document_title: Photon

question_text: who introduced the term photon to represent a packet of light energy

question_tokens: who introduced the term photon to represent a packet of light energy

root

text: Photon

text: Nomenclature[edit]

text: In 1900, the German physicist Max Planck was studying black-body radiation and suggested that the energy carried by electromagnetic waves could only be released in "packets" of energy. In his 1901 article [9] in Annalen der Physik he called these packets "energy elements". The word quanta (singular quantum, Latin for how much) was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1905, Albert Einstein suggested that electromagnetic waves could only exist as discrete wave-packets.[10] He called such a wave-packet the light quantum (German: das Lichtquant).[Note 1] The name photon derives from the Greek word for light, φῶς (transliterated phôs). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis.[11] The same name was used earlier, by the American physicist and psychologist Leonard T. Troland, who coined the word in 1916, in 1921 by the Irish physicist John Joly, in 1924 by the French physiologist René Wurmser (1890-1993) and in 1926 by the French physicist Frithiof Wolfers (1891-1971).[7] The name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolfers's and Lewis's theories were contradicted by many experiments and never accepted, the new name was adopted very soon by most physicists after Compton used it.[7][Note 2]

text: In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard,[12][13] named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade.[14] In chemistry and optical engineering, photons are usually symbolized by hν, which is the photon energy, where h is Planck constant and the Greek letter ν (nu) is the photon's frequency.[15] Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f.

text: Physical properties[edit]

text: A photon is massless,[Note 3] has no electric charge,[16] and is a stable particle. A photon has two possible polarization states.[17] In the momentum representation of the photon, which is preferred in quantum field theory, a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation. A photon's wave vector may not be zero and can be represented either as a spatial 3-vector or as a (relativistic) four-vector; in the latter case it belongs to the light cone (pictured). Different signs of the four-vector denote different circular polarizations, but in the 3-vector representation one should account for the polarization state separately; it actually is a spin quantum number. In both cases the space of possible wave vectors is three-dimensional.

text: The photon is the gauge boson for electromagnetism,[18]:29–30 and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero.[19] Also, the photon does not obey the Pauli exclusion principle.[20]:1221

text: Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons of various energy will be emitted, ranging from radio waves to gamma rays. Photons can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron–positron annihilation).[20]:572, 1114, 1172

text: In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[21]

text: The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):

text: where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[22]

text: Since p points in the direction of the photon's propagation, the magnitude of the momentum is

text:
The photon also carries a quantity called spin angular momentum that does not depend on its frequency.[23] The magnitude of its spin is

2

ℏ

{\displaystyle \scriptstyle {{\sqrt {2}}\hbar }}

 and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon.[24]

text: To illustrate the significance of these formulae, the annihilation of a particle with its antiparticle in free space must result in the creation of at least two photons for the following reason. In the center of momentum frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since, as we have seen, it is determined by the photon's frequency or wavelength, which cannot be zero). Hence, conservation of momentum (or equivalently, translational invariance) requires that at least two photons are created, with zero net momentum. (However, it is possible if the system interacts with another particle or field for the annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.)[25]:64–65 The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production, is the dominant mechanism by which high-energy photons such as gamma rays lose energy while passing through matter.[26] That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus.

text: The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.[27]

text:
Each photon carries two distinct and independent forms of angular momentum of light. The spin angular momentum of light of a particular photon is always either

+
ℏ

{\displaystyle +\hbar }

 or

−
ℏ

{\displaystyle -\hbar }

. The light orbital angular momentum of a particular photon can be any integer N, including zero.[28]

text: Experimental checks on photon mass[edit]

text: Current commonly accepted physical theories imply or assume the photon to be strictly massless. If the photon is not a strictly massless particle, it would not move at the exact speed of light, c in vacuum. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the upper bound on speed that any object could theoretically attain in space-time.[29] Thus, it would still be the speed of space-time ripples (gravitational waves and gravitons), but it would not be the speed of photons.

text: If a photon did have non-zero mass, there would be other effects as well. Coulomb's law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb's law is not exactly valid, then that would allow the presence of an electric field to exist within a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb's law to very high precision.[30] A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2.[31]

text:
Sharper upper limits on the speed of light have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very great length scales, only the magnetic field would be observable if the photon is massless. In the case that the photon has mass, the mass term

1
2

m

2

A

μ

A

μ

{\displaystyle \scriptstyle {\frac {1}{2}}m^{2}A_{\mu }A^{\mu }}

 would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 6973300000000000000♠3×10−27 eV/c2.[32] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[33] Such methods were used to obtain the sharper upper limit of 10−18eV/c2 (the equivalent of 6973107000000000000♠1.07×10−27 atomic mass units) given by the Particle Data Group.[34]

text: These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent.[35] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb's law is valid.

text: Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors.[36]

text: Historical development[edit]

text: In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637),[37] Robert Hooke (1665),[38] and Christiaan Huygens (1678);[39] however, particle models remained dominant, chiefly due to the influence of Isaac Newton.[40] In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted.[41] In 1865, James Clerk Maxwell's prediction[42] that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves[43]—seemed to be the final blow to particle models of light.

text: The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.[44][Note 4]

text: At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers[45] culminated in Max Planck's hypothesis[9][46] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = hν. As shown by Albert Einstein,[10][47] some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.[48]

text: Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.[10] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space.[10] In 1909[47] and 1916,[49] Einstein showed that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum p = h/λ, making them full-fledged particles. This photon momentum was observed experimentally[50] by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell's wave theory of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life,[51] and was solved in quantum electrodynamics and its successor, the Standard Model (see Second quantization and The photon as a gauge boson, below).

text: Einstein's light quantum[edit]

text: Unlike Planck, Einstein entertained the possibility that there might be actual physical quanta of light—what we now call photons. He noticed that a light quantum with energy proportional to its frequency would explain a number of troubling puzzles and paradoxes, including an unpublished law by Stokes, the ultraviolet catastrophe, and the photoelectric effect. Stokes's law said simply that the frequency of fluorescent light cannot be greater than the frequency of the light (usually ultraviolet) inducing it. Einstein eliminated the ultraviolet catastrophe by imagining a gas of photons behaving like a gas of electrons that he had previously considered. He was advised by a colleague to be careful how he wrote up this paper, in order to not challenge Planck, a powerful figure in physics, too directly, and indeed the warning was justified, as Planck never forgave him for writing it.[52]

text: Early objections[edit]

text: Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture.[53] However, before Compton's experiment[50] showed that photons carried momentum proportional to their wave number (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien,[45] Planck[46] and Millikan.[53]) Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbed or emitted radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.[54]

text: Even after Compton's experiment, Niels Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model.[55] To account for the data then available, two drastic hypotheses had to be made:

text:
Energy and momentum are conserved only on the average in interactions between matter and radiation, but not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (the jump between energy states) with the continuous release of energy as radiation.
Causality is abandoned. For example, spontaneous emissions are merely emissions stimulated by a "virtual" electromagnetic field.

