An Etymological Dictionary of Astronomy and Astrophysics

1. Math.: An → eigenvector for a linear → operator on a → vector space whose vectors are → functions. Also known as proper function.
   

2. Quantum mechanics: A → wave function corresponding to an → eigenvalue. Eigenfunctions represent the stationary → quantum states of a system.

Etymology (EN): From Ger. Eigenfunktion, from eigen- “characteristic, particular, own” (from P.Gmc. *aigana- “possessed, owned,” Du. eigen, O.E. agen “one’s own”) + → function.

Etymology (PE): Viž-karyâ, from viž, contraction of vižé “particular, charcteristic” + karyâ, → function. Vižé, from Mid.Pers. apēcak “pure, sacred,” from *apa-vēcak “set apart,” from prefix apa- + vēcak, from vēxtan (Mod.Pers. bixtan) “to detach, separate, sift, remove,” Av. vaēk- “to select, sort out, sift,” pr. vaēca-, Skt. vic-, vinakti “to sift, winnow, separate; to inquire.”

1. Math.: An → eigenvector for a linear → operator on a → vector space whose vectors are → functions. Also known as proper function.
   

2. Quantum mechanics: A → wave function corresponding to an → eigenvalue. Eigenfunctions represent the stationary → quantum states of a system.

Etymology (EN): From Ger. Eigenfunktion, from eigen- “characteristic, particular, own” (from P.Gmc. *aigana- “possessed, owned,” Du. eigen, O.E. agen “one’s own”) + → function.

Etymology (PE): Viž-karyâ, from viž, contraction of vižé “particular, charcteristic” + karyâ, → function. Vižé, from Mid.Pers. apēcak “pure, sacred,” from *apa-vēcak “set apart,” from prefix apa- + vēcak, from vēxtan (Mod.Pers. bixtan) “to detach, separate, sift, remove,” Av. vaēk- “to select, sort out, sift,” pr. vaēca-, Skt. vic-, vinakti “to sift, winnow, separate; to inquire.”

Quantum mechanics: A dynamical state whose state vector (or wave function) is an → eigenvector of an → operator corresponding to a specified physical quantity.

See also: → eigenfunction; → state.

Quantum mechanics: A dynamical state whose state vector (or wave function) is an → eigenvector of an → operator corresponding to a specified physical quantity.

See also: → eigenfunction; → state.

1. Math.: The one of the → scalars λ such that T(v) = λv, where T is a linear → operator on a → vector space, and v is an → eigenvector.
   

2. Quantum mechanics: The specified values of → quantized energy for which the → Schrodinger equation is soluble, subject to the appropriate → boundary conditions.

See also: → eigenfunction; → value.

1. Math.: The one of the → scalars λ such that T(v) = λv, where T is a linear → operator on a → vector space, and v is an → eigenvector.
   

2. Quantum mechanics: The specified values of → quantized energy for which the → Schrodinger equation is soluble, subject to the appropriate → boundary conditions.

See also: → eigenfunction; → value.

Math.: A nonzero vector v whose direction is not changed by a given linear transformation T; that is, T(v) = λ v for some scalar λ.

See also: → eigenfunction; → vector.

Math.: A nonzero vector v whose direction is not changed by a given linear transformation T; that is, T(v) = λ v for some scalar λ.

See also: → eigenfunction; → vector.

A → cardinal number between → seven and → nine.

Etymology (EN): M.E. eighte, from O.E. eahta, æhta, related to O.Norse atta, Swed. åtta, Du. acht, O.H.G. Ahto, Ger. acht; Pars. hašt, as below, from PIE *okto(u) “eight.”

Etymology (PE): Hašt, from Mid.Pers. hašt; Av. ašta; cognate with Skt. asta; Gk. okto; L. octo (from which It. otto, Sp. ocho, Fr. huit).

A → cardinal number between → seven and → nine.

Etymology (EN): M.E. eighte, from O.E. eahta, æhta, related to O.Norse atta, Swed. åtta, Du. acht, O.H.G. Ahto, Ger. acht; Pars. hašt, as below, from PIE *okto(u) “eight.”

Etymology (PE): Hašt, from Mid.Pers. hašt; Av. ašta; cognate with Skt. asta; Gk. okto; L. octo (from which It. otto, Sp. ocho, Fr. huit).

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.

See also: Named for Albert Einstein (1879-1955).

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.

See also: 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.

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

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.

See also: 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.

See also: → Einstein; → cross.

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.

See also: → 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.

See also: → Einstein; → equivalence; → principle.

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.

See also: → 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.

See also: Albert Einstein in 1907; → model.

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.

See also: 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.

See also: → Einstein; → notation.

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.

See also: → 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.

See also: → Einstein; → radius.

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.

See also: → 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.

See also: → Einstein; → ring.

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.

See also: → Einstein; → ring.

Same as → Einstein model.

See also: → Einstein; → solid.

Same as → Einstein model.

See also: → 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.

See also: → Einstein;
→ static; arr; universe.

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.

See also: → Einstein;
→ static; arr; universe.

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

See also: → Einstein; → temperature.

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

See also: → 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.

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

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.

See also: 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.

See also: → Einstein; → time-scale.

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.

See also: → Einstein; → time-scale.

Same as → geodetic precession.

See also: → Einstein-de Sitter Universe; → effect.

Same as → geodetic precession.

See also: → Einstein-de Sitter Universe; → effect.

The → Friedmann-Lemaitre model of → expanding Universe that only contains matter and in which space is → Euclidean (Ω_M > 0, Ω_R = 0, Ω_Λ = 0, k = 0). The Universe will expand at a decreasing rate for ever.

See also: → Einstein; de Sitter, after the Dutch mathematician and physicist Willem de Sitter (1872-1934) who worked out the model in 1917; → Universe.

The → Friedmann-Lemaitre model of → expanding Universe that only contains matter and in which space is → Euclidean (Ω_M > 0, Ω_R = 0, Ω_Λ = 0, k = 0). The Universe will expand at a decreasing rate for ever.

See also: → Einstein; de Sitter, after the Dutch mathematician and physicist Willem de Sitter (1872-1934) who worked out the model in 1917; → Universe.

In → general relativity, the → action that yields → Einstein’s field equations. It is expressed by:
S_{EH</SUB = (1/2κ)∫d⁴x (-g)^1/2R + S^m,
where κ ≡ 8πG and S^m is the matter part of the action.}

See also: → Einstein; → Hilbert space; → action.

In → general relativity, the → action that yields → Einstein’s field equations. It is expressed by:
S_{EH</SUB = (1/2κ)∫d⁴x (-g)^1/2R + S^m,
where κ ≡ 8πG and S^m is the matter part of the action.}

See also: → Einstein; → Hilbert space; → action.

→ EPR paradox.

See also: A. Einstein, B. Podolsky, N. Rosen: “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 41, 777 (15 May 1935); → paradox.

→ EPR paradox.

See also: A. Einstein, B. Podolsky, N. Rosen: “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 41, 777 (15 May 1935); → paradox.

A hypothetical structure that can join two distant regions of → space-time through a tunnel-like shortcut, as predicted by → general relativity. The Einstein-Rosen bridge is based on the → Schwarzschild solution of → Einstein’s field equations. It is the simplest type of → wormholes.

See also: Albert Einstein & Nathan Rosen (1935, Phys.Rev. 48, 73); → bridge.

A hypothetical structure that can join two distant regions of → space-time through a tunnel-like shortcut, as predicted by → general relativity. The Einstein-Rosen bridge is based on the → Schwarzschild solution of → Einstein’s field equations. It is the simplest type of → wormholes.

See also: Albert Einstein & Nathan Rosen (1935, Phys.Rev. 48, 73); → bridge.

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.

Etymology (EN): → 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.

Etymology (PE): Bâlâbar, → lift.

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.

Etymology (EN): → 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.

Etymology (PE): 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.

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

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.

See also: 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.

See also: → einstein; → gravitational; → constant.

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.

See also: → einstein; → gravitational; → constant.

Same as → Einstein model.

See also: → Einstein; → theory; → specific heat.

Same as → Einstein model.

See also: → Einstein; → theory; → specific heat.

The laws of physics are the same in all → inertial reference frames and are invariant under the → Lorentz transformation. The → speed of light is a → physical constant, i.e. it is
the same for all observers in uniform motion. Einsteinian relativity is prompted by the → Newton-Maxwell incompatibility. See also: → Galilean relativity, → Newtonian relativity.

See also: → Einstein; → relativity.

The laws of physics are the same in all → inertial reference frames and are invariant under the → Lorentz transformation. The → speed of light is a → physical constant, i.e. it is
the same for all observers in uniform motion. Einsteinian relativity is prompted by the → Newton-Maxwell incompatibility. See also: → Galilean relativity, → Newtonian relativity.

See also: → Einstein; → relativity.

A radioactive metallic → transuranium element belonging to the → actinides; symbol Es. → Atomic number 99, → mass number of most stable
→ isotope 254 (→ half-life 270 days). Eleven isotopes are known. The element was first identified by A. Ghiorso and collaborators in the debris of first hydrogen bomb explosion in 1952.

See also: Named after Albert Einstein, → einstein + → -ium.

A radioactive metallic → transuranium element belonging to the → actinides; symbol Es. → Atomic number 99, → mass number of most stable
→ isotope 254 (→ half-life 270 days). Eleven isotopes are known. The element was first identified by A. Ghiorso and collaborators in the debris of first hydrogen bomb explosion in 1952.

See also: Named after Albert Einstein, → einstein + → -ium.