De Broglie extended duality from light to matter, implying that particles should also show:

1. The symmetry runs in both directions. 2. Light was already known to behave as both wave and particle. 3. In 1923 de Broglie made a radical proposal. 4. It rested on the hope that nature is symmetric. 5. So if waves can act as particles, particles should show wave behaviour. _Source: OpenStax College Physics for AP Courses 2e (CC BY 4.0), Ch 29 'Quantum Physics', sections 29.1-29.8_