An interactive visualisation of the double-slit experiment from the perspective of David Bohm's pilot wave theory (de Broglie-Bohm / Bohmian mechanics).
Particles have definite positions at all times. Their trajectories are guided by a real physical field — the pilot wave ψ — through the quantum potential Q. The interference pattern is not a mystery; it is the natural consequence of Q's topology.
| Element | Description |
|---|---|
| Blue field | The pilot wave |ψ|² — probability density. Passes through ALL slits simultaneously |
| Green trajectories | Deterministic Bohmian particle paths guided by v = (ħ/m) Im(∇ψ/ψ) |
| Detector strip | The fringe pattern building up particle by particle, with the theoretical |ψ|² curve overlaid for comparison |
| Q potential (toggle) | Quantum potential Q = −(ħ²/2m)∇²R/R — the non-local field that organises trajectories |
| Flow field (toggle) | The guidance velocity field as arrows — the "current" every particle rides |
- Trajectories never cross the symmetry axis — provable from the guidance equation
- Bunching into bright fringes — Q has valleys at high |ψ|² regions, pulling particles in
- No wave function collapse — the wave is a real field; detection is just a particle reaching the screen
- Copenhagen contrast — toggle to see the same field with no trajectories, particles "teleporting" to the detector
Q potential (plasma overlay) and the guidance flow field together — particles ride the arrows straight into Q's valleys.
The guidance equation determines particle velocity from the wave function:
v = (ħ/m) · Im(∇ψ / ψ)
The quantum potential is derived from the amplitude R = |ψ|:
Q = −(ħ²/2m) · ∇²R / R
The wave function is computed via Huygens-Fresnel superposition with the Rayleigh-Sommerfeld obliquity factor cos θ, using adaptive source counts per slit (source spacing stays far below λ/2, so the discretisation is exact for display purposes while staying fast enough to recompute live as you drag a slider). The guidance velocity comes purely from the phase gradient — the outgoing-wave kernel already carries the forward momentum ħk, so no drift term is added. Near wave nodes the true Bohmian speed diverges; the field is regularised and speed-capped so the fixed-step 4th-order Runge-Kutta integrator stays stable while keeping the characteristic whip around dark fringes.
Single slit: pure diffraction. No second path to interfere with, so no fringes — only the diffraction envelope.
Three slits sharpen the primary maxima and add faint secondary maxima between them — the same physics as a diffraction grating, one slit at a time.
Toggle to Copenhagen and the trajectories vanish — particles simply appear at the detector, Born-rule sampled from |ψ|², with no path in between.
| Control | Effect |
|---|---|
| Slits (1 / 2 / 3) | Single-slit pure diffraction, the classic double slit, or a triple-slit grating |
| Slit width | Narrower = wider diffraction, fewer fringes. Updates live while dragging |
| Separation | Larger = more fringes packed closer. Updates live while dragging |
| Presets | Classic · Wide fringes · Fine fringes · Single slit · Triple slit |
| Interpretation | Toggle Bohm (trajectories) vs Copenhagen (probability cloud only) |
| Wave shows | |ψ|² probability density or Re(ψ) oscillating crests |
| Layers | ψ wave · Q potential · Flow field · Trajectories · Labels · Axis |
| Fire burst / Fire 1 / Clear | Launch particles sampled from the Born distribution |
| Speed / Pause / Auto-fire | Simulation pacing |
| 3D Perspective | CSS perspective transform — drag to rotate the view |
Keyboard: space pause · f fire burst · c clear · q toggle Q · t toggle trajectories.
Hover any control for a plain-English explanation of what it does physically. Hover the canvas for a live readout of |ψ|², Q and v at the cursor.
- Vite + TypeScript — no framework, zero runtime dependencies
- HTML5 Canvas 2D (HiDPI/retina aware), static fields cached offscreen; finished trajectories are stamped once onto a persistent layer so per-frame cost scales with active particles only
- Pure physics: no physics library, all equations derived from first principles
npm install
npm run devOpen http://localhost:5173.
- Bohm, D. (1952). A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. Physical Review, 85(2), 166-179.
- Holland, P.R. (1993). The Quantum Theory of Motion. Cambridge University Press.
- Philippidis, C., Dewdney, C., & Hiley, B.J. (1979). Quantum interference and the quantum potential. Il Nuovo Cimento B, 52(1), 15-28. (The original Bohmian trajectory paper with the double-slit)