An Etymological Dictionary of Astronomy and Astrophysics
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A state of matter in which a group of atoms or subatomic particles, cooled to within → absolute zero, coalesce into a single quantum mechanical entity that can be described by a → wave function. When a group of atoms are cooled down to very near absolute zero, the atoms hardly move relative to each other, because they have almost no free energy to do so. Hence the atoms clump together and enter the same → ground energy states. They become identical and the whole group starts behaving as though it were a single atom. A Bose-Einstein condensate results from a → quantum transition phase called the → Bose-Einstein condensation. This form of matter was predicted in 1924 by Albert Einstein on the basis of the quantum formulations of the Indian physicist Satyendra Nath Bose.
Bose-Einstein condensate was created for the first time in the laboratory in 1995. The three physicist who succeeded in producing BEC, Eric A. Cornell, Wolfgang Ketterle, and Carl E. Wieman, were awarded the 2001 Nobel Prize in Physics. Cornell and Wieman managed to do that with about 2,000 → rubidium atoms cooled down to 20 nano K, while Ketterle used more than 100,000 → sodium atoms.

→ boson; → Einstein; → condensate.

A → quantum phase transition during which the → bosons constituting a sufficiently cooled boson gas are all clustered in the → ground energy state. The phase transition results in a → Bose-Einstein condensate. This phenomenon occurs when the temperature becomes smaller than a critical value given by: T_c = (2πħ² / km)(n / 2.612)^2/3, where m is mass of each boson, ħ is the → reduced Planck's constant, k is → Boltzmann's constant, and n is the particle number density. When T  ≤  T_c, the → de Broglie wavelength of bosons becomes comparable to the distance between bosons.

→ boson; → Einstein; → condensation.

For a → population of independent → bosons, a function that specifies the number of particles in each of the allowed → energy states.

→ boson; → Einstein; → distribution.

Same as → Bose-Einstein distribution.

→ boson; → Einstein; → statistics.

A unit of radiation energy sometimes used in the investigation of photochemical processes. The unit is defined as N_Ahν, where N_A is → Avogadro's number and hν is the energy of a → quantum of the radiation. One einstein (or Einstein unit) is the energy per → mole of photons carried by a beam of monochromatic light.

Named for Albert Einstein (1879-1955).

A measure of the probability that a particular atomic transition leading to the formation of an atomic spectral line occurs. The coefficient of spontaneous emission is denoted by A_ij, and the coefficient of stimulated emission by B_ij, i representing the lower level and j is the upper level.

Named after Albert Einstein (1879-1955) who introduced the coefficients in 1916; → coefficient.

An image of a distant quasar (redshift 1.7) formed by a foreground spiral galaxy (redshift 0.039) through gravitational lensing. The image of the quasar is split into four point sources forming a cross at the center of the galaxy.

→ Einstein; → cross.

The → equivalence principle as stated by Einstein, on which is based the theory of → general relativity. It comprises the three following items:
1) The → weak equivalence principle is valid.
2) The outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling → reference frame in which it is performed. Also known as → local Lorentz invariance.
3) The outcome of any local non-gravitational experiment is independent of where and when in the Universe it is performed. Also called → local position invariance.

→ Einstein; → equivalence; → principle.

A model for the → specific heat of solids in which the specific heat is due to the vibrations of the atoms of the solids. The vibration energy is → quantized and the atoms have a single frequency, ν. Put forward in 1907 by Einstein, this model was the first application of → quantum theory to the solid state physics. The expression for the specific heat is given by: C_V = 3Rx²e^x/(e^x -1)², where R is the → gas constant, x = T_E/T, T_E = hν/k, h is → Planck's constant, and k is → Boltzmann's constant. T_E is called the → Einstein temperature. This model could explain the temperature behavior of specific heat but not very satisfactorily at low temperatures. It has therefore been superseded by the → Debye model. See also → Dulong-Petit law.

Albert Einstein in 1907; → model.

A notation convention in → tensor analysis whereby whenever there is an expression with a repeated → index, the summation is done over that index from 1 to 3 (or from 1 to n, where n is the space dimension). For example, the dot product of vectors a and b is usually written as: a.b = Σ (i = 1 to 3) a_i.b_i. In the Einstein notation this is simply written as a.b = a_i.b_i. This notation makes operations much easier. Same as Einstein summation convention.

