Quantum evidence / Light from moving atoms

Canal-Ray Doppler Spectrometer

How does the light from fast-moving hydrogen atoms reveal their speed? Through its Doppler shift. Hydrogen atoms flying in a canal-ray beam emit light that is bluer when you watch them coming toward you and redder when you watch from behind. Atoms at rest leave an unshifted line in the original place. The size of the shift tells you how fast the moving atoms travel, and so their kinetic energy.

Collect hydrogen light from behind a perforated cathode. Swing the receiving arm from forward to backward, record the Doppler-shifted light and the unshifted light from atoms at rest, and estimate the kinetic energy of the moving atoms.

The source is a teaching beam of neutral hydrogen atoms that all share one energy, plus emitters at rest. The rest wavelength is a rounded vacuum value. The Doppler shift uses relativistic kinematics, and each line has a Gaussian response. Charge exchange, discharge fields, energy spreads and the historical photographic records are not reconstructed.

Schematic geometry with enlarged gaps and parts. The colors and moving markers do not show visible light or measured trajectories. Drag to orbit.

Exposure: signal and reference counted separately

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

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Moving-line shift · source

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Atom speed · source

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Measured spectrum in counts per second

Which structure survives measurement?

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

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 with a joint Poisson likelihood

Estimate from both exposures.

Inferred atom kinetic energy

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Inferred source rate

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Deviance per degree

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Stationary-only alternative

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

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 its settings and seed, for as long as this page stays open.

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

The latest six points are shown. The CSV has every raw count, exposure, setting and unit, plus the seed. Moving the probe never changes data already taken.

Scientific scope, geometry & primary sources

Atoms travel along scene positive x. The angle is measured in the laboratory between this velocity and the photon path to the counter. Forward observation shifts the moving line upward in frequency, backward observation downward. At a right angle the retained time-dilation shift is much smaller than the selected linewidth; a visually merged spectrum can give a weak or boundary estimate.

The discharge and the perforated cathode show how positive ions upstream feed the glowing beam downstream. The light is modeled as coming from neutral hydrogen, not from bare protons. The input is the kinetic energy of the neutral atoms, not a measured discharge voltage. Neutralization and excitation are only marked on the drawing; collisions, charge exchange and the mass-to-charge ratio of the ions are not modeled.

A rounded vacuum wavelength of 486.3 nm stands for one isolated Balmer-like transition; it is not an isotope or fine-structure centroid. The hydrogen mass is the proton mass plus the electron mass, with the binding mass neglected. The moving line uses exact relativistic Doppler kinematics at the laboratory collection angle. The stationary component is a separate line whose share of the photons collected in this arm you choose; it is not calculated from the discharge. Beaming and angular collection are folded into that share and into the source rate.

Both components have the selected Gaussian FWHM; there is no velocity distribution or angle acceptance integration. Each spectral channel integrates 0.15 THz. A whole-line reference bypasses the spectral selector along the same optical arm. The counter receives light; the atoms continue to a separate beam stop. The apparatus is schematic and does not reconstruct Stark’s historical tube, plates, data or interpretation of emitting charge states.

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.

Stark 1906 · original report preview UCSD · laboratory-angle Doppler derivation Nobel · 1919 contribution

Start with the essentials

Focus question: How does the light from fast-moving hydrogen atoms reveal their speed?
One-sentence intuition: Keep every signal and reference count. Fit them together with one Poisson likelihood, and estimate the source rate from those same counts.

Core mathematical model

Energy fixes the speed

\gamma=1+\frac{K}{m_{\mathrm H}c^2},\qquad\beta=\sqrt{1-\gamma^{-2}}

The kinetic energy you set is that of the moving neutral emitter. The Lab does not reconstruct the discharge potential.

Doppler shift at the laboratory angle

\nu=\frac{\nu_0}{\gamma(1-\beta\cos\theta)},\qquad\Delta\nu=\nu-\nu_0

The angle is measured in the laboratory frame, between the atom's velocity and the emitted photon. Even at a right angle, a small transverse red shift remains.

Moving and stationary light in each channel

g_i=f_0 G_i(0,w)+(1-f_0)G_i(\Delta\nu,w)

In this inversion, the fraction of light from atoms at rest is known independently. Both components are integrated over each calibrated channel.

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]

The background rate is known in advance. The source rate and the spectral parameter are fitted together, and the uncertainty of the reference counts is included. Counts are drawn as Poisson numbers, never rounded from a Gaussian.

Common difficulties

Recovering a parameter does not test the law

Typical misconceptionIf the fit is good, the law built into the simulator has been independently confirmed.

Better mental modelThe simulator is given the source response in advance. Recovering the parameter shows only that this simulated measurement and fit work correctly together. The deviance and residuals describe the fit; they are not confidence intervals, significance tests or outside scientific certification.

Run the experiment

01
Acquire a forward spectrum
Scan, save the counts and look at the fitted energy.
What to observe: The recorded spectrum contains both an unshifted component and a shifted one.
02
Move the receiver
Choose Atoms moving away to look from behind, and acquire a new spectrum.
What to observe: The shifted component moves to the negative-frequency side, even though the atoms still travel forward.
03
What can still be inferred?
Compare the Transverse view and No moving emitters presets.
What to observe: Viewed at right angles, the energy is only weakly resolved. With no light from moving atoms, the energy cannot be determined and no estimate is reported.

Canal-Ray Doppler Spectrometer

Give the spectrum a record.

Which structure survives measurement?

Estimate from both exposures.

Keep the original counts.