tag: ol

text: However, refined Compton experiments showed that energy–momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible".[51] Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics.[56]

text: A few physicists persisted[57] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum mechanics. Although the evidence from chemical and physical experiments for the existence of photons was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, and a sufficiently complete theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photon-correlation experiments.[Note 5] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven.

text: Wave–particle duality and uncertainty principles[edit]

text: Photons, like all quantum objects, exhibit wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment exhibits interference phenomena but only if no measure was made at the slit. A single photon passing through a double-slit experiment lands on the screen with a probability distribution given by its interference pattern determined by Maxwell's equations.[58] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.[59] Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below).

text: A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum.

text: An elegant illustration of the uncertainty principle is Heisenberg's thought experiment for locating an electron with an ideal microscope.[60] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics

text:
where θ is the aperture angle of the microscope and λ is the wavelength of the light used to observe the electron. Thus, the position uncertainty

Δ
x

{\displaystyle \Delta x}

 can be made arbitrarily small by reducing the wavelength λ. Even if the momentum of the electron is initially known, the light impinging on the electron will give it a momentum "kick"

Δ
p

{\displaystyle \Delta p}

 of some unknown amount, rendering the momentum of the electron uncertain. If light were not quantized into photons, the uncertainty

Δ
p

{\displaystyle \Delta p}

 could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals

text:
giving the product

Δ
x
Δ
p

∼

h

{\displaystyle \Delta x\Delta p\,\sim \,h}

, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.[61]

text:
The analogous uncertainty principle for photons forbids the simultaneous measurement of the number

n

{\displaystyle n}

 of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase

ϕ

{\displaystyle \phi }

 of that wave

text: See coherent state and squeezed coherent state for more details.

text:
Both photons and electrons create analogous interference patterns when passed through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles (electron), this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations describing the photon's electromagnetic wave are simply Schrödinger's equation for photons, most physicists do not agree.[62][63] For one thing, they are mathematically different; most obviously, Schrödinger's one equation for the electron solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons.[64] As photons are massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate

|

r

⟩

{\displaystyle |\mathbf {r} \rangle }

, and, thus, the normal Heisenberg uncertainty principle

Δ
x
Δ
p
>
h

/

2

{\displaystyle \Delta x\Delta p>h/2}

 does not pertain to photons. A few substitute wave functions have been suggested for the photon,[65][66][67][68] but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

text: Another interpretation, that avoids duality, is the De Broglie–Bohm theory: known also as the pilot-wave model. In that theory, the photon is both, wave and particle.[69] "This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored",[70] J.S.Bell.

text: Bose–Einstein model of a photon gas[edit]

text: In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism, but rather by using a modification of coarse-grained counting of phase space.[71] Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction",[72][73] now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995.[74] It was later used by Lene Hau to slow, and then completely stop, light in 1999[75] and 2001.[76]

text: The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi–Dirac statistics).[77]

text: Stimulated and spontaneous emission[edit]

text:
In 1916, Albert Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a link between the rates at which atoms emit and absorb photons. The condition follows from the assumption that functions of the emission and absorption of radiation by the atoms are independent of each other, and that thermal equilibrium is made by way of the radiation's interaction with the atoms. Consider a cavity in thermal equilibrium with all parts of itself and filled with electromagnetic radiation and that the atoms can emit and absorb that radiation. Thermal equilibrium requires that the energy density

ρ
(
ν
)

{\displaystyle \rho (\nu )}

 of photons with frequency

ν

{\displaystyle \nu }

 (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate at which they absorb them.[78]

text:
Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate

R

j
i

{\displaystyle R_{ji}}

 for a system to absorb a photon of frequency

ν

{\displaystyle \nu }

 and transition from a lower energy

E

j

{\displaystyle E_{j}}

 to a higher energy

E

i

{\displaystyle E_{i}}

 is proportional to the number

N

j

{\displaystyle N_{j}}

 of atoms with energy

E

j

{\displaystyle E_{j}}

 and to the energy density

ρ
(
ν
)

{\displaystyle \rho (\nu )}

 of ambient photons of that frequency,

text:
where

B

j
i

{\displaystyle B_{ji}}

 is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, or the emission of a photon initiated by the interaction of the atom with a passing photon and the return of the atom to the lower-energy state. Following Einstein's approach, the corresponding rate

R

i
j

{\displaystyle R_{ij}}

 for the emission of photons of frequency

ν

{\displaystyle \nu }

 and transition from a higher energy

E

i

{\displaystyle E_{i}}

 to a lower energy

E

j

{\displaystyle E_{j}}

 is

text:
where

A

i
j

{\displaystyle A_{ij}}

 is the rate constant for emitting a photon spontaneously, and

B

i
j

{\displaystyle B_{ij}}

 is the rate constant for emissions in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state i and those in state j must, on average, be constant; hence, the rates

R

j
i

{\displaystyle R_{ji}}

 and

R

i
j

{\displaystyle R_{ij}}

 must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of

N

i

{\displaystyle N_{i}}

 and

N

j

{\displaystyle N_{j}}

 is

g

i

/

g

j

exp

(

E

j

−

E

i

)

/

(
k
T
)

,

{\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},}

 where

g

i
,
j

{\displaystyle g_{i,j}}

 are the degeneracy of the state i and that of j, respectively,

E

i
,
j

{\displaystyle E_{i,j}}

 their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that

g

i

B

i
j

=

g

j

B

j
i

{\displaystyle g_{i}B_{ij}=g_{j}B_{ji}}

 and

text: The A and Bs are collectively known as the Einstein coefficients.[79]

text:
Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients

A

i
j

{\displaystyle A_{ij}}

,

B

j
i

{\displaystyle B_{ji}}

 and

B

i
j

{\displaystyle B_{ij}}

 once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".[80] In fact, in 1926, Paul Dirac derived the

B

i
j

{\displaystyle B_{ij}}

 rate constants by using a semiclassical approach,[81] and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory.[82][83] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;[84][85][86] earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field.

text: Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which of the two paths a single photon would take.[40] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[51] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function[87][88] was inspired by Einstein's later work searching for a more complete theory.[89]

text: Second quantization and high energy photon interactions[edit]

text:
In 1910, Peter Debye derived Planck's law of black-body radiation from a relatively simple assumption.[90] He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of

h
ν

{\displaystyle h\nu }

, where

ν

{\displaystyle \nu }

 is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, which were derived by Einstein in 1909.[47]

text:
In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way.[91] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be

E
=
n
h
ν

{\displaystyle E=nh\nu }

, where

ν

{\displaystyle \nu }

 is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy

E
=
n
h
ν

{\displaystyle E=nh\nu }

 as a state with

n

{\displaystyle n}

 photons, each of energy

h
ν

{\displaystyle h\nu }

. This approach gives the correct energy fluctuation formula.

text:
Dirac took this one step further.[82][83] He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's

A

i
j

{\displaystyle A_{ij}}

 and

B

i
j

{\displaystyle B_{ij}}

 coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of black-body radiation by assuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics.

text:
Dirac's second-order perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and magnetic interactions are mediated by such virtual photons. In such quantum field theories, the probability amplitude of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy

E
=
p
c

{\displaystyle E=pc}

, and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such second-order and higher-order perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization.

text: Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron–positron pairs.[92] In fact, such photon-photon scattering (see two-photon physics), as well as electron-photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider.[93]

text: In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode

text:
where

|

n

k

i

⟩

{\displaystyle |n_{k_{i}}\rangle }

 represents the state in which

n

k

i

{\displaystyle \,n_{k_{i}}}

 photons are in the mode

k

i

{\displaystyle k_{i}}

. In this notation, the creation of a new photon in mode

k

i

{\displaystyle k_{i}}

 (e.g., emitted from an atomic transition) is written as

|

n

k

i

⟩
→

|

n

k

i

+
1
⟩

{\displaystyle |n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle }

. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.

text: The hadronic properties of the photon[edit]

text: Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons[94] in spite of the fact that the electric charge structures of protons and neutrons are substantially different. A theory called Vector Meson Dominance (VMD) was developed to explain this effect. According to VMD, the photon is a superposition of the pure electromagnetic photon which interacts only with electric charges and vector meson.[95] However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasi-free according to asymptotic freedom in QCD and described by the photon structure function.[96][97] A comprehensive comparison of data with theoretical predictions was presented in a review in 2000.[98]

text: The photon as a gauge boson[edit]

text: The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime.[99] For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of complex numbers of absolute value 1, which reflects the ability to vary the phase of a complex field without affecting observables or real valued functions made from it, such as the energy or the Lagrangian.

text:
The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be

±
ℏ

{\displaystyle \pm \hbar }

. These two spin components correspond to the classical concepts of right-handed and left-handed circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states.[99]

text: In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W− and Z0 and are responsible for the weak interaction. Unlike the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics.[100][101][102] Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.[103]

text: Contributions to the mass of a system[edit]

text:
The energy of a system that emits a photon is decreased by the energy

E

{\displaystyle E}

 of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount

E

/

c

2

{\displaystyle {E}/{c^{2}}}

. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form

E

/

c

2

{\displaystyle {E}/{c^{2}}}

 for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).[104]

text: This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.[105]

text: Since photons contribute to the stress–energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.[106]

text: Photons in matter[edit]

text: Light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. For example, photons engage in so many collisions on the way from the core of the sun that radiant energy can take about a million years to reach the surface;[107] however, once in open space, a photon takes only 8.3 minutes to reach Earth. The factor by which the speed is decreased is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and that new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter to produce quasi-particles known as polariton (other quasi-particles are phonons and excitons); this polariton has a nonzero effective mass, which means that it cannot travel at c. Light of different frequencies may travel through matter at different speeds; this is called dispersion (not to be confused with scattering). In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering.[108]

text: Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal (C20H28O), which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and co-workers. The absorption provokes a cis-trans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[109][110]

text: Technological applications[edit]

text: Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.

text: Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon of sufficient energy strikes a metal plate and knocks free an electron, initiating an ever-amplifying avalanche of electrons. Semiconductor charge-coupled device chips use a similar effect: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules contained in the device, causing a detectable change of conductivity of the gas.[111]

text:
Planck's energy formula

E
=
h
ν

{\displaystyle E=h\nu }

 is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to determine the frequency of the light emitted from a given photon emission. For example, the emission spectrum of a gas-discharge lamp can be altered by filling it with (mixtures of) gases with different electronic energy level configurations.

text: Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the spectrum where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.[112]

text: In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins.[113]

text: Several different kinds of hardware random number generators involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beam-splitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".[114][115]

text: Recent research[edit]

text: Much research has been devoted to applications of photons in the field of quantum optics. Photons seem well-suited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.[Note 6]


document_title: Politics of the United States during World War II

question_text: who was president during world war 2 e

question_tokens: who was president during world war 2 e

text: Overview[edit]

text: The United States entered World War II with the same Administration that had been at the helm of the nation since 1932, that of Franklin Delano Roosevelt. This Administration had been preparing for war for a while by the time of the attack on Pearl Harbor.

tag: p

text: President of the United States[edit]

text: President Franklin Delano Roosevelt and Vice President Henry A. Wallace won the election of 1940, and were at the helm of the nation as it prepared for and entered World War II. Roosevelt sought and won an unprecedented fourth term in office in 1944, but this time with Harry S. Truman as his Vice President. Roosevelt, who had been a victim of Polio early in life, died in April 1945, and Truman assumed the Presidency through the end of the war.

text: Cabinet[edit]

text:
Secretary of State

Cordell Hull pre-war to November 1944
Edward Stettinius to war's end

Secretary of the Interior

Harold Ickes throughout the war

Secretary of Commerce

Jesse H. Jones pre-war to June 1945
Henry A. Wallace to war's end

Secretary of the Treasury

Henry Morgenthau Jr. pre-war to June 1945
Carl Vinson to war's end

Secretary of Labor

Francis Perkins pre-war to June 1945
Schwellenback to war's end

Secretary of War

Henry L. Stimson throughout the war

Secretary of the Navy

Frank Knox pre-war to May 1944
James V. Forrestal to war's end

Secretary of Agriculture

Claude Wickard pre-war to June 1945
Anderson to war's end

Postmaster General

Frank C. Walker pre-war to June 1945
Hannegan to war's end

Attorney General

Francis Biddle pre-war to June 1945
Tom C. Clark to war's end

Director of the Federal Bureau of Investigation

J. Edgar Hoover throughout the war

tag: ul

text: Executive Agencies[edit]

