Double-Slit Experiment Simulator: Quantum Interference Pattern

simulator beginner ~10 min
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Fringe spacing = 55.0 mm — visible interference fringes

With green light (550 nm), 10 um slit separation, and 1 m screen distance, the interference fringes are spaced 55 mm apart. After 500 photons, the classic double-slit interference pattern clearly emerges from individual particle detections.

Formula

Interference pattern: I(theta) = I_0 cos^2(pi d sin(theta)/lambda) sinc^2(pi a sin(theta)/lambda)
Fringe spacing: Delta_y = lambda D / d
Single-slit envelope width: w = 2 lambda D / a
de Broglie wavelength: lambda = h / p

The Double-Slit Experiment

Richard Feynman called the double-slit experiment 'a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics.' When particles pass through two narrow slits, they create an interference pattern — even when sent through one at a time. This simulator lets you watch this iconic experiment unfold.

Wave-Particle Duality in Action

Each photon in this simulation arrives at a definite point on the detection screen — that's the particle aspect. But the probability of where it lands is determined by the wave equation. With just a few photons, the pattern looks random. As hundreds and thousands accumulate, the familiar bright and dark interference fringes emerge from the statistical distribution. This is wave-particle duality made visible.

The Physics of Interference

The interference pattern combines two effects. Double-slit interference (the cos^2 term) creates regularly spaced bright fringes, with spacing determined by the ratio of wavelength to slit separation. Single-slit diffraction (the sinc^2 envelope) modulates these fringes, creating a broader pattern governed by the individual slit width. Together, I(theta) = I_0 cos^2(pi d sin theta / lambda) sinc^2(pi a sin theta / lambda).

What the Parameters Control

Wavelength affects fringe spacing — longer wavelengths produce wider fringes and different colors on the detection screen. Slit separation controls the interference pattern spacing inversely — wider separation means closer fringes. Slit width affects the diffraction envelope — narrower slits spread light more widely. Photon count controls how many particles are detected — start with just a few to see the randomness of individual detections, then increase to watch the pattern emerge.

A Deep Mystery

The double-slit experiment raises the deepest question in quantum mechanics: how does each individual particle 'know' about both slits? If you block one slit, the interference pattern vanishes. If you try to determine which slit the particle went through, the pattern also vanishes. The particle seems to explore all possible paths simultaneously, only 'choosing' a definite outcome when detected. Different interpretations of quantum mechanics (Copenhagen, many-worlds, pilot wave) offer different answers to this profound puzzle.

FAQ

What is the double-slit experiment?

The double-slit experiment demonstrates wave-particle duality: when particles (photons, electrons) pass through two narrow slits, they create an interference pattern on a detection screen — even when sent one at a time. Each particle is detected at a single point, but over many detections the pattern matches the wave prediction. Feynman called it 'the only mystery' of quantum mechanics.

How does the interference pattern form?

The intensity at angle theta is I(theta) = I_0 * cos^2(pi d sin(theta)/lambda) * sinc^2(pi a sin(theta)/lambda). The cos^2 factor comes from double-slit interference (path difference between slits), while the sinc^2 factor is the single-slit diffraction envelope. Together they produce bright and dark fringes modulated by a broader envelope.

What happens when you observe which slit the particle goes through?

If you determine which slit each particle passes through, the interference pattern disappears and you get two single-slit patterns. This is the essence of complementarity: wave behavior (interference) and particle behavior (which-path information) are mutually exclusive. This has been confirmed in numerous experiments with photons, electrons, and even molecules.

Can large objects show interference?

Yes. Double-slit interference has been demonstrated with electrons, neutrons, atoms, and even large molecules like C60 fullerenes (Arndt et al., 1999). The de Broglie wavelength lambda = h/p decreases with momentum, making interference harder to observe for macroscopic objects but never fundamentally impossible.

Sources

Embed

<iframe src="https://homo-deus.com/lab/quantum-mechanics/double-slit/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub