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Spin (physics)
Title: Spin (physics)
Subject: Spinmechatronics, Condensed matter physics, Wave function, Higgs boson, Elementary particle
Collection: Concepts in Physics, Physical Quantities, Quantum Field Theory, Rotational Symmetry, Spintronics
Standard Model of particle physics
Large Hadron Collider tunnel at CERN
Gauge theory
Spontaneous symmetry breaking
Higgs mechanism
Electroweak interaction
Quantum chromodynamics
CKM matrix
Strong CP problem
Hierarchy problem
Neutrino oscillations
See also: Physics beyond the Standard Model
Sudarshan · Koshiba · Davis, Jr. · Anderson · Fermi · Dirac · Feynman · Rubbia · Gell-Mann · Kendall · Taylor · Friedman · Powell · P. W. Anderson · Glashow · Meer · Cowan · Nambu · Chamberlain · Cabibbo · Schwartz · Perl · Majorana · Weinberg · Lee · Ward · Salam · Kobayashi · Maskawa · Yang · Yukawa · 't Hooft · Veltman · Gross · Politzer · Wilczek · Cronin · Fitch · Vleck · Higgs · Englert · Brout · Hagen · Guralnik · Kibble · Ting · Richter
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.[1][2]
Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. Orbital angular momentum is the quantum-mechanical counterpart to the classical notion of angular momentum: it arises when a particle executes a rotating or twisting trajectory (such as when an electron orbits a nucleus).[3][4] The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which particles are observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone.[5]
In some ways, spin is like a vector quantity; it has a definite magnitude, and it has a "direction" (but quantization makes this "direction" different from the direction of an ordinary vector). All elementary particles of a given kind have the same magnitude of spin angular momentum, which is indicated by assigning the particle a spin quantum number.[2]
The SI unit of spin is the joule-second, just as with classical angular momentum. In practice, however, it is written as a multiple of the reduced Planck constant ħ, usually in natural units, where the ħ is omitted, resulting in a unitless number. Spin quantum numbers are unitless numbers by definition.
When combined with the spin-statistics theorem, the spin of electrons results in the Pauli exclusion principle, which in turn underlies the periodic table of chemical elements.
Samuel Goudsmit at Leiden University suggested a physical interpretation of particles spinning around their own axis. The mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it.
Quantum number 1
Fermions and bosons 1.1
Spin-statistics theorem 1.2
Magnetic moments 2
Spin projection quantum number and multiplicity 3.1
Vector 3.2
Mathematical formulation 4
Operator 4.1
Pauli matrices 4.2
Pauli exclusion principle 4.3
Rotations 4.4
Lorentz transformations 4.5
Metrology along the x, y, and z axes 4.6
Metrology along an arbitrary axis 4.7
Compatibility of metrology 4.8
Parity 5
Quantum number
As the name suggests, spin was originally conceived as the rotation of a particle around some axis. This picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta:
Spin quantum numbers may take half-integer values.
Although the direction of its spin can be changed, an elementary particle cannot be made to spin faster or slower.
The spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur classically if the internal charge of the particle were distributed differently from its mass.
The conventional definition of the spin quantum number, s, is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 0, 1/2, 1, 3/2, 2, etc. The value of s for an elementary particle depends only on the type of particle, and cannot be altered in any known way (in contrast to the spin direction described below). The spin angular momentum, S, of any physical system is quantized. The allowed values of S are:
S = \frac{h}{2\pi} \, \sqrt{s (s+1)}=\frac{h}{4\pi} \, \sqrt{n(n+2)},
where h is the Planck constant. In contrast, orbital angular momentum can only take on integer values of s; i.e., even-numbered values of n.
Fermions and bosons
Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons. The two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle; that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning roughly, being in the same place with the same velocity). In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may "bunch" together even if in identical states. Also, composite particles can have spins different from the particles which comprise them. For example, a helium atom can have spin 0 and therefore can behave like a boson even though the quarks and electrons which make it up are all fermions.
This has profound practical applications:
Quarks and leptons (including electrons and neutrinos), which make up what is classically known as matter, are all fermions with spin 1/2. The common idea that "matter takes up space" actually comes from the Pauli exclusion principle acting on these particles to prevent the fermions that make up matter from being in the same quantum state. Further compaction would require electrons to occupy the same energy states, and therefore a kind of pressure (sometimes known as degeneracy pressure of electrons) acts to resist the fermions being overly close. It is also this pressure which prevents stars collapsing inwardly, and which, when it finally gives way under immense gravitational pressure in a dying massive star, triggers inward collapse and the dramatic explosion into a supernova.
Elementary fermions with other spins (3/2, 5/2 etc.) are not known to exist, as of 2014.
Elementary particles which are thought of as carrying forces are all bosons with spin 1. They include the photon which carries the electromagnetic force, the gluon (strong force), and the W and Z bosons (weak force). The ability of bosons to occupy the same quantum state is used in the laser, which aligns many photons having the same quantum number (the same direction and frequency), superfluid liquid helium resulting from helium-4 atoms being bosons, and superconductivity where pairs of electrons (which individually are fermions) act as single composite bosons.
Elementary bosons with other spins (0, 2, 3 etc.) were not historically known to exist, although they have received considerable theoretical treatment and are well established within their respective mainstream theories. In particular theoreticians have proposed the graviton (predicted to exist by some quantum gravity theories) with spin 2, and the Higgs boson (explaining electroweak symmetry breaking) with spin 0. Since 2013 the Higgs boson with spin 0 has been considered proven to exist. It is the first scalar particle (spin 0) known to exist in nature.
Theoretical and experimental studies have shown that the spin possessed by elementary particles cannot be explained by postulating that they are made up of even smaller particles rotating about a common center of mass analogous to a classical electron radius; as far as can be presently determined, these elementary particles have no inner structure. The spin of an elementary particle is therefore seen as a truly intrinsic physical property, akin to the particle's electric charge and rest mass.
Spin-statistics theorem
The proof that particles with half-integer spin (fermions) obey Fermi–Dirac statistics and the Pauli Exclusion Principle, and particles with integer spin (bosons) obey Bose–Einstein statistics, occupy "symmetric states", and thus can share quantum states, is known as the spin-statistics theorem. The theorem relies on both quantum mechanics and the theory of special relativity, and this connection between spin and statistics has been called "one of the most important applications of the special relativity theory".[6]
Magnetic moments
Magnetic field lines around a magnetostatic dipole; the magnetic dipole itself is in the center and is seen from the side.
Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment, or by measuring the magnetic fields generated by the particles themselves.
The intrinsic magnetic moment μ of a spin-1/2 particle with charge q, mass m, and spin angular momentum S, is[7]
\boldsymbol{\mu} = \frac{g_s q}{2m} \mathbf{S}
where the dimensionless quantity gs is called the spin g-factor. For exclusively orbital rotations it would be 1 (assuming that the mass and the charge occupy spheres of equal radius).
The electron, being a charged elementary particle, possesses a nonzero magnetic moment. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron g-factor, which has been experimentally determined to have the value −2.0023193043622(15), with the digits in parentheses denoting measurement uncertainty in the last two digits at one standard deviation.[8] The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319304... arises from the electron's interaction with the surrounding electromagnetic field, including its own field.[9] Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle. In fact, it is made up of quarks, which are electrically charged particles. The magnetic moment of the neutron comes from the spins of the individual quarks and their orbital motions.
Neutrinos are both elementary and electrically neutral. The minimally extended Standard Model that takes into account non-zero neutrino masses predicts neutrino magnetic moments of:[10][11][12]
\mu_{\nu}\approx 3\times 10^{-19}\mu_\mathrm{B}\frac{m_{\nu}}{\text{eV}}
where the μν are the neutrino magnetic moments, mν are the neutrino masses, and μB is the Bohr magneton. New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. It can be shown in a model independent way that neutrino magnetic moments larger than about 10−14 μB are unnatural, because they would also lead to large radiative contributions to the neutrino mass. Since the neutrino masses cannot exceed about 1 eV, these radiative corrections must then be assumed to be fine tuned to cancel out to a large degree.[13]
The measurement of neutrino magnetic moments is an active area of research. As of 2001, the latest experimental results have put the neutrino magnetic moment at less than 1.2×10−10 times the electron's magnetic moment.
In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar.
In paramagnetic materials, the magnetic dipole moments of individual atoms spontaneously align with an externally applied magnetic field. In diamagnetic materials, on the other hand, the magnetic dipole moments of individual atoms spontaneously align oppositely to any externally applied magnetic field, even if it requires energy to do so.
The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions.
Spin projection quantum number and multiplicity
In classical mechanics, the angular momentum of a particle possesses not only a magnitude (how fast the body is rotating), but also a direction (either up or down on the axis of rotation of the particle). Quantum mechanical spin also contains information about direction, but in a more subtle form. Quantum mechanics states that the component of angular momentum measured along any direction can only take on the values [14]
S_i = \hbar s_i, \quad s_i \in \{ - s, -(s-1), \dots, s-1, s \} \,\!
where Si is the spin component along the i-axis (either x, y, or z), si is the spin projection quantum number along the i-axis, and s is the principal spin quantum number (discussed in the previous section). Conventionally the direction chosen is the z-axis:
S_z = \hbar s_z, \quad s_z \in \{ - s, -(s-1), \dots, s - 1, s \} \,\!
where Sz is the spin component along the z-axis, sz is the spin projection quantum number along the z-axis.
One can see that there are 2s+1 possible values of sz. The number "2s + 1" is the multiplicity of the spin system. For example, there are only two possible values for a spin-1/2 particle: sz = +1/2 and sz = −1/2. These correspond to quantum states in which the spin is pointing in the +z or −z directions respectively, and are often referred to as "spin up" and "spin down". For a spin-3/2 particle, like a delta baryon, the possible values are +3/2, +1/2, −1/2, −3/2.
