A scientist is conducting an experiment to measure the position and velocity of an electron in a hydrogen atom. She finds that as she gets more accurate measurements of the position, the uncertainty in the electron's velocity increases significantly. Which principle of quantum mechanics best explains this phenomenon?

The phenomenon is explained by the Heisenberg uncertainty principle, which states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision at the same time. When the scientist measures the electron’s position more accurately, the measurement process forces the wavefunction to become sharply localized in space, which mathematically means the wavefunction must spread out in momentum space. As a result, the momentum (and thus velocity, since momentum is mass times velocity) becomes highly uncertain. For example, if the electron’s position is narrowed to within a few picometers, the velocity uncertainty can grow to thousands of meters per second, making the velocity essentially unpredictable. This trade‑off between position and momentum accuracy is a fundamental feature of quantum mechanics.