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Validating · emergence

Blackbody radiation · the birth of quanta

Why does a hot object glow the colour it does — and why did classical physics predict it should radiate infinite energy?

▶ Launch the interactive simulation

How the lab tests it

Plot the Planck spectral radiance B_λ(λ,T) = (2hc²/λ⁵)/(e^{hc/λk_BT}−1) for several temperatures, alongside the classical Rayleigh–Jeans curve. Then measure the laws directly: find each curve's peak wavelength numerically (Wien), integrate ∫B dλ across many temperatures and log–log fit the exponent (Stefan–Boltzmann), and compare classical vs quantum at short wavelength.

What it checks

Wien's displacement law λ_peak·T = 2898 µm·K (constant ⇒ hotter is bluer, recovered to machine precision); the Stefan–Boltzmann law P ∝ T⁴ (fitted exponent 4.000, with σ = 5.67×10⁻⁸ W m⁻²K⁻⁴ backed out); and the ultraviolet catastrophe — Rayleigh–Jeans over-predicts Planck by ~10¹¹× at 100 nm and diverges as λ→0, while Planck's quantization of energy (E=hν, so short-wavelength modes are too costly to excite) turns the curve over and keeps it finite. The 1900 result that forced energy to come in lumps and started quantum theory

This is one world in the PHS lab — 91 interactive simulations, each posing a question and measuring the answer. See the catalogued findings.