For a given quantum state, one could think of a spin vector \lang S \rang whose components are the expectation values of the spin components along each axis, i.e., \lang S \rang = [\lang S_x \rang, \lang S_y \rang, \lang S_z \rang]. This vector then would describe the "direction" in which the spin is pointing, corresponding to the classical concept of the axis of rotation. It turns out that the spin vector is not very useful in actual quantum mechanical calculations, because it cannot be measured directly: sx, sy and sz cannot possess simultaneous definite values, because of a quantum uncertainty relation between them. However, for statistically large collections of particles that have been placed in the same pure quantum state, such as through the use of a Stern–Gerlach apparatus, the spin vector does have a well-defined experimental meaning: It specifies the direction in ordinary space in which a subsequent detector must be oriented in order to achieve the maximum possible probability (100%) of detecting every particle in the collection. For spin-1/2 particles, this maximum probability drops off smoothly as the angle between the spin vector and the detector increases, until at an angle of 180 degrees—that is, for detectors oriented in the opposite direction to the spin vector—the expectation of detecting particles from the collection reaches a minimum of 0%.
As a qualitative concept, the spin vector is often handy because it is easy to picture classically. For instance, quantum mechanical spin can exhibit phenomena analogous to classical gyroscopic effects. For example, one can exert a kind of "torque" on an electron by putting it in a magnetic field (the field acts upon the electron's intrinsic magnetic dipole moment—see the following section). The result is that the spin vector undergoes precession, just like a classical gyroscope. This phenomenon is known as electron spin resonance (ESR). The equivalent behaviour of protons in atomic nuclei is used in nuclear magnetic resonance (NMR) spectroscopy and imaging.
Mathematically, quantum mechanical spin states are described by vector-like objects known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-1/2 particle by 360 degrees does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720 degree rotation. A spin-zero particle can only have a single quantum state, even after torque is applied. Rotating a spin-2 particle 180 degrees can bring it back to the same quantum state and a spin-4 particle should be rotated 90 degrees to bring it back to the same quantum state. The spin 2 particle can be analogous to a straight stick that looks the same even after it is rotated 180 degrees and a spin 0 particle can be imagined as sphere which looks the same after whatever angle it is turned through.
Mathematical formulation
Spin obeys commutation relations analogous to those of the orbital angular momentum:
[S_i, S_j ] = i \hbar \epsilon_{ijk} S_k
where \epsilon_{ijk} is the Levi-Civita symbol. It follows (as with angular momentum) that the eigenvectors of S2 and Sz (expressed as kets in the total S basis) are:
\begin{align} S^2 |s,m\rangle &= \hbar^2 s(s + 1) |s,m\rangle \\ S_z |s,m\rangle &= \hbar m |s,m\rangle. \end{align}
The spin raising and lowering operators acting on these eigenvectors give:
S_\pm |s,m\rangle = \hbar\sqrt{s(s+1)-m(m\pm 1)} |s,m\pm 1 \rangle, where S_\pm = S_x \pm i S_y.
But unlike orbital angular momentum the eigenvectors are not spherical harmonics. They are not functions of θ and φ. There is also no reason to exclude half-integer values of s and m.
In addition to their other properties, all quantum mechanical particles possess an intrinsic spin (though it may have the intrinsic spin 0, too). The spin is quantized in units of the reduced Planck constant, such that the state function of the particle is, say, not \psi = \psi(\mathbf r), but \psi =\psi(\mathbf r,\sigma)\,, where \sigma is out of the following discrete set of values:
\sigma \in \{-s\hbar, -(s - 1)\hbar, \cdots, +(s - 1)\hbar, +s\hbar\}.
One distinguishes bosons (integer spin) and fermions (half-integer spin). The total angular momentum conserved in interaction processes is then the sum of the orbital angular momentum and the spin.
Pauli matrices
The quantum mechanical operators associated with spin observables are:
S_x = {\hbar \over 2} \sigma_x,\quad S_y = {\hbar \over 2} \sigma_y,\quad S_z = {\hbar \over 2} \sigma_z.
In the special case of spin-1/2 particles, σx, σy and σz are the three Pauli matrices, given by:
\sigma_x = \begin{pmatrix} 0 & 1\\ 1 & 0 \end{pmatrix} ,\quad \sigma_y = \begin{pmatrix} 0 & -i\\ i & 0 \end{pmatrix} ,\quad \sigma_z = \begin{pmatrix} 1 & 0\\ 0 & -1 \end{pmatrix}.
Pauli exclusion principle
For systems of N identical particles this is related to the Pauli exclusion principle, which states that by interchanges of any two of the N particles one must have
\psi ( \cdots \mathbf r_i,\sigma_i\cdots \mathbf r_j,\sigma_j\cdots ) = (-1)^{2s}\psi ( \cdots \mathbf r_j,\sigma_j\cdots \mathbf r_i,\sigma_i\cdots ) .
Thus, for bosons the prefactor (−1)2s will reduce to +1, for fermions to −1. In quantum mechanics all particles are either bosons or fermions. In some speculative relativistic quantum field theories "supersymmetric" particles also exist, where linear combinations of bosonic and fermionic components appear. In two dimensions, the prefactor (−1)2s can be replaced by any complex number of magnitude 1 such as in the Anyon.
The above permutation postulate for N-particle state functions has most-important consequences in daily life, e.g. the periodic table of the chemists or biologists.
As described above, quantum mechanics states that components of angular momentum measured along any direction can only take a number of discrete values. The most convenient quantum mechanical description of particle's spin is therefore with a set of complex numbers corresponding to amplitudes of finding a given value of projection of its intrinsic angular momentum on a given axis. For instance, for a spin 1/2 particle, we would need two numbers a±1/2, giving amplitudes of finding it with projection of angular momentum equal to ħ/2 and −ħ/2, satisfying the requirement
\left|a_\frac{1}{2}\right|^2 + \left|a_{-\frac{1}{2}}\right|^2 \, = 1.
For a generic particle with spin s, we would need 2s+1 such parameters. Since these numbers depend on the choice of the axis, they transform into each other non-trivially when this axis is rotated. It's clear that the transformation law must be linear, so we can represent it by associating a matrix with each rotation, and the product of two transformation matrices corresponding to rotations A and B must be equal (up to phase) to the matrix representing rotation AB. Further, rotations preserve the quantum mechanical inner product, and so should our transformation matrices:
\sum_{m=-j}^{j} a_m^* b_m = \sum_{m=-j}^{j} \left(\sum_{n=-j}^j U_{nm} a_n\right)^* \left(\sum_{k=-j}^j U_{km} b_k\right)
\sum_{n=-j}^j \sum_{k=-j}^j U_{np}^* U_{kq} = \delta_{pq}.
Mathematically speaking, these matrices furnish a unitary projective representation of the rotation group SO(3). Each such representation corresponds to a representation of the covering group of SO(3), which is SU(2).[15] There is one n-dimensional irreducible representation of SU(2) for each dimension, though this representation is n-dimensional real for odd n and n-dimensional complex for even n (hence of real dimension 2n). For a rotation by angle θ in the plane with normal vector \hat{\theta}, U can be written
U = e^{-\frac{i}{\hbar} \vec{\theta} \cdot \vec{S}},
where \vec{\theta} = \theta \hat{\theta} and \vec{S} is the vector of spin operators.
(Click "show" at right to see a proof or "hide" to hide it.)
Working in the coordinate system where \hat{\theta} = \hat{z}, we would like to show that Sx and Sy are rotated into each other by the angle θ. Starting with Sx. Using units where ħ = 1:
\begin{align} S_x \rightarrow U^\dagger S_x U &{}= e^{i \theta S_z} S_x e^{-i \theta S_z} \\ &{} = S_x + (i \theta) [S_z, S_x] + \left(\frac{1}{2!}\right) (i \theta)^2 [S_z, [S_z, S_x]] + \left(\frac{1}{3!}\right) (i \theta)^3 [S_z, [S_z, [S_z, S_x]]] + \cdots\\ \end{align}
Using the spin operator commutation relations, we see that the commutators evaluate to iSy for the odd terms in the series, and to Sx for all of the even terms. Thus:
\begin{align} U^\dagger S_x U &{}= S_x \left[ 1 - \frac{\theta^2}{2!} + ... \right] - S_y \left[ \theta - \frac{\theta^3}{3!} \cdots \right] \\ &{} = S_x \cos\theta - S_y \sin\theta\\ \end{align}
as expected. Note that since we only relied on the spin operator commutation relations, this proof holds for any dimension (i.e., for any principal spin quantum number s).[16]
A generic rotation in 3-dimensional space can be built by compounding operators of this type using Euler angles:
\mathcal{R}(\alpha,\beta,\gamma) = e^{-i\alpha S_x}e^{-i\beta S_y}e^{-i\gamma S_z}
An irreducible representation of this group of operators is furnished by the Wigner D-matrix:
D^s_{m'm}(\alpha,\beta,\gamma) \equiv \langle sm' | \mathcal{R}(\alpha,\beta,\gamma)| sm \rangle = e^{-im'\alpha} d^s_{m'm}(\beta)e^{-i m\gamma},
d^s_{m'm}(\beta)= \langle sm' |e^{-i\beta s_y} | sm \rangle
is Wigner's small d-matrix. Note that for γ = 2π and α = β = 0; i.e., a full rotation about the z-axis, the Wigner D-matrix elements become
D^s_{m'm}(0,0,2\pi) = d^s_{m'm}(0) e^{-i m 2 \pi} = \delta_{m'm} (-1)^{2m}.
Recalling that a generic spin state can be written as a superposition of states with definite m, we see that if s is an integer, the values of m are all integers, and this matrix corresponds to the identity operator. However, if s is a half-integer, the values of m are also all half-integers, giving (−1)2m = −1 for all m, and hence upon rotation by 2π the state picks up a minus sign. This fact is a crucial element of the proof of the spin-statistics theorem.
Lorentz transformations
We could try the same approach to determine the behavior of spin under general Lorentz transformations, but we would immediately discover a major obstacle. Unlike SO(3), the group of Lorentz transformations SO(3,1) is non-compact and therefore does not have any faithful, unitary, finite-dimensional representations.
In case of spin 1/2 particles, it is possible to find a construction that includes both a finite-dimensional representation and a scalar product that is preserved by this representation. We associate a 4-component Dirac spinor \psi with each particle. These spinors transform under Lorentz transformations according to the law
\psi' = \exp{\left(\frac{1}{8} \omega_{\mu\nu} [\gamma_{\mu}, \gamma_{\nu}]\right)} \psi
where \gamma_{\mu} are gamma matrices and \omega_{\mu\nu} is an antisymmetric 4×4 matrix parametrizing the transformation. It can be shown that the scalar product
\langle\psi|\phi\rangle = \bar{\psi}\phi = \psi^{\dagger}\gamma_0\phi
is preserved. It is not, however, positive definite, so the representation is not unitary.
Metrology along the x, y, and z axes
Each of the (Hermitian) Pauli matrices has two eigenvalues, +1 and −1. The corresponding normalized eigenvectors are:
\begin{array}{lclc} \psi_{x+}=\displaystyle\frac{1}{\sqrt{2}}\!\!\!\!\! & \begin{pmatrix}{1}\\{1}\end{pmatrix}, & \psi_{x-}=\displaystyle\frac{1}{\sqrt{2}}\!\!\!\!\! & \begin{pmatrix}{1}\\{-1}\end{pmatrix}, \\ \psi_{y+}=\displaystyle\frac{1}{\sqrt{2}}\!\!\!\!\! & \begin{pmatrix}{1}\\{i}\end{pmatrix}, & \psi_{y-}=\displaystyle\frac{1}{\sqrt{2}}\!\!\!\!\! & \begin{pmatrix}{1}\\{-i}\end{pmatrix}, \\ \psi_{z+}= & \begin{pmatrix}{1}\\{0}\end{pmatrix}, & \psi_{z-}= & \begin{pmatrix}{0}\\{1}\end{pmatrix}. \end{array}
By the postulates of quantum mechanics, an experiment designed to measure the electron spin on the x, y or z axis can only yield an eigenvalue of the corresponding spin operator (Sx, Sy or Sz) on that axis, i.e. ħ/2 or –ħ/2. The quantum state of a particle (with respect to spin), can be represented by a two component spinor:
\psi = \begin{pmatrix} {a+bi}\\{c+di}\end{pmatrix}.
When the spin of this particle is measured with respect to a given axis (in this example, the x-axis), the probability that its spin will be measured as ħ/2 is just \left\vert \langle \psi_{x+} \vert \psi \rangle \right\vert ^2. Correspondingly, the probability that its spin will be measured as –ħ/2 is just \left\vert \langle \psi_{x-} \vert \psi \rangle \right\vert ^2. Following the measurement, the spin state of the particle will collapse into the corresponding eigenstate. As a result, if the particle's spin along a given axis has been measured to have a given eigenvalue, all measurements will yield the same eigenvalue (since \left\vert \langle \psi_{x+} \vert \psi_{x+} \rangle \right\vert ^2 = 1 , etc), provided that no measurements of the spin are made along other axes.
Metrology along an arbitrary axis
The operator to measure spin along an arbitrary axis direction is easily obtained from the Pauli spin matrices. Let u = (ux, uy, uz) be an arbitrary unit vector. Then the operator for spin in this direction is simply
S_u = \frac{\hbar}{2}(u_x\sigma_x + u_y\sigma_y + u_z\sigma_z).
The operator Su has eigenvalues of ±ħ/2, just like the usual spin matrices. This method of finding the operator for spin in an arbitrary direction generalizes to higher spin states, one takes the dot product of the direction with a vector of the three operators for the three x, y, z axis directions.
A normalized spinor for spin-1/2 in the (ux, uy, uz) direction (which works for all spin states except spin down where it will give 0/0), is:
\frac{1}{\sqrt{2+2u_z}}\begin{pmatrix} 1+u_z \\ u_x+iu_y \end{pmatrix}.
The above spinor is obtained in the usual way by diagonalizing the \sigma_u matrix and finding the eigenstates corresponding to the eigenvalues. In quantum mechanics, vectors are termed "normalized" when multiplied by a normalizing factor, which results in the vector having a length of unity.
Compatibility of metrology
Since the Pauli matrices do not commute, measurements of spin along the different axes are incompatible. This means that if, for example, we know the spin along the x-axis, and we then measure the spin along the y-axis, we have invalidated our previous knowledge of the x-axis spin. This can be seen from the property of the eigenvectors (i.e. eigenstates) of the Pauli matrices that:
\mid \langle \psi_{x\pm} \mid \psi_{y\pm} \rangle \mid ^ 2 = \mid \langle \psi_{x\pm} \mid \psi_{z\pm} \rangle \mid ^ 2 = \mid \langle \psi_{y\pm} \mid \psi_{z\pm} \rangle \mid ^ 2 = \frac{1}{2}.
So when physicists measure the spin of a particle along the x-axis as, for example, ħ/2, the particle's spin state collapses into the eigenstate \mid \psi_{x+} \rangle. When we then subsequently measure the particle's spin along the y-axis, the spin state will now collapse into either \mid \psi_{y+} \rangle or \mid \psi_{y-} \rangle, each with probability 1/2. Let us say, in our example, that we measure –ħ/2. When we now return to measure the particle's spin along the x-axis again, the probabilities that we will measure ħ/2 or –ħ/2 are each 1/2 (i.e. they are \mid \langle \psi_{x+} \mid \psi_{y-} \rangle \mid ^ 2 and \mid \langle \psi_{x-} \mid \psi_{y-} \rangle \mid ^ 2 respectively). This implies that the original measurement of the spin along the x-axis is no longer valid, since the spin along the x-axis will now be measured to have either eigenvalue with equal probability.
In tables of the spin quantum number s for nuclei or particles, the spin is often followed by a "+" or "−". This refers to the parity with "+" for even parity (wave function unchanged by spatial inversion) and "−" for odd parity (wave function negated by spatial inversion). For example, see the isotopes of bismuth.
Spin has important theoretical implications and practical applications. Well-established direct applications of spin include:
Nuclear magnetic resonance spectroscopy in chemistry;
Electron spin resonance spectroscopy in chemistry and physics;
Magnetic resonance imaging (MRI) in medicine, which relies on proton spin density;
Giant magnetoresistive (GMR) drive head technology in modern hard disks.
Electron spin plays an important role in magnetism, with applications for instance in computer memories. The manipulation of nuclear spin by radiofrequency waves (nuclear magnetic resonance) is important in chemical spectroscopy and medical imaging.
Spin-orbit coupling leads to the fine structure of atomic spectra, which is used in atomic clocks and in the modern definition of the second. Precise measurements of the g-factor of the electron have played an important role in the development and verification of quantum electrodynamics. Photon spin is associated with the polarization of light.
A possible future direct application of spin is as a binary information carrier in spin transistors. Original concept proposed in 1990 is known as Datta-Das spin transistor.[17] Electronics based on spin transistors is called spintronics, which includes the manipulation of spins in semiconductor devices.
There are many indirect applications and manifestations of spin and the associated Pauli exclusion principle, starting with the periodic table of chemistry.
Spin was first discovered in the context of the emission spectrum of alkali metals. In 1924 Wolfgang Pauli introduced what he called a "two-valued quantum degree of freedom" associated with the electron in the outermost shell. This allowed him to formulate the Pauli exclusion principle, stating that no two electrons can share the same quantum state at the same time.
Wolfgang Pauli
The physical interpretation of Pauli's "degree of freedom" was initially unknown. Ralph Kronig, one of Landé's assistants, suggested in early 1925 that it was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. This would violate the theory of relativity. Largely due to Pauli's criticism, Kronig decided not to publish his idea.
In the autumn of 1925, the same thought came to two Dutch physicists, Samuel Goudsmit at Leiden University. Under the advice of Paul Ehrenfest, they published their results. It met a favorable response, especially after Llewellyn Thomas managed to resolve a factor-of-two discrepancy between experimental results and Uhlenbeck and Goudsmit's calculations (and Kronig's unpublished ones). This discrepancy was due to the orientation of the electron's tangent frame, in addition to its position.
Mathematically speaking, a fiber bundle description is needed. The tangent bundle effect is additive and relativistic; that is, it vanishes if c goes to infinity. It is one half of the value obtained without regard for the tangent space orientation, but with opposite sign. Thus the combined effect differs from the latter by a factor two (Thomas precession).
Despite his initial objections, Pauli formalized the theory of spin in 1927, using the modern theory of quantum mechanics invented by Schrödinger and Heisenberg. He pioneered the use of Pauli matrices as a representation of the spin operators, and introduced a two-component spinor wave-function.
Pauli's theory of spin was non-relativistic. However, in 1928, Paul Dirac published the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a "Dirac spinor") was used for the electron wave-function. In 1940, Pauli proved the spin-statistics theorem, which states that fermions have half-integer spin and bosons integer spin.
In retrospect, the first direct experimental evidence of the electron spin was the Stern–Gerlach experiment of 1922. However, the correct explanation of this experiment was only given in 1927.[18]
Spinor
Stern–Gerlach experiment
Einstein–de Haas effect
Spin-orbital
Angular momentum
Chirality (physics)
Dynamic nuclear polarisation
Helicity (particle physics)
Pauli equation
Pauli–Lubanski pseudovector
Rarita–Schwinger equation
Representation theory of SU(2)
Spin-½
Spin-flip
Spin isomers of hydrogen
Spin magnetic moment
Spin quantum number
Spin tensor
Spin wave
Spin Engineering
Spintronics
Yrast
Zitterbewegung
^ Merzbacher, Eugen (1998). Quantum Mechanics (3rd ed.). pp. 372–3.
^ a b Griffiths, David (2005). Introduction to Quantum Mechanics (2nd ed.). pp. 183–4.
^ "Angular Momentum Operator Algebra", class notes by Michael Fowler
^ , by Townsend, p. 31 and p. 80A modern approach to quantum mechanics
^ Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). pp. 272–3.
^ Physics of Atoms and Molecules, B.H. Bransden, C.J.Joachain, Longman, 1983, ISBN 0-582-44401-2
^ "CODATA Value: electron g factor". The NIST Reference on Constants, Units, and Uncertainty.
"After some years, it was discovered that this value [−g/2] was not exactly 1, but slightly more—something like 1.00116. This correction was worked out for the first time in 1948 by Schwinger as j*j divided by 2 pi [sic] [where j is the square root of the fine-structure constant], and was due to an alternative way the electron can go from place to place: instead of going directly from one point to another, the electron goes along for a while and suddenly emits a photon; then (horrors!) it absorbs its own photon."
^ W.J. Marciano, A.I. Sanda (1977). "Exotic decays of the muon and heavy leptons in gauge theories".
^ B.W. Lee, R.E. Shrock (1977). "Natural suppression of symmetry violation in gauge theories: Muon- and electron-lepton-number nonconservation".
^ K. Fujikawa, R. E. Shrock (1980). "Magnetic Moment of a Massive Neutrino and Neutrino-Spin Rotation".
^ N.F. Bell et al.; Cirigliano, V.; Ramsey-Musolf, M.; Vogel, P.; Wise, Mark (2005). "How Magnetic is the Dirac Neutrino?".
^ Quanta: A handbook of concepts, P.W. Atkins, Oxford University Press, 1974, ISBN 0-19-855493-1
^ B.C. Hall (2013). Quantum Theory for Mathematicians. Springer. pp. 354–358.
^ , by J. J. Sakurai, p159Modern Quantum Mechanics
^ Datta. S and B. Das (1990). "Electronic analog of the electrooptic modulator". Applied Physics Letters 56 (7): 665–667.
^ B. Friedrich, D. Herschbach (2003). "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics".
Cohen-Tannoudji, Claude; Diu, Bernard; Laloë, Franck (2006). Quantum Mechanics (2 volume set ed.). John Wiley & Sons.
Condon, E. U.; Shortley, G. H. (1935). "Especially Chapter 3". The Theory of Atomic Spectra. Cambridge University Press.
Hipple, J. A.; Sommer, H.; Thomas, H.A. (1949). A precise method of determining the faraday by magnetic resonance. https://www.academia.edu/6483539/John_A._Hipple_1911-1985_technology_as_knowledge
Edmonds, A. R. (1957). Angular Momentum in Quantum Mechanics. Princeton University Press.
Jackson, John David (1998). Classical Electrodynamics (3rd ed.). John Wiley & Sons.
Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole.
Thompson, William J. (1994). Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems. Wiley.
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W. H. Freeman.
Sin-Itiro Tomonaga, The Story of Spin, 1997
"Spintronics. Feature Article" in Scientific American, June 2002.
Goudsmit on the discovery of electron spin.
Nature: " Milestones in 'spin' since 1896."
ECE 495N Lecture 36: Spin Online lecture by S. Datta
Operator (physics)
Space and time
Time evolution
D'Alembert operator
C-symmetry
Operators for operators
Ladder operator
Anti-symmetric operator
Total energy
Hamiltonian
Transition dipole moment
Quantum correlator
Hanbury Brown and Twiss effect
Creation and annihilation
Casimir invariant
Concepts in physics
Rotational symmetry
Quantum mechanics, Periodic table, Electron, Proton, Quantum field theory
Electromagnetism, Quantum field theory, Cern, Particle physics, Quantum chromodynamics
Spinmechatronics
Spintronics, Proton, Spin (physics), Electron, Magnetism
Electron, Electromagnetism, Matter, Standard Model, Boson


