A Quantum Is Both Wave and Particle
A single electron or particle of light behaves like a spread-out wave when no one is watching, yet the instant it is detected it becomes a particle that lands at one tiny point. The double-slit experiment shows both faces on one screen. In the first widget, particles arrive one at a time as dots, and as the dots pile up they form bright and dark fringes before your eyes.
Each dot is the mark of a particle arriving at one place, yet the whole accumulated pattern is wave interference. Lowering the slit separation d widens the fringe spacing, because of the relation Δy = λL/d. Here λ is the de Broglie wavelength λ = h/p, the crest-to-crest distance of the wave (its wavelength), and the wavenumber is k = 2π/λ. The astonishing part is that even sending particles one at a time, however sparsely, the same fringes still build up, which means each particle interferes with itself rather than with other particles. Each press of fire piles on a batch of dots weighted by the interference intensity.
Even with a single slit the wave nature does not disappear. When light or an electron passes through one narrow gap it spreads into a single wide central band, shaped like a sinc² envelope. The narrower the gap, the wider the spread. This trade-off, where a narrower gap spreads wider, is one face of the uncertainty principle in which confining position blurs momentum, and it is also the diffraction limit that caps the resolution of every lens and microscope. Move the slit-width slider and watch a narrower slit spread more broadly.
What happens if you switch on a which-path detector to learn which slit it went through? With the detector off the fringes survive and it looks like a wave; with it on the fringes vanish and only two plain bands remain. The key is that it is not the detector roughly shoving the particle but the mere fact that which path becomes knowable that erases the interference, and it has also been confirmed in experiment that erasing that path information afterward brings the fringes back. Flip the toggle ON and OFF and feel directly that the act of observing erases the interference.
Before it is detected, a particle travels not as a point but as a tightly bunched lump of wave, a wave packet. As time passes and distance grows, this lump spreads sideways and drops in height. This spreading happens because the several wavelength components inside it each travel at slightly different speeds, and so a free particle's position grows more and more uncertain as time goes on. Increase the propagation-distance slider and watch the wave packet widen and fade.
The two faces are complementary pictures of the same quantum. Set the toggle to the wave side and a smooth wave appears; set it to the particle side and it becomes a single dot carrying a momentum arrow. Both pictures are needed, yet they never appear together at once. This is complementarity. The idea that which face appears depends not on the object itself but on which experiment we choose is what Niels Bohr crystallized as the complementarity principle. Switch the toggle back and forth to see the two sides of one object in turn.