## Spin: The Quantum Property That Should Have Been Impossible

“However, as Goudsmit realized in May 1925, there was a problem with using pure integers to characterize the quantum states. If you did, the exclusion principle couldn’t be maintained. Two electrons in the ground state (lowest energy level) of an atom would have identical set of those three quantum numbers. Goudsmit found that by introducing a fourth quantum number, representing a kind of intrinsic or extra angular momentum, that could take on only one of two possible values — either +½ or -½ — he could preserve the Pauli exclusion principle. The ground state could still have two electrons, but their fourth quantum numbers would be opposite: if one was +½, the other would be -½.”

If you want to describe nature accurately, you can only get so far by following your classical intuition. For many of our most fundamental properties, you have to resort to a quantum set of rules. These quantum instructions that nature has given us are often unintuitive, such as probabilistic locations of a particle, fractional properties, and statistics that didn’t obey simple counting rules. Perhaps the most puzzling rule came in the mid-1920s, when two young physicists submitted a paper hypothesizing the existence of spin: a small amount of angular momentum intrinsic to a particle. Just before publication, they showed their work to the famous Hendrik Lorentz, who calculated that a spinning electron, in order to achieve the necessary angular momentum, must spin faster than light. Nevertheless, Paul Ehrenfest, advisor to the two young reserachers, told them it was too late, and he had already submitted the paper.