Which of the following statements accurately reflect the implications of the Heisenberg Uncertainty Principle in quantum mechanics? (Select all that apply)

The Heisenberg Uncertainty Principle says that certain pairs of properties, like position and momentum, cannot both be measured with arbitrary precision at the same time; the more precisely you know one, the less precisely you know the other. This limits our ability to predict a particle’s exact state, so we must describe particles using probability waves instead of fixed paths. Because of this inherent fuzziness, even a particle at rest still has a nonzero “zero‑point” energy, and energy measurements over very short times become uncertain. The principle also explains why electrons in atoms occupy fixed orbitals rather than spiraling into the nucleus; the uncertainty in momentum keeps them from collapsing. These ideas show that quantum mechanics replaces deterministic trajectories with probabilistic descriptions and sets fundamental limits on measurement.