The (Mostly) Quantum Physics Of Making Colors

A week or so ago, I got a question on Facebook that was relayed from one of the kids of a college friend, which I'll paraphrase as "What's the physics explanation of what gives objects their color?" It's a good question, but unfortunately there isn't a compact answer other than the weaselly-sounding "It's complicated..." Which makes it a decent basis for a blog post...

In order to start answering, though, it's important to be clear about what we mean when we talk about "the color" of something. When we talk about an object having a color in the normal sense (not the quantum chromodynamics sense, in which interacting quarks have "color," where "color" is just a placeholder word for a three-valued property), we're really talking about light, specifically the light that reaches our eyes from that object. Depending on the exact condition of the object, there are a bunch of different physics processes that can be involved, and probably are at some level; nearly all of these involve quantum mechanics.

1) The Wave Nature of Electrons: If the object in question is a smallish amount of diffuse vapor that's emitting its own light, the color we see is determined by quantum physics. Atoms are made up of negatively charged electrons bound to a positively charged nucleus, and the wave nature of these things picks out a unique set of special states having well-defined energy due to their interaction. When the electrons in an atom are excited to one of the higher-energy states (say by being heated in a fire, or excited in a plasma discharge like you find in a fluorescent light), they will eventually drop back down to lower energy states by spontaneously emitting photons of light whose frequency depends on the energy difference between the initial and final state.

Every element has a different number of electrons, and the interactions between those shift the allowed energy states around so that every element has a unique set of energy levels. This means that every element has a unique set of differences between levels, which means that every element has a unique set of "spectral lines," narrow ranges of frequency that it will emit. This collection of lines determines the color we see from a sample of that element, a fact that's been used to identify chemicals since the 1860's (roughly six decades before anybody understood the quantum physics that determines the spectral lines).

2) The Particle Nature of Light: If the object in question is a sufficiently big collection of atoms, and very hot, another essential quantum phenomenon comes into play, causing the object to emit colored light in a very different way. This produces a broad "black-body spectrum," emitting light over a huge range of frequencies.

Unlike the spectral lines of atoms, this black-body spectrum does not depend on the composition of the material, only its temperature— this is the characteristic red glow of a hot object, which is the same for all materials. A black iron rod and a clear glass one heated to the same temperature will emit the same spectrum of light.

The simple and universal nature of this problem suggests that it should have a simple and universal explanation, which was pursued by a lot of physicists in the late 1800's. In the end, the explanation found by Max Planck is simple and elegant, but it's not what 19th-century physicists were expecting: it comes from the particle nature of light, where a beam of light is a stream of photons, each carrying a discrete amount of energy determined by the frequency. So, if you're looking at the color of light from a toaster element or an incandescent bulb, you have the quantum nature of light to thank for it.

3) The Wave Nature of Electrons II: If the object of interest is made up of more than one kind of atom, but not hot enough to be emitting visible black-body radiation, you can see broad bands of color emitted that are associated not with individual atoms, but with multi-atom molecules, like the fluorescent proteins biologists use to label different parts of cells under a microscope. When you bring together multiple atoms, their electrons end up being shared between atoms, and there are lots of very similar ways to do that sharing, with very slightly different energies. This causes the extremely narrow energy states of atoms to broaden into collections of enormous numbers of very closely spaced states. This, in turn, leads to enormous numbers of very closely spaced spectral lines, which sort of smear together to look like continuous bands of color. As with atoms, each molecule has a unique collection of these, and will thus emit a unique set of colors.

4) The Wave Nature of Electrons IIa: If the object of interest isn't getting energy pumped into it in a way that causes it to emit light, the light we see is reflected instead. In that case, much of the color comes from the opposite process to that described above: the absorption of light taking electrons from low-energy states to high-energy ones.

As with the emission properties described above, the color you get this way ultimately depends on the quantum physics of the atoms and molecules making up the object, but in this case, the effect isn't to add light of a characteristic color, but to remove it. Light of a frequency that falls within the right range will be absorbed by the object, while the rest of the light gets reflected, so the color we see reflects the absence of the absorbed frequencies.