→ Einstein; → notation.

In gravitational lens phenomenon, the critical distance from the → lensing object for which the light ray from the source is deflected to the observer, provided that the source, the lens, and the observer are exactly aligned. Consider a massive object (the lens) situated exactly on the line of sight from Earth to a background source. The light rays from the source passing the lens at different distances are bent toward the lens. Since the bending angle for a light ray increases with decreasing distance from the lens, there is a critical distance such that the ray will be deflected just enough to hit the Earth. This distance is called the Einstein radius. By rotational symmetry about the Earth-source axis, an observer on Earth with perfect resolution would see the source lensed into an annulus, called Einstein ring, centered on its position. The size of an Einstein ring is given by the Einstein radius: θ_E = (4GM/c²)^0.5 (d_LS/(d_L.d_S)^0.5, where G is the → gravitational constant, M is the mass of the lens, c is the → speed of light, d_L is the angular diameter distance to the lens, d_S is the angular diameter distance to the source, and d_LS is the angular diameter distance between the lens and the source. The equation can be simplified to: θ_E = (0''.9) (M/10¹¹Msun)^0.5 (D/Gpc)^-0.5. Hence, for a dense cluster with mass M ~ 10 × 10¹⁵ Msun at a distance of 1 Gigaparsec (1 Gpc) this radius is about 100 arcsec. For a gravitational → microlensing event (with masses of order 1 Msun) at galactic distances (say D ~ 3 kpc), the typical Einstein radius would be of order milli-arcseconds.

→ Einstein; → radius.

The apparent shape of a background source unsergoing the effect of → gravitational lensing as seen from Earth, provided that the source, the intervening lens, and the observer are in perfect alignement through → Einstein radius.

→ Einstein; → ring.

Same as → Einstein model.

→ Einstein; → solid.

A cosmological model in which a static (neither expanding nor collapsing) Universe is maintained by introducing a cosmological repulsion force (in the form of the cosmological constant) to counterbalance the gravitational force.

→ Einstein; → static; arr; universe.

A characteristic parameter occurring in the → Einstein model of → specific heats.

→ Einstein; → temperature.

A mathematical entity describing the → curvature of → space-time in → Einstein's field equations, according to the theory of → general relativity. It is expressed by G_μν = R_μν - (1/2) g_μνR, where R_μν is the Ricci tensor, g_μν is the → metric tensor, and R the scalar curvature. This tensor is both symmetric and divergence free.

Named after Albert Einstein (1879-1955); → tensor.

The time during which a → microlensing event occurs. It is given by the equation t_E = R_E/v, where R_E is the → Einstein radius, v is the magnitude of the relative transverse velocity between source and lens projected onto the lens plane. The characteristic time-scale of → microlensing events is about 25 days.

→ Einstein; → time-scale.

A → thought experiment, involving an elevator, first conceived by Einstein to show the → principle of equivalence. According to this experiment, it is impossible for an observer situated inside a closed elevator to decide if the elevator is being pulled upward by a constant force or is subject to a gravitational field acting downward on a stationary elevator. Einstein used this experiment and the principle of equivalence to deduce the bending of light by the force of gravity.

→ einstein; elevator, from L. elevator, agent noun from p.p. stem of elevare "to lift up, raise," from → ex- "out" + levare "lighten, raise," from levis "light" in weight, → lever.

Bâlâbar, → lift.

A system of ten non-linear → partial differential equations in the theory of → general relativity which relate the curvature of → space-time with the distribution of matter-energy. They have the form: G_μν = -κ T_μν, where G_μν is the → Einstein tensor (a function of the → metric tensor), κ is a coupling constant called the → Einstein gravitational constant, and T_μν is the → energy-momentum tensor. The field equations mean that the curvature of space-time is due to the distribution of mass-energy in space. A more general form of the field equations proposed by Einstein is: G_μν + Λg_μν = - κT_μν, where Λ is the → cosmological constant.

Named after Albert Einstein (1879-1955); → field; → equation.

The coupling constant appearing in → Einstein's field equations, expressed by: κ = 8πG/c⁴, where G is the Newtonian → gravitational constant and c the → speed of light.

→ einstein; → gravitational; → constant.