What it is
Wave–particle duality means that the same object, light or an electron, gives results like a wave in some experiments and like a particle in others. Neither classical picture is enough by itself.
For light:
- Wave: light passing through two narrow slits makes a pattern of bright and dark bands, interference; see double-slit interference.
- Particle: in the photoelectric effect light is absorbed in packets, photons, with energy E = hf; see photons.
For matter it is the other way round. Particles have a wavelength, de Broglie’s hypothesis: λ = h/p = h/(mv); see de Broglie wavelength.
- Electron at 1.0 · 10⁶ m/s. With electron mass 9.1093837 · 10⁻³¹ kg and h = 6.62607015 · 10⁻³⁴ J·s, λ ≈ 7.27 · 10⁻¹⁰ m, about 0.73 nm. That is the same order as the spacing of atoms in a crystal, which is why electrons make interference patterns off crystals.
- A baseball, 0.145 kg at 40 m/s. p = 5.8 kg·m/s and λ ≈ 1.1 · 10⁻³⁴ m. A wavelength that small cannot be noticed in any experiment.
What is not duality:
- “A wave sometimes and a particle sometimes, depending on mood.” It is the same object; the experiment decides which side shows.
- Classical water waves. They are a medium in motion, not a probability distribution for a particle.
Why it matters
Duality is the doorway to quantum physics. Because a particle has a wavelength, position and momentum cannot both be given exactly; see the Heisenberg uncertainty principle. A particle trapped in a box is allowed only certain wavelengths and so only certain energies; see particle in a box. The electron microscope works because electron waves have a much shorter wavelength than visible light and so resolve more detail.
Common misconceptions
- “Only light has duality.” Electrons, atoms and molecules have it too; we just do not notice it for large objects because λ = h/p is so small.
- “An electron’s wavelength means the electron is smeared out like a water wave.” Each electron is registered as a dot on a detector; the pattern builds up from many electrons.
- “Photons are little balls riding in a wave.” The wave and particle pictures are both models; neither is the whole description.
Common questions
What is de Broglie’s hypothesis?
That every particle with momentum p has a wavelength λ = h/p. It was confirmed when electrons produced interference off crystals.
Why can’t we see a ball behave like a wave?
Its wavelength is around 10⁻³⁴ m, far smaller than an atomic nucleus, and no experiment can detect it.
Which experiments show the wave side and the particle side?
Interference and diffraction show the wave. The photoelectric effect and Compton scattering show the particle; see Compton scattering.