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You are at:Home»News»The dead are coming in the new Game of Thrones: Season 6 trailer – watch
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The dead are coming in the new Game of Thrones: Season 6 trailer – watch
By Natalie Fordham	on	 April 11, 2016 News
There's a brand new Game of Thrones trailer with a goblet-load of new footage. And the dead are coming.
Things are looking very ominous for pretty much every character in the HBO series, but especially Arya (Maisie Williams) and Daenerys (Emilia Clarke) in scenes that show that not even these two strong women are safe.
The promo for 'The Red Woman' serves like a Greatest Hits compilation for every single character this season, and the challenges that await them when the show returns on 24th April.
Highlights include Sansa seeking revenge on the Boltons, Cersei promising blood and preparing an army and the White Walkers on the comeback trail. It also seems that Theon's sister isn't quite ready give up on her sibling and Tyrion finally comes face to face with one of Dany's ferocious dragons. We've already got some quotable lines too – "That's what I do. I drink and I know things."
Game of Thrones: Season 6 will be simulcast on Sky Atlantic at 2am on April 25, at the same time as it airs in the US, and will be repeated at 9pm the same day.
Watch the new trailer below.
Natalie Fordham
BA English student at University of Southampton and Editor for The Edge (2015-16). A deep love of reading, theatre and all things entertainment.
Nostalgic News: Moana Turns Five!
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Nostalgic News: Space Jam (1996) was released 25 years ago

