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Sandbox Physics

QUANTUM EVIDENCE / MOVING EMITTERS

Canal-Ray Doppler Spectrometer

Collect hydrogen light behind a perforated cathode. Swing the receiving arm from forward to backward, record the shifted and stationary components and estimate the kinetic energy of the moving atoms.

Interactive modelCanal-Ray Doppler Spectrometer

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

00

Moving-line shift · source

00

Atom speed · source

00

ACQUIRED SPECTRUM / COUNTS PER SECOND

Which structure survives measurement?

Δν/THz\Delta\nu/\mathrm{THz} · Ni/τi  (s−1)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 atom kinetic energy

—\text{—}

Inferred source rate

—\text{—}

Deviance per degree

—\text{—}

Stationary-only alternative

—\text{—}

ri=(Ni−μ^i)/μ^ir_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.

#Δν/THz\Delta\nu/\mathrm{THz}SignalWhole-line monitorτ/s\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

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 perforated cathode show how positive precursors feed a downstream emitting beam. The optical emission model is neutral hydrogen, not a bare proton spectrum. The input is the neutral atom kinetic energy, not a measured discharge voltage. Neutralization and excitation are only indicated, with no collision, charge-exchange or precursor mass-to-charge inference.

A rounded 486.3 nm vacuum wavelength represents an isolated Balmer-like transition, not an isotope or fine-structure centroid. The hydrogen mass is the proton-plus-electron mass with binding mass neglected. The moving line uses exact relativistic Doppler kinematics at the laboratory collection angle. An independent stationary component has a selected fraction of the photons collected in this arm, not a solved discharge population. Beaming and angular throughput are absorbed into that chosen fraction and 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.

Physics tutorial

Canal-Ray Doppler Spectrometer

BackgroundCollect hydrogen light behind a perforated cathode. Swing the receiving arm from forward to backward, record the shifted and stationary components and estimate the kinetic energy of the moving atoms.

Why it mattersA line becomes evidence only through a measurement and a stated response model.

Start with the essentials

Focus question
Follow the atoms. Watch the line move.
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

Energy fixes the speed

γ=1+KmHc2,β=1−γ−2\gamma=1+\frac{K}{m_{\mathrm H}c^2},\qquad\beta=\sqrt{1-\gamma^{-2}}

The controlled kinetic energy belongs to the moving neutral emitter. It is not a reconstruction of the discharge potential.

Use the laboratory angle

ν=ν0γ(1−βcos⁡θ),Δν=ν−ν0\nu=\frac{\nu_0}{\gamma(1-\beta\cos\theta)},\qquad\Delta\nu=\nu-\nu_0

Angle is between atom velocity and the outgoing photon in the laboratory frame. A right-angle view retains the small transverse red shift.

Separate moving and stationary light

gi=f0Gi(0,w)+(1−f0)Gi(Δν,w)g_i=f_0 G_i(0,w)+(1-f_0)G_i(\Delta\nu,w)

The stationary fraction is independently known in this inverse problem. Both components are integrated over each calibrated channel.

Two independent exposures

Ni∼Poisson⁡ ⁣[τi(Sgi+b)],Mi∼Poisson⁡ ⁣[τi(S+b)]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

  1. 01

    Acquire a forward spectrum

    Scan, save the counts and inspect the fitted energy.

    What to observe: A fixed component and a shifted component share the recorded spectrum.
  2. 02

    Move the receiver

    Choose the backward view and acquire a new spectrum.

    What to observe: The shifted component crosses to the negative-frequency side; atom velocity still points forward.
  3. 03

    Ask what can be inferred

    Compare transverse collection and the no-moving-emitter preset.

    What to observe: Transverse resolution is weak. With no moving photons the energy is unidentifiable and no estimate is reported.
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