## Definition **Wave–particle duality** is the empirical fact that every quantum entity — photon, electron, atom — exhibits behaviour characteristic of a wave (interference, diffraction, extension through space) and also behaviour characteristic of a particle (localised detection, discrete energy exchange), depending on how it is observed. The duality is not a deficiency in our description; it signals that quantum objects belong to a category of reality for which classical concepts like "wave" and "particle" are both partially correct and partially insufficient. ## The Two Faces of a Quantum Entity When a quantum system is left undisturbed — when no measurement interaction pins it to a definite state — it evolves according to a wavefunction $\psi(\mathbf{x}, t)$ that spreads through space. The squared modulus $|\psi|^2$ gives the probability density of finding the entity at a given location. An electron travelling toward a double-slit barrier passes through both slits simultaneously, and the resulting probability distribution on a screen shows an interference pattern — a hallmark of waves. Yet the moment a detector catches the electron, it arrives at a single, definite point. The extended wavefunction instantly updates to reflect that the electron has been found here and nowhere else — a process described as the *collapse of the wavefunction*, or *wavefunction reduction*. This localised arrival is the hallmark of a particle. The same duality holds for photons: a single photon passing through a double-slit apparatus builds up an interference pattern one dot at a time (particle-like individual arrivals, wave-like statistical distribution), a result confirmed in laboratory experiments since the early twentieth century. ## The Role of Observation A subtlety explored at length by Galfard: as long as there is *no way* — even in principle — to determine through which slit a particle passed, the interference pattern appears. The moment any physical interaction allows the path to be inferred (whether a human observes it or not), the interference is destroyed. This is not mysticism: it reflects the physical fact that a which-path measurement necessarily disturbs the system's quantum state. The deeper reason, as the Wikipedia note that Galfard himself cites in the context of the uncertainty principle, is that quantum properties exist in a state of superposition. The wavefunction is not a description of ignorance about a pre-existing trajectory; the electron *has* no definite trajectory before interaction. Observation does not reveal a pre-existing fact; it participates in bringing one into existence. ## Formal Expression For a particle with momentum $p$, de Broglie (1924) proposed that the associated wavelength is: $ \lambda = \frac{h}{p} $ where $h$ is Planck's constant. This relation unifies the particle property (momentum $p$) with the wave property (wavelength $\lambda$). The smaller the particle's momentum (or mass), the longer its associated wavelength and the more prominently wave-like its behaviour — which is why quantum effects are conspicuous for electrons but imperceptible for footballs. ## Relation to the Uncertainty Principle Wave–particle duality is the intuitive underpinning of the [[Heisenberg Uncertainty Principle]]. A well-defined wavelength (definite momentum) requires an extended, spread-out wave — so position is undefined. A sharply localised particle (definite position) is built from a superposition of many wavelengths — so momentum is undefined. The two descriptions are complementary, not contradictory. ## Related - [[Heisenberg Uncertainty Principle]] - [[Quantum Mechanics]] - [[Photon]] - [[Standard Model of Particle Physics]] ## Sources - [[The Universe in Your Hand (Galfard 2015)]]