redpajama_set_name: RedPajamaCommonCrawl


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Saturday, Jan 16th 2021 7PM 40°F 10PM 38°F 5-Day Forecast
Beyond the Footsie: Thursday close
SMALLER company shares ended a gloomy session in negative territory, undermined by sharp losses in the UK and the US. At the close, the FTSE SmallCap index was down 8.7 points at 2202.2.
Transport Systems was the session's biggest riser, with shares up 7p to 15 1/2p after revealing interim profits to September should significantly exceed expectations, thanks to a profitable first quarter and very successful trading at its Forrest Highway operating unit, which has secured a number of new contracts.
Universe Group rose 2 1/2p to 33p after announcing that its international money transfer division has opened in a further nine countries.
Silk Industries jumped 6p to 32 1/2p after revealing that it is in preliminary takeover talks, while news of a trial contract boosted DCS Group by 2 1/4p to 14 3/4p.
And Mouchel jumped 12 to 160 1/2p after the support services group promised a very positive set of results for the year ending this month, and predicted a 'strong and secure' order book for the coming year.
Financially restructured Marconi Corp was also under the spotlight after the company revealed that tough markets and weaker demand were behind a 38% year-on-year fall in first quarter sales to £367m.
It also revealed that gross profit margins dropped two percentage points year-on-year in the first quarter to June, though it gave no hint as to how this might alter the company's previously-stated financial targets for the year.
Chief executive Mike Parton warned he held a 'cautious view' of short-term market conditions. But, after initial sharp falls, its shares ended the day up 1 1/4p at 69p.
AIM Group was cheaper by 7 1/2p at 80p after skipping its final dividend and warning of 'extremely difficult' trading in the aviation industry.
Beyond the Footsie: Thursday close - Jul 17, 2003


