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Add spin to one of your lists below, or create a new one. Improve your vocabulary with English Vocabulary in Use from Cambridge. Learn the words you need to communicate with confidence.

Spotless or squalid? Definitions Clear explanations of natural written and spoken English. Click on the arrows to change the translation direction.

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My word lists. Tell us about this example sentence:. The word in the example sentence does not match the entry word.

The sentence contains offensive content. Cancel Submit. Your feedback will be reviewed. C1 [ I or T ] to cause to turn around and around, especially fast :.

The earth spins on its axis. He was killed when his car hit a tree and spun off the road. If your head or the room spins, you feel as if it is turning around and around, and you cannot balance :.

The room started spinning and I felt faint. The car spun on the ice. She spun the globe , and pointed to the Solomon Islands. The revolving door spun too fast and knocked him over.

He spun his partner around until she was dizzy. The children spun the carousel round as fast as they could. Revolving, rotating and spinning.

Want to learn more? The final stage of the production of cotton is when it is spun into thread. 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. 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: [13] [14] [15].

New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. Experimental results have put the neutrino magnetic moment at less than 1.

On the other hand elementary particles with spin but without electric charge, such as a photon or a Z boson, do not have a 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, with the overall average being very near zero.

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. 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 for a spin-s particle measured along any direction can only take on the values [17].

Conventionally the direction chosen is the z -axis:. 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: s x , s y and s z cannot possess simultaneous definite values, because of a quantum uncertainty relation between them.

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.

To return the particle to its exact original state, one needs a degree rotation. The Plate trick and Möbius strip give non-quantum analogies.

A spin-zero particle can only have a single quantum state, even after torque is applied. Rotating a spin-2 particle 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 degrees and a spin-0 particle can be imagined as sphere, which looks the same after whatever angle it is turned through.

Spin obeys commutation relations analogous to those of the orbital angular momentum :. It follows as with angular momentum that the eigenvectors of S 2 and S z expressed as kets in the total S basis are:.

The spin raising and lowering operators acting on these eigenvectors give:. But unlike orbital angular momentum the eigenvectors are not spherical harmonics.

There is also no reason to exclude half-integer values of s and m s. In addition to their other properties, all quantum mechanical particles possess an intrinsic spin though this value may be equal to zero.

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.

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.

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.

The above permutation postulate for N -particle state functions has most-important consequences in daily life, e. 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.

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:. 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.

Starting with S x. Using the spin operator commutation relations , we see that the commutators evaluate to i S y for the odd terms in the series, and to S x for all of the even terms.

Note that since we only relied on the spin operator commutation relations, this proof holds for any dimension i. A generic rotation in 3-dimensional space can be built by compounding operators of this type using Euler angles :.

An irreducible representation of this group of operators is furnished by the Wigner D-matrix :. 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.

This fact is a crucial element of the proof of the spin-statistics theorem. 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.

These spinors transform under Lorentz transformations according to the law. It can be shown that the scalar product. The corresponding normalized eigenvectors are:.

Because any eigenvector multiplied by a constant is still an eigenvector, there is ambiguity about the overall sign. In this article, the convention is chosen to make the first element imaginary and negative if there is a sign ambiguity.

The present convention is used by software such as sympy; while many physics textbooks, such as Sakurai and Griffiths, prefer to make it real and positive.

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 S x , S y or S z on that axis, i.

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The car spun on the ice. She spun the globe , and pointed to the Solomon Islands. The revolving door spun too fast and knocked him over.

He spun his partner around until she was dizzy. The children spun the carousel round as fast as they could.

Revolving, rotating and spinning. Want to learn more? The final stage of the production of cotton is when it is spun into thread.

Spiders spin webs. He spun some tale about needing to take time off work because his mother was ill. We were spinning along , when suddenly one of our tyres burst.

Chris spun past in a flashy new car. Moving quickly. Idioms spin a coin. Phrasal verbs spin sb around. I hit something on the road , which sent the car into a spin.

Suddenly, the plane went into a spin. They have tried to put a positive spin on the situation. This report puts a different spin on the issue. Rupert took me for a spin in his new car.

Idiom in a spin. Cotton is spun into thread. Idiom spin your wheels. Phrasal verbs spin off something. To understand spin, he said, is to understand that you get your story told without getting your fingerprints on it.

Examples of spin. However, immortality does not come easy on this spinning earth. From the Cambridge English Corpus. They also like to up-end push and pull toys for imaginary mending, and wheels can be spun at different speeds.

These examples are from the Cambridge English Corpus and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

In spinning the position by had become truly remarkable. Finding enough spinners at the peak periods of clothmaking must have been no easy task, given the prevailing wage levels for spinning yarn.

Is it in the least surprising, therefore, that spinning was seen as work for women or children? In the sixteenth century commentators were clear that a livelihood could not be gained from spinning alone.

The type of fiber used and the end-product desired determine the technique of spinning and the tools utilized.

