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Rutherford did say something like this but suggesting a barmaid instead of a six-year-old, while Hilbert suggested the first man on the street. Technically, if we assume the statement correct, then nobody has understood anything about science, ever. But I'd like to have my go at explaining Physics-y stuff as simply as I can, and, perhaps equally importantly, without too much of the "woaaah quantum mechanics is so weird, you just have to accept it like this even though it's completely non-intuitive" crap one often finds in science articles written for the laymen.

Monday, January 18, 2016

Let me teal you about the cyansce of color

If you were among the asocial few who actually listened to their Physics teacher, you'll probably know most of what follows. But maybe you were cool instead, and even if not, surely some of the details go beyond what you know. In any case, this is one more post (after this one) on the way of explaining what I did during my PhD. Enjoy.

What gives objects color?

Color, of course, has everything to do with light. Now, light is actually electromagnetic radiation, and as such propagates in waves, and every wave has an associated wavelength. Classically, this is the distance between two consecutive crests. Quantum mechanically, the wavelength also determines the smallest amount of energy that a beam of light can carry - namely, the energy of one light 'quantum', commonly called a photon. The higher the wavelength, the lower the photon energy. I’ll get back to this later on. Importantly, individual wavelengths, or photon energies, are also associated to various colors. Or, rather, the other way round - to every color, a particular wavelength can be associated, but not every wavelength has an associated color. This is simply due to the limitation of our perception - we cannot register all the wavelengths, and the concept of color is only associated to the ones we do. You should be familiar with some version of the following image, which illustrates the full range of possible wavelengths, