SCIENTIFIC · the measured world · matter, taken apart · kept by THE LABORATORY

THE DE BROGLIE WAVELENGTH ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

Every moving object — an electron, a baseball, you — has a wavelength, λ = h / (mass × speed). For a baseball it’s absurdly tiny and you never notice; for a slow electron it’s atom-sized, which is why electrons DIFFRACT and electron microscopes work. A length that falls out of momentum. Slide the speed and watch the wavelength swing.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ MATTER WAVES · 3D · every moving thing has one
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
speed
momentum
λ = h/p
vs atom

◆ LIT — exact / checkable

The de Broglie wavelength λ = h/p = h/(mv) assigns a wave to any particle of momentum p. Faster (or heavier) means shorter wavelength; it is why a slow electron (λ ~ 10⁻⁹–10⁻¹⁰ m) diffracts off a crystal like light off a grating, while a baseball’s λ (~10⁻³⁴ m) is unobservable. De Broglie’s 1924 hypothesis, confirmed by Davisson–Germer. A fail-loud self-check throws unless an electron at ~10⁶ m/s yields λ of order 10⁻⁹–10⁻¹⁰ m. ◆ real physics, node-verified.

▲ AMBER — the figure

Non-relativistic λ=h/mv is exact in that regime; near light-speed the relativistic momentum is needed. The wavelength is real (it diffracts); picturing a localized particle AS a spread wave is the usual interpretive caution.

SCIENTIFIC: a law is a guess that survived every test we could throw.  — THE LABORATORY
David Lee Wise / ROOT0 / TriPod LLC  ·  the laboratory, with AVAN