Shoot silver atoms between the poles of a shaped magnet. Each one is a tiny magnet itself, pointing any which way, so you would expect a smear. You get exactly two spots. Then chain the magnets together and things get stranger.
This is the famous one. Magnet 1 keeps only the atoms that went up along Z. Magnet 2 sorts them along X. Magnet 3 asks about Z again, and half of them now come out down, even though every down atom was removed at the start.
An oven boils off silver atoms. Each has one unpaired electron, and that electron's spin makes the atom a tiny magnet. The magnet's poles are shaped so the field is stronger near one pole, which pushes an atom up or down depending on how its little magnet is tilted along the magnet's axis.
A classical tilted compass needle could have any tilt, so the atoms should spread into a continuous band. Instead every atom lands in one of two spots. Along any axis you ask about, the spin is only ever up or down.
An atom can't have a definite spin along Z and along X at the same time. Measuring one throws away the other, just as position and momentum trade off. So the atom isn't carrying a hidden arrow that each magnet reads. Each magnet asks a question, and the act of asking sets the answer that the next magnet sees.
Otto Stern and Walther Gerlach saw the split in February 1922, before spin had been proposed. Uhlenbeck and Goudsmit explained it as electron spin in 1925. Stern received the 1943 Nobel Prize.
The discovery that spin only ever comes in "up" or "down" along an axis turned into a toolkit. Flipping spins, reading them and sorting by them runs through medicine, timekeeping and every computer.
The protons in your body's water are spin-½, just like these silver atoms. In a 3 tesla scanner their two energy levels are split by a radio frequency of about 128 MHz. Radio pulses tip the spins, and the signal they send back as they relax builds the image.
In the demo: the magnet's two beams are the two energy levels MRI flips between.The same physics in a test tube. A nucleus's exact flip frequency depends slightly on the electrons and atoms around it, so chemists read a molecule's structure from its spectrum. It is a standard tool for checking new drugs and materials.
In the demo: every spin answers only "up" or "down", which makes the frequencies sharp.The second is defined by a caesium transition at exactly 9,192,631,770 cycles per second. Classic caesium beam clocks use Stern–Gerlach-style magnets: one to pick out atoms in one state, a microwave cavity to flip them, and a second magnet to send only the flipped atoms to the detector.
In the demo: block one beam, change the atoms, then sort again.Giant magnetoresistance, found independently by Albert Fert and Peter Grünberg in 1988 (Nobel Prize 2007), makes a layered metal's resistance depend on electron spin. Read heads built on it from 1997 let hard drives pack in far more data, and their successors still read every hard drive today.
In the demo: spin-up and spin-down electrons are treated differently, like the two beams.Magnetic RAM stores each bit as the up or down magnetization of a tiny layer, read through a spin-dependent tunnelling current. It keeps data with the power off and survives endless rewrites, so it is used in satellites, industrial controllers and some chip foundries' embedded memory.
In the demo: two states, chosen by spin, read by how electrons pass through.A single electron spin in a diamond defect (an NV centre) can sense magnetic fields from single cells and tiny circuits. Electron spins in silicon chips are being built into qubits. In both, measuring along an axis tilted by θ gives "up" with probability cos²(θ/2), the rule you can test here.
In the demo: turn magnet 2 and watch the counts follow cos²(θ/2).