The Rydberg Constant — read off starlight

spectral plate · light

1/n² plot · number

Measure the Rydberg constant from noisy starlight. A blind line-fitter that knows zero atomic physics reads R off four smudged hydrogen lines — plot 1/λ against u=1/n² and the Balmer law is a straight line, slope −R, intercept R/4. It names the constant twice, and the two must agree.

Noise σ — smudge the starlight

noiseFrac0.000

Drags each plate line off its vacuum-truth ghost, scatters the dots, fattens the t·SE band, drops R² below 1, and separates the two R-markers. At σ=0 the band is a hairline (R²=1 is geometry, not a measurement).

The draw — reproducible seed

◀

seed 1

▶

🎲

copy state

The loss — best is a choice

L2 · Σr²

L1 · Σ|r|

Click a plate line to yank it (an outlier blunder). Recommended: interior Hγ (n=5). At ×1.20 L2 lurches while robust L1 holds — L2 chases the blunder; L1 ignores it and reads R right.

The medium — mind your vacuum

vacuum

air

The band — ±t·SE (n=4 ⇒ 2 d.o.f.)

68% · t=1.32

95% · t=4.30

With only four points and two fitted params there are 2 degrees of freedom — Student-t, not normal. A naive ±1·SE band covers just ~57.5%; the t-band is the honest one.

The constant, twice

R from −slope—

R from 4·intercept—

−0.5%

+0.5%

CODATA R_H (the spectroscope's own constant)—

recovered: R ± t·SE

At σ=0 these are the SAME number by algebra; under noise they are two INDEPENDENT estimates of it.

Legend

the fit line (slate) · slope −R

L1 / robust (dashed violet) — a choice

R · the recovered constant + the u=0 intercept (gilt)

±t·SE prediction band

↔ the cross

← The Spectroscope · the lines where these four wavelengths come from — 1/λ = R_H(¼ − 1/n²), computed from the Rydberg constant. Here we run that arrow backwards. ← The Plumbline · the fitter the blind least-squares core that reads R off these points — the same Σr² minimum that fits any noisy cloud. It knows no atomic physics.