The double-slit experiment and the quantum nature of light and matter
Is light a wave or a particle? Quantum mechanics answers: both. Fire a few particles and see for yourself.
Click "Fire Particles" and watch single dots build up interference bands. Then switch to 1 slit, and drag Slit Width and Slit Separation to change the fringe spacing.
Is light a wave or a particle? Quantum mechanics answers: both. Photons and electrons behave as waves when unobserved, producing interference patterns. But the moment you measure them, they appear as discrete particles at definite positions.
This wave-particle duality isn't just a strange fact — it's the gateway to understanding all of quantum mechanics.
Richard Feynman called this "the only mystery" of quantum mechanics. Fire particles one at a time through two slits and watch — each particle lands at a single point, yet over thousands of particles, an interference pattern emerges. Each particle interferes with itself.
Try it: Start with 2 slits and watch the interference bands emerge. Then switch to 1 slit — the pattern becomes a simple diffraction envelope. Adjust slit width and separation to see how they affect the fringe spacing.
Click "Run", then toggle the which-path detector on and off. With the detector on, the interference pattern vanishes into two plain bumps.
Detector OFF — No which-path information. Each particle interferes with itself, building up the quantum interference pattern.
What happens if we try to figure out which slit each particle goes through? Place a detector near the slits and the interference pattern vanishes. The very act of gaining which-path information destroys the quantum superposition that created the interference.
Key insight: This isn't about physically disturbing the particle. Even the possibility of knowing which path was taken is enough to collapse the interference. Information and physics are deeply connected in quantum mechanics.
Start with Particle in Box and step up the energy level to count the nodes. Then switch to Wave Packet and turn on Time Evolution to watch the complex phase rotate.
Quantum mechanics describes particles using a wave function ψ(x,t) — a complex-valued function whose squared magnitude |ψ|² gives the probability density of finding the particle at position x. The real and imaginary parts oscillate, but the probability density tells us what we'll actually measure.
Particle in a Box: Energy is quantized — only certain standing waves fit between the walls. Higher energy levels n have more nodes (zero crossings). The probability |ψ|² shows where you're most likely to find the particle.
Wave Packet: A Gaussian wave packet is a more realistic "localized" particle. Turn on time evolution to see the complex phase rotate. Higher momentum k means faster oscillation — the de Broglie relation λ = h/p.
Slide from "very precise position" to "very uncertain position". As the position spread narrows, the momentum spread grows.
Drag the slider to localize the particle's position. The more precisely you know where a particle is (narrow Δx), the less you can know about its momentum (wide Δp) — and vice versa. This isn't a limitation of measurement; it's a fundamental feature of nature.
You cannot simultaneously know a particle's exact position and exact momentum. This isn't a limitation of our instruments — it's a fundamental property of nature encoded in the wave function. A narrow position distribution (well-localized particle) requires many momentum components, making momentum uncertain.
Click "Send Photons" and change the phase between the two arms. At φ = 0 every photon reaches D₁; at φ = π every photon reaches D₂.
A single photon enters the interferometer and takes both paths simultaneously. At φ = 0, constructive interference sends every photon to D₁. At φ = π, every photon goes to D₂. In between, the photon's quantum amplitudes interfere to produce a probabilistic mixture.
A single photon enters a beam splitter and takes both paths at once. After recombining at a second beam splitter, the photon's probability of reaching each detector depends on the phase difference between the two arms. This is quantum interference with a single particle.
The punchline: At φ = 0, the photon always goes to D₁ — the amplitudes for reaching D₂ perfectly cancel. At φ = π, it always goes to D₂. This happens even though only one photon is in the interferometer. The photon interferes with itself.
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