Photon polarization

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Photon_polarization 

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two.

The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well. Polarization is an example of a qubit degree of freedom, which forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through lossless media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.

Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with polaroid sunglass lenses.

The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (called spin), as well as energy, with the photon.

Polarization of classical electromagnetic waves

Main article: Polarization (waves)

Polarization states

Linear polarization

Main article: Linear polarization

 

Effect of a polarizer on reflection from mud flats. In the first picture, the polarizer is rotated to minimize the effect; in the second it is rotated 90° to maximize it: almost all reflected sunlight is eliminated.

The wave is linearly polarized (or plane polarized) when the phase angles ${\displaystyle \alpha _{x}^{},\alpha _{y}}$ are equal,

${\displaystyle \alpha _{x}=\alpha _{y}\ {\stackrel {\mathrm {def} }{=}}\ \alpha .}$

This represents a wave with phase ${\displaystyle \alpha }$ polarized at an angle ${\displaystyle \theta }$ with respect to the x axis. In this case the Jones vector

${\displaystyle |\psi \rangle ={\begin{pmatrix}\cos \theta \exp \left(i\alpha _{x}\right)\\\sin \theta \exp \left(i\alpha _{y}\right)\end{pmatrix}}}$

can be written with a single phase:

${\displaystyle |\psi \rangle ={\begin{pmatrix}\cos \theta \\\sin \theta \end{pmatrix}}\exp \left(i\alpha \right).}$

The state vectors for linear polarization in x or y are special cases of this state vector.

If unit vectors are defined such that

${\displaystyle |x\rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}1\\0\end{pmatrix}}}$

and

${\displaystyle |y\rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}0\\1\end{pmatrix}}}$

then the linearly polarized polarization state can be written in the "x-y basis" as

${\displaystyle |\psi \rangle =\cos \theta \exp \left(i\alpha \right)|x\rangle +\sin \theta \exp \left(i\alpha \right)|y\rangle =\psi _{x}|x\rangle +\psi _{y}|y\rangle .}$

Circular polarization

Main article: Circular polarization

If the phase angles ${\displaystyle \alpha _{x}}$ and ${\displaystyle \alpha _{y}}$ differ by exactly ${\displaystyle \pi /2}$ and the x amplitude equals the y amplitude the wave is circularly polarized. The Jones vector then becomes

${\displaystyle |\psi \rangle ={\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\\pm i\end{pmatrix}}\exp \left(i\alpha _{x}\right)}$

where the plus sign indicates left circular polarization and the minus sign indicates right circular polarization. In the case of circular polarization, the electric field vector of constant magnitude rotates in the x-y plane.

If unit vectors are defined such that

${\displaystyle |\mathrm {R} \rangle \ {\stackrel {\mathrm {def} }{=}}\ {1 \over {\sqrt {2}}}{\begin{pmatrix}1\\i\end{pmatrix}}}$

and

${\displaystyle |\mathrm {L} \rangle \ {\stackrel {\mathrm {def} }{=}}\ {1 \over {\sqrt {2}}}{\begin{pmatrix}1\\-i\end{pmatrix}}}$

then an arbitrary polarization state can be written in the "R-L basis" as

${\displaystyle |\psi \rangle =\psi _{\rm {R}}|\mathrm {R} \rangle +\psi _{\rm {L}}|\mathrm {L} \rangle }$

where

${\displaystyle \psi _{\rm {R}}=\langle \mathrm {R} |\psi \rangle ={\frac {1}{\sqrt {2}}}(\cos \theta \exp(i\alpha _{x})-i\sin \theta \exp(i\alpha _{y}))}$

and

${\displaystyle \psi _{\rm {L}}=\langle \mathrm {L} |\psi \rangle ={\frac {1}{\sqrt {2}}}(\cos \theta \exp(i\alpha _{x})+i\sin \theta \exp(i\alpha _{y})).}$

We can see that

${\displaystyle 1=|\psi _{\rm {R}}|^{2}+|\psi _{\rm {L}}|^{2}.}$

Elliptical polarization

Main article: Elliptical polarization

The general case in which the electric field rotates in the x-y plane and has variable magnitude is called elliptical polarization. The state vector is given by

${\displaystyle |\psi \rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}\psi _{x}\\\psi _{y}\end{pmatrix}}={\begin{pmatrix}\cos \theta \exp \left(i\alpha _{x}\right)\\\sin \theta \exp \left(i\alpha _{y}\right)\end{pmatrix}}.}$

Geometric visualization of an arbitrary polarization state

To get an understanding of what a polarization state looks like, one can observe the orbit that is made if the polarization state is multiplied by a phase factor of ${\displaystyle e^{i\omega t}}$ and then having the real parts of its components interpreted as x and y coordinates respectively. That is:

${\displaystyle {\begin{pmatrix}x(t)\\y(t)\end{pmatrix}}={\begin{pmatrix}\Re (e^{i\omega t}\psi _{x})\\\Re (e^{i\omega t}\psi _{y})\end{pmatrix}}=\Re \left[e^{i\omega t}{\begin{pmatrix}\psi _{x}\\\psi _{y}\end{pmatrix}}\right]=\Re \left(e^{i\omega t}|\psi \rangle \right).}$

If only the traced out shape and the direction of the rotation of (x(t), y(t)) is considered when interpreting the polarization state, i.e. only

${\displaystyle M(|\psi \rangle )=\left.\left\{{\Big (}x(t),\,y(t){\Big )}\,\right|\,\forall \,t\right\}}$

(where x(t) and y(t) are defined as above) and whether it is overall more right circularly or left circularly polarized (i.e. whether |ψ_R| > |ψ_L| or vice versa), it can be seen that the physical interpretation will be the same even if the state is multiplied by an arbitrary phase factor, since

${\displaystyle M(e^{i\alpha }|\psi \rangle )=M(|\psi \rangle ),\ \alpha \in \mathbb {R} }$

and the direction of rotation will remain the same. In other words, there is no physical difference between two polarization states ${\displaystyle |\psi \rangle }$ and ${\displaystyle e^{i\alpha }|\psi \rangle }$, between which only a phase factor differs.

It can be seen that for a linearly polarized state, M will be a line in the xy plane, with length 2 and its middle in the origin, and whose slope equals to tan(θ). For a circularly polarized state, M will be a circle with radius 1/√2 and with the middle in the origin.

Energy, momentum, and angular momentum of a classical electromagnetic wave

Energy density of classical electromagnetic waves

Energy in a plane wave

Main article: Energy density

The energy per unit volume in classical electromagnetic fields is (cgs units) and also Planck unit

${\displaystyle {\mathcal {E}}_{c}={\frac {1}{8\pi }}\left[\mathbf {E} ^{2}(\mathbf {r} ,t)+\mathbf {B} ^{2}(\mathbf {r} ,t)\right].}$

For a plane wave, this becomes

${\displaystyle {\mathcal {E}}_{c}={\frac {\mid \mathbf {E} \mid ^{2}}{8\pi }}}$

where the energy has been averaged over a wavelength of the wave.

Fraction of energy in each component

The fraction of energy in the x component of the plane wave is

${\displaystyle f_{x}={\frac {\mid \mathbf {E} \mid ^{2}\cos ^{2}\theta }{\mid \mathbf {E} \mid ^{2}}}=\psi _{x}^{*}\psi _{x}=\cos ^{2}\theta }$

with a similar expression for the y component resulting in ${\displaystyle f_{y}=\sin ^{2}\theta }$.

The fraction in both components is

${\displaystyle \psi _{x}^{*}\psi _{x}+\psi _{y}^{*}\psi _{y}=\langle \psi |\psi \rangle =1.}$

Momentum density of classical electromagnetic waves

The momentum density is given by the Poynting vector

${\displaystyle {\boldsymbol {\mathcal {P}}}={1 \over 4\pi c}\mathbf {E} (\mathbf {r} ,t)\times \mathbf {B} (\mathbf {r} ,t).}$

For a sinusoidal plane wave traveling in the z direction, the momentum is in the z direction and is related to the energy density:

${\displaystyle {\mathcal {P}}_{z}c={\mathcal {E}}_{c}.}$

The momentum density has been averaged over a wavelength.

Angular momentum density of classical electromagnetic waves

Main article: Angular momentum of light

Electromagnetic waves can have both orbital and spin angular momentum. The total angular momentum density is

${\displaystyle {\boldsymbol {\mathcal {L}}}=\mathbf {r} \times {\boldsymbol {\mathcal {P}}}={1 \over 4\pi c}\mathbf {r} \times \left[\mathbf {E} (\mathbf {r} ,t)\times \mathbf {B} (\mathbf {r} ,t)\right].}$

For a sinusoidal plane wave propagating along ${\displaystyle z}$ axis the orbital angular momentum density vanishes. The spin angular momentum density is in the ${\displaystyle z}$ direction and is given by

${\displaystyle {\mathcal {L}}={{\mid \mathbf {E} \mid ^{2}} \over {8\pi \omega }}\left(\mid \langle \mathrm {R} |\psi \rangle \mid ^{2}-\mid \langle \mathrm {L} |\psi \rangle \mid ^{2}\right)={1 \over \omega }{\mathcal {E}}_{c}\left(\mid \psi _{\rm {R}}\mid ^{2}-\mid \psi _{\rm {L}}\mid ^{2}\right)}$

where again the density is averaged over a wavelength.

Optical filters and crystals

Passage of a classical wave through a polaroid filter

Linear polarization

A linear filter transmits one component of a plane wave and absorbs the perpendicular component. In that case, if the filter is polarized in the x direction, the fraction of energy passing through the filter is

${\displaystyle f_{x}=\psi _{x}^{*}\psi _{x}=\cos ^{2}\theta .\,}$

Example of energy conservation: Passage of a classical wave through a birefringent crystal

An ideal birefringent crystal transforms the polarization state of an electromagnetic wave without loss of wave energy. Birefringent crystals therefore provide an ideal test bed for examining the conservative transformation of polarization states. Even though this treatment is still purely classical, standard quantum tools such as unitary and Hermitian operators that evolve the state in time naturally emerge.

Initial and final states

A birefringent crystal is a material that has an optic axis with the property that the light has a different index of refraction for light polarized parallel to the axis than it has for light polarized perpendicular to the axis. Light polarized parallel to the axis are called "extraordinary rays" or "extraordinary photons", while light polarized perpendicular to the axis are called "ordinary rays" or "ordinary photons". If a linearly polarized wave impinges on the crystal, the extraordinary component of the wave will emerge from the crystal with a different phase than the ordinary component. In mathematical language, if the incident wave is linearly polarized at an angle ${\displaystyle \theta }$ with respect to the optic axis, the incident state vector can be written

${\displaystyle |\psi \rangle ={\begin{pmatrix}\cos \theta \\\sin \theta \end{pmatrix}}}$

and the state vector for the emerging wave can be written

${\displaystyle |\psi '\rangle ={\begin{pmatrix}\cos \theta \exp \left(i\alpha _{x}\right)\\\sin \theta \exp \left(i\alpha _{y}\right)\end{pmatrix}}={\begin{pmatrix}\exp \left(i\alpha _{x}\right)&0\\0&\exp \left(i\alpha _{y}\right)\end{pmatrix}}{\begin{pmatrix}\cos \theta \\\sin \theta \end{pmatrix}}\ {\stackrel {\mathrm {def} }{=}}\ {\hat {U}}|\psi \rangle .}$

While the initial state was linearly polarized, the final state is elliptically polarized. The birefringent crystal alters the character of the polarization.

Dual of the final state

A calcite crystal laid upon a paper with some letters showing the double refraction

The initial polarization state is transformed into the final state with the operator U. The dual of the final state is given by

${\displaystyle \langle \psi '|=\langle \psi |{\hat {U}}^{\dagger }}$

where ${\displaystyle U^{\dagger }}$ is the adjoint of U, the complex conjugate transpose of the matrix.

Unitary operators and energy conservation

The fraction of energy that emerges from the crystal is

${\displaystyle \langle \psi '|\psi '\rangle =\langle \psi |{\hat {U}}^{\dagger }{\hat {U}}|\psi \rangle =\langle \psi |\psi \rangle =1.}$

In this ideal case, all the energy impinging on the crystal emerges from the crystal. An operator U with the property that

${\displaystyle {\hat {U}}^{\dagger }{\hat {U}}=I,}$

where I is the identity operator and U is called a unitary operator. The unitary property is necessary to ensure energy conservation in state transformations.

Hermitian operators and energy conservation

Doubly refracting Calcite from Iceberg claim, Dixon, New Mexico. This 35 pound (16 kg) crystal, on display at the National Museum of Natural History, is one of the largest single crystals in the United States.