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Sights and Attractions near Young Frankenstein
THIS EVENT ENDED ON THE 25TH AUGUST 2018
Garrick Theatre, 2 Charing Cross Road, Soho, London WC2H 0HH
28th September 2017 until 25th August 2018
Mon-Sat 7.30pm, mats Wed, Sat 3pm
Mon-Thu £20-£69.50, Fri-Sun £20-£74.50, Premium Seats £97.50, Sep 28-30, Oct 1-9 Mon-Thu previews £20-£59.50, Fri and Sat previews £20-£64.50, Premium Seats previews £97.50
All Activities for Kids Art and Design Art Galleries Attractions for Kids Boats Boats and Bridges Historic Buildings House and Garden Museums Other Attractions Parks and Gardens Sights Sightseeing Tours Venue Hire
Admiralty Arch
The Mall, Westminster, London SW1A | 4 minutes walk from Young Frankenstein
Admiralty Arch, a grade I listed building just off Trafalgar Square, was commissioned by Edward VII in memory of his mother, Queen Victoria. The inscription... More
Alan Cristea Gallery
43 Pall Mall, Mayfair, London SW1Y | 9 minutes walk from Young Frankenstein
Alan Cristea Gallery is the largest publisher and dealer of artists' prints and editions in Europe. Set up by Alan Cristea, who brings with him... More
London > Attractions > House and Garden
36 Bedford Square, Bloomsbury, London WC1B | 11 minutes walk from Young Frankenstein
The Architectural Association School of Architecture, the UK's oldest school of architecture, was originally set up in 1847 and moved to Bedford Square in 1917.... More
All Souls Church Langham Place
2 All Souls Place, Fitzrovia, London W1B | 17 minutes walk from Young Frankenstein
All Souls Church was the creation of the Prince Regent's favourite designer, John Nash. It was erected in 1824 and formed the pivotal point for... More
Apsley House
149 Piccadilly, Hyde Park Corner, Belgravia, London W1J | 22 minutes walk from Young Frankenstein
Originally the London residence of the first Duke of Wellington, Apsley House was designed and built by Robert Adam between 1771 and 1778 and retains... More
Alma Enterprises
38-40 Glasshill Street, SE1 | 26 minutes walk from Young Frankenstein
After five years at 1 Vyner Street Alma Enterprises, the project-space which began as a base for successful young artists' collective 'Land', moved to this... More
Ambika P3
35 Marylebone Road, Marylebone, London NW1 | 27 minutes walk from Young Frankenstein
Located within the University of Westminster - Marylebone's campus, the vast 14,000 foot P3 exhibition and performance space - a former concrete-testing facility - is... More
Angel Building
407 St John Street, Clerkenwell, London EC1V | 33 minutes walk from Young Frankenstein
Launched in late 2010, the Angel Building in Islington transformed from an under-used early 1980s commercial block into an award-winning office space, reinvented by... More
All Hallows by the Tower
Byward Street, City, London EC3R | 2.1 miles from Young Frankenstein
All Hallows, the oldest church in the City of London, is 1300 years old with a crypt museum, Roman pavement and Saxon and Roman artefacts.... More
Albert Memorial
Kensington Gardens, 27 Princes Square, South Kensington, London W2 | 2.2 miles from Young Frankenstein
This 180ft Victorian bronze gilt statue in Kensington Gardens is a tribute to Queen Victoria's husband, Prince Albert, and was erected following his death through... More
Art Work Space: The Hempel Hotel
31-35 Craven Hill Gardens, Paddington, London W2 | 2.4 miles from Young Frankenstein
Art Work Space is an independent art gallery on the lower ground floor of The Hempel hotel, showcasing emerging artists working in a variety of... More
APT Gallery
Harold Works, 6 Creekside, SE8 | 5.1 miles from Young Frankenstein
Charity organisation and gallery A.P.T. in Harold Wharf, on the banks of Deptford Creek, was set up in 1995 by a group of artists to... More
ArcelorMittal Orbit
Olympic Park, Stratford, E20 | 5.3 miles from Young Frankenstein
Presiding over the former Olympic Park the Anish Kapoor-designed ArcelorMittal Orbit observation tower, was described by Mayor Boris Johnson as that "something extra" needed to... More
Annex East
Unit 2, Hutchins Close, Stratford, London E15 | 5.6 miles from Young Frankenstein
Annex East is a warehouse arts centre located just 100 metres from London's Olympic Park. The space will incorporate an exhibition space, a bespoke bar... More
Alexandra Palace Ice Rink
Alexandra Palace Way, N22 | 5.9 miles from Young Frankenstein
The biggest (it has a total capacity of 1,250) and best permanent ice rink in London, Alexandra Palace Ice Rink within Alexandra Palace is an... More
Alphabetti Spaghetti
Caxton Works, E16 | 6.1 miles from Young Frankenstein
We've all used the excuse "it must have got stuck in the post" and this knotted post box might explain where all the... More
Avenue House
17 East End Road, N3 | 6.7 miles from Young Frankenstein
An imposing grade II listed mid Victorian mansion with extensive grounds landscaped by Robert Marnock, Avenue House is now available to hire for weddings, conferences... More
Covent Garden, Covent Garden, London WC2E | 3 minutes walk from Young Frankenstein
The first hundred names are now down on London's answer to the Hollywood Walk of Fame. On the pavement outside St Paul's church in Covent... More
51 Chiltern Street, Soho, London W1B5AB | 7 minutes walk from Young Frankenstein
55-57 Great Marlborough Street, Soho, London W1F | 10 minutes walk from Young Frankenstein
30 Museum Street, Bloomsbury, London WC1A | 11 minutes walk from Young Frankenstein
London School of Economics & Political Science, Old Building, Houghton Street, Holborn, London WC2A | 11 minutes walk from Young Frankenstein
The gallery at London School of Economics (LSE) hosts exhibitions by students connected with the college. Since it's foundation in 1895 the LSE students and... More
Australia House
Strand, Holborn, London WC2B | 11 minutes walk from Young Frankenstein
Home of the Australian High Commission in London, Australia House is a landmark building on the corner of Aldwych and the Strand.... More
Adam Gallery
24 Cork Street, Mayfair, London W1S | 11 minutes walk from Young Frankenstein
20th century and contemporary works of art.... More
Albemarle Gallery
49 Albemarle Street, Mayfair, London W1S | 12 minutes walk from Young Frankenstein
One of the best small galleries in London, the Albemarle has a tradition of supporting controversial artists, and of beautifully mounted, carefully curated exhibitions. ... More
Alexia Goethe Gallery
5-7 Dover Street, Mayfair, London W1S | 12 minutes walk from Young Frankenstein
Austin/Desmond Fine Art
Pied Bull Yard, Great Russell Street, Bloomsbury, London WC1B | 12 minutes walk from Young Frankenstein
Alison Jacques Gallery
16-18 Berners Street, Fitzrovia, London W1T | 12 minutes walk from Young Frankenstein
This architecturally designed space for the Alison Jacques Gallery, opened in 2007, is an improvement on the previous location on Clifford Street. Artists represented include... More
Association of Anaesthetists of Great Britain and Ireland
BOC Museum, 9 Bedford Square, Camden, Bloomsbury, London WC1B | 13 minutes walk from Young Frankenstein
The museum collection contains over 2000 objects relating to the story of anaesthesia. Its collections date from 1774 to the present day and provide a... More
All Saints Margaret Street
7 Margaret Street, Westminster, Fitzrovia, London W1W | 13 minutes walk from Young Frankenstein
This church is the most influential of all the buildings of its architect, William Butterfield, being the first important example of the constructional use of... More
Near Young Frankenstein	 All London hotels
Near Young Frankenstein
Fourth Plinth: Heather Phillipson THE END
Exhibitions | Until 26th March 2022
Trafalgar Square 3 minutes walk from Young Frankenstein
London born artist Heather Philipson puts an ice cream with a cherry on top on The Fourth Plinth in Trafalgar ...More
Theatre | Until 6th March 2021
Adelphi Theatre 4 minutes walk from Young Frankenstein
Multi Olivier and BAFTA Award winning Imelda Staunton plays meddlesome socialite turned matchmaker Dolly Levi, taking the title role in ...More
Palace Theatre 5 minutes walk from Young Frankenstein
From the 36,000 retweets Harry Potter creator J.K. Rowling got when she announced the ...More
Theatre | Until 2nd May 2021
Duchess Theatre 7 minutes walk from Young Frankenstein
Presented by the award-winning, international comedy company Mischief Theatre, The Play That Goes Wrong follows the inept and accident prone ...More
Theatre | Until 27th March 2021
Fortune Theatre 7 minutes walk from Young Frankenstein
One of the less well-known West End fixtures, this adaptation of Susan Hill's gothic novel has been packing out houses ...More
From cheap budget hotels to luxury 5 star suites see our deals for Garrick Theatre hotels, including Holiday Inn Express London Hammersmith from 70% off.
Hotels near Cebu Trade Hall, SMX Convention Center, Philippines
Hotels near Congress Beaune, France


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Danbury » Directory » Venue » Ridgefield Playhouse
Ridgefield Playhouse
80 East Ridge Avenue
em. [email protected]
Danbury New Haven Poughkeepsie Hartford
Mar20Sat
Apr13Tue
Official Tower of Power Band, Tower of Power
Apr16Fri
Felix Cavaliere's Rascals
Oct16Sat
The Ridgefield Playhouse is a not for profit 501 (c)(3) whose mission is to present a variety of performing arts to the community and the surrounding area that they can enjoy and experience at a varied price point. The Playhouse presents national and local acts and is the cultural hub for the town of Ridgefield.
After many years of planning, fundraising, and building, the dream of restoring the Cass Gilbert Jr.-designed theater in Ridgefield became a reality with our December 2000 opening night performance by Jose Feliciano.
Since our opening, enthusiastic, sold-out audiences have enjoyed Peter Yarrow, Marcel Marceau, Barbara Cook, Moscow Boys Choir, Joan Baez, and The Bacon Brothers and more recently, Michael Feinstein, Gregg Allman, Clint Black, The Doobie Brothers, Brian Wilson, Diana Krall and more. Film-goers have been treated to question and answer sessions with many of the movie industries finest- including Ron Howard, Harvey Keitel, Tim Robbins, Barry Levinson and more, as part of our film society events, which screens both feature and documentary films. Community events such as the Ridgefield High School Orchestra Concert and the Annual Town Meeting found a new home at The Playhouse, not to mention a place for local dance companies to perform. Children have been enjoying our children series as well as our after school programs and summer camp. Comedians such as Martin Short, Dana Carvey, Jackie Mason, Joan Rivers, Kathy Griffen, Robert Klein, Ron White and many others have been making audiences laugh here while speakers such as Ira Glass, David Sedaris, and Stephen Sondheim have shared their insight and journey.
Our Arts in Education and outreach programs in addition to various series that deal with real teen issues are something that not only fulfill our mission, but also complete our sense of purpose. And of course our free outdoor Shakespeare on the Green and Green expo has become an annual "thank you" to all who support us.
While we can all agree with Shakespeare that "the play's the thing," we also know that this beautiful theater adds a great deal to the experience of a performance or movie. In an age of multiplexes and stadiums, what a pleasure to be in an impeccably renovated, historic theater with near-perfect acoustics!
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Eric Packer (Robert Pattinson) is a 28-year-old finance billionaire who sets out to cross New York City in his luxurious white stretch limo to get to a hairdressing appointment. His anxious eyes are glued to the Chinese yuan's exchange rate: it is mounting against all expectations, destroying Eric's bet against it. Eric Packer is losing his empire with every tick of the clock. It soon becomes apparent that the city is in turmoil, and Packer's journey is obstructed by various traffic jams caused by a presidential visit to the city, widespread rioting, and several uncanny encounters with his ex-wife. During the course of his cross-town odyssey, his paranoia intensifies and he becomes increasingly certain that someone is trying to kill him. Writer/director David Cronenberg revisits subjects that fascinate him: how the organic and the psychological are inextricably intertwined, society's anxieties and phobias, and letting repressed impulses and paranoia run wild. With Paul Giamatti, Juliette Binoche and Samantha Morton. Based on the novel by Don DeLillo.
Genre: Art House Cinema, Drama
Starring: Juliette Binoche, Mathieu Amalric, Samantha Morton, Paul Giamatti, Jay Baruchel, Emily Hampshire, Robert Pattinson, Kevin Durand, Sarah Gadon, K'Naan
Rating: R16 - Contains violence and sex scenes
Location in store: Art House Cinema
DVD AVAILABLE NOW!
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Tom Graves & Paul Gosar
Compare the voting records of Tom Graves and Paul Gosar in 2017-18.
Tom Graves
Represented Georgia's 14th Congressional District. This was his 5th term in the House.
Paul Gosar
Tom Graves and Paul Gosar are from the same party and agreed on 91 percent of votes in the 115th Congress (2017-18).
Disagree: 9%
But they didn't always agree. Out of 1139 votes in the 115th Congress, they disagreed on 97 votes, including 13 major votes.
Here are the votes they disagreed on
June 21, 2018 — Securing America's Future Act of 2018
May 18, 2018 — Agriculture and Nutrition Act of 2018
Jan. 18, 2018 — Federal Register Printing Savings Act
Dec. 21, 2017 — Department of Homeland Security Blue Campaign Authorization Act of 2017
Dec. 7, 2017 — Making further continuing appropriations for fiscal year 2018, and for other purposes
Oct. 12, 2017 — Providing for the concurrence by the House in the Senate amendment to H.R. 2266, with an amendment
On Motion to Concur in the Senate Adt to the House Adt to the Senate Adt
Sept. 8, 2017 — Reinforcing Education Accountability in Development Act
On Motion to Concur in Senate Amendments Nos. 2 and 3, and in No. 1 with Amendment
May 3, 2017 — HIRE Vets Act
Dec. 21, 2018 — National Flood Insurance Program Extention Act
Dec. 21, 2018 — Correct Enrollment to S. 3628
Dec. 20, 2018 — Codifying Useful Regulatory Definitions Act
Dec. 19, 2018 — Museum and Library Services Act
Dec. 12, 2018 — Agriculture and Nutrition Act of 2018
Sept. 26, 2018 — Providing for consideration for the conference report to accompany H.R. 6157, making appropriations for the Department of Defense for FY ending September 30, 2019; and H.Res. 1071, recognizing allowing illegal immigrants the right to vote devalues the franchise and diminishes the voting power of U.S. citizens
July 25, 2018 — The American Legion 100th Anniversary Commemorative Coin Act
June 28, 2018 — Courtney of Connecticut Amendment No. 29
June 27, 2018 — Langevin of Rhode Island Part A Amendment No. 9
June 20, 2018 — Individuals in Medicaid Deserve Care that is Appropriate and Responsible in its Execution Act
June 7, 2018 — Gosar of Arizona Part B Amendment No. 29
May 23, 2018 — Nolan of Minnesota Amendment No. 2
May 18, 2018 — Russell of Oklahoma Amendment No. 17
May 17, 2018 — McClintock of California Amendment No. 3
May 16, 2018 — Protect and Serve Act of 2018
April 27, 2018 — McClintock of California Part A Amendment No. 112
April 12, 2018 — Proposing a balanced budget amendment to the Constitution of the United States
On Ordering the Previous Question
Sept. 27, 2017 — Providing for consideration of H.R. 3823, Disaster Tax Relief and Airport and Airway Extension Act of 2017; and providing for consideration of motions to suspend the rules
Sept. 13, 2017 — Lewis of Minnesota Amendment No. 167
Sept. 8, 2017 — Palmer of Alabama Amendment No. 56
Sept. 6, 2017 — McClintock of California Part B Amendment No. 25
March 24, 2017 — Providing for consideration of H.R. 1628, the American Health Care Act of 2017
Jan. 11, 2017 — Peterson of Minnesota Part A Amendment No. 5


