# The spins

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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: New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments.

The measurement of neutrino magnetic moments is an active area of research. 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 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: 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: 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.

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The spins are often reported when alcohol is mixed with cannabis , since both may cause dizziness [2] and magnify each other's effects.

Since at least some of the symptoms of "the spins" can be attributed to alcohol's disturbance of the vestibular system, many symptom relief strategies are based on increasing the body's ability to use other senses to regain balance.

In addition to the vestibular system, vision and touch information from the body are extremely important in maintaining balance.

In fact, the vestibular system is not necessary at all to maintain standing balance unless information from the other two systems becomes inadequate.

Keeping one foot flat on the ground while trying to sleep is one popular self-treatment for people whose dizziness is exacerbated by lying down with eyes closed.

One way to mask the symptoms of the spins is to avoid staring at moving objects, such as people who are dancing or ceiling fans. Instead, it helps to stare at a non-moving object and slowly blink a few times.

However, it will make things worse to keep one's eyes closed for an extended period. In minor cases of the spins, simply sitting alone in a quiet place or taking a walk is all it takes to make them subside.

The best ways to avoid the spins are to continuously keep monitoring one's alcohol intake, which involves limiting one's intake to a reasonable level [18] [ unreliable source?

Someone getting or having the spins is mentioned in several books, including: The cause of the spins is also described in Season 1, Episode 10 of the Netflix Original Series Marvel's Daredevil during a discussion between two main characters, Matt Murdock and Foggy Nelson, after a night of drinking.

Murdock confirms when asked by Nelson that he still gets the spins despite being blind due to disturbed equilibrium of the fluid in the inner ear.

The Pittsburgh rapper , Mac Miller 's album K. S featured a track titled "The Spins". Danger Ronnie and the Spins associate this into their name and music.

Rock musician Brian Head Welch references experiencing the spins during his time as an alcoholic and drug addict. He mentions the symptoms were particularly noticeable when laying down with his eyes closed.

These references were made in his self-debuted album track "Flush". From Wikipedia, the free encyclopedia. This article is about intoxication.

For other uses of the word "spins", see Spin disambiguation. Women's Voices on College Drinking: Discovery Channel Ask the Expert: 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. 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: New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments.

The measurement of neutrino magnetic moments is an active area of research. 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 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: 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: 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.

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.

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.

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