Heisenberg wondered if this kind of trade-off between measuring an object’s position and its momentum was unavoidable, or if it was just an artifact of his thought experiment. To his delight, he discovered that these limits on measurement were fundamental: buried in the mathematics of Schrödinger’s wave mechanics, Heisenberg found a precise formulation of how much information you have to give up about an object’s momentum in order to learn more about its position, and vice versa.