} Therein Lies the Rub.

&--Thursday, April 30, 2009 ; 12:05 AM
EldwinSchrodinger @ What exactly are "spins" in subatomic particles?

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"When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets. In the classical world, a charged, spinning object has magnetic properties that are very much like those exhibited by these elementary particles. Physicists love analogies, so they described the elementary particles too in terms of their 'spin.'

"Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid 'objects' that can 'rotate' in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term 'spin,' however, still remains."

"Spin is the total angular momentum, or intrinsic angular momentum, of a body. The spins of elementary particles are analogous to the spins of macroscopic bodies. In fact, the spin of a planet is the sum of the spins and the orbital angular momenta of all its elementary particles. So are the spins of other composite objects such as atoms, atomic nuclei and protons (which are made of quarks).

"In classical physics, angular momentum is a continuous variable. In quantum mechanics, angular momenta are discrete, quantized in units of Planck's constant divided by 4 pi. Niels Bohr proposed that angular momentum is quantized in 1913 and used this to explain the line spectrum of hydrogen.

"At our current level of understanding, the elementary particles are quarks, leptons (such as the electron) and bosons (such as the photon). These particles are all imagined as pointlike, so you might wonder how they can have spins. A simple answer might be, perhaps they are composite, too. But deep theoretical reasons having to do with the rotational symmetry of nature lead to the existence of spins for elementary objects and to their quantization. Of particular significance is the difference between fermions, particles that, like the electron, have half-integer spins (half-integer multiples of Planck's constant divided by 2 pi), and bosons, particles that have integer spins. Fermions obey the Pauli exclusion principle, which states that two identical fermions cannot exist in the same state; without the Pauli exclusion principle, chemistry would have no Periodic Table. Bosons, on the other hand, tend to congregate in the same state, leading to phenomena such as superconductivity and Bose-Einstein condensation.

"Spin has served as the prototype for other, even more abstract notions that seem to have the mathematical properties of angular momentum but do not have a simple classical analogue. For example, isotopic spin is used in nuclear physics to represent the two states of a 'nucleon,' the proton and neutron. Similarly, quarks are paired as isospin 'up' and 'down,' which are the names given to the two quarks that make up ordinary matter. The rotational symmetry of space and time is generalized to include symmetries in more abstract 'inner' dimensions, with the result that much of the complex structure of the microworld can be seen as resulting from symmetry breaking, connecting profoundly to ideas describing the spontaneous formation of structure in the macroworld. "

Extracted from: Scientific American

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