Quantum evidence / Thermal radiation

Blackbody Radiation Observatory

Can one temperature and one emissivity explain the measured spectrum? In this simulated measurement, yes. Fit Planck's law with one temperature and one emissivity to the power measured in each wavelength band, and it reproduces the whole spectrum. Classical equipartition cannot: at best it follows the long-wave end, and it blows up toward short wavelengths.

Pass thermal radiation through a scanning monochromator and take an open and a dark reading at each wavelength. Fit the temperature and emissivity to the spectrum you collect, and see where classical equipartition fails.

The source is gray and isothermal, and the detector is an ideal power meter. The simulated readings include a finite spectral bandwidth and independent Gaussian read noise. This is a teaching instrument; it does not use historical data and is not a calibrated reproduction of a NIST facility.

Schematic cutaway with the aperture and slit enlarged. Amber paths also stand for invisible infrared. Drag to orbit.

Acquire readings, 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 on a log wavelength axis

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 only

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 each candidate law to the same measured powers through the same passband. A law that works well at short wavelengths can still fail at long ones.

Core mathematical model

Radiance per wavelength

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

Wavelength is the vacuum wavelength in metres and temperature is in kelvin. Radiance is power per unit area, solid angle and wavelength, which is different from 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}

The passband is a top hat, and its throughput is constant and known independently. The source fills the field the instrument accepts, and the detector measures the power integrated over the band.

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 is the peak of radiance per wavelength. Total exitance adds up all wavelengths and all directions in the outward hemisphere. Both values shown here come straight from the model; they are not estimated from the 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 observations are generated from Planck radiation. Real evidence needs an independently calibrated instrument response, historical or new observations, an account of systematic uncertainties and a comparison with 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 and the spectrum gets brighter. A gray emissivity changes the height of the curve but does not move the ideal peak.
02
Test an approximation
Compare the short-wave preset with the full scan. Switch the fitted law and look at the standardized residuals.
What to observe: Every fit uses only the recorded net power. With emissivity unknown, the classical law cannot pin down a unique temperature, because only their product enters.
03
Test the instrument settings
Widen the passband, shorten the integration time and export the open and dark records. Then restore a saved run.
What to observe: The fit integrates over the finite passband. A shorter integration time raises the noise, and subtracting the dark reading from the open one adds their variances. Net powers that noise pushes below zero are kept.

Blackbody Radiation Observatory

Build the spectrum, one reading at a time.

Does the shape agree?

Keep a comparison

Testing a radiation law with one spectrum

Core mathematical model

Radiance per wavelength

What reaches the detector

Two useful limits

Peak and total power are different tests

Common difficulties

A simulation is not an independent discovery

Run the experiment

Predict the peak

Test an approximation

Test the instrument settings

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