QUANTUM EVIDENCE / MISSING ATOMS

Lamb Shift Microwave Bench

Drive a beam of metastable hydrogen toward a short-lived state. Record the loss of surviving atoms, compare microwave-off counts and locate an effective Lamb resonance.

A weak-drive, single-resonance rate model with a rounded reference center. Hyperfine and Zeeman components, coherent transients, velocity distributions and QED corrections are omitted. The center is an input, not a first-principles QED calculation or historical data.

Schematic geometry · enlarged gaps and components · colors and moving markers do not represent visible light or measured trajectories. Drag to orbit.

EXPOSURE / TWO INDEPENDENT COUNTS

Give the spectrum a record.

Each coordinate has a signal exposure and a separate reference: microwaves off. Exposure time controls Poisson noise; scan playback is accelerated.

Ready. Predict, then acquire.

Recorded points

0

Metastable survival · model

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Effective energy gap · source

0

ACQUIRED SPECTRUM / COUNTS PER SECOND

Which structure survives measurement?

$\nu/\mathrm{MHz}$ · $N_i/\tau_i\;(\mathrm{s^{-1}})$

Teal: source expectation. Gold: acquired rates with fitted Poisson standard deviations, once a fit exists. Purple dashes: inference from records. Gray dots: saved run. Background is included.

Click or drag to move the probe; its slider supports keyboard input. The vertical scale follows the data.

INFERENCE / JOINT POISSON LIKELIHOOD

Estimate from both exposures.

Inferred center

\text{—}

Inferred source rate

\text{—}

Deviance per degree

\text{—}

Flat alternative

\text{—}

$r_i=(N_i-\widehat\mu_i)/\sqrt{\widehat\mu_i}$

Gold: signal residuals. Blue: reference residuals. Known response, splitting/width controls and background; unknown source rate and spectral parameter. At least sixteen distinct probe positions are required. Descriptive residuals and deviance do not establish identifiability, confidence intervals or discovery significance.

Keep the original counts.

Save a full or partial run with settings and seed in this page session.

#	$\nu/\mathrm{MHz}$	Signal	Microwaves off	$\tau/\mathrm{s}$

Latest six points shown. CSV includes all raw counts, exposures, settings, units and seed. Changing the probe never changes acquired records.

Scientific scope, geometry & primary sources

Prepared metastable hydrogen travels from the source through a microwave interaction gap without static fields to a metal collector. Only surviving metastable atoms contribute to the signal. Atoms transferred to the short-lived state radiatively decay before collection; the collector is not a photon detector.

An effective isolated transition uses a rounded 1057.8 MHz reference center and a 100 MHz natural full width. The source-center control also represents a hypothetical frequency offset. Weak-drive adiabatic elimination gives exponential loss during the selected interaction time. The largest drive is four percent of the decay width; the shortest interaction is much longer than the short-lived-state lifetime.

Hyperfine and Zeeman structure, velocity distributions, coherent transients, stray-field quenching and collector calibration are omitted. The reference exposure switches microwaves off. This is not a reconstruction of the historical magnetic-field experiment or a calculation of radiative corrections. Fitting the supplied resonance cannot independently verify QED.

Independent Poisson exposures, fixed calibrated background and stable source. No drift, dead time or calibration uncertainty. The source follows the displayed model; successful recovery validates the simulator, not the historical discovery.

Lamb & Retherford · 1947 Lamb & Retherford · 1950 Washington · optical comparison

Start with the essentials

Focus question: Tune the microwaves. Count who survives.
One-sentence intuition: Keep the signal and reference counts. Fit their joint Poisson likelihood while estimating the source rate from the same records.

Core mathematical model

Rapid decay, slow depletion

R(\nu)=\frac{\Omega^2\Gamma}{\Gamma^2+4[2\pi(\nu-\nu_0)]^2},\qquad \Gamma=2\pi\,(100\,\mathrm{MHz})

Rabi frequency and decay rate in this equation are angular quantities. The displayed frequency controls are ordinary frequencies.

Survivors are the signal

g(\nu)=e^{-R(\nu)t},\qquad \Delta E=h\nu_0

Weak-drive elimination assumes a rapidly decaying destination and an interaction long compared with its lifetime. The metal collector counts metastable survivors.

Two independent exposures

N_i\sim\operatorname{Poisson}\!\left[\tau_i(Sg_i+b)\right],\qquad M_i\sim\operatorname{Poisson}\!\left[\tau_i(S+b)\right]

Background is independently known. Source rate and the spectral parameter are jointly inferred; reference uncertainty is included. Counts are never Gaussian-rounded.

Common difficulties

Recovery is not discovery

Typical misconceptionA good fit independently confirms the law used by the simulator.

Better mental modelThe source response is supplied. Parameter recovery validates this synthetic measurement loop. Descriptive deviance and residuals are not confidence intervals, significance tests or external scientific certification.

Run the experiment

01
Find a dip
Scan the microwave frequency and compare each signal exposure with its separate microwave-off exposure.
What to observe: A loss of collected metastable atoms marks the effective resonance. The instrument measures survival rather than direct microwave absorption.
02
Change the interaction
Save the default run. Extend the interaction time, scan again, and inspect the depth and wings.
What to observe: Exponential depletion changes the spectral shape. The inverse problem uses that response, rather than fitting an arbitrary Lorentzian dip.
03
Turn the microwaves off
Use the zero-drive preset, scan, then restore the saved records and export the CSV.
What to observe: Without coupling there is no resonance information. The estimated center is withheld even if random counts form an accidental dip.