Why hot things glow

A poker left in a fire goes dull red, then orange, then white. Nothing is burning; the metal is simply warm, and warm matter shines. Working out why it shines with that spectrum began quantum theory.

What thermal radiation is

Every object warmer than absolute zero radiates light — at room temperature infrared, felt by skin but invisible to the eye. Heat it enough and it glows. In 1859 Kirchhoff argued that an ideal absorber — a black body, which swallows all incoming light — must emit a spectrum that depends only on its temperature, not its shape or material. The spectrum became a universal curve, its formula a set problem for physics.

Why it mattered

By 1900 the measurements were excellent and the theory in trouble. Classical physics shares a warm cavity's energy equally among all possible vibrations of the light inside it. Short wavelengths have far more vibrations than long, so equal shares pile energy toward the short end without limit: a warm oven should pour out unbounded ultraviolet. It does not. Ehrenfest later called this the ultraviolet catastrophe. The textbook story that Planck set out to fix it is not quite right — the classical formula was only published in full in 1905 — but the gap is genuine, shown below.

Planck's count

Planck modelled the cavity walls as oscillators: charged particles each vibrating at one frequency and trading energy with light at it. The spectrum then hangs on one number: an oscillator's average energy at temperature T.

He had guessed the right formula in October 1900 by fitting new long-wavelength data. To derive it he used Boltzmann's idea that entropy counts arrangements, so he had to count the ways a total energy can be shared among N oscillators. Counting requires pieces: infinitely divisible energy gives infinite arrangements. Planck cut energy into elements of size ε, counted, and got a finite formula.

It matched. But the element could not then shrink to zero — that limit gave back the wrong classical curve. Worse, an older thermodynamic result of Wien's required the average oscillator energy to depend only on the ratio of frequency to temperature, forcing the element to be proportional to frequency: ε = hν, with h a new constant. That is the crack: high-frequency oscillators need a big first element to start vibrating and at ordinary temperatures rarely get one. The short-wavelength end starves; the catastrophe never arrives.

Whether Planck himself believed energy was physically lumpy is still argued by historians; his writing is ambiguous. In 1905 Einstein took the lumps seriously: light itself comes in quanta.

What the colour tells you

Heating changes two things. Total power climbs as the fourth power of temperature. And the curve tilts: the short-wavelength side rises faster than the long. That tilt is the colour. A star at about 4000 K is orange because its spectrum falls sharply across the visible band, red to blue. A star at 30,000 K is blue-white for the opposite reason. Between them the curve is almost flat across the visible range, which is why the Sun, at about 5800 K, is white — despite the popular claim that its peak sits in the green. The peak is broad, its position depends on how you plot the curve, and your eye responds to the slope.

In one breath

Warm matter shines because its jiggling charges radiate, with a spectrum set only by temperature. Classical physics predicted unlimited ultraviolet. The real spectrum turns over because energy is exchanged in elements proportional to frequency, so high-frequency oscillators mostly stay quiet. Planck introduced that element to make a count finite; the rest of quantum theory followed from taking it literally.