de Broglie hypothesis
The de Broglie hypothesis is Louis de Broglie's 1924 proposal, made in his doctoral thesis, that wave-particle duality is not a quirk of light alone but a universal feature of nature. If light, long thought purely a wave, also behaves as particles, then perhaps electrons and all other matter, long thought purely particles, also have a wave nature. He dared to give that matter wave a definite wavelength, set by the particle's momentum.
It was a bold leap of symmetry rather than a result forced by data. De Broglie reasoned that the universe should not play favourites between light and matter, and he showed that a wave following his rule could naturally explain why the electron orbits in Bohr's model of the atom were quantised: only orbits whose circumference fit a whole number of wavelengths would survive, like a standing wave on a loop of string.
The idea was so unexpected that de Broglie's examiners sought Einstein's opinion before accepting the thesis; Einstein praised it. Within a few years experiments on electron diffraction confirmed the matter waves directly, and Schrödinger built his wave equation on de Broglie's foundation. A speculation grounded in beauty and symmetry had become one of the load-bearing pillars of quantum mechanics.
De Broglie extended duality from light to all matter, with momentum setting the wavelength.
De Broglie's own picture imagined a real pilot wave guiding a particle, an idea later revived in Bohmian mechanics. Mainstream quantum mechanics keeps his wavelength but interprets the wave as a probability amplitude, not a physical fluid.