What is Spin?

Spin, when applied to fundamental particles, is a property rather than a description. The basic components of matter are not tiny spinning tops, like coins that are stood on edge then flicked on opposite sides to make them rotate. Instead, spin is a physical property that can be demonstrated and also a numerical value that explains particles’ behaviour.

Although it is not part of the AQA A-Level Physics syllabus, spin is an interesting property that deserves a brief discussion. The key points are:

• Particles with half-integer spin (1/2, 3/2, 5/2) are categorised as fermions and must always exist in a unique state
• Particles with integer spin (including zero) are categorised as bosons and can accumulate without limit in any single state.

The fact that all particles are either fermions or bosons is a mathematical theory and it is possible that a different type of particle might be discovered in the future but, so far, every observation supports the mathematical theory. (A nice non-mathematical description of the theory by John Baez is available at https://math.ucr.edu/home/baez/spin_stat.html)

Photons are bosons and this is what makes LASER beams possible, where the photons all have exactly the same energy and are precisely in-phase with each other. Electrons, on the other hand, are fermions; they are held in discrete orbits (energy levels) around atoms instead of all collapsing into the lowest energy state. Electrons can exist in pairs but only because their half-integer spin can be either positive or negative. This restriction is embedded in Wolfgang Pauli’s exclusion principle.

Mesons are a special category of bosons comprising an even number of quarks and therefore integral spin. The fact that mesons are immune from the Pauli exclusion principle explains why Hideki Yukawa was able to propose them as carriers of the strong nuclear force – although this is now known to be incorrect and that role belongs to a different type of boson, the gluons.

• For more about the strong nuclear force, see https://physbang.com/2024/10/14/what-is-the-strong-nuclear-force/.
• There is more about bosons in general on the Modern Physics website at https://modern-physics.org/bosons/

Neutrons also have half-integer spin, with a magnitude similar to that of a proton, but they display an effect suggesting the existence of a negative charge, which neutrons do not have. This hints at an internal structure for neutrons, which we now know to be the case, but it’s still weird to think of electrically-neutral neutrons having a spin property that seems to come from a residual negative charge.

(Be warned that magnitudes of proton and neutron spin are not a simple addition of quark spins! For more about this, see https://physicsworld.com/a/the-spin-of-a-proton/)

Electron spin was first suggested in 1925 by Samuel Goudsmit and George Uhlenbeck when they were both young students in their mid-twenties but two previous experiments paved their way;

• In 1897, fellow Dutch physicist Pieter Zeeman demonstrated that seemingly-single spectral lines could be revealed as doublets by the action of an external magnetic field.
• In 1920, Otto Stern and Walter Gerlach discovered that passing a beam of vaporised silver atoms through a highly non-uniform magnetic field caused it to split into two components. (There is a detailed account of the Stern-Gerlach experiment in the Stanford Encyclopedia of Philosophy, at https://plato.stanford.edu/entries/physics-experiment/app5.html)

Goudsmit knew of Zeeman’s work and in conversation with Uhlenbeck it dawned on him, “if one now allows the electron to be magnetic with the appropriate magnetic moment, then one can understand all those complicated Zeeman-effects”. Goudsmit’s 1971 lecture, from which this quote is taken, can be read online at https://www.lorentz.leidenuniv.nl/history/spin/goudsmit.html

But in trying to explain a mechanism for the magnetic moment in terms of physical spin, Goudsmit and Uhlenbeck had to deal with the issue of a required rotation speed that was faster than the speed of light. This awkwardness was resolved in 1928 when Paul Dirac produced his relativistic wave equation that explained the behaviour of particles moving close to the speed of light. Although it was not the intended purpose, Dirac’s equation predicted all the properties that derive from an electron’s spin.

Despite knowing that it is not a true rotation, we still refer to electron spin in this manner but now incorporating the electron’s overall movement, resulting in either right-handed or left-landed corkscrew motions. And this is where things get really weird.

Being electrically charged, electrons are affected by the electromagnetic force, which acts equally on both right-handed and left-handed electrons. But electrons are also affected by the weak nuclear force (which is responsible for beta decay) and it happens that W bosons (carriers of the weak nuclear force) act only on left-handed particles!

To make matters even worse, the Higgs field, which gives particles their mass, causes electrons to flip between right-handedness and left-handedness.

Nobody knows why any of this should be the case but that’s how things are.

And as if all of this were not bad enough, spin has one final trick up its sleeve in the form of entanglement, which was explained very briefly and clearly a few months ago in Symmetry magazine.

Experiments have shown that if there are two entangled particles, both with spin magnitude of 1/2 (either up or down but not previously determined) then as soon as the spin of one particle is measured, the other acquires the opposite sign instantaneously – faster than information can possibly travel between the two particles.

This is a tricky and hard-to-explain effect that Albert Einstein labelled as spooky action at a distance (but in German, in a letter sent to Max Born in 1947).

A nice explanation of the problem was provided by Andreas Muller for The Conversation in 2022, celebrating the award of that year’s Nobel Prize for Physics to Alain Aspect, John Clauser and Anton Zeilinger for their work with entangled photons. The key extract is given below but the full article, and a link to David Bohm’s original paper mentioned in the extract, can be found at https://theconversation.com/what-is-quantum-entanglement-a-physicist-explains-the-science-of-einsteins-spooky-action-at-a-distance-191927 

“A simplified version of this thought experiment, attributed to David Bohm, considers the decay of a particle called the pi meson. When this particle decays, it produces an electron and a positron that have opposite spin and are moving away from each other. Therefore, if the electron spin is measured to be up, then the measured spin of the positron could only be down, and vice versa. This is true even if the particles are billions of miles apart.

“This would be fine if the measurement of the electron spin were always up and the measured spin of the positron were always down. But because of quantum mechanics, the spin of each particle is both part up and part down until it is measured. Only when the measurement occurs does the quantum state of the spin ‘collapse’ into either up or down – instantaneously collapsing the other particle into the opposite spin.”

No further explanation is required because the described effect is simply a result of the quantum mechanics principles involved. Einstein regarded this as spooky (“spukhafte” to be exact) but that’s just the way things are in the quantum world and spin is simply one of the properties that are caught in its web.

Further Reading

• For a non-technical explanation of entanglement by Los Alamos National Laboratory researchers Andrew Sornborger and Patrick Coles, see https://www.realclearscience.com/articles/2022/04/14/spooky_action_at_a_distance_not_a_chance_827017.html 
• For details of an entanglement experiment using photons, conducted in 2015 at the US National Institute of Standards and Technology, see https://www.nist.gov/news-events/news/2015/11/nist-team-proves-spooky-action-distance-really-real)