Quantum double slit

Quantum Double Slit, published by @hyle, evolves a single nonrelativistic electron wave packet on a 192 × 160 plane. It is ordinary editable Hyle source. The third coordinate is fixed at zero; this is a two-dimensional cross-section, not a full three-dimensional electron apparatus.

Watch the experiment

Open the simulation from Atlas in Studio. Use CPU-64 as the numerical reference, or GPU-32 on a supported device. Run about 800 ticks to collect most of the transmitted packet; the first visible splitting happens much earlier. A CPU run can take several minutes. Use the timeline to compare stages or restore the initial packet by recompiling the saved source and world recipe. The full run can exceed the 512 MiB timeline budget, so preserve useful stages with bake downloads and fork from a frame when you need a fresh session to continue.

• Cyan: probability density, proportional to real² + imag². Brighter cells have larger probability; the color scale saturates for visibility.
• Grey barrier: an ideal reflecting wall, with two openings.
• Amber strip: an absorbing detector. Its exposure accumulates as probability reaches it; bright and dark fringes form across its height.

Rotate toward a top view for the clearest picture. This is already a single layer; cutting along Z can hide the entire experiment. Select a cell to inspect real, imag, received and sink. The detector becomes amber as exposure accumulates.

The detector displays expected probability, not individual random electron hits. Sampling discrete outcomes and modeling which-path measurement are separate features; looking at the viewport does not change the physics.

What Hyle is calculating

Two Float fields represent the complex wavefunction. Neighbor reads and nine ordered phases approximate the time-dependent Schrödinger equation. Alternating pairs exchange complex amplitude through unitary rotations, in a symmetric Suzuki–Trotter sequence. This is a real-space finite-difference method; interference emerges from amplitude propagation rather than a painted fringe formula. See the solver method.

The units set ℏ = m = Δx = 1, with Δt = 0.4. The initial packet has mean momentum 0.55 and is normalized to total probability one. Slits are 8 cells wide, separated by 28 cells, in a two-cell-thick ideal wall. A gradually absorbing detector starts 96 cells after the barrier. Other outer edges also absorb to reduce reflections.

received accounts for detector absorption and sink for other losses. Summing real² + imag² + received + sink over the whole lattice should remain approximately one. The constant kinetic-energy diagonal is omitted: it changes only a global phase, not the density or measured fringes. Compiler interval guards at ±2 are inactive for the normalized packet and are not a stabilization technique.

Accuracy and limits

The reference checks cover probability accounting, a completely closed barrier, both individual slits, comparison with exact evolution on a small lattice, and timestep refinement. Halving the timestep reduces the exact-Hamiltonian error by roughly four, as expected for a second-order scheme. The full GPU-32 validation is separate from CPU-64; matching float widths never guarantees identical devices.

This is an idealized quantum model. It omits electron spin, interactions between electrons, material-scale scattering, realistic detector electronics and which-path dephasing. Absorbing boundaries approximate an open domain. Finite lattice spacing also introduces dispersion. In the recorded checks, halving the timestep changed integrated detector probability by about 0.0022 in absolute L1 distance; halving cell spacing changed it by about 0.0085. Total incident probability is one. These are resolution-sensitivity measurements, not certified error bounds, so this example is not a calibrated laboratory prediction.

Painting empty-default Wave cells does not inject another normalized electron and can invalidate the geometry’s parity information. For controlled variants, change the fixture geometry and regenerate its initial state. Ordinary edits remain useful for exploring, but the validation claims apply to the published starting state.