Matter is a wave too. Every moving thing has a wavelength λ = h/p set purely by its momentum — inverse in p, so the harder you push it the shorter its wave. A baseball's wave is unmeasurably tiny; an electron's, at atomic momenta, is the size of an atom — which is exactly why electrons diffract off crystals, and exactly the standing wave that fits Bohr's orbits. Down the center: a momentum goes in, the engine returns λ, and the scale comes out. Blue builds it; red tries to break it.
source L. de Broglie, Recherches sur la théorie des quanta, doctoral thesis (Paris, 1924); pub. Ann. de Physique (10) 3, 22–128 (1925). No stable DOI — ADS 1925AnPh...10...22D AMBER. Rendered, not quoted.
The whole engine is one equation, applied three ways:
1 · matter wave λ = h/p. Momentum in, wavelength out. Double p → halve λ.
2 · accelerated electron a charge dropped through voltage V gains p = √(2 me e V), so λ = h/√(2 me e V) — the Davisson–Germer scale.
3 · photon same law, with p = E/c, giving λ = hc/E — light and matter obey one rule.
Live for the current object, the exponents that matter:
| quantity | value |
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De Broglie's leap answered Bohr's riddle. Bohr postulated that angular momentum is quantized; de Broglie derived it. If the electron is a wave, a stable orbit must close on itself — fit a whole number of wavelengths:
2π rn = n λn
The engine checks this to machine precision (window 7). That standing wave is the seed of the-schrodinger-equation, and the ring it closes is the-bohr-model. Each sphere is the next one's premise.
The blue team's live check: re-derive the inverse law, both scale regimes, the 54 V electron, the Bohr standing-wave fit, and the photon — against known values. If red tampers, this badge turns red.
Everything the engine needs is a single number: momentum p (kg·m/s). You can hand it p directly by choosing an object (mass × speed), or let the machine build it — from a voltage V for an electron, or from a photon's energy E.
Constants (SI, exact where defined): h = 6.62607015×10−34 J·s, c = 299792458 m/s, e = 1.602176634×10−19 C, me = 9.109×10−31 kg, α = 1/137.036.
λ = h/p. The dot on the plot is the current object; the line is the inverse law.
Change any control — every number is computed from λ = h/p on the spot, never looked up.
What the machine proves: λ is inverse in p (doubling p halves λ); a baseball lands near 10−34 m — below the nucleus, forever hidden — while an electron at atomic momenta lands near 10−10 m, the size of an atom. A 54 V electron gives ≈0.167 nm (Davisson–Germer, 1927), and the Bohr orbit fits a whole number of these waves.
The blue witness (left) confirms these live; the red team (right) tries to invert the law.
At relativistic speeds p ≠ mv; you need the relativistic momentum. The single-number λ here is the non-relativistic, monochromatic idealization — true as a scale, incomplete as a full state. The complete story is the wave equation.
"The de Broglie wavelength is the size of the particle." Cut. It is set by momentum, not size — a slow heavy object has a huge mass yet an infinitesimal λ.
"Only electrons show it." Cut. Neutrons, atoms, and molecules up to C60 and beyond diffract; the law is universal, just crushed to nothing for large p.
"λ grows when you speed a particle up." Cut — this is the tamper. Faster means larger p means shorter λ. Window 6 plants exactly this error; window 7 catches it.
The red team's move: flip the law to λ = h·p (product, not quotient), so faster particles wrongly get longer waves. The blue witness (window 7) is watching.
Flip quotient to product and the inverse-in-p check fails: doubling p now doubles λ instead of halving it. The witness recomputes, disagrees with the known scales, and turns red. Nothing is faked; the attack is real and it is caught.