text:
Foreign Economic Administration under Director Crowley, formed September 1943 from the Office of Economic Warfare, the Office of Lend Lease Administration, and the Office of Foreign Relief and Rehabilitation Operations.
Office of Price Administration under Administrators Henderson, Brown, and Bowles, formed April 1941 (originally named the Office of Price Administration and Civilian Supply).
Office of War Mobilization and Reconversion under Chairmen Byrnes and Vinson, formed in May 1943 as the Office of War Mobilization.
War Production Board under Chairmen Nelson and King, formed in January 1942 from the Office of Production Management and the Supply Priorities and Allocation Board.
Economic Stabilization Board under Chairmen Byrnes and Vinson, formed in October 1942 as the Office of Economic Stabilization.
War Manpower Commission under Chairman McNuff, formed in April 1942.
United States Maritime Commission under Chairman Land.
War Shipping Administration under Administrator Land, formed in February 1942.
Office of Defense Transportation under Chairman Eastman, formed in December 1941.
Petroleum Administration for War under Administrator Ickes, formed in December 1942.
War Food Administration formed in December 1942.
National War Labor Board under Chairman Davis, formed in January 1942.
Office of Scientific Research and Development under Chairman Bush, formed in July 1941.
Office of War Information under Chairman Davis, formed in June 1942.
Office of Civilian Defense under Chairmen LaGuardia and Landis, formed in May 1941.

text: Joint Chiefs of Staff[edit]

text: The Joint Chiefs were military officers, as opposed to the above, who were for the most part civilians.

text:
Chairman of the Joint Chiefs of Staff William D. Leahy
Army Commander-in-Chief and Chief of Staff George C. Marshall
Navy Commander-in-Chief and Chief of Operations Ernest King
Army Air Force Commander Henry Arnold
Marine Corps Commandant Alexander Vandegrift
Army Air Force Chief of Staff Giles
Army Ground Forces Commander Lear
Army Service Forces Commander Somervell

text: In addition, the following offices reported to the Joint Chiefs of Staff:

text:
Operations Division, formerly the War Plans Division.
Military Intelligence Division
Office of Naval Intelligence

text: Politics of World War IIUnited States home front during World War IIPolitics of the United States

text: Articles lacking sources from December 2009All articles lacking sources


document_title: Local government in California

question_text: at the county level of government in california power is held by

text: Local government in California

text: Counties[edit]

text: The basic political subdivision of California are the 58 counties. The county government provides countywide services such as law enforcement, jails, elections and voter registration, vital records, property assessment and records, tax collection, public health, health care, social services, libraries, flood control, fire protection, animal control, agricultural regulations, building inspections, ambulance services, and education departments in charge of maintaining statewide standards.[1][2] In addition the county serves as the local government for all unincorporated areas (those areas not within any incorporated city), providing services such as police, parks, street maintenance, land use regulations, zoning, and waste disposal.[3] Counties have taxing and police powers. Counties may promulgate ordinances which are usually codified in a county code, and violations of the ordinances are misdemeanor crimes unless otherwise specified as an infraction.[4]

text:
Major county governments

County
Largest city
Government

Alameda
Oakland
Government of Alameda County

Fresno
Fresno
Government of Fresno County

Los Angeles
Los Angeles
Government of Los Angeles County

Sacramento
Sacramento
Government of Sacramento County

San Diego
San Diego
Government of San Diego County

San Francisco
Government of San Francisco

San Joaquin
Stockton
Government of San Joaquin County

Solano
Vallejo
Government of Solano County

Stanislaus
Modesto
Government of Stanislaus County

tag: table

text: Thirteen counties are "charter" counties while the rest are "general law" counties.[5] Other than San Francisco, which is a consolidated city-county, California's counties are governed by an elected five-member Board of Supervisors, who appoint executive officers to manage the various functions of the county.[5] In San Francisco, there is an eleven-member Board of Supervisors,[5] but the executive branch of the government is headed by an elected mayor, department heads are responsible to the mayor, and there is both a city police department and a county sheriff, the latter mostly responsible for operating the county jail and for most jail bookings.[6] Most counties elect all of their supervisors by district except San Mateo and Tehama.[5] (San Francisco had at-large supervisors from 1980 to 2000, but in 2000 the county was once again divided into 11 districts, whose updated borders roughly followed those of the old 1970s-era districts, although the districts themselves were renumbered.) All counties elect their treasurers except Los Angeles, Sacramento, Santa Clara, and Glenn.[5] Forty-seven counties have an appointed county administrative officer, while five counties have a more powerful official such as a county manager, chief executive officer, or county mayor, and five rural counties do not have a full-time county administrative officer.[5] All counties elect their district attorneys and their sheriffs.[citation needed] Counties may also have an assessor, a recorder, an auditor, a controller, a treasurer, a tax collector, a county clerk, a registrar of voters, a coroner, and/or a medical examiner.[citation needed]

text: California's judicial system is organized along county lines, but the county courts are a part of the state court system, and are not part of the county government. Historically, counties were responsible for providing courthouses and courthouse security for the Superior Courts of California (there is one superior court for each county), even though the superior courts were actually divisions of the state government, not the county governments. This unfunded mandate was a perennial source of frustration for both the superior courts and the counties. The Legislature finally responded by enacting the Trial Court Funding Act of 1997 and then the Trial Court Facilities Act of 2002 to transfer all courthouses to the state government and to relieve the counties of the burden of providing facilities to state courts. However, because the state government was not prepared to assume the burden of developing its own statewide courthouse security force, the superior courts were allowed to establish agreements with county sheriffs by which the courts would reimburse counties for continuing to provide deputy sheriffs to serve as bailiffs in the courthouses.

text: Because of historical problems with fragmentation of local government as a result of the formation of too many special districts by enthusiastic local officials, all counties currently have a corresponding Local Agency Formation Commission (LAFCO), one for each county. A LAFCO regulates the creation of special districts and annexation of unincorporated land to cities within the county. No incorporated city may cross county boundaries, and special districts that span county lines must be specially approved by the state Legislature.

text: California also uses grand juries, with at least one per county.[7] These county-level grand juries are often called civil grand juries because their primary focus is on oversight of government institutions at the county level and lower. They meet at least once per year.

