QUANTUM EVIDENCE / THERMAL RADIATION

Blackbody Radiation Observatory

Send thermal radiation through a scanning monochromator. Record open and dark readings, fit temperature and emissivity from the collected spectrum, and see where classical equipartition fails.

A gray, isothermal source and an ideal power detector. Simulated readings include finite spectral bandwidth and independent Gaussian read noise. This is a teaching instrument, not historical data or a calibrated reproduction of a NIST facility.

Schematic cutaway · enlarged aperture and slit · amber paths include invisible infrared. Drag to orbit.

ACQUIRE / NOT JUST A CURVE

Build the spectrum, one reading at a time.

Each point records an open exposure and an independent shuttered dark exposure. Playback is accelerated; integration time controls noise.

Ready. Predict the peak, then scan.

Recorded points

0

Wavelength peak · model

0

Probe power · model

0

Total exitance · model

0

SPECTRUM / LOG WAVELENGTH

Does the shape agree?

$\lambda/\mathrm{\mu m}$ · $\overline L_\lambda/(\mathrm{W\,m^{-2}\,sr^{-1}\,\mu m^{-1}})$

Teal: Planck source reference through the passband. Gold: dark-subtracted records, one standard uncertainty. Purple dashes: selected fit. Gray: saved run. Negative records are kept.

Click or drag the spectrum to move the probe; the wavelength slider also supports keyboard input. The vertical scale follows the curves.

INFERENCE / FROM THE RECORDS

Candidate law

Fitted temperature

\text{—}

Fitted emissivity / classical product

\text{—}

Reduced chi-squared

\text{—}

$r_i=(P_i^{\mathrm{net}}-P_i^{\mathrm{fit}})/u_i$

Fits integrate the same passband. Planck and Wien fit temperature and gray emissivity; the classical fit identifies only their product. No confidence interval or discovery significance is claimed.

Keep a comparison

Save one complete or partial run with its settings and raw readings.

#	$\lambda/\mathrm{\mu m}$	Open $/\mathrm{nW}$	Dark $/\mathrm{nW}$	Net $/\mathrm{nW}$

Latest six readings shown; CSV includes every reading, uncertainty, source setting, passband and seed. Save and restore work in this page session.

Scientific scope & primary sources

Uniform gray radiance; zero incident background, ideal shutter and known constant throughput. No atmospheric bands, stray light, wavelength-dependent emissivity, photon bunching, shot noise, saturation or thermal transients. Independent additive Gaussian read noise is the only detector noise. The 0.5–12 micrometre range is an ideal broadband instrument, not the stated range of FASCAL. Cavity glow and moving markers are presentation, not calibrated color or photon trajectories.

The source uses Planck’s law. Recovering it from these synthetic readings tests the simulator; it does not provide independent evidence for quantization. Absolute detector response is assumed known independently. A response calibrated by assuming Planck’s law cannot independently test that same law.

NIST · FASCAL NIST · Planck and radiometry CODATA · constants

Read the quantum evidence collection

Start with the essentials

Focus question: Which parts of the spectrum distinguish the three laws?
One-sentence intuition: Fit every candidate to the same acquired powers through the same passband. A good short-wave approximation can fail on the long-wave side.

Core mathematical model

Radiance per wavelength

B_\lambda(T)=\frac{2hc^2}{\lambda^5}\frac{1}{\exp(hc/\lambda k_{\mathrm B}T)-1}

Vacuum wavelength in metres, temperature in kelvin. Radiance is per area, solid angle and wavelength; it is not radiant exitance.

What reaches the detector

P_i=G\varepsilon\int_{\lambda_i-\Delta\lambda_i/2}^{\lambda_i+\Delta\lambda_i/2}B_\lambda(T)\,\mathrm d\lambda,\quad G=10^{-10}\,\mathrm{m^2\,sr}

A top-hat passband with independently known, constant throughput. The source fills the accepted field. The detector measures band-integrated power.

Two useful limits

B_\lambda^{\mathrm W}=\frac{2hc^2}{\lambda^5}e^{-hc/\lambda k_{\mathrm B}T},\qquad B_\lambda^{\mathrm{RJ}}=\frac{2ck_{\mathrm B}T}{\lambda^4}

Wien describes the short-wave limit. Rayleigh–Jeans describes the long-wave limit, where temperature and gray emissivity enter only as their product.

Peak and total power are different tests

\lambda_{\mathrm{peak}}T=2897.771955\,\mathrm{\mu m\,K},\qquad M=\varepsilon\sigma T^4

The peak refers to radiance per wavelength. Total exitance integrates all wavelengths and the outward hemisphere. Both readouts here are model references, not estimates from a finite scan.

Common difficulties

A simulation is not an independent discovery

Typical misconceptionA good Planck fit proves that the real world follows this law.

Better mental modelThese are synthetic observations generated from Planck radiation. Real evidence needs independently calibrated response, historical or new observations, systematic uncertainties and competing explanations.

Run the experiment

01
Predict the peak
Scan the default cavity, save the sample, then choose the hotter source and scan again.
What to observe: The peak moves to shorter wavelengths while brightness rises. A gray emissivity changes amplitude, not the ideal peak position.
02
Challenge an approximation
Compare the short-wave preset with the full scan. Switch the fitted law and inspect standardized residuals.
What to observe: Every fit uses the recorded net power. The classical law cannot uniquely infer temperature when emissivity is unknown.
03
Audit the instrument
Widen the passband, lower integration time, and export the open and dark records. Restore a saved run.
What to observe: The fit integrates the finite passband. Shorter integration raises noise; subtracting two readings adds their variances. Negative noisy powers are retained.