What Exactly Is the 'Spin' of Subatomic Particles such as Electrons?

Morton Tavel, a professor of physics at Vassar College, responds:

"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."

Kurt T. Bachmann of Birmingham-Southern College adds some historical background and other details:

"Starting in the 1920s, Otto Stern and Walther Gerlach of the University of Hamburg in Germany conducted a series of important atomic beam experiments. Knowing that all moving charges produce magnetic fields, they proposed to measure the magnetic fields produced by the electrons orbiting nuclei in atoms. Much to their surprise, however, the two physicists found that electrons themselves act as if they are spinning very rapidly, producing tiny magnetic fields independent of those from their orbital motions. Soon the terminology 'spin' was used to describe this apparent rotation of subatomic particles.

"Spin is a bizarre physical quantity. It is analogous to the spin of a planet in that it gives a particle angular momentum and a tiny magnetic field called a magnetic moment. Based on the known sizes of subatomic particles, however, the surfaces of charged particles would have to be moving faster than the speed of light in order to produce the measured magnetic moments. Furthermore, spin is quantized, meaning that only certain discrete spins are allowed. This situation creates all sorts of complications that make spin one of the more challenging aspects of quantum mechanics.

"In a broader sense, spin is an essential property influencing the ordering of electrons and nuclei in atoms and molecules, giving it great physical significance in chemistry and solid-state physics. Spin is likewise an essential consideration in all interactions among subatomic particles, whether in high-energy particle beams, low-temperature fluids or the tenuous flow of particles from the sun known as the solar wind. Indeed, many if not most physical processes, ranging from the smallest nuclear scales to the largest astrophysical distances, depend greatly on interactions of subatomic particles and the spins of those particles."

Victor J. Stenger, professor of physics at the University of Hawaii at Manoa, offers another, more technical perspective:

"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.

--Originally published: Scientific American Online, October 21, 1999