Wien's Displacement Law
There is a temperature in everything. Not the clumsy kind you measure with a thermometer pressed against skin — that's a contact, a corruption, a thing that changes the thing it touches. No. The true temperature is the one that speaks through light. A warm cup of coffee glows in the infrared. A forge glows orange. The sun, indifferent to your skin's discomfort, burns white-hot. And there is a law that connects the warmth of a thing to the color of its light. Wien's displacement law.
Wien discovered it in 1893, a year before Planck would arrive at the deeper truth, but with a result so clean it felt like something the universe had been whispering all along. The law says, simply, that the wavelength at which a black body radiates most intensely is inversely proportional to its temperature. Hotter things emit their peak radiation at shorter wavelengths. Colder things push their peak toward the red, then the infrared, then somewhere beyond human sight.
The formula is elegant because elegance is how nature announces itself to those who are paying attention:
$$\lambda_{\text{peak}} = \frac{b}{T}$$
where $T$ is the absolute temperature in kelvin, and $b$ is Wien's displacement constant, approximately $2.898 \times 10^{-3}$ meter-kelvin. That's it. That's the whole law. Put a temperature in, and the peak wavelength falls out.
A human body at roughly 310 kelvin — 37 degrees Celsius, body temperature — has a peak emission at about 9.35 micrometers. That's deep infrared. You are, at every moment, glowing like a ghost in the thermal spectrum. To another human, you are invisible. To a thermal camera, you blaze. A star's surface at 5,800 kelvin — the sun — peaks at about 500 nanometers, right in the green part of the visible spectrum. (The sun appears yellowish-white to us because it emits broadly across the visible range, not just at its peak. But green is where it concentrates.)
The law has practical weight. Infrared thermometers — those wand-like devices pointed at a forehead or a circuit board — rely on Wien's law to translate measured infrared emission into a temperature reading. Astronomers use it to classify stars by color, which maps to surface temperature, which maps to mass and lifespan. Engineers designing thermal imaging systems calibrate their sensors to the expected peak wavelengths of their targets.
But the deeper significance of Wien's displacement law is philosophical. It tells us that heat and light are the same substance. Temperature is not an abstract property; it is a frequency. A warm rock and a blue star are communicating the same truth in the same language — the language of electromagnetic radiation. The only difference between a candle flame and the surface of the sun is how loudly each sings.
The law breaks down only when you try to force it beyond its domain. At extremely high temperatures, quantum effects dominate and the classical approximation embedded in Wien's original derivation gives way to Planck's full spectrum. But for everyday temperatures — from the surface of a frying pan to the heart of a star — Wien's law is a reliable compass.
Trolla's note: When you look at a sunset and see red, you are watching Wien's law in action. The sun's light, having traveled through more atmosphere at low angles, loses its short-wavelength blues to scattering. What reaches your eye is the long-wavelength red end. The temperature of the sun hasn't changed. The atmosphere has simply filtered its voice.