I’ve been reading about quantum spin for awhile and taking notes. Hobson’s book1, for example, discusses the foundational experiment which discovered spin. In the mean time, Space.com posted an article today which may serve as a placeholder for the topic while my draft notes on other topics develop.
The Space.com article “The Weird Quantum Property of ‘Spin’” is another one by Paul Sutter, astrophysicist, in the Expert Voices series.2 The article includes a video.
While I have reservations about Sutter’s “particle” frame of reference in this article, clearly he’s trying to connect with our everyday (macroscopic) experience of the world rather than get into Quantum Field Theory (QFT) and a perspective where “there are no particles, there are only fields.” 3 So, he discusses classical object properties such as mass (rather than “bundled” energy which has inertia) and charge (quantum symmetry of gauge bosons). Regarding spin, however, Sutter does conclude that there is “no classical description of this enigmatic property” — just the math.
Like Hobson4, he cites the 1922 Stern-Gerlach experiment, which remains a pedagogical mainstay in physics (with variations of the original experiment).
Keep in mind that the actual direction of the spin could point anywhere — imagine a little arrow tagged onto each and every particle. The length of that arrow is fixed for each kind of particle, but we’re only ever allowed to measure a limited number of directions. If the arrow is pointing even slightly up it will register in any experiment as +1/2. If it’s a little bit down or very much down, it doesn’t matter, we get -1/2. And that’s it.
… a certain theoretical physicist named Paul Adrien Maurice Dirac was also puzzling out the quantum world and went full bore with an approach to quantum mechanics that included special relativity. And unlike his buddy Erwin [Schrodinger], he was able to crack the mathematical code and figure out its implications. One of those implications of uniting quantum mechanics with special relativity was — you guessed it — spin. His mathematics automatically included a description of spin. If he had worked it out a few years before the experiments of Stern and Gerlach, he could’ve predicted their results!
As tempting as it may be, we have to totally discard any thoughts of subatomic particles being tiny, little spinning metal balls; their behavior is much more complex than that metaphor might suggest. Indeed, there are probably no useful [macroscopic] metaphors at all.
Update: This humorous YouTube video “What is Quantum Spin?” by The Science Asylum (published on September 23, 2017) also explains why classical metaphors are not useful.
Small particles like protons, neutrons, and electrons are often shown to be spinning on an axis like a planet, but this simply cannot be the case. Quantum mechanical spin is actually an intrinsic property like charge, so how does that work?
Although Schrödinger’s equation provides a firm foundation for the quantum physics of slow-moving matter, it runs into problems at higher energies because it happens not to conform with the principles of special relativity. Paul Dirac fixed this in 1928 by inventing an equation that generalized Schrödinger’s equation so that it incorporated the principles of special relativity and thus described high-energy relativistic matter correctly. Dirac’s equation was even more accurate than Schrödinger’s in predicting the hydrogen spectrum and also incorporating a new, distinctly quantum, aspect of the electron known as spin. — Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (Kindle Locations 2157 – 2162). Oxford University Press. Kindle Edition.
 Paul Sutter is an astrophysicist at The Ohio State University and the chief scientist at COSI science center. Sutter is also host of Ask a Spaceman and Space Radio, and leads AstroTours around the world. Sutter contributed this article to Space.com’s Expert Voices: Op-Ed & Insights.
 I’m working on a post titled “Float like a butterfly, sting like a bee” regarding this QFT perspective as discussed in Hobson’s book.
 Hobson uses a variation of the Stern-Gerlach experiment to resolve the irreversibility problem (after exploring local states and decoherence and the definite outcomes and measurement problems).
A variation on an experiment first performed in 1922 by German physicists Otto Stern and Walther Gerlach demonstrates the connection between quantum measurements and the second law. — Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (Kindle Locations 4948 – 4950). Oxford University Press. Kindle Edition.
Our discussion of the Stern–Gerlach experiment … suggested that the answer lies in the irreversible nature of the macroscopic detection process. This suggestion resembles the resolution of the irreversibility problem for environmental measurements: Environmental measurements are “recorded” by innumerable environmental quanta whereas lab measurements are recorded by detection screens, electronic clicks, or, perhaps, cats. — Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (Kindle Locations 5115 – 5119). Oxford University Press. Kindle Edition.