= Wave-particle duality
Wave-particle duality names the coexistence of localized detection events and wave-like <interference> in <quantum mechanics>. A <photon> or <electron> is detected as an individual event, yet the distribution of many events depends on <probability amplitudes> from alternative paths. If the alternatives remain coherent, adding the <probability amplitudes> before applying the <Born rule> gives an <interference> term; simply adding the separate path <probabilities> does not.
In the single-<electron> experiment of <Akira Tonomura> and collaborators, an electrostatic biprism divided and overlapped the <electron> wave, and a position-sensitive detector recorded individual arrivals. Successive accumulated records developed <interference fringes>. This makes the apparent tension concrete: localization describes the detector events, while <matter-wave interference> describes their statistical distribution.<Demonstration of single-electron buildup of an interference pattern by Akira Tonomura and others>[American Journal of Physics 57 (1989), pp. 117–120, apparatus and accumulated electron-count images]{ref}
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