text: On January 4, 1850, the California constitutional committee recommended the formation of 18 counties. They were Benicia, Butte, Fremont, Los Angeles, Mariposa, Monterey, Mount Diablo, Oro, Redding, Sacramento, San Diego, San Francisco, San Joaquin, San Jose, San Luis Obispo, Santa Barbara, Sonoma, and Sutter. On April 22, the counties of Branciforte, Calaveras, Coloma, Colusi, Marin, Mendocino, Napa, Trinity, and Yuba were added. Benicia was renamed Solano, Coloma to El Dorado, Fremont to Yolo, Mt. Diablo to Contra Costa, San Jose to Santa Clara, Oro to Tuolumne, and Redding to Shasta. One of the first state legislative acts regarding counties was to rename Branciforte County to Santa Cruz, Colusi to Colusa, and Yola to Yolo. The last county in California to be established is Imperial County on August 7, 1907.

text: Since 1911, counties in California have been allowed limited home rule, with the Government of Los Angeles County the first in the nation to be granted home rule by charter in 1912.[8][9][10] The county governments were originally molded around property recording and assessment, law enforcement, judicial administration, and tax collection, but more recently other functions have been added by the state such as public welfare, public health, water conservation, and flood protection.[8] In 1933, county supervisors gained authority to fix salaries for all county officers other than themselves.[11]

text: Cities and towns[edit]

text: As of July 1, 2011, there were 482 incorporated municipalities in the state.[12] Under California law, the terms "city" and "town" are explicitly interchangeable; the name of an incorporated municipality in the state can either be "City of (Name)" or "Town of (Name)".[13] Counties exercise the powers of cities in unincorporated areas.[3]

text:
Major city governments

City
County
Government

Los Angeles
Los Angeles
Government of Los Angeles

San Francisco
Government of San Francisco

Sacramento
Sacramento
Government of Sacramento

text: California municipalities are either charter or general-law. General-law municipalities have powers defined by the state's Government Code;[note 3] charter municipalities may have increased powers, but adoption and amendment of city charters requires a popular vote. Most small cities have a council–manager government, where the elected city council appoints a city manager to supervise the operations of the city. Some larger cities have a mayor–council government, with a directly-elected mayor who oversees the city government. In many council–manager cities, the city council selects one of its members as a mayor, sometimes rotating through the council membership—but this type of mayoral position is primarily ceremonial.

text: Incorporated cities and towns have the power to levy taxes. They are responsible for providing police service, zoning, issuing building permits, and maintaining public streets. Municipalities may also provide parks, public housing, and various utility services, though all of these are sometimes provided by special districts, and some utilities are provided privately. Incorporated cities may promulgate ordinances which are usually codified in a city code, and violations of the ordinances are misdemeanor crimes unless otherwise specified as an infraction.[14]

text: Residents of a sufficiently large piece of unincorporated county land can incorporate a city. The city government then takes some of the tax revenue that would have gone to the county, and can impose additional taxes on its residents. It can then choose to provide almost all the services usually provided by the county (and more), or provide only a few and pay the county to do the rest. A city in this last arrangement is called a contract city; this type of contract is generally known among lawyers as the "Lakewood Plan", because it was pioneered by the city of Lakewood in 1954.[15]

text: School districts[edit]

text: Public education of children is provided by school districts, which are governed independently from cities. Each county has a board of education and superintendent that oversee school districts within the county. There are about 1,102 school districts.[16]

text: California school districts may be organized as elementary districts, high school districts, unified school districts combining elementary and high school grades, or community college districts.[16] Union districts are formed by joining two or more elementary districts.[16] School districts are governed by an elected school board (sometimes called a "board of education" or "board of trustees"), which manages the schools within its jurisdiction.[16] There are also county special service schools and regional occupational programs provide vocational and technical education.[16] Historically, school districts were organized at the primary level (Kindergarten through 8th grade, approximately ages 5–13), and the secondary (high school) level (9th through 12th grade, approximately ages 14–17).

text: School district and community college district boards may determine their own fiscal requirements—the counties levy and collect the taxes required, possibly subject to constitutional tax limitations and voter approval.[16] Historically, school districts were funded through local property tax revenue, but due to Serrano v. Priest, school districts are funded through the State government through various funding formulas that allocate local property tax revenues and other revenue.

text: Community colleges[edit]

text: The State of California operates the University of California and the California State University as statewide systems. However, community colleges, which provide the first two years of post-secondary education and adult vocational courses, are organized in community college districts, which operate one or more community colleges within their jurisdiction. Community college districts in California are governed by elected boards.

text: California's first community colleges were established as extensions of high schools.[17] Through legislation enacted in 1907, high schools were allowed to create "junior colleges" to provide a general undergraduate education to local students, approximating the first two years of university courses.[17] In the early 1920s, the Legislature authorized the creation of separate colleges, in addition to the programs offered in high schools.[17] In 1967, the Governor and Legislature created the Board of Governors for the Community Colleges to oversee the community colleges and formally established the California Community Colleges System, requiring all areas of the state to be included within a community college district.[17]

text: Special districts[edit]

text: A special district is defined as "any agency of the state for the local performance of governmental or proprietary functions within limited boundaries"[18] and provides a limited range of services within a defined geographic area. Most of California's special districts are single-purpose districts, and provide one service. Most special districts have no police powers.

text: Independent special districts have elected boards. Dependent special districts are governed by the city or county that created them. Regional bodies have boards appointed by the city and county governments they encompass. Some districts, often referred to as assessment districts, have voting based on the assessed values of the property contained within the district, rather than popular vote; that was ruled constitutional for districts that provide benefits to the land in rough proportion to the value of the land, rather than to people within the district.[note 4]

text: Districts are categorized as enterprise districts and non-enterprise districts. Enterprise districts operate as a business, and obtain most of their revenue from user fees or sales of a product or service. Enterprise districts include those that provide water, waste disposal, electric power, hospitals, public transit, and similar services.

text: The most common type of special district is the utility district, which provides public utility services to residents within the district boundaries. Among the largest of these are the Sacramento Municipal Utility District, which provides electric power in the Sacramento area, the Metropolitan Water District, which provides water to local water agencies in the Los Angeles area, and the Imperial Irrigation District, which provides water for agriculture and electric power in Imperial County.

text: Another very common type of special district is the transit agency, which provides public transportation. The Los Angeles County Metropolitan Transportation Authority provides bus and train services and funds some transportation projects, including bicycle paths, HOV lanes, and other road improvements. By contrast, the San Francisco Bay Area Rapid Transit District only operates a commuter rail service and buses to locations beyond the range of the rail service.

text: There are at least 3000 special districts, and possibly as many as 5000, depending on how they are counted. Special districts spend over $26 billion each year (over $700 per person in California), though some significant amount of that is double-counted as some districts purchase services from others, and some subsidize others.