If the crystal is very thin, the final state will be only slightly different from the initial state. The unitary operator will be close to the identity operator. We can define the operator H by

${\displaystyle {\hat {U}}\approx I+i{\hat {H}}}$

and the adjoint by

${\displaystyle {\hat {U}}^{\dagger }\approx I-i{\hat {H}}^{\dagger }.}$

Energy conservation then requires

${\displaystyle I={\hat {U}}^{\dagger }{\hat {U}}\approx \left(I-i{\hat {H}}^{\dagger }\right)\left(I+i{\hat {H}}\right)\approx I-i{\hat {H}}^{\dagger }+i{\hat {H}}.}$

This requires that

${\displaystyle {\hat {H}}={\hat {H}}^{\dagger }.}$

Operators like this that are equal to their adjoints are called Hermitian or self-adjoint.

The infinitesimal transition of the polarization state is

${\displaystyle |\psi '\rangle -|\psi \rangle =i{\hat {H}}|\psi \rangle .}$

Thus, energy conservation requires that infinitesimal transformations of a polarization state occur through the action of a Hermitian operator.

Photons: The connection to quantum mechanics

Main article: Photon

Energy, momentum, and angular momentum of photons

Energy

The treatment to this point has been classical. It is a testament, however, to the generality of Maxwell's equations for electrodynamics that the treatment can be made quantum mechanical with only a reinterpretation of classical quantities. The reinterpretation is based on the theories of Max Planck and the interpretation by Albert Einstein of those theories and of other experiments.

Einstein's conclusion from early experiments on the photoelectric effect is that electromagnetic radiation is composed of irreducible packets of energy, known as photons. The energy of each packet is related to the angular frequency of the wave by the relation

${\displaystyle \epsilon =\hbar \omega }$

where ${\displaystyle \hbar }$ is an experimentally determined quantity known as Planck's constant. If there are ${\displaystyle N}$ photons in a box of volume ${\displaystyle V}$, the energy in the electromagnetic field is

${\displaystyle N\hbar \omega }$

and the energy density is

${\displaystyle {N\hbar \omega \over V}}$

The photon energy can be related to classical fields through the correspondence principle which states that for a large number of photons, the quantum and classical treatments must agree. Thus, for very large ${\displaystyle N}$, the quantum energy density must be the same as the classical energy density

${\displaystyle {N\hbar \omega \over V}={\mathcal {E}}_{c}={\frac {\mid \mathbf {E} \mid ^{2}}{8\pi }}.}$

The number of photons in the box is then

${\displaystyle N={\frac {V}{8\pi \hbar \omega }}\mid \mathbf {E} \mid ^{2}.}$

Momentum

The correspondence principle also determines the momentum and angular momentum of the photon. For momentum

${\displaystyle {\mathcal {P}}_{z}={N\hbar \omega \over cV}={N\hbar k_{z} \over V}}$

where ${\displaystyle k_{z}}$ is the wave number. This implies that the momentum of a photon is

${\displaystyle p_{z}=\hbar k_{z}.\,}$

Angular momentum and spin

Similarly for the spin angular momentum

${\displaystyle {\mathcal {L}}={1 \over \omega }{\mathcal {E}}_{c}\left(\mid \psi _{\rm {R}}\mid ^{2}-\mid \psi _{\rm {L}}\mid ^{2}\right)={N\hbar \over V}\left(\mid \psi _{\rm {R}}\mid ^{2}-\mid \psi _{\rm {L}}\mid ^{2}\right)}$

where ${\displaystyle {\mathcal {E}}_{c}}$ is field strength. This implies that the spin angular momentum of the photon is

${\displaystyle l_{z}=\hbar \left(\mid \psi _{\rm {R}}\mid ^{2}-\mid \psi _{\rm {L}}\mid ^{2}\right).}$

the quantum interpretation of this expression is that the photon has a probability of ${\displaystyle \mid \psi _{\rm {R}}\mid ^{2}}$ of having a spin angular momentum of ${\displaystyle \hbar }$ and a probability of ${\displaystyle \mid \psi _{\rm {L}}\mid ^{2}}$ of having a spin angular momentum of ${\displaystyle -\hbar }$. We can therefore think of the spin angular momentum of the photon being quantized as well as the energy. The angular momentum of classical light has been verified. A photon that is linearly polarized (plane polarized) is in a superposition of equal amounts of the left-handed and right-handed states.

Spin operator

The spin of the photon is defined as the coefficient of ${\displaystyle \hbar }$ in the spin angular momentum calculation. A photon has spin 1 if it is in the ${\displaystyle |R\rangle }$ state and -1 if it is in the ${\displaystyle |L\rangle }$ state. The spin operator is defined as the outer product

${\displaystyle {\hat {S}}\ {\stackrel {\mathrm {def} }{=}}\ |\mathrm {R} \rangle \langle \mathrm {R} |-|\mathrm {L} \rangle \langle \mathrm {L} |={\begin{pmatrix}0&-i\\i&0\end{pmatrix}}.}$

The eigenvectors of the spin operator are ${\displaystyle |\mathrm {R} \rangle }$ and ${\displaystyle |\mathrm {L} \rangle }$ with eigenvalues 1 and -1, respectively.

The expected value of a spin measurement on a photon is then

${\displaystyle \langle \psi |{\hat {S}}|\psi \rangle =\mid \psi _{\rm {R}}\mid ^{2}-\mid \psi _{\rm {L}}\mid ^{2}.}$

An operator S has been associated with an observable quantity, the spin angular momentum. The eigenvalues of the operator are the allowed observable values. This has been demonstrated for spin angular momentum, but it is in general true for any observable quantity.

Spin states

See also: Circular polarization § Quantum mechanics

We can write the circularly polarized states as

${\displaystyle |s\rangle }$

where s=1 for ${\displaystyle |\mathrm {R} \rangle }$ and s= -1 for ${\displaystyle |\mathrm {L} \rangle }$. An arbitrary state can be written

${\displaystyle |\psi \rangle =\sum _{s=-1,1}a_{s}\exp \left(i\alpha _{x}-is\theta \right)|s\rangle }$

where ${\displaystyle \alpha _{1}}$ and ${\displaystyle \alpha _{-1}}$ are phase angles, θ is the angle by which the frame of reference is rotated, and

${\displaystyle \sum _{s=-1,1}\mid a_{s}\mid ^{2}=1.}$

Spin and angular momentum operators in differential form

When the state is written in spin notation, the spin operator can be written

${\displaystyle {\hat {S}}_{d}\rightarrow i{\partial \over \partial \theta }}$

${\displaystyle {\hat {S}}_{d}^{\dagger }\rightarrow -i{\partial \over \partial \theta }.}$

