Quantum Particles Aren’t Spinning. So Where Does Their Spin Come From?No, this is wrong. Electrons do spin. You only get that paradox if you assume that electrons are very tiny spheres or point particles, but quantum mechanics teaches that electron are non-classical entities with wave-like properties.
A new proposal seeks to solve the paradox of quantum spin ...
But despite appearances, electrons don’t spin. They can’t spin; proving that it’s impossible for electrons to be spinning is a standard homework problem in any introductory quantum physics course. If electrons actually spun fast enough to account for all of the spinlike behavior they display, their surfaces would be moving much faster than the speed of light (if they even have surfaces at all). Even more surprising is that for nearly a century, this seeming contradiction has just been written off by most physicists as yet another strange feature of the quantum world, nothing to lose sleep over.
The article goes on to give the history of quantum spin, and how crucial it is for understanding chemistry and many other things.
But all of these fabulous discoveries, applications, and explanations still leave Goudsmit and Uhlenbeck’s question on the table: what is spin? If electrons must have spin, but can’t be spinning, then where does that angular momentum come from? The standard answer is that this momentum is simply inherent to subatomic particles, and doesn’t correspond to any macroscopic notion of spinning.No, this is silly. The QM textbooks teach that position, momentum, energy, angular momentum, and spin are observables that correspond to the classical variables, but cannot be taken literally about electrons as point particles, as the uncertainty principle prevents such a literal treatment. There is not really any difference between spin and the other variables in this respect.
Yet this answer is not satisfying to everyone. “I never loved the account of spin that you got in a quantum mechanics class,” says Charles Sebens, a philosopher of physics at the California Institute of Technology.
Peter Woit explains:
Despite what Sebens and Carroll claim, it has nothing to do with quantum field theory. The spin phenomenon is already there in the single particle theory, with the free QFT just providing a consistent multi-particle theory. In addition, while relativity and four-dimensional space-time geometry introduce new aspects to the spin phenomenon, it’s already there in the non-relativistic theory with its three-dimensional spatial geometry.Asking whether electrons really spin is a like asking whether they orbit the nucleus of an atom. A century ago, physicists tried to model an atom as classical electron orbits, and figured out that it doesn't work. You need a quantum model. But it is still correct to say that the electrons orbit the nucleus.