Definition
Wave-particle duality is the empirical fact that every quantum object — photon, electron, neutron, atom, even small molecules — behaves as a wave in some experiments (showing interference and diffraction) and as a particle in others (depositing localized energy and momentum). Both descriptions apply; neither one is the whole story.
In modern quantum mechanics the apparent paradox dissolves: the underlying object is a quantum field whose excitations sometimes act wave-like and sometimes particle-like depending on the measurement.
Why it matters
How it works
A monochromatic beam of light passing through two narrow slits produces a striped interference pattern on a distant screen — the hallmark of waves. The same happens with electrons, neutrons, or atoms: send them through a double slit and the cumulative arrival pattern shows interference fringes, as if each particle were a wave passing through both slits at once.
Yet if you reduce the intensity until particles arrive one at a time, each individual electron registers as a single localized hit on the detector. The pattern that emerges from many such hits is the interference pattern. Each electron behaves as a particle on detection but as a wave between source and detector.
If you install detectors at the slits to determine which slit each electron passed through, the interference pattern disappears. The detection itself, no matter how gently done, collapses the wave-like behavior. Bohr articulated this as complementarity: wave and particle pictures are both essential but mutually exclusive — you can probe one or the other, never both fully at once in the same experiment.
The modern interpretation: there are no "real waves" or "real particles" — there are quantum fields whose excitations evolve according to the Schrödinger equation (a wave equation) and are detected as discrete quanta (particle-like events). The wave function ψ encodes the wave-like aspect; |ψ|² gives the probability of finding a localized particle at a given location. Wave-particle duality is just the dual personality of a quantum field — wave-like in evolution, particle-like in detection.