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Spin
Spin (physics)
Spin is an intrinsic
angular momentum associated with
quantum mechanical
particles. Unlike
classical "spinning" objects, which derive their
angular momentum from the rotation of their constituent parts, spin angular
momentum is not associated with any rotating internal masses. For example,
elementary particles, such as the
electron, possess spin angular momentum, even though they are point
particles. Also, unlike classical mechanical spinning, the spin is not described
by a
vector, but by a two-component object (for spin-1/2 particles): there is an
observable difference in how it transforms under
coordinate rotations.
Other
subatomic particles, such as
neutrons, which have zero electrical charge, also possess spin.
When applied to
spatial rotations, the principles of quantum mechanics state that the
observed values of angular momentum (which are
eigenvalues of the angular momentum operator) are restricted to integer or
half-integer multiples of
h/2π. This applies to spin angular momentum as well. Furthermore,
the
spin-statistics theorem states that particles with integer spin correspond
to bosons, and particles with half-integer spin correspond to
fermions.
A rotating
charged body in an inhomogenous
magnetic field will experience a
force. Electrons in an inhomogenous magnetic field also experience a force,
and this is why people have imagined the electron as "spinning around". The
observed forces vary for different electrons, and these differences are
attributed to differences in spin. The spin of electrons is therefore typically
measured by observing their deflection in an inhomogenous magnetic field. In
accordance with the predictions of theory, only half-integer multiples of h/2π
are ever observed for electrons.
Spin was first discovered in the context of the emission
spectrum of
alkali metals. In
1924,
Wolfgang Pauli (who was possibly the most influential physicist in the
theory of spin) 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.
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 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 L.H. 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).
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.
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.
A possible application of spin is as a binary information
carrier in
spin transistors. Electronics based on spin transistors is called
spintronics.
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