Do Quantum Particles Really Spin?

Frankfurt, 1922. Otto Stern and Walther Gerlach fired silver atoms between the poles of a lopsided magnet. If each atom is a little compass tilted at random, each should be nudged by an amount set by its tilt, and the beam should smear into a band – the safest bet classical physics ever placed. The plate said otherwise: two clean spots. However the magnet is turned, every atom answers fully along it or fully against it, and nothing in between, ever.

Now, a compass is a magnet, and classical physics knows exactly one way to make a magnet: electric charge going round in a loop. So when the electron turned out to be magnetic, the natural reading was that its charge circulates – that the electron spins. A spinning charge should also carry ordinary angular momentum, the quantity a flywheel stores, and we will see shortly that it truly does. The name stuck before anyone checked whether a ball that small could turn that fast. The machine below is the chapter’s analyzer chain, live – worth a minute of play before we do the checking, if only to feel how absolute the two-ness is.

The spinning electron was proposed twice. In January 1925 Ralph Kronig, twenty years old, showed Pauli his calculation: let the electron rotate, and the alkali spectra come out right. Pauli called it “a very witty idea” – but nature, he said, was not like that – and Kronig put it in a drawer. That autumn in Leiden, George Uhlenbeck and Samuel Goudsmit had the same idea and told their supervisor, Paul Ehrenfest. They also showed the great H. A. Lorentz, who returned a week later with pages of arithmetic: the picture was fatal. The pair rushed to withdraw their note. Ehrenfest had already posted it to the journal, and consoled them with one of physics’ kindest sentences: “You are both young enough to be able to afford a stupidity.”

The fatal arithmetic, in plain words: for a ball the electron’s size to store the electron’s turning, its surface would have to move at about 171 times the speed of light. It gets worse. Experiments since have found the electron smaller than the size Lorentz used – at least a thousand times smaller – and the smaller the ball, the faster its surface must go: the modern figure is half a million times light speed. To keep its equator merely at light speed, the ball would need to be five hundred times wider than a proton, which nothing that hides inside atoms can be. And on top of all that, a spinning ball’s magnetism comes out at half the measured strength. Every road out is blocked. Only the name survived.

Before concluding that spin is a mere accounting fiction, meet the only experiment Albert Einstein ever published from his own laboratory bench. Berlin, 1915, with Wander de Haas: an iron rod hangs from a fine glass fibre inside a coil. Switch the coil’s current one way and the atomic compasses inside the rod all point up; reverse it, and they all flip down. And each time they flip – the rod itself begins to turn.

It has to. Angular momentum is conserved: all that atomic turning-power pointed one way, and if every atom reverses, something must take up the difference. The only thing available is the rod as a whole. The kick is tiny – for a rod the size of a matchstick, one full revolution every twenty-one minutes – which is why the experiment needs the fibre and a resonance trick, flipping the field in time with the rod’s own gentle twisting period, like pushing a swing. Twenty-one years later Richard Beth did the same with light: circularly polarised light, passed through a crystal plate hanging from a fibre, measurably twists the plate. Spin can be cashed into ordinary, visible rotation. Whatever it is, it is not a metaphor.

There is one more disqualification, and it is the strangest. Every actual object – a top, a compass needle, a planet – comes back to itself after one full turn. Turn it through 360 degrees and nothing remembers the journey. The electron is not like that. Rotate an electron’s state through one full turn and it comes back subtly wrong – “minus itself”, a change invisible if the electron is alone, but detectable the moment you compare it with an untouched twin.

In 1975 two groups did exactly that with neutrons, which carry the same kind of spin. Split a beam in two, let a magnetic field turn the spins on one path through a full turn, and recombine: the two halves cancel where they used to reinforce, as if one had been flipped upside down. Only after two full turns – 720 degrees – does everything return to normal. There is even a party trick for it: twist a belt through one full turn and the twist is trapped, however you slide the belt around; give it two full turns and the twist can be walked out without rotating either end. Electrons live on the belt’s rhythm, not the wheel’s. No spinning ball of any size, at any speed, behaves like that – this is the final proof that spin is not a picture of motion, deeper than any argument about speed limits.

So what is left, once the ball is gone? A property, not a motion. Every electron carries a fixed, unchangeable amount of turning-power, exactly as it carries a fixed charge – you can no more spin an electron up or slow it down than you can drain its charge. All you can ever change is the direction of its compass, and all any measurement ever gets back is one of the two readings. “The electron spins” is, in the end, grammar left over from a dead picture. “The electron has spin” is the truth: it behaves, in every conserved and measurable way, exactly as if something were turning – with nothing there to turn.

And that property runs an astonishing amount of the world. The magnet on your fridge holds because trillions of electron compasses in the iron agree on a direction: everyday magnetism is spin, in bulk. An MRI scanner works by tipping the compasses inside your body’s hydrogen atoms and listening to them wobble back – if you have ever had a scan, this page’s physics has been performed on you. And the two readings are why atoms fill their rungs in pairs, which is where chemistry gets its shape. Chapter 5 of the quantum course puts the compass to work – the Bloch sphere, and the measurement chains where one look erases another.