The eigenvectors of the differential spin operator are

${\displaystyle \exp \left(i\alpha _{x}-is\theta \right)|s\rangle .}$

To see this note

${\displaystyle {\hat {S}}_{d}\exp \left(i\alpha _{x}-is\theta \right)|s\rangle \rightarrow i{\partial \over \partial \theta }\exp \left(i\alpha _{x}-is\theta \right)|s\rangle =s\left[\exp \left(i\alpha _{x}-is\theta \right)|s\rangle \right].}$

The spin angular momentum operator is

${\displaystyle {\hat {l}}_{z}=\hbar {\hat {S}}_{d}.}$

The nature of probability in quantum mechanics

Probability for a single photon

There are two ways in which probability can be applied to the behavior of photons; probability can be used to calculate the probable number of photons in a particular state, or probability can be used to calculate the likelihood of a single photon to be in a particular state. The former interpretation violates energy conservation. The latter interpretation is the viable, if nonintuitive, option. Dirac explains this in the context of the double-slit experiment:

Some time before the discovery of quantum mechanics people realized that the connection between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place. The importance of the distinction can be made clear in the following way. Suppose we have a beam of light consisting of a large number of photons split up into two components of equal intensity. On the assumption that the beam is connected with the probable number of photons in it, we should have half the total number going into each component. If the two components are now made to interfere, we should require a photon in one component to be able to interfere with one in the other. Sometimes these two photons would have to annihilate one another and other times they would have to produce four photons. This would contradict the conservation of energy. The new theory, which connects the wave function with probabilities for one photon gets over the difficulty by making each photon go partly into each of the two components. Each photon then interferes only with itself. Interference between two different photons never occurs.
—Paul Dirac, The Principles of Quantum Mechanics, 1930, Chapter 1

Probability amplitudes

The probability for a photon to be in a particular polarization state depends on the fields as calculated by the classical Maxwell's equations. The polarization state of the photon is proportional to the field. The probability itself is quadratic in the fields and consequently is also quadratic in the quantum state of polarization. In quantum mechanics, therefore, the state or probability amplitude contains the basic probability information. In general, the rules for combining probability amplitudes look very much like the classical rules for composition of probabilities: 

1. The probability amplitude for two successive probabilities is the product of amplitudes for the individual possibilities. For example, the amplitude for the x polarized photon to be right circularly polarized and for the right circularly polarized photon to pass through the y-polaroid is ${\displaystyle \langle R|x\rangle \langle y|R\rangle ,}$ the product of the individual amplitudes.
2. The amplitude for a process that can take place in one of several indistinguishable ways is the sum of amplitudes for each of the individual ways. For example, the total amplitude for the x polarized photon to pass through the y-polaroid is the sum of the amplitudes for it to pass as a right circularly polarized photon, ${\displaystyle \langle y|R\rangle \langle R|x\rangle ,}$ plus the amplitude for it to pass as a left circularly polarized photon, ${\displaystyle \langle y|L\rangle \langle L|x\rangle \dots }$
3. The total probability for the process to occur is the absolute value squared of the total amplitude calculated by 1 and 2.

Uncertainty principle

Main article: Uncertainty principle

Cauchy–Schwarz inequality in Euclidean space. ${\displaystyle \mathbf {V} \cdot \mathbf {W} =\|\mathbf {V} \|\|\mathbf {W} \|\cos a.}$ This implies ${\displaystyle \mathbf {V} \cdot \mathbf {W} \leq \|\mathbf {V} \|\|\mathbf {W} \|.}$

Mathematical preparation

For any legal operators the following inequality, a consequence of the Cauchy–Schwarz inequality, is true.

${\displaystyle {\frac {1}{4}}|\langle ({\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}})x|x\rangle |^{2}\leq \|{\hat {A}}x\|^{2}\|{\hat {B}}x\|^{2}.}$

If B A ψ and A B ψ are defined, then by subtracting the means and re-inserting in the above formula, we deduce

${\displaystyle \Delta _{\psi }{\hat {A}}\,\Delta _{\psi }{\hat {B}}\geq {\frac {1}{2}}\left|\left\langle \left[{\hat {A}},{\hat {B}}\right]\right\rangle _{\psi }\right|}$

where

${\displaystyle \left\langle {\hat {X}}\right\rangle _{\psi }=\left\langle \psi |{\hat {X}}|\psi \right\rangle }$

is the operator mean of observable X in the system state ψ and

${\displaystyle \Delta _{\psi }{\hat {X}}={\sqrt {\langle {\hat {X}}^{2}\rangle _{\psi }-\langle {\hat {X}}\rangle _{\psi }^{2}}}.}$

Here

${\displaystyle \left[{\hat {A}},{\hat {B}}\right]\ {\stackrel {\mathrm {def} }{=}}\ {\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}}}$

is called the commutator of A and B.

This is a purely mathematical result. No reference has been made to any physical quantity or principle. It simply states that the uncertainty of one operator times the uncertainty of another operator has a lower bound.

Application to angular momentum

The connection to physics can be made if we identify the operators with physical operators such as the angular momentum and the polarization angle. We have then

${\displaystyle \Delta _{\psi }{\hat {l}}_{z}\,\Delta _{\psi }{\theta }\geq {\frac {\hbar }{2}},}$

which means that angular momentum and the polarization angle cannot be measured simultaneously with infinite accuracy. (The polarization angle can be measured by checking whether the photon can pass through a polarizing filter oriented at a particular angle, or a polarizing beam splitter. This results in a yes/no answer which, if the photon was plane-polarized at some other angle, depends on the difference between the two angles.)

States, probability amplitudes, unitary and Hermitian operators, and eigenvectors

Much of the mathematical apparatus of quantum mechanics appears in the classical description of a polarized sinusoidal electromagnetic wave. The Jones vector for a classical wave, for instance, is identical with the quantum polarization state vector for a photon. The right and left circular components of the Jones vector can be interpreted as probability amplitudes of spin states of the photon. Energy conservation requires that the states be transformed with a unitary operation. This implies that infinitesimal transformations are transformed with a Hermitian operator. These conclusions are a natural consequence of the structure of Maxwell's equations for classical waves.

Quantum mechanics enters the picture when observed quantities are measured and found to be discrete rather than continuous. The allowed observable values are determined by the eigenvalues of the operators associated with the observable. In the case angular momentum, for instance, the allowed observable values are the eigenvalues of the spin operator.

