Interfera: Path Unchosen / Quantum Interference
Quantum Foundations arc, page 6 of 193. Back to The Pixelated Physics Universe
Who they are
Send particles through two paths, one at a time, and stripes still appear. Quantum interference: probability amplitudes add or cancel, so even single particles build wave patterns. Interfera wears it in pixel art on a unisex tee.
Interfera is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
When a particle can reach the screen by two paths, you add the amplitudes before squaring them, and the cross term creates bright and dark fringes. The fringe spacing is set by the particle's de Broglie wavelength, even when particles arrive one at a time.
$$ \begin{gathered} P = \lvert\psi_1 + \psi_2\rvert^{2} = \lvert\psi_1\rvert^{2} + \lvert\psi_2\rvert^{2} + 2\,\mathrm{Re}\!\left(\psi_1^{*}\psi_2\right) \\ \Delta y = \frac{\lambda L}{d}, \qquad \lambda = \frac{h}{p} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\psi_1, \psi_2$ | amplitudes for the two paths (unit for a 1-D wavefunction; dimensionless if normalized over discrete outcomes) | m^{-1/2} |
| $P$ | detection probability density | m⁻¹ |
| $\Delta y$ | fringe spacing | m |
| $\lambda$ | de Broglie wavelength | m |
| $L$ | slit-to-screen distance | m |
| $d$ | slit separation | m |
| $h$ | Planck constant | J·s |
| $p$ | momentum | kg·m/s |
Sources
- Feynman Lectures on Physics Vol. III Ch. 1: Quantum Behavior
- Merli, Missiroli, Pozzi (1976) On the statistical aspect of electron interference phenomena, Am. J. Phys. 44, 306
- Tonomura et al. (1989) Demonstration of single-electron buildup of an interference pattern, Am. J. Phys. 57, 117
- Encyclopaedia Britannica — Interference
Crossovers
Interfera meets Decoherex (Interference / Quantum Decoherence). Interfera sends each particle down both paths, and the stripes build up. Decoherex only has to leave a record of which path was taken, even in a stray photon, and the stripes wash out. Path information and interference cannot both be had in full.
Interfera meets Arago (Spot of Arago). Interfera's stripes come from probability amplitudes adding and cancelling. Arago's bright spot comes from light waves around a disc's edge adding in step. It is the same superposition, once for quantum amplitudes and once for classical light.
Wear the lore
- Interfera – The Path Unchosen / Quantum Interference Physics T-Shirt
- Related infographic poster: One Electron at a Time – Plate 037 Physics Poster
Concept keywords: Path Unchosen / Quantum Interference, Interfera, Quantum Foundations, physics lore, Pixelated Physics