportionality is the Planck constant.

determinism principle

The principle that if one knows the state to an infinite accuracy of a system at one point in time, one would be able to predict the state of that system with infinite accuracy at any other time, past or future. For example, if one were to know all of the positions and velocities of all the particles in a closed system, then determinism would imply that one could then predict the positions and velocities of those particles at any other time. This principle has been disfavored due to the advent of quantum mechanics, where probabilities take an important part in the actions of the subatomic world, and the uncertainty principle implies that one cannot know both the position and velocity of a particle to arbitrary precision.

Dirac constant; Planck constant, modified form; hbar

A sometimes more convenient form of the Planck constant, defined as

hbar = h/(2 pi).

Doppler effect (C.J. Doppler)

Waves emitted by a moving object as received by an observer will be blueshifted (compressed) if approaching, redshifted (elongated) if receding. It occurs both in sound as well as electromagnetic phenomena, although it takes on different forms in each.

Compare cosmological redshift.

Drake equation (F. Drake; 1961)

A method of estimating the number of intelligent, technological species (i.e., able to communicate with other species) in existence in our Galaxy.

N = R fp ne fl fi ft L.

N is the number of species described above at any given moment in our Galaxy. The parameters it is computed from are as follows:

R

the rate of star formation in our Galaxy (in stars per year);

fp

the fraction of stars which have planets;

ne

the number of habitable planets per system with planets;

fl

the fraction of habitable planets upon which life arises;

fi

the fraction of these planets upon which life develops intelligence;

ft

the fraction of these planets where the intelligence develops into a technological civilization capable of communication; and

L

the mean lifetime of such a technological civilization.

Of these quantities, only the first — R — is known with anything like any reliability; it is on the order of 10 stars per year. The others, most notably the fractions, are almost entirely pure speculation at this point. Calculations made by respectable astronomers differ by something like ten orders of magnitude in the final estimation of the number of species out there.

Dulong-Petit law (P. Dulong, A.T. Petit; 1819)

The molar heat capacity is approximately equal to the three times the ideal gas constant:

C = 3 R.

Eddington limit (Sir A. Eddington)

The theoretical limit at which the photon pressure would exceed the gravitational attraction of a light-emitting body. That is, a body emitting radiation at greater than the Eddington limit would break up from its own photon pressure.

Edwards-Casimir quantum vacuum drive

A hypothetical drive exploiting the peculiarities of quantum mechanics by restricting allowed wavelengths of virtual photons on one side of the drive (the bow of the ship); the pressure generated from the unrestricted virtual photons toward the aft generates a net force and propels the drive.

See Casimir effect.

Ehrenfest paradox (Ehernfest, 1909)

The special relativistic “paradox” involving a rapidly rotating disc. Since any radial segment of the disc is perpendicular to the direction of motion, there should be no length contraction of the radius; however, since the circumference of the disc is parallel to the direction of motion, it should contract.

Einstein field equation

The cornerstone of Einstein’s general theory of relativity, relating the gravitational tensor G to the stress-energy tensor T by the simple equation

G = 8 pi T.

Einstein-Podolsky-Rosen effect; EPR effect

Consider the following quantum mechanical thought-experiment: Take a particle which is at rest and has spin zero. It spontaneously decays into two fermions (spin 1/2 particles), which stream away in opposite directions at high speed. Due to the law of conservation of spin, we know that one is a spin +1/2 and the other is spin -1/2. Which one is which? According to quantum mechanics, neither takes on a definite state until it is observed (the wavefunction is collapsed).

The EPR effect demonstrates that if one of the particles is detected, and its spin is then measured, then the other particle — no matter where it is in the Universe — instantaneously is forced to choose as well and take on the role of the other particle. This illustrates that certain kinds of quantum information travel instantaneously; not everything is limited by the speed of light.

However, it can be easily demonstrated that this effect does not make faster-than-light communication or travel possible.

electric constant

See permeability of free space.

Eotvos law of capillarity (Baron L. von Eotvos; c. 1870)

The surface tension gamma of a liquid is related to its temperature T, the liquid’s critical temperature, T*, and its density rho by

gamma ~= 2.12 (T* – T)/rho3/2.

EPR effect

See Einstein-Podolsky-Rosen effect.

epsilon_0

See permittivity of free space.

equivalence principle

The basic postulate of A. Einstein’s general theory of relativity, which posits that an acceleration is fundamentally indistinguishable from a gravitational field. In other words, if you are in an elevator which is utterly sealed and protected from the outside, so that you cannot “peek outside,” then if you feel a force (weight), it is fundamentally impossible for you to say whether the elevator is present in a gravitational field, or whether the elevator has rockets attached to it and is accelerating “upward.”

Although that in practical situations — say, sitting in a closed room — it would be possible to determine whether the acceleration felt was due to uniform thrust or due to gravitation (say, by measuring the gradient of the field; if nonzero, it would indicate a gravitational field rather than thrust); however, such differences could be made arbitrarily small. The idea behind the equivalence principle is that it acts around the vicinity of a point, rather than over macroscopic distances. It would be impossible to say whether or not a given (arbitrary) acceleration field was caused by thrust or gravitation by the use of physics alone.

The equivalence principle predicts intere

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