text: A short list of the types of special districts includes:[19]

text:
Air pollution control districts
Air quality management districts
Airport districts
Bridge or highway districts

The headquarters building of the Sacramento Municipal Utility District

California water districts
Mello-Roos (community facilities districts)
Community services districts
County sanitation districts
County service areas
County water districts
County waterworks districts
Fire protection districts
Harbor and port districts
Health care districts
Improvement districts
Irrigation districts
Joint power agencies
Joint highway districts
Library districts
Metropolitan water districts
Mosquito abatement districts

A meadow in the Russian Ridge Open Space Preserve of the Midpeninsula Regional Open Space District

Municipal utility districts
Municipal water districts
Permanent road divisions
Pest control districts
Police protection districts
Public cemetery districts
Public utility districts
Reclamation districts
Recreation and park districts
Redevelopment agencies
Resource conservation districts
Sanitary districts
Separation of grade districts
Service zones of special districts
Sewer districts
Sewer maintenance districts
Special assessment districts
Transit or rapid transit districts
Unified or union high school library districts
Vector control districts


document_title: Electron transport chain

question_text: where does electron transport system occur in mitochondria

text: Electron transport chain

text: In mitochondria[edit]

text: Most eukaryotic cells have mitochondria, which produce ATP from products of the citric acid cycle, fatty acid oxidation, and amino acid oxidation. At the mitochondrial inner membrane, electrons from NADH and FADH2 pass through the electron transport chain to oxygen, which is reduced to water. The electron transport chain comprises an enzymatic series of electron donors and acceptors. Each electron donor will pass electrons to a more electronegative acceptor, which in turn donates these electrons to another acceptor, a process that continues down the series until electrons are passed to oxygen, the most electronegative and terminal electron acceptor in the chain. Passage of electrons between donor and acceptor releases energy, which is used to generate  a proton gradient across the mitochondrial membrane by actively "pumping" protons into the intermembrane space, producing a thermodynamic state that has the potential to do work. This entire process is called oxidative phosphorylation, since ADP is phosphorylated to ATP using the energy of hydrogen oxidation in many steps.

text: A small percentage of electrons do not complete the whole series and instead directly leak to oxygen, resulting in the formation of the free-radical superoxide, a highly reactive molecule that contributes to oxidative stress and has been implicated in a number of diseases and aging.

text: Mitochondrial redox carriers[edit]

text: Energy obtained through the transfer of electrons down the ETC is used to pump protons from the mitochondrial matrix into the intermembrane space, creating an electrochemical proton gradient (ΔpH) across the inner mitochondrial membrane (IMM). This proton gradient is largely but not exclusively responsible for the mitochondrial membrane potential (ΔΨM). It allows ATP synthase to use the flow of H+ through the enzyme back into the matrix to generate ATP from adenosine diphosphate (ADP) and inorganic phosphate. Complex I (NADH coenzyme Q reductase; labeled I) accepts electrons from the Krebs cycle electron carrier nicotinamide adenine dinucleotide (NADH), and passes them to coenzyme Q (ubiquinone; labeled Q), which also receives electrons from complex II (succinate dehydrogenase; labeled II). Q passes electrons to complex III (cytochrome bc1 complex; labeled III), which passes them to cytochrome c (cyt c). Cyt c passes electrons to Complex IV (cytochrome c oxidase; labeled IV), which uses the electrons and hydrogen ions to reduce molecular oxygen to water.

text: Four membrane-bound complexes have been identified in mitochondria. Each is an extremely complex transmembrane structure that is embedded in the inner membrane.  Three of them are proton pumps. The structures are electrically connected by lipid-soluble electron carriers and water-soluble electron carriers. The overall electron transport chain:

text: Complex I[edit]

text: In Complex I (NADH:ubiquinone oxidoreductase, NADH-CoQ reductase, or NADH dehydrogenase; EC 1.6.5.3), two electrons are removed from NADH and ultimately transferred to a lipid-soluble carrier, ubiquinone (UQ). The reduced product, ubiquinol (UQH2), freely diffuses within the membrane, and Complex I translocates four protons (H+) across the membrane, thus producing a proton gradient. Complex I is one of the main sites at which premature electron leakage to oxygen occurs, thus being one of the main sites of production of superoxide.[3]

text: The pathway of electrons is as follows:

text:
NADH is oxidized to NAD+, by reducing Flavin mononucleotide to FMNH2 in one two-electron step. FMNH2 is then oxidized in two one-electron steps, through a semiquinone intermediate. Each electron thus transfers from the FMNH2 to an Fe-S cluster, from the Fe-S cluster to ubiquinone (Q). Transfer of the first electron results in the free-radical (semiquinone) form of Q, and transfer of the second electron reduces the semiquinone form to the ubiquinol form, QH2. During this process, four protons are translocated from the mitochondrial matrix to the intermembrane space.
[4] As the electrons become continuously oxidized and reduced throughout the complex an electron current is produced along the 180 Angstrom width of the complex within the membrane. This current powers the active transport of four protons to the intermembrane space per two electrons from NADH.[5]

text: This complex is inhibited by Alkylguanides (Example : Guanethidine), Rotenone, Barbiturates, Chlorpromazine, Piericidin.

text: Complex II[edit]

text: In Complex II (succinate dehydrogenase or succinate-CoQ reductase; EC 1.3.5.1) additional electrons are delivered into the quinone pool (Q) originating from succinate and transferred (via flavin adenine dinucleotide (FAD)) to Q. Complex II consists of four protein subunits:  succinate dehydrogenase, (SDHA);  succinate dehydrogenase [ubiquinone] iron-sulfur subunit, mitochondrial, (SDHB);  succinate dehydrogenase complex subunit C, (SDHC) and succinate dehydrogenase complex, subunit D, (SDHD). Other electron donors (e.g., fatty acids and glycerol 3-phosphate) also direct electrons into Q (via FAD). Complex 2 is a parallel electron transport pathway to complex 1, but unlike complex 1, no protons are transported to the intermembrane space in this pathway. Therefore, the pathway through complex 2 contributes less energy to the overall electron transport chain process.

text: This complex is inhibited by Carboxin.

text: Complex III[edit]

text:
In Complex III (cytochrome bc1 complex or CoQH2-cytochrome c reductase; EC 1.10.2.2), the Q-cycle contributes to the proton gradient by an asymmetric absorption/release of protons. Two electrons are removed from QH2 at the QO site and sequentially transferred to two molecules of cytochrome c, a water-soluble electron carrier located within the intermembrane space. The two other electrons sequentially pass across the protein to the Qi site where the quinone part of ubiquinone is reduced to quinol. A proton gradient is formed by one quinol (

2

H

2

+

e

−

{\displaystyle {\ce {2H+2e-}}}

) oxidations at the Qo site to form one quinone (

2

H

2

+

e

−

{\displaystyle {\ce {2H+2e-}}}

) at the Qi site. (in total four protons are translocated: two protons reduce quinone to quinol and two protons are released from two ubiquinol molecules).

text: When electron transfer is reduced (by a high membrane potential or respiratory inhibitors such as antimycin A), Complex III may leak electrons to molecular oxygen, resulting in superoxide formation.

text: This complex is inhibited by British Antilewisite(BAL), Napthoquinone and Antimycin.

text: Complex IV[edit]

text: In Complex IV (cytochrome c oxidase; EC 1.9.3.1), sometimes called cytochrome AA3, four electrons are removed from four molecules of cytochrome c and transferred to molecular oxygen (O2), producing two molecules of water.  At the same time, eight protons are removed from the mitochondrial matrix (although only four are translocated across the membrane), contributing to the proton gradient. The activity of cytochrome c oxidase is inhibited by cyanide, carbon monoxide, azide, hydrogen sulphide(H2S).

text: Coupling with oxidative phosphorylation[edit]

text:
According to the  chemiosmotic coupling hypothesis, proposed by Nobel Prize in Chemistry winner Peter D. Mitchell, the electron transport chain and oxidative phosphorylation are coupled by a proton gradient across the inner mitochondrial membrane. The efflux of protons from the mitochondrial matrix creates an electrochemical gradient (proton gradient). This gradient is used by the FOF1 ATP synthase complex to make ATP via oxidative phosphorylation. ATP synthase is sometimes described as Complex V of the electron transport chain.[6] The FO component of ATP synthase acts as an ion channel that provides for a proton flux back into the mitochondrial matrix. It is composed of a, b and c subunits. Protons in the inter-membranous space of mitochondria first enters the ATP synthase complex through a subunit channel. Then protons move to the c subunits.[7] The number of c subunits it has determines how many protons it will require to make the FO turn one full revolution. For example, in humans, there are 8 c subunits, thus 8 protons are required.[8] After c subunits, protons finally enters matrix using a subunit channel that opens into the mitochondrial matrix.[7] This reflux releases free energy produced during the generation of the oxidized forms of the electron carriers (NAD+ and Q). The free energy is used to drive ATP synthesis, catalyzed by the F1 component of the complex.[9]

Coupling with oxidative phosphorylation is a key step for ATP production. However, in specific cases, uncoupling the two processes may be biologically useful. The uncoupling protein, thermogenin—present in the inner mitochondrial membrane of brown adipose tissue—provides for an alternative flow of protons back to the inner mitochondrial matrix. Thyroxine is also a natural uncoupler. This alternative flow results in thermogenesis rather than ATP production.[10] Synthetic uncouplers (e.g., 2,4-dinitrophenol, 2,4-dinitrocresol, CCCP) also exist, and can be lethal at high doses.[citation needed]

text: Summary[edit]

text: In the mitochondrial electron transport chain electrons move from an electron donor (NADH or QH2) to a terminal electron acceptor (O2) via a series of redox reactions. These reactions are coupled to the creation of a proton gradient across the mitochondrial inner membrane. There are three proton pumps: I, III, and IV.  The resulting transmembrane proton gradient is used to make ATP via ATP synthase.

text: The reactions catalyzed by Complex I and Complex III work roughly at equilibrium.  This means that these reactions are readily reversible, by increasing the concentration of the products relative to the concentration of the reactants (for example, by increasing the proton gradient).  ATP synthase is also readily reversible.  Thus ATP can be used to build a proton gradient, which in turn can be used to make NADH.   This process of reverse electron transport is important in many prokaryotic electron transport chains.[11]

text: In bacteria[edit]

text: In eukaryotes, NADH is the most important electron donor.  The associated electron transport chain is

text:
NADH → Complex I → Q → Complex III → cytochrome c → Complex IV → O2
where Complexes I, III and IV are proton pumps, while Q and cytochrome c are mobile electron carriers.  The electron acceptor is molecular oxygen.

text: In prokaryotes (bacteria and archaea) the situation is more complicated, because there are several different electron donors and several different electron acceptors.  The generalized electron transport chain in bacteria is:

text: Note that electrons can enter the chain at three levels: at the level of a dehydrogenase, at the level of the quinone pool, or at the level of a mobile cytochrome electron carrier.  These levels correspond to successively more positive redox potentials, or to successively decreased potential differences relative to the terminal electron acceptor.  In other words, they correspond to successively smaller Gibbs free energy changes for the overall redox reaction Donor → Acceptor.

text: Individual bacteria use multiple electron transport chains, often simultaneously.  Bacteria can use a number of different electron donors, a number of different dehydrogenases, a number of different oxidases and reductases, and a number of different electron acceptors.  For example, E. coli (when growing aerobically using glucose as an energy source) uses two different NADH dehydrogenases and two different quinol oxidases, for a total of four different electron transport chains operating simultaneously.

text: A common feature of all electron transport chains is the presence of a proton pump to create a transmembrane proton gradient.  Bacterial electron transport chains may contain as many as three proton pumps, like mitochondria, or they may contain only one or two.  They always contain at least one proton pump.

text: Electron donors[edit]

text: In the present day biosphere, the most common electron donors are organic molecules.  Organisms that use organic molecules as an energy source are called organotrophs.  Organotrophs (animals, fungi, protists) and phototrophs (plants and algae) constitute the vast majority of all familiar life forms.

text: Some prokaryotes can  use inorganic matter as an energy source.  Such an organism is called a lithotroph ("rock-eater").  Inorganic electron donors include hydrogen, carbon monoxide, ammonia, nitrite, sulfur, sulfide, manganese oxide, and ferrous iron.  Lithotrophs have been found growing in rock formations thousands of meters below the surface of Earth.  Because of their volume of distribution, lithotrophs may actually outnumber organotrophs and phototrophs in our biosphere.

text: The use of inorganic electron donors as an energy source is of particular interest in the study of evolution.  This type of metabolism must logically have preceded the use of organic molecules as an energy source.

