Infinity and Beyond

10 July 2013

Blackbody radiation Brian Koberlein
Blackbody radiation

Objects around us come in a variety of colors. The reason for this is that most objects will absorb certain wavelengths of light, while other wavelengths reflect off the object. So if you are wearing a red shirt for example, the colors such as green and blue are absorbed by the shirt, but red reflects off the shirt, so you only see red.

Some objects appear white, and this is because they reflect most of the wavelengths in the visible spectrum. Because of the way our eyes work, when the different colors of light are mixed together it appears white to us, so when objects reflect all those colors we see it as white. Other objects appear black because they absorb all the wavelengths in the visible spectrum. Because the object doesn’t reflect much light, we see it as black.

Most of the black objects around us aren’t really that black. If you look at them closely you might see a bit of glossy reflection, or you can see it’s really more of a dark gray, or maybe it has just a hint of color to it. It’s hard to find objects that are really black. The closest example you might have experienced is candle soot (also known as lampblack or carbon black), which is a particularly dark black, but even this isn’t perfectly black.

Suppose then that you had a perfectly black object, meaning that all light striking it (at any wavelength) would be completely absorbed by the material. Absolutely no light would be reflected off the object’s surface. Such an object would be a perfect blackbody. Because a perfect blackbody absorbs all the light that strikes it, you might think it is similar to a black hole, but this is not the case. A black hole traps anything that enters it, but a blackbody simply doesn’t reflect any light. Any light produced within the blackbody is perfectly free to leave the object. A blackbody is not only a perfect absorber of light, it is also a perfect emitter of light.

This is an important distinction because it means a blackbody doesn’t have to appear black. If it is creating light within itself it will freely emit that light. So candle soot is a good approximation of a blackbody, but so is the Sun. It might seem odd to think of the Sun as a blackbody, but we know that objects give off light when they get hot. The filament in your toaster, for example, glows red when it is making toast. Likewise, the sun glows because it is very hot. This is why blackbody objects are studied. The light a blackbody emits is produced entirely within the object itself, so by studying light from a blackbody we can better understand how light is produced.

By the mid-1800s, studies by Gustav Kirchhoff and others had found that the light given off by any blackbody is a continuous spectrum. It is dim at the shortest wavelengths, brightens at longer wavelengths reaching some maximum brightness at a particular wavelength, then gradually growing dimmer at ever longer wavelengths. The overall brightness increases at higher temperatures. The wavelength at which the spectrum is brightest also depdends on temperature. It is shorter (more toward the blue) at higher temperatures. We see this effect when metal is heated, first glowing dim red, then brighter orange, then bright yellow-white as it is heated. By measuring the spectrum of a blackbody (or an approximate blackbody) we can determine its temperature. This is how we determine the temperatures of stars, for example.

In 1900 John Strutt (Lord Rayleigh) and James Jeans attempted to model the blackbody spectrum using Newton’s mechanics and Maxwell’s equations. In their model, the atoms of a blackbody were bound together like small masses connected by springs. (They did not actually think the atoms were connected by springs, simply that the atomic forces behaved in a similar way.) The atoms would then oscillate back and forth like little pendulums. As the atoms oscillated they would create electromagnetic waves. Of course some of the atoms would oscillate slowly, while others would oscillate quickly. This would produce the distribution of wavelengths seen in a blackbody spectrum.

While this model worked relatively well for longer wavelengths, it was problematic at shorter wavelengths. According to Newton, there was no limit to how quickly or slowly the atoms could oscillate. So some atoms should be able to oscillate extremely quickly, and thus produce a tremendous amount of electromagnetic waves at short wavelengths. As a result, the Rayleigh-Jeans model predicted that at shorter and shorter wavelengths the spectrum should get brighter and brighter. At the shortest wavelengths the brightness would be almost infinite. This disagreed completely with what was observed, and was known as the ultraviolet catastrophe (because ultraviolet light has a short wavelength). Once again, the physics of Newton and Maxwell disagreed with experimental observation.

But around the same time Max Planck had a different idea. Rather than assuming atoms could emit any amount of light energy, he proposed that atoms could only emit light energy in packets. The amount of energy in each packet increases at shorter wavelengths. At shorter and shorter wavelengths, the amount of energy a packet of light has gets bigger and bigger, making it more difficult for the atom to emit. As a result, at short wavelengths the atoms would rarely emit light. The result of this model is given in the equation below.

Here B the brightness of light at different frequencies, nu (the v-looking symbol) is the frequency of light, c is the speed of light, T is temperature of the blackbody, and k is a constant known as Boltzmann’s constant. The h in the equation is the constant that determines the size of the light’s energy packets. It is now known as Planck’s constant. Although this equation looks complicated, it describes the light emitted by a blackbody perfectly.

While objects like stars are approximate blackbodies, we know of one physical object that is an almost perfect blackbody. We call it the universe. This fact was first discovered in 1964 when the Arno Penzias and Robert Wilson discovered the entire sky emitted a faint radio noise. When this cosmic background signal was analyzed it was found to have the spectrum of a blackbody with a temperature of just under 3 Kelvin. It is the temperature remnant of the big bang.

Planck’s equation gave us an understanding of the age of the universe. The blackbody spectrum of the cosmic background is one of the clues that tells us the universe is 13.77 billion years old. But the constant Planck introduced does more than solve the ultraviolet catastrophe. It is a constant that tells us about the scale of quantum mechanics. Planck’s constant is necessary to the understanding of the tiniest of particles. The most elementary particles and the entire universe are connected through this single constant.

It takes us to infinity and beyond.

Tomorrow: Einstein enters the game to prove beyond a shadow of doubt that light is made of particles. But it’s long been verified that light is a wave. What’s going on here? The plot thickens, next time.