The simplest but deepest questions of the philosophy of quantum mechanics are these: Are quantum systems waves, or are they particles? Are they both or are they neither?

When light bounces an electron out of the surface of an alkali metal it behaves like a particle. Light carries momentum but also a punch. Just as there is no such thing as half a punch, so there is no such thing as half a quantum of light.

On the other hand, the shadow formed on a screen by an object has soft edges, edges which get softer as the object is moved away from the screen. Light exhibits the phenomena of diffraction and interference and so is wavelike.

This dual behaviour of light, and indeed of matter itself, is called wave-particle duality. The wave nature of a quantum system is reflected in wave mechanics which assigns a wave-function to the system. But the dual nature of light was noticed before Schrodinger developed the wave-mechanical formalism in 1926. In fact, it goes back at least as far as Einsteins explanation of the photoelectric effect in 1905.

Wave-particle duality is not something that arises within the quantum mechanical formalism. It is something which is expressed within it, and is something which is best discussed in terms of the paradoxes that quantum experiments force upon physics.

In fact, the simplest and most immediately disturbing of the quantummechanical paradoxes arise out of wave-particle duality. We take the two-slit experiment and the delayed-choice experiment as examples.