She also found that women spun, and presumably wove, maguey and cotton in both commoner and elite households. The parasite passes the winter inside its host, emerging in the spring and spinning its cocoon inside that of its host.

On the proximal arm segment the arm spines meet midradially forming a single fan. On the proximal arm segment the arm spines almost meet midventrally forming a fan.

What, for example, are we to make of the spinning glands of one of the scale-worm groups the sigalionids , which produce fibres employed in tube-building?

Ferromagnetic couplings tend to align the spins, antiferromagnetic couplings make them point in opposite directions. One takes from this the idea that it has hardly begun before it swiftly spins along.

Even feathers and the hair of rabbit and humans may have been spun, along with other materials. See all examples of spin. Because any eigenvector multiplied by a constant is still an eigenvector, there is ambiguity about the overall sign.

In this article, the convention is chosen to make the first element imaginary and negative if there is a sign ambiguity.

The present convention is used by software such as sympy; while many physics textbooks, such as Sakurai and Griffiths, prefer to make it real and positive.

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 S x , S y or S z on that axis, i.

The quantum state of a particle with respect to spin , can be represented by a two component spinor :. Following the measurement, the spin state of the particle will collapse into the corresponding eigenstate.

The operator to measure spin along an arbitrary axis direction is easily obtained from the Pauli spin matrices. Then the operator for spin in this direction is simply.

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.

In quantum mechanics, vectors are termed "normalized" when multiplied by a normalizing factor, which results in the vector having a length of unity.

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. 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.

By taking Kronecker products of this representation with itself repeatedly, one may construct all higher irreducible representations. That is, the resulting spin operators for higher spin systems in three spatial dimensions, for arbitrarily large s , can be calculated using this spin operator and ladder operators.

The resulting irreducible representations yield the following spin matrices and eigenvalues in the z-basis. Also useful in the quantum mechanics of multiparticle systems, the general Pauli group G n is defined to consist of all n -fold tensor products of Pauli matrices.

The analog formula of Euler's formula in terms of the Pauli matrices :. For example, see the isotopes of bismuth in which the List of isotopes includes the column Nuclear spin and parity.

Spin has important theoretical implications and practical applications. Well-established direct applications of spin include:.

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 photon polarization. An emerging application of spin is as a binary information carrier in spin transistors.

The original concept, proposed in , is known as Datta-Das spin transistor. The manipulation of spin in dilute magnetic semiconductor materials , such as metal-doped ZnO or TiO 2 imparts a further degree of freedom and has the potential to facilitate the fabrication of more efficient electronics.

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 , Wolfgang Pauli introduced what he called a "two-valuedness not describable classically" [23] associated with the electron in the outermost shell.

This allowed him to formulate the Pauli exclusion principle , stating that no two electrons can have the same quantum state in the same quantum system.

The physical interpretation of Pauli's "degree of freedom" was initially unknown. 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. 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 results.

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 , known to Ludwik Silberstein in Despite his initial objections, Pauli formalized the theory of spin in , 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 , 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.

Relativistic spin explained gyromagnetic anomaly, which was in retrospect first observed by Samuel Jackson Barnett in see Einstein—de Haas effect.

In , Pauli proved the spin-statistics theorem , which states that fermions have half-integer spin and bosons have integer spin.

In retrospect, the first direct experimental evidence of the electron spin was the Stern—Gerlach experiment of However, the correct explanation of this experiment was only given in From Wikipedia, the free encyclopedia.

This article is about spin in quantum mechanics. For rotation in classical mechanics, see angular momentum. Elementary particles of the Standard Model.

Main article: Spin quantum number. Main article: Spin magnetic moment. Further information: Angular momentum operator. Main article: Pauli matrices.

See also: Symmetry in quantum mechanics. Click "show" at right to see a proof or "hide" to hide it. Quantum Mechanics 3rd ed. Introduction to Quantum Mechanics 2nd ed.

Niels Bohr's Times. Oxford: Clarendon Press. Bibcode : PhRv Bransden, C. Retrieved Physics Letters. B67 3 : — Bibcode : PhLB Physical Review.

D16 5 : — Bibcode : PhRvD.. Fujikawa, R. Shrock Physical Review Letters. Bibcode : PhRvL.. Hall Quantum Theory for Mathematicians.

S and B. Das Applied Physics Letters. Bibcode : ApPhL.. N; Hanaor, D. H Journal of Applied Physics. Bibcode : JAP Nobel Lecture.

Nobel Prize. Friedrich, D. Herschbach Physics Today. Bibcode : PhT Quantum Mechanics 2 volume set ed. Condon, E. The Theory of Atomic Spectra.

Cambridge University Press. Hipple, J. Edmonds, A. Angular Momentum in Quantum Mechanics. Princeton University Press. Jackson, John David Classical Electrodynamics 3rd ed.

Serway, Raymond A. Physics for Scientists and Engineers 6th ed. Thompson, William J. Tipler, Paul

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