QUANTUM EVIDENCE / MAGNETIC LIGHT

Zeeman Polarization Spectrometer

Observe a spin-zero atomic line across a magnetic field and along it. Rotate the analyzer, collect spectral counts and infer the field from the surviving components.

An ideal normal Zeeman triplet inspired by the red cadmium singlet. Equal upper populations, a Gaussian spectral selector and an ideal linear analyzer are assumed. No anomalous Zeeman structure, isotope shifts, self-absorption or Fabry–Pérot ring reconstruction is included.

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: whole-line monitor. Exposure time controls Poisson noise; scan playback is accelerated.

Ready. Predict, then acquire.

Recorded points

0

Outer-line separation · source

0

Single-side shift per field

0

ACQUIRED SPECTRUM / COUNTS PER SECOND

Which structure survives measurement?

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

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 field magnitude

\text{—}

Inferred source rate

\text{—}

Deviance per degree

\text{—}

Zero-field alternative

\text{—}

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

Gold: signal residuals. Blue: reference residuals. Known width, viewing angle, analyzer or stationary fraction, and background; unknown source rate and target field or energy. 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.

#	$\Delta\nu/\mathrm{GHz}$	Signal	Whole-line monitor	$\tau/\mathrm{s}$

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

The spin-zero orbital model groups nine allowed singlet transitions into three frequencies. The upper magnetic sublevels have equal populations. A linear analyzer transmits the projection of each dipole radiation pattern; transverse parallel selection leaves only the field-insensitive central line. Along the field, the central component vanishes and rotating a linear analyzer leaves equal outer components. Circular handedness is not measured here.

Physical field is scene up. A lamp sits in the gap of two bored pole pieces; the optical arm collects either across the gap or through their axial aperture. Analyzer bars rotate in the same plane used by the response. The incoming ray reaches the upstream counter face. Gaps, source, apertures and supports are schematic and enlarged.

The scan uses an ideal calibrated Gaussian spectral selector followed by a photon counter, not a simulated Fabry–Pérot image. Each channel integrates 0.875 GHz. A separate whole-line reference bypasses the spectral selector after the same analyzer. The source rate means total post-analyzer collected flux; throughput and background are assumed calibrated.

The line is inspired by the approximately 643.8 nm cadmium singlet, but no absolute wavelength or isotope centroid is inferred. Linear orbital Zeeman shifts alone are retained. No spin, isotope structure, finite angular acceptance, lamp kinetics, self-absorption or magnetic calibration uncertainty is included. The normal triplet also has a classical oscillator explanation; observing this ideal pattern alone does not establish electron spin.

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.

Basel / PHYWE · normal Zeeman apparatus NIST · CODATA constants

Start with the essentials

Focus question: One line. Three frequencies. Two directions.
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

Normal orbital shifts

\Delta\nu_q=q\,\frac{\mu_{\mathrm B}B}{h},\qquad q\in\{-1,0,1\}

The two outer components move oppositely. The field magnitude, rather than its sign, is estimated; a linear analyzer does not resolve helicity.

Project the dipoles

w_0=\sin^2\theta\cos^2\alpha,\quad w_{\pm}=\frac{\cos^2\theta\cos^2\alpha+\sin^2\alpha}{2},\quad\sum_q w_q=1

Viewing angle is from the field; analyzer angle is from its transverse projection. At longitudinal incidence, use the fixed lab transverse reference.

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
Resolve and count
Scan the transverse triplet, then save the run.
What to observe: Three source peaks become noisy channel counts and a fitted field.
02
Remove the information
Choose only the central line and scan again.
What to observe: Counts remain, but all field sensitivity is removed. No field estimate is reported.
03
Look down the field
Switch to the longitudinal view and rotate the analyzer.
What to observe: The central line is absent. The two outer weights stay equal.