ICAO's Fang Liu has stated that the future of aviation depends on the actions we take now, to ensure the longevity of the industry, especially when it comes to both passenger and freight capacity.
Dr. Fang Liu emphasised the importance of the upcoming 40th Assembly, especially in view of the ever changing nature of civil aviation that necessitates ICAO be prepared for changes that will occur, be cognisant of emerging issues and have contingencies in place. Among those emerging issues in global civil aviation, the Secretary General highlighted the increased use of Unmanned Aeronautical Systems (UAS), Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA), Cybersecurity and Trust Framework, Aviation Infrastructure/system financing, Big data analytics for aviation and commercial space transport and higher airspace operations.
To achieve significant, targeted improvements in its work, to benefit global civil aviation and Member States, ICAO will focus on Improved Aviation Safety, Strengthened Regulatory Capacity, Increased Air Navigation Capacity, Reduced Aviation Security Risk, Improved Environmental Performance of Aviation and Strengthened Aviation Professional Skills.
Besides the status report on the EUR/NAT 2017-2019 work programme, Dr. Liu and the attending DGCAs were also updated during their meeting on how to strengthen State safety and security oversight capabilities, as well as a review of some new suggestions aimed at enhancing EUR/NAT Air Traffic Management (ATM) safety.
Dr. Liu concluded by reminding her audience that 2019 is the 75th Anniversary of ICAO and the Chicago Convention which established it, and noted that given the dramatic new developments in aircraft design and operations now coming to light, ICAO would be using the occasion to look to aviation's exciting future as much as to its storied past.


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NHRA Notebook: For Junior Dragsters, seeing is dreaming
Terrill Coveysports@seacoastonline.com
Jul 7, 2019 at 10:36 PM Jul 7, 2019 at 10:36 PM
EPPING — Many of the biggest stars in the NHRA got their start in the Junior Dragsters. Names such as JR Todd, Shawn Langdon, Erica Enders and Leah Pritchett famously kicked their careers off in the entry-level division in which students age 6-18 compete.
This weekend, the current crop of New England Dragway up-and-comers were part of the Sunday show at the NHRA New England Nationals.
Ten of the 30 Junior Dragster competitors that compete regularly at New England Dragway were in attendance this weekend, complete with photographs to sign for their fans. The kids were set up in the pits amid the professional drivers and had a front row seat to what their future might be.
"It means a lot because that's what I want to do," said 15-year old Abbie Croteau. "Hopefully I will be one of them one day."
Olivia Karaguezian is in her final season in the Junior Dragsters, as the 18-year old is set to enter college in the fall. She said she hopes to stay involved in drag racing, though she will move up from the Junior Dragsters.
"It's a cool experience to be able to talk to (the professional drivers) and see what it takes to get to the top," Karaguezian said. "I don't know if I will go pro, but I definitely want to continue bracket racing. It's in my blood now."
Eleven-year old Tyler Beaulieu said the best part of the weekend for him was being able to meet and talk with the professional drivers, while 6-year old Makenna Mason said she enjoyed driver introductions where the Junior Dragster drivers were called up on the same stage that the professional drivers were called up to and introduced to fans.
"It's fun meeting new people and getting introduced was cool," said 7-year old Jacob Biron, whose father also started his racing career in a Junior Dragster.
"The best part is being treated like any other driver," said 11-year old Seth Noble. "It's cool to be treated like the pros out here."
Aiden Baker is 11, and he won the Junior Dragster division at last year's national event. Each of the kids was staged by drivers from the professional divisions when they came to the line for exhibition runs this weekend, and Baker was backed up by former champion Antron Brown.
In addition to the driver introductions and the large crowd, the Junior Dragster drivers were also excited to meet their racing heroes.
Greyson St. Jean, 7, said getting to race was the best part of the weekend, while 8-year old Cody Cumming said being able to talk with John Force and have reigning Top Fuel champion Steve Torrence sign his race car were the best parts of the weekend. For Jaylee Soucy, meeting her heroes now gives her even more hope that she will be beating them one day.
"I've got plans to race against them one day," said 13-year old Soucy. "I want to race Leah (Pritchett)."
John Parenteau of Brentwood, Timothy Stickles of Dover and Hampton's Nick Meloni were the class of the local drivers this weekend. Meloni won several rounds on the weekend, eventually falling in the final round of the 32-car Top Dragster field.
Parenteau won the Pro Stock Snowmobile race, becoming the first person to defeat Canada's Tina Duncanson at the New England Nationals. It was the second national event win for Parenteau and it came after he struggled a bit in qualifying earlier in the day.
Stickles won his first three races of the weekend in the Stock Eliminator category before falling in the quarterfinals. He said he looks forward to performing on the big stage of the NHRA event each year.
"This is my biggest race every year," Stickles said. "At the national events, guys who go out there and do this for a living come in, and competing with them is really fun. To hang with those guys is an honor."
Stickles said the packed stands are exciting, but he had to manufacture blinders for himself to block out distractions during Saturday's racing.
"My nerves were working against me a little bit, but the blinders seemed to help," he said. "This is like getting to play in the major league for a day. Me and my father Pete built this car and my father basically handed it down to me. We've owned it for 25 years, so to be doing well this weekend is special."


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Marc Secchia: Congratulations to the Goodreads winners!
I would like to congratulate the winners of the Goodreads giveaway for Shioni of Sheba: The Enchanted Castle. I am looking forward to making the Addis Ababa post office a tad busier on Monday morning.
And to the 1195 good people who entered and did not win - thank you for participating! Lots of copies going begging here, both paperback and electronic, why don't you treat yourself to a breath of ancient Africa?


text:
Coulter Woodmansey (born August 1, 1997) is a professional Canadian football offensive lineman for the Hamilton Tiger-Cats of the Canadian Football League (CFL).

University career
Woodmansey played U Sports football for the Guelph Gryphons from 2016 to 2019, where he appeared in 32 regular season games, including 28 starts at guard, over the course of four seasons.

Professional career
Woodmansey was selected fifth overall in the 2020 CFL Draft by the Hamilton Tiger-Cats, but did not play in 2020 due to the cancellation of the 2020 CFL season. He then signed with the team on January 21, 2021. Woodmansey made the team's active roster following training camp in 2021 and played in his first career professional game on August 5, 2021, against the Winnipeg Blue Bombers. He earned his first career start on October 2, 2021, against the Montreal Alouettes.

References

External links
Hamilton Tiger-Cats bio

1997 births
Living people
Canadian football offensive linemen
Guelph Gryphons football players
Hamilton Tiger-Cats players
Players of Canadian football from Ontario
Canadian football people from Toronto

redpajama_set_name: RedPajamaWikipedia