These concepts have emerged naturally from Maxwell's equations and Planck's and Einstein's theories. They have been found to be true for many other physical systems. In fact, the typical program is to assume the concepts of this section and then to infer the unknown dynamics of a physical system. This was done, for instance, with the dynamics of electrons. In that case, working back from the principles in this section, the quantum dynamics of particles were inferred, leading to Schrödinger's equation, a departure from Newtonian mechanics. The solution of this equation for atoms led to the explanation of the Balmer series for atomic spectra and consequently formed a basis for all of atomic physics and chemistry.

This is not the only occasion in which Maxwell's equations have forced a restructuring of Newtonian mechanics. Maxwell's equations are relativistically consistent. Special relativity resulted from attempts to make classical mechanics consistent with Maxwell's equations (see, for example, Moving magnet and conductor problem).

Intergenerational equity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Intergenerational_equity 

 

Grandfather and grandchild

 

The U.S. National Debt is often cited as an example of intergenerational inequity, as future generations will have the responsibility of paying it off. The U.S. National Debt has grown substantially over the past several decades. Relative to total GDP, the debt burden has worsened in the past several years.

Intergenerational equity in economic, psychological, and sociological contexts, is the idea of fairness or justice between generations. The concept can be applied to fairness in dynamics between children, youth, adults, and seniors. It can also be applied to fairness between generations currently living and future generations.

Conversations about intergenerational equity occur across several fields. It is often discussed in public economics, especially with regard to transition economics, social policy, and government budget-making. Many cite the growing U.S. national debt as an example of intergenerational inequity, as future generations will shoulder the consequences. Intergenerational equity is also explored in environmental concerns, including sustainable development, and climate change. The continued depletion of natural resources that has occurred in the past century will likely be a significant burden for future generations. Intergenerational equity is also discussed with regard to standards of living, specifically on inequities in the living standards experienced by people of different ages and generations. Intergenerational equity issues also arise in the arenas of elderly care and social justice.

Public economics usage

History

Since the first recorded debt issuance in Sumaria in 1796 BC, one of the penalties for failure to repay a loan has been debt bondage. In some instances, this repayment of financial debt with labor included the debtor's children, essentially condemning the debtor family to perpetual slavery. About one millennium after written debt contracts were created, the concept of debt forgiveness appears in the Old Testament, called Jubilee (Leviticus 25), and in Greek law when Solon introduces Seisachtheia. Both of these historical examples of debt forgiveness involved freeing children from slavery caused by their parents' debt.

While slavery is illegal in all countries today, North Korea has a policy called, "Three Generations of Punishment" which has been documented by Shin Dong-hyuk and used as an example of punishing children for parents' mistakes. Stanley Druckenmiller and Geoffrey Canada have applied this concept (calling it "Generational Theft") to the large increase in government debt being left by the Baby Boomers to their children.

Investment management

In the context of institutional investment management, intergenerational equity is the principle that an endowed institution's spending rate must not exceed its after-inflation rate of compound return, so that investment gains are spent equally on current and future constituents of the endowed assets. This concept was originally set out in 1974 by economist James Tobin, who wrote that "The trustees of endowed institutions are the guardians of the future against the claims of the present. Their task in managing the endowment is to preserve equity among generations."

In an economical context intergenerational equity refers to the relationship that a particular family has with resources. An example is the forest-dwelling civilians in Papua New Guinea, who for generations have lived in a certain part of the forest which thus becomes their land. The adult population sell the trees for palm oil to make money. If they cannot make a sustainable development on managing their resources, their next or future generations will lose this resource.

U.S. national debt

See also: National debt of the United States

One debate about the national debt relates to intergenerational equity. If one generation is receiving the benefit of government programs or employment that is enabled by deficit spending and debt accumulation, to what extent does the resulting higher debt impose risks and costs on future generations? There are several factors to consider:

• For every dollar of debt held by the public, there is a government obligation (generally marketable Treasury securities) counted as an asset by investors. Future generations benefit to the extent these assets are passed on to them, which by definition must correspond to the level of debt passed on.
• As of 2010, approximately 72% of financial assets were held by the wealthiest 5% of the population. This presents a wealth and income distribution question, as only a fraction of the people in future generations will receive principal or interest from investments related to the debt incurred today.
• To the extent the U.S. debt is owed to foreign investors (approximately half the "debt held by the public" during 2012), principal and interest are not directly received by U.S. heirs.
• Higher debt levels imply higher interest payments, which create costs for future taxpayers (e.g., higher taxes, lower government benefits, higher inflation, or increased risk of fiscal crisis).
• To the extent that borrowed funds are invested today to improve the long-term productivity of the economy and its workers, such as via useful infrastructure projects, future generations may benefit.
• For every dollar of intragovernmental debt, there is an obligation to specific program recipients, generally non-marketable securities such as those held in the Social Security Trust Fund. Adjustments that reduce future deficits in these programs may also apply costs to future generations, via higher taxes or lower program spending.

Economist Paul Krugman wrote in March 2013 that by neglecting public investment and failing to create jobs, we are doing far more harm to future generations than merely passing along debt: "Fiscal policy is, indeed, a moral issue, and we should be ashamed of what we’re doing to the next generation's economic prospects. But our sin involves investing too little, not borrowing too much." Young workers face high unemployment and studies have shown their income may lag throughout their careers as a result. Teacher jobs have been cut, which could affect the quality of education and competitiveness of younger Americans.

Australian politician Christine Milne made similar statements in the lead-up to the 2014 Carbon Price Repeal Bill, naming the Liberal National Party (elected to parliament in 2013) and inherently its ministers, as intergenerational thieves; her statement was based on the party's attempts to roll back progressive carbon tax policy and the impact this would have on the intergenerational equity of future generations.

U.S. Social Security

See also: Social Security (United States)

The U.S. Social Security system has provided a greater net benefit to those who reached retirement closest to the first implementation of the system. The system is unfunded, meaning the elderly who retired right after the implementation of the system did not pay any taxes into the social security system, but reaped the benefits. Professor Michael Doran estimates that cohorts born previous to 1938 will receive more in benefits than they pay in taxes, while the reverse is true to cohorts born after. Also, that the long-term insolvency of Social Security will likely lead to further intergenerational transfers. However, Broad concedes that other benefits have been introduced into U.S. society via the welfare system, like Medicare and government-financed medical research, that benefit current and future elderly cohorts.

