In classical physics, all variables commute: it doesn't matter whether you measure position and then momentum, or momentum and then position. It's impossible to know any quantity that obeys this quantum relation to an arbitrary accuracy. There are plenty of physical quantities out there -- often for esoteric reasons in quantum physics -- that have that same uncertainty relation between them. It's true: if you took all of those spin +ℏ/2 particles and passed them through another, identical magnet, they'd all deflect upwards. The existence of that uncertainty, the amount/magnitude of that uncertainty, and which variables that uncertainty occurs between, is what the quantum mechanical commutation relation tells you.

Source: Forbes August 12, 2017 13:52 UTC