Quantum & Wave Double-Slit Simulator

Live Interactive Wavefield Space Wave Mode

Emitter Nozzle

Detector Plate Area

Probability Density Profile |\psi(x)|^2

Theory (Born Rule) Live Hits (Histogram)

Fringe Spacing (Δy) - Formula: λL / d

Path Difference Max - For peak separation

Observed State No Decoherence toggle

Diffraction Limit - Width of main lobe

Simulation Preset

Wave-Particle Duality Mode

Wavelength (λ) 532 nm

Slit Separation (d) 40 µm

Slit Width (w) 10 µm

Screen Distance (L) 200 mm

Frequency Speed 1.5x

Observe the Slits Measure which slit each photon/wave goes through.

The Mechanics of Double-Slit Diffraction

In continuous wave optics, the classical electromagnetic field propagates as spherical wavefronts from each of the slits, forming an interference pattern. When these wave fronts overlap at the screen, they undergo coherent superposition.

Superposition Field Formula $$\Psi_{\text{total}} = \Psi_1 + \Psi_2$$ $$I \propto |\Psi_1 + \Psi_2|^2 = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos(\Delta\phi)$$

The fringe spacing $\Delta y$ represents the distance between consecutive interference maxima (bright bands) and is given by the classic grating equation:

Fringe Distance $$\Delta y = \frac{\lambda L}{d}$$

Quantum Wave-Particle Duality

When the source is attenuated such that particles (photons, electrons, or molecules) pass through one at a time, each particle lands as a localized, discrete mark on the screen. There is no continuous wave medium.

Yet, as particles accumulate, they mathematically construct the identical wave-interference pattern. This demonstrates that the wave represents a probability amplitude, governed by **Born's Rule**:

$$P(x) = |\psi(x)|^2$$

The Measurement Problem & Decoherence

If we place a detector to "observe" which slit the particle traverses, the state of the particle entangles with the macroscopic state of the detector. This physical interaction triggers quantum decoherence.

The phase coherence is lost, collapsing the superposition state $\Psi_1 + \Psi_2$ into a localized mixed statistical ensemble. The cross-interference term $2\sqrt{I_1 I_2}\cos(\Delta\phi)$ vanishes entirely:

$$I(x) = I_1(x) + I_2(x)$$

Observe the live difference by enabling the "Observe the Slits" sensor on the control tab. Notice how the interference fringes morph instantly into two classical diffraction curves.