text: Dehydrogenases[edit]

text: Bacteria can use a number of different electron donors.  When organic matter is the energy source, the donor may be NADH or succinate, in which case electrons enter the electron transport chain via NADH dehydrogenase (similar to Complex I in mitochondria) or succinate dehydrogenase (similar to Complex II).  Other dehydrogenases may be used to process different energy sources:   formate dehydrogenase, lactate dehydrogenase, glyceraldehyde-3-phosphate dehydrogenase, H2 dehydrogenase (hydrogenase), etc.  Some dehydrogenases  are also proton pumps; others funnel electrons into the quinone pool. Most dehydrogenases show induced expression in the bacterial cell in response to metabolic needs triggered by the environment in which the cells grow.[citation needed]

text: Quinone carriers[edit]

text: Quinones are mobile, lipid-soluble carriers that shuttle electrons (and protons) between large, relatively immobile macromolecular complexes embedded in the membrane.  Bacteria use ubiquinone (the same quinone that mitochondria use) and related quinones such as menaquinone. Another name for ubiquinone is Coenzyme Q10.

text: Proton pumps[edit]

text: A proton pump is any process that creates a proton gradient across a membrane.  Protons can be physically moved across a membrane; this is seen in mitochondrial Complexes I and IV.  The same effect can be produced by moving electrons in the opposite direction. The result is the disappearance of a proton from the cytoplasm and the appearance of a proton in the periplasm.   Mitochondrial Complex III uses this second type of proton pump, which is mediated by a quinone (the Q cycle).

text: Some dehydrogenases are proton pumps; others are not.  Most oxidases and reductases are proton pumps, but some are not.  Cytochrome bc1 is a proton pump found in many, but not all, bacteria (it is not found in E. coli).  As the name implies, bacterial bc1 is similar to mitochondrial bc1 (Complex III).

text: Proton pumps are the heart of the electron transport process.  They produce the transmembrane electrochemical gradient that enables ATP Synthase to synthesize ATP.

text: Cytochrome electron carriers[edit]

text: Cytochromes are pigments that contain iron.  They are found in two very different environments.

text: Some cytochromes are water-soluble carriers that shuttle electrons to and from large, immobile macromolecular structures imbedded in the membrane. The mobile cytochrome electron carrier in mitochondria is cytochrome c.  Bacteria use a number of different mobile cytochrome electron carriers.

text: Other cytochromes are found within macromolecules such as Complex III and Complex IV.  They also function as electron carriers, but in a very different, intramolecular, solid-state environment.

text: Electrons may enter an electron transport chain at the level of a mobile cytochrome or quinone carrier.  For example, electrons from inorganic electron donors (nitrite, ferrous iron, etc.) enter the electron transport chain at the cytochrome level. When electrons enter at a redox level greater than NADH, the electron transport chain must operate in reverse to produce this necessary, higher-energy molecule.

text: Terminal oxidases and reductases[edit]

text: When bacteria grow in aerobic environments, the terminal electron acceptor (O2) is reduced to water by an enzyme called an oxidase.  When bacteria  grow in anaerobic environments, the terminal electron acceptor is reduced by an enzyme called a reductase.

text: In mitochondria the terminal membrane complex (Complex IV) is cytochrome oxidase.  Aerobic bacteria use a number of different terminal oxidases.  For example, E. coli does not have a cytochrome oxidase or a bc1 complex.  Under aerobic conditions, it uses two different terminal quinol oxidases (both proton pumps) to reduce oxygen to water.

text: Anaerobic bacteria, which do not use oxygen as a terminal electron acceptor, have terminal reductases individualized to their terminal acceptor.  For example, E. coli can use fumarate reductase, nitrate reductase, nitrite reductase, DMSO reductase, or trimethylamine-N-oxide reductase, depending on the availability of these acceptors in the environment.

text: Most terminal oxidases and reductases are inducible.  They are synthesized by the organism as needed, in response to specific environmental conditions.

text: Electron acceptors[edit]

text: Just as there are a number of different electron donors (organic matter in organotrophs, inorganic matter in lithotrophs), there are a number of different  electron acceptors, both organic and inorganic.  If oxygen is available, it is invariably used as the terminal electron acceptor, because it generates the greatest Gibbs free energy change and produces the most energy.[citation needed]

text: In anaerobic environments, different electron acceptors are used, including nitrate, nitrite, ferric iron, sulfate, carbon dioxide, and small organic molecules such as fumarate.

text: Since electron transport chains are redox processes, they can be described as the sum of two redox pairs.  For example, the mitochondrial electron transport chain can be described as the sum of the NAD+/NADH redox pair and the O2/H2O redox pair.  NADH is the electron donor and O2 is the electron acceptor.

text: Not every donor-acceptor combination is thermodynamically possible.  The redox potential of the acceptor must be more positive than the redox potential of the donor.  Furthermore, actual environmental conditions may be far different from standard conditions (1 molar concentrations, 1 atm partial pressures, pH = 7), which apply to standard redox potentials.  For example, hydrogen-evolving bacteria grow at an ambient partial pressure of hydrogen gas of 10−4  atm.  The associated redox reaction, which is thermodynamically favorable in nature, is thermodynamic impossible under "standard" conditions.[citation needed]

text: Summary[edit]

text: Bacterial electron transport pathways are, in general, inducible.  Depending on their environment, bacteria can synthesize different transmembrane complexes and produce different electron transport chains in their cell membranes.  Bacteria select their electron transport chains from a DNA library containing multiple possible dehydrogenases, terminal oxidases and terminal reductases.  The situation is often summarized by saying that electron transport chains in bacteria are branched, modular, and inducible.

text: Photosynthetic[edit]

text: In oxidative phosphorylation, electrons are transferred from a low-energy electron donor (e.g., NADH) to an acceptor (e.g., O2) through an electron transport chain.   In photophosphorylation, the energy of sunlight is used to create a high-energy electron donor and an electron acceptor.  Electrons are then transferred from the donor to the acceptor through another electron transport chain.

text: Photosynthetic electron transport chains have many similarities to the oxidative chains discussed above.  They use mobile, lipid-soluble carriers (quinones) and mobile, water-soluble carriers (cytochromes, etc.).  They also contain a proton pump.  It is remarkable that the proton pump in all photosynthetic chains resembles mitochondrial Complex III.

text: Photosynthetic electron transport chains are discussed in greater detail in the articles Photophosphorylation, Photosynthesis, Photosynthetic reaction center and Light-dependent reaction.

text: Summary[edit]

text:
Electron transport chains are redox reactions that transfer electrons from an electron donor to an electron acceptor.  The transfer of electrons is coupled to the translocation of protons across a membrane, producing a proton gradient.  The proton gradient is used to produce useful work.
About 30 work units are produced per electron transport.