Spin (physics)

In physics, spin is an intrinsic angular momentum associated with microscopic particles. It is a purely quantum mechanical phenomenon without any analogy in classical mechanics. Whereas classical angular momentum arises from the rotation of an extended object, spin is not associated with any rotating internal masses, but is intrinsic to the particle itself. Elementary particles such as the electron can have non-zero spin, even though they are believed to be point particles possessing no internal structure. The concept of spin was introduced in 1925 by Ralph Kronig, and independently by George Uhlenbeck and Samuel Goudsmit.

History

Wolfgang Pauli was possibly the most influential physicist in the theory of spin. Spin was first discovered in the context of the emission spectrum of alkali metals. In 1924 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 numbers.

Related Topics:
Wolfgang Pauli - Emission spectrum - Alkali metal - 1924 - Shell - Pauli exclusion principle

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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.

Related Topics:
Ralph Kronig - Landé - 1925 - Speed of light - Theory of relativity

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In the fall of that year, the same thought came to two young Dutch physicists, George Uhlenbeck and Samuel Goudsmit. Under the advice of Paul Ehrenfest, they published their results in a small paper. 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a factor of two discrepancy between experimental results and Uhlenbeck and Goudsmit's calculations (and Kronig's unpublished ones).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 necessity to take into account 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 (i.e. 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).

Related Topics:
George Uhlenbeck - Samuel Goudsmit - Paul Ehrenfest - Llewellyn Thomas - Fiber bundle - Tangent bundle - Thomas precession

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Despite his initial objections to the idea, Pauli formalized the theory of spin in 1927, using the modern theory of quantum mechanics discovered 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.

Related Topics:
1927 - Quantum mechanics - Schrödinger - Heisenberg - Pauli matrices - Representation - Spinor

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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.

Related Topics:
1928 - Paul Dirac - Dirac equation - Electron

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In 1940, Pauli proved the spin-statistics theorem, which states that fermions have half-integer spin and bosons integer spin.

Related Topics:
1940 - Spin-statistics theorem

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Magnetic material may be modelled by a system of spins located at positions in a lattice, where the interaction of neighboring spins contributes to the total energy of the system and the states of the spins change according to some non-deterministic (probabilistic) rule (the dynamics of the system). In the Ising model spins have only two possible states (up and down), whereas in the Potts model they may have more than two possible states. This is discussed in detail in Spin Models (http://www.hermetic.ch/compsci/thesis/chap1.htm), particularly in the section Modelling Magnetic Material (http://www.hermetic.ch/compsci/thesis/chap1.htm#s1.3) and subsequent sections.

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