This is what's going on with most dyes and pigments, so the vast majority of the colors we see in everyday objects are due to this process.

5) The Wave Nature of Light: This is the one entry in the list that isn't really quantum. There are two ways of making color that don't depend on the quantum properties of atoms and molecules, but instead on the structure of the material making up the object on microscopic scale. Both rely on the fact that light waves from two nearby sources can add together in a way that reinforces the waves, or cancels them out.

The simplest case uses a structure consisting of lots of (nearly) overlapping flat sheets or scales. These reflect all colors of light in all directions, but for particular reflection angles, the distance traveled by the light from two neighboring surfaces on its way to your eye will be different by an exact multiple of a particular wavelength. In that case, those waves reinforce each other, and you see a bright reflection of that particular color from that particular spot on the surface. A different spot a short distance away will reflect light to your eyes at a slightly different angle, and thus you'll see a different color reflected. This leads to the shimmery color of an iridescent object, that shifts depending on the angle you're looking at.

There's also a non-iridescent version of a similar process, which is responsible for the blue colors in the feathers of many species of birds. In this case, the structure responsible is a complicated web of filaments spaced by an amount similar to the wavelength of blue light. Waves of that wavelength trying to pass through that material will cancel each other out, making a "band gap" that excludes those frequencies; since the incident light can't enter the material, it must be reflected, and that gives the characteristic color.

6) The Wave Nature of Electrons III: It's maybe a stretch to call "shiny" a color, but the final process related to the composition of a material object is that responsible for the broad reflection from many metals. This again has to do with the quantum nature of electrons, specifically what happens when you put vast numbers of them into a solid crystal.

The key process is similar to what I described above regarding molecules: the electrons are shared among all the atoms in the crystal, leading to an uncountably huge number of extremely closely spaced states that behave like a continuous band of energies. If the energy of the allowed bands in a material and the number of electrons in those bands break out in the right way, you end up with an electrical conductor, in which the electrons are effectively free to move through the material with very little resistance.

If you apply an electric field to a conductor, electrons that start out uniformly distributed through the crystal will very quickly re-arrange themselves in response to the field, until the new unequal distribution creates its own field that cancels out the field you're trying to apply. This works both for a static distribution like a charged object brought nearby, and also for an oscillating field like a light wave, which is why electrical conductors also tend to be shiny metals, reflecting light of a broad range of wavelengths.

Of course, "very little resistance" isn't no resistance, so there's a limit to how quickly the electrons in any real conductor can re-arrange themselves. This means that there's a maximum frequency of light for which any given conductor can stop light from entering; at higher frequencies, the electrons move too slowly, and the reflectivity drops because some of the light can, in fact, penetrate. Which is (part of) why different shiny metals have different colors: the maximum frequency for gold is a bit lower than than for silver, so gold is a better reflector for low-frequency red and yellow light than high-frequency blue light, making it appear yellowish. Silver reflects blue light about as well as red, so it doesn't have as much of a tint.

7) Messy Quantum Biology: The final determinant of the color we see does not depend on the object being seen, but the observer doing the seeing. The various processes described above determine the spectrum of the light coming to our eyes from a given object, but ultimately the "color" we see is a function of interpretation by our brain.

This process also has a quantum component, in that our eyes detect light using different molecular receptors that absorb characteristic ranges of wavelengths (one mostly-red, one mostly-yellow, one mostly-blue-green). Our brains take the signals from those three receptors and combine them to produce a single sensation of "color."

This system is kind of a hack, which leads to a few quirks that can be exploited to great effect. Since we process color based on the response of three different receptors, we can trick the eye into seeing a color that isn't there by using a mix of three other colors. Whatever device you're reading this on is using a display that produces light at three wavelengths corresponding to red, green, and blue, and cleverly mixing them in ways that convince your brain that you're seeing light of wavelengths that aren't actually there.

So, you can see that, as weaselly as it may sound, the only true answer to "What's the physics explanation of what gives objects their color?" is "It's complicated..."