Environmental usage

Further information: Climate justice

 

Global warming is an example of intergenerational inequity, see climate justice

Intergenerational equity is often referred to in environmental contexts, as younger age cohorts will disproportionately experience the negative consequences of environmental damage. For instance, it is estimated that children born in 2020 (e.g. "Generation Alpha") will experience 2–7 as many extreme weather events over their lifetimes, particularly heat waves, compared to people born in 1960, under current climate policy pledges. Moreover, on average, the elderly played "a leading role in driving up GHG emissions in the past decade and are on the way to becoming the largest contributor" due to factors such as demographic transition, low informed concern about climate change and high expenditures on carbon-intensive products like energy which is used i.a. for heating rooms and private transport.

Ethical perspectives on amelioration

Two perspectives have been proposed on what should be done to ameliorate environmental intergenerational equity: the "weak sustainability" perspective and the "strong sustainability" perspective. From the "weak" perspective, intergenerational equity would be achieved if losses to the environment that future generations face were offset by gains in economic progress (as measured by contemporary mechanisms/metrics). From the "strong" perspective, no amount of economic progress (or as measured by contemporary metrics) can justify leaving future generations with a degraded environment. According to Professor Sharon Beder, the "weak" perspective is undermined by a lack of knowledge of the future, as we do not know which intrinsically valuable resources will not be able to be replaced by technology. We also do not know to what extent environmental damage is irreversible. Further, more harm cannot be avoided to many species of plants and animals. Other scholars contest Beder's point of view. Professor Wilfred Beckerman insists that "strong sustainability" is "morally repugnant", particularly when it overrides other moral concerns about those alive today. Beckerman insists that the optimal choice for society is to prioritize the welfare of current generations – albeit, depending e.g. on lifespans, these are also affected by unsustainability – above future generations. He suggests placing a discount rate on outcomes for future generations when accounting for generational equity. Beckerman is extensively criticized by Brian Barry and Nicholas Vrousalis.

Climate-related lawsuit

See also: Climate change litigation and Right to a healthy environment

In September 2015, a group of youth environmental activists filed a lawsuit against the U.S. federal government for insufficiently protecting against climate change: Juliana v. United States. Their statement emphasized the disproportionate cost of climate-related damage younger generations would bear: “Youth Plaintiffs represent the youngest living generation, beneficiaries of the public trust. Youth Plaintiffs have a substantial, direct, and immediate interest in protecting the atmosphere, other vital natural resources, their quality of life, their property interests, and their liberties. They also have an interest in ensuring that the climate system remains stable enough to secure their constitutional rights to life, liberty, and property, rights that depend on a livable Future.” In November 2016, the case was allowed to go to trial after US District Court Judge Ann Aiken denied the federal government’s motion to dismiss the case. In her opinion and order, she said, "Exercising my ‘reasoned judgment,’ I have no doubt that the right to a climate system capable of sustaining human life is fundamental to a free and ordered society." As of April 2017, the trial was put on hold with a stay. The Ninth Circuit heard oral arguments on the stay in November of 2017 and a ruling is expected in February of 2018.

Standards of living usage

Discussions of intergenerational equity in standards of living reference differences between people of different ages or of different generations. Two perspectives on intergenerational equity in living standards have been distinguished by Rice, Temple, and McDonald. The first perspective – a "cross-sectional" perspective – focuses how living standards at a particular point in time vary between people of different ages. The relevant issue is the degree to which, at a particular point in time, people of different ages enjoy equal living standards. The second perspective – a "cohort" perspective – focuses on how living standards over a lifetime vary between people of different generations. For intergenerational equity, the relevant issue becomes the degree to which people of different generations enjoy equal living standards over their lifetimes. Three indicators of intergenerational equity in economic flows, such as income, have been proposed by d'Albis, Badji, El Mekkaoui, and Navaux. Their first indicator originates from a cross-sectional perspective and describes the relative situation of an age group (retirees) with respect to the situation of another age group (younger people). Their second indicator originates from a cohort perspective and compares the standards of living of successive generations at the same age. D'Albis, Badji, El Mekkaoui, and Navaux's third indicator is a combination of the two previous criteria and is both an inter-age indicator and an intergenerational indicator.

In Australia, notable equality has been achieved in living standards, as measured by consumption, among people between the ages of 20 and 75 years. Substantial inequalities exist, however, between different generations, with older generations experiencing lower living standards in real terms at particular ages than younger generations. One way to illustrate these inequalities is to look at how long different generations took to achieve a level of consumption of $30,000 per year (2009–10 Australian dollars). At one extreme, people born in 1935 achieved this level of consumption when they were roughly 50 years of age, on average. At the other extreme, Millennials born in 1995 had achieved this level of consumption by the time they were around 10 years of age.

Considerations such as this have led some scholars to argue that standards of living have tended to increase generation over generation in most countries, as development and technology have progressed. When taking this into account, younger generations may have inherent privileges over older generations, which may offset the redistribution of wealth towards older generations.

Elderly care usage

Some scholars consider the cultural decay of the norm of adult children caring for elderly parents to be an intergenerational equity issue. Older generation had to care for their parents, as well as their own children, while the younger generation must only care for their children. This is especially true in countries with weak social security systems. Professor Sang-Hyop Lee describes this phenomenon in South Korea, explaining that the current elderly have the highest poverty rate among any developed country. He notes that it is particularly frustrating because the elderly usually invest a lot in their children's education, and they now feel betrayed.

Other scholars express different opinions on which generation is disadvantaged by elderly care. Professor Steven Wisensale describes the burden on current working age adults in developed economies, who must care for more elderly parents and relatives for a longer period of time. This problem is exacerbated by the increasing involvement of women in the workforce, and by the dropping fertility rate, leaving the burden for caring for parents, as well as aunts, uncles, and grandparents, on fewer children.

Social justice usage

Conversations about intergenerational equity are also relevant to social justice arenas, where issues such as health care are equal in importance to youth rights and youth voice are pressing and urgent. There is a strong interest within the legal community towards the application of intergenerational equity in law.

Advocacy groups

Generation Squeeze is a Canadian not-for-profit organization that advocates for intergenerational equity.

Urushiol

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Urushiol 

 

Urushiol

R = (CH2)14CH3 or R = (CH2)7CH=CH(CH2)5CH3 or R = (CH2)7CH=CHCH2CH=CH(CH2)2CH3 or R = (CH2)7CH=CHCH2CH=CHCH=CHCH3 or R = (CH2)7CH=CHCH2CH=CHCH2CH=CH2 and others

Urushiol /ʊˈruːʃi.ɒl/ is an oily mixture of organic compounds with allergenic properties found in plants of the family Anacardiaceae, especially Toxicodendron spp. (e.g., poison oak, Chinese lacquer tree, poison ivy, poison sumac), Comocladia ssp. (maidenplums) and also in parts of the mango tree as well as the fruit of the cashew tree.

