# Hydrogen Matrix Lab 0.5.0 — electromagnetic correction ladder

## Bounded question

The old fixed-proton Schrödinger clock missed the NIST Lyman-alpha centroid by about `-0.05325%`. Does that discrepancy require a new force, or is it mostly the result of standard electromagnetic structure omitted from the baseline?

The correction begins with terminology: the old model did **not** omit electromagnetism. Its Coulomb potential

\[
V(r)=-\frac{e^2}{4\pi\epsilon_0 r}
\]

is the nonrelativistic electromagnetic interaction. It omitted proton motion, relativistic spin structure, and precision radiative/nuclear corrections.

## Frozen ladder and real-data comparison

NIST lists the neutral-hydrogen levels `2p 2P°1/2 = 82258.9191 cm^-1` and `2p 2P°3/2 = 82259.2850 cm^-1`. Those correspond to `121.567364480 nm` and `121.566823733 nm`. Using the NIST strong-line intensity ratio 500:1000 gives the declared comparison centroid `121.567003982 nm`.

| Model | Physical content | Centroid (nm) | Error (ppm) |
|---|---|---:|---:|
| H0 | Fixed-proton Schrödinger Coulomb | 121.502273411 | -532.4683 |
| H1 | H0 plus electron-proton reduced mass | 121.568445617 | +11.8588 |
| H2 | Reduced-mass point-nucleus Dirac-Coulomb | 121.566602395 | -3.3034 |

Reduced mass alone removes `97.7729%` of H0's centroid absolute error. H2 removes `99.3796%`, predicts two distinct lines, and predicts a fine-structure wavelength split of `0.000539476 nm`, versus NIST's `0.000540747 nm` (`-0.2351%` relative split error).

This is a written mathematical model plus deterministic finite computation compared with critically compiled measured spectroscopy. It is not new measured evidence. An independent implementation using 50-digit Decimal arithmetic reproduced all six central wavelengths/centroids within `2e-8 nm`; all 35 unit tests passed.

## What the residual does and does not mean

H2 is not a complete precision calculation. It omits complete relativistic recoil, radiative self-energy and vacuum polarization (Lamb/QED corrections), finite proton charge radius, hyperfine structure, linewidth, and external-field effects. Therefore the remaining `-3.3034 ppm` centroid residual is first a budget for omitted standard physics. It does not identify a unique new force, a fourth spatial dimension, a string/rotor mechanism, or a theological cause.

The extra-dimensional proposal remains admissible only in a testable form,

\[
H_{\mathrm{candidate}}=H_{\mathrm{standard}}+\lambda\mathcal O_4,
\]

where the extra coordinate, field equation or action, operator units, coupling to charge/current, gauge or conservation law, parameter budget, and fresh falsifying observable are fixed before fitting. No `O_4` has yet been derived, so release 0.5 does not manufacture one from the residual.

## Next test

Add the complete standard precision ladder—recoil, Lamb/QED, finite-size, and hyperfine contributions—and validate it against multiple independently sourced hydrogen transitions, not only Lyman-alpha. Only then freeze one explicit higher-dimensional operator and test whether it predicts a state-dependent residual pattern that cannot be absorbed by the standard constants.

## Sources

- NIST, *Energy Levels of Neutral Hydrogen*: https://physics.nist.gov/PhysRefData/Handbook/Tables/hydrogentable5.htm
- NIST, *Strong Lines of Hydrogen*: https://physics.nist.gov/PhysRefData/Handbook/Tables/hydrogentable2.htm
- Mohr, Newell, Taylor, and Tiesinga, *CODATA Recommended Values of the Fundamental Physical Constants: 2022*: https://arxiv.org/abs/2409.03787