In most individuals, urushiol causes an allergic skin rash on contact, known as urushiol-induced contact dermatitis.

The name urushiol is derived from the Japanese word for the lacquer tree, Toxicodendron vernicifluum (漆, urushi). The oxidation and polymerization of urushiol in the tree's sap in the presence of moisture allows it to form a hard lacquer, which is used to produce traditional Chinese, Korean and Japanese lacquerware.

History

Although urushiol-containing lacquers and their skin-irritating properties were well known in East Asia for several millennia, its first recorded Western texts were in 1624 by John Smith and he initially likened poison ivy to English Ivy. He did not classify it as a poison at first due to the speed with which its rash disappeared and Smith hypothesized that there may actually be medicinal uses for the plant. In the 18th and 19th centuries, many experiments were done in this area to determine whether or not this theory was true. Because that era's medicinal culture was dominated by plant-based treatments, physicians were hopeful that the strong effect this chemical produced on the body could be effective in some way. André-Ignace-Joseph Dufresnoy was one of the first to come up with a medicinal use for this chemical in 1780 when he boiled poison ivy to produce an infusion for internal use. This led to a distilled extract of poison ivy which he prescribed to many people suffering from skin problems and even paralysis. He claimed this treatment to have yielded several positive results.

For many years, poison ivy was thought to fall into the Rhus genus; however, in the 1900s, it was reclassified into a more appropriate genus, Toxicodendron, meaning poison tree. There were many documented cases of irritations and allergic reactions from the plant, and its propensity for medicinal use quickly dwindled. After this new categorization, scientists began attempts to determine what it was that rendered plants of this genus noxious, starting with a hypothesis of a volatile oil present in the plants. While this proved incorrect, Rikou Majima from Japan was able to determine that the chemical urushiol was the irritant. Further, he determined that the substance was a type of alkyl catechol, and due to its structure it was able to penetrate the skin and survive on surfaces for months to years. Urushiol's ability to polymerise into a hard glossy coating is the chemical basis for traditional lacquerware in many Asian countries. After urushiol comes in contact with oxygen, under certain conditions it become a black lacquer and has been named urushi lacquer.

Characteristics

Urushiol in its pure form is a pale-yellow liquid with a specific gravity of 0.968 and a boiling point of 200 °C (392 °F). It is soluble in diethyl ether, acetone, ethanol, carbon tetrachloride, and benzene.

Urushiol is a mixture of several closely related organic compounds. Each consists of a catechol substituted in the 3 position with a hydrocarbon chain that has 15 or 17 carbon atoms. The hydrocarbon group may be saturated or unsaturated. The exact composition of the mixture varies, depending on the plant source. Whereas western poison oak urushiol contains chiefly catechols with C₁₇ side-chains, poison ivy and poison sumac contain mostly catechols with C₁₅ sidechains.

The likelihood and severity of allergic reaction to urushiol is dependent on the degree of unsaturation of the hydrocarbon chain. Less than half of the general population experience a reaction with the saturated urushiol alone, but over 90% do so with urushiol that contains at least two degrees of unsaturation (double bonds). Longer side chains tend to produce a stronger reaction.

Urushiol is an oleoresin contained within the sap of poison ivy and related plants, and after injury to the plant, or late in the fall, the sap leaks to the surface of the plant, where under certain temperature and humidity conditions the urushiol becomes a blackish lacquer after being in contact with oxygen. Urushi lacquer is very stable. It is able to withstand disturbances from alkali, acid, and alcohol, while also being able to resist temperatures of over 300 °C. However, the lacquer can be degraded by UV rays from the sun and other sources.

Within the United States, urushiol-containing plants are distributed throughout. Poison ivy can be found in all states except California, Alaska, and Hawaii. Poison Oak can be found on the west coast or some states in the southeast, while poison sumac can be found only in the eastern half of the country.

These plants all have distinguishing features that will help in identification. Poison ivy always grows with three shiny, pointy leaves. Poison oak has a similar look, but with larger and more rounded leaves that are hairy and grow in groups of 3, 5, or 7. Poison sumac grows in groups of 7 to 13 leaves, but always in an odd number. The leaves are feather-shaped and shiny.

Allergic response and treatment

Before the urushiol has been absorbed by the skin, it can be removed with soap and water. Substantial amounts of urushiol may be absorbed within minutes. Once urushiol has penetrated the skin, attempting to remove it with water is ineffective. After being absorbed by the skin, it is recognized by the immune system's dendritic cells, otherwise called Langerhans cells. These cells then migrate to the lymph nodes, where they present the urushiol to T-lymphocytes and thus recruit them to the skin, and the T-lymphocytes cause pathology through the production of cytokines and cytotoxic damage to the skin. This causes the painful rash, blisters, and itching.

Once this response starts, only a few treatments, such as cortisone or prednisone, are effective. Medications that can reduce the irritation include antihistamines (diphenhydramine (Benadryl) or cetirizine (Zyrtec)). Other treatments include applying cold water or calamine lotion to soothe the pain and stop the itching.

Mechanism of action

Main article: Urushiol-induced contact dermatitis

To cause an allergic dermatitis reaction, the urushiol is first oxidized to create two double-bonded oxygens on the chemical. It then reacts with a protein nucleophile to trigger a reaction within the skin. Dermatitis is mediated by an induced immune response. Urushiol is too small a molecule to directly activate an immune response. Instead, it attaches to certain proteins of the skin, where it acts as a hapten, leading to a type IV hypersensitive reaction.

Hydrocortisone, the active ingredient in cortisone, works to alleviate this condition by stopping the release of chemicals that cause the dermatitis reaction. Hydrocortisone itself does not react with urushiol in any way.

Basic mechanism of Urushiol causing allergic dermatitis

Use as lacquer

A Chinese six-pointed tray, red lacquer over wood, from the Song Dynasty (960–1279), 12th–13th century, Metropolitan Museum of Art.

Urushiol-based lacquers differ from most others, being slow-drying, and set by oxidation and polymerization, rather than by evaporation alone. The active ingredient of the resin is urushiol, a mixture of various phenols suspended in water, plus a few proteins. In order for it to set properly it requires a humid and warm environment. The phenols oxidize and polymerize under the action of laccase enzymes, yielding a substrate that, upon proper evaporation of its water content, is hard. These lacquers produce very hard, durable finishes that are both beautiful and very resistant to damage by water, acid, alkali or abrasion. The resin is derived from trees indigenous to East Asia, like lacquer tree Toxicodendron vernicifluum, and wax tree Toxicodendron succedaneum. The fresh resin from the T. vernicifluum trees causes urushiol-induced contact dermatitis and great care is therefore required in its use. The Chinese treated the allergic reaction with crushed shellfish, which supposedly prevents lacquer from drying properly. Lacquer skills became very highly developed in Asia, and many highly decorated pieces were produced.

It has been confirmed that the lacquer tree has existed in Japan since 12,600 years ago in the incipient Jōmon period. This was confirmed by radioactive carbon dating of the lacquer tree found at the Torihama shell mound, and is the oldest lacquer tree in the world found as of 2011. Lacquer was used in Japan as early as 7000 BCE, during the Jōmon period. Evidence for the earliest lacquerware was discovered at the Kakinoshima "B" Excavation Site in Hokkaido. The ornaments woven with lacquered red thread were discovered in a pit grave dating from the first half of the Initial Jōmon period. Also, at Kakinoshima "A" Excavation Site, earthenware with a spout painted with vermilion lacquer, which was made 3200 years ago, was found almost completely intact.

During the Shang Dynasty (1600–1046 BC), the sophisticated techniques used in the lacquer process were first developed and it became a highly artistic craft, although various prehistoric lacquerwares have been unearthed in China dating back to the Neolithic period. The earliest extant Chinese lacquer object, a red wooden bowl, was unearthed at a Hemudu culture (5000–4500 BC) site in China. By the Han Dynasty (206 BC – 220 AD), many centres of lacquer production became firmly established. The knowledge of the Chinese methods of the lacquer process spread from China during the Han, Tang and Song dynasties. Eventually it was introduced to Korea and Japan.

Trade of lacquer objects travelled through various routes to the Middle East. Known applications of lacquer in China included coffins, music instruments, furniture, and various household items. Lacquer mixed with powdered cinnabar is used to produce the traditional red lacquerware from China.

A maki-e and mother-of-pearl inlay cabinet that was exported from Japan to Europe in the 16th century.

From the 16th century to the 17th century, lacquer was introduced to Europe on a large scale for the first time through trade with Japanese. Until the 19th century, lacquerware was one of Japan's major exports, and European royalty, aristocrats and religious people represented by Marie-Antoinette, Maria Theresa and The Society of Jesus collected Japanese lacquerware luxuriously decorated with maki-e. The terms related to lacquer such as "Japanning", "Urushiol" and "maque" which means lacquer in Mexican Spanish, are derived from Japanese.

The trees must be at least ten years old before cutting to bleed the resin. It sets by a process called "aqua-polymerization", absorbing oxygen to set; placing in a humid environment allows it to absorb more oxygen from the evaporation of the water.

Lacquer-yielding trees in Thailand, Vietnam, Burma and Taiwan, called Thitsi, are slightly different; they do not contain urushiol, but similar substances called laccol or thitsiol. The result is similar but softer than the Chinese or Japanese lacquer. Burmese lacquer sets slower, and is painted by craftsmen's hands without using brushes.

Raw lacquer can be "coloured" by the addition of small amounts of iron oxides, giving red or black depending on the oxide. There is some evidence that its use is even older than 8,000 years from archaeological digs in Japan and China. Later, pigments were added to make colours. It is used not only as a finish, but mixed with ground fired and unfired clays applied to a mould with layers of hemp cloth, it can produce objects without need for another core like wood. The process is called "kanshitsu" in Japan. In the lacquering of the Chinese musical instrument, the guqin, the lacquer is mixed with deer horn powder (or ceramic powder) to give it more strength so it can stand up to the fingering.

There are a number of forms of urushiol. They vary by the length of the R chain, which depends on the species of plant producing the urushiol. Urushiol can also vary in the degree of saturation in the carbon chain. Urushiol can be drawn as follows: , where:

R = (CH₂)₁₄CH₃ or
R = (CH₂)₇CH=CH(CH₂)₅CH₃ or
R = (CH₂)₇CH=CHCH₂CH=CH(CH₂)₂CH₃ or
R = (CH₂)₇CH=CHCH₂CH=CHCH=CHCH₃ or
R = (CH₂)₇CH=CHCH₂CH=CHCH₂CH=CH₂

Gallery

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  Armorial screen

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  A Chinese carved lacquer oval tray, Yuan Dynasty, ca. 13th century.

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  Ming Dynasty Chinese lacquerware container, dated 16th century.

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  Clothing box decorated with peony scrolls, Joseon Dynasty Korea, 17th century.

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  Inro in maki-e Lacquer, Edo period Japan, 18th century

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  Picnic Box with Design of the Scene from The Tale of Genji in Maki-e Lacquer, Edo or Meiji period Japan, 19th century

Types of lacquer

Lacquer mixed with water and turpentine, ready for applying to surface.

Types of lacquer vary from place to place but they can be divided into unprocessed and processed categories.

The basic unprocessed lacquer is called raw lacquer (生漆: ki-urushi in Japanese, shengqi in Chinese). This is directly from the tree itself with some impurities filtered out. Raw lacquer has a water content of around 25% and appears in a light brown colour. This comes in a standard grade made from Chinese lacquer, which is generally used for ground layers by mixing with a powder, and a high quality grade made from Japanese lacquer called kijomi-urushi (生正味漆) which is used for the last finishing layers.

The processed form (in which the lacquer is stirred continuously until much of the water content has evaporated) is called guangqi (光漆) in Chinese but comes under many different Japanese names depending on the variation, for example, kijiro-urushi (木地呂漆) is standard transparent lacquer sometimes used with pigments and roiro-urushi (黒呂色漆) is the same but pre-mixed with iron hydroxide to produce a black coloured lacquer. Nashiji-urushi (梨子地漆) is the transparent lacquer but mixed with gamboge to create a yellow-tinged lacquer and is especially used for the sprinkled-gold technique. These lacquers are generally used for the middle layers. Japanese lacquers of this type are generally used for the top layers and are prefixed by the word jo- (上) which means 'top (layer)'.

Processed lacquers can have oil added to them to make them glossy, for example, shuai-urushi (朱合漆) is mixed with linseed oil. Other specialist lacquers include ikkake-urushi (釦漆) which is thick and used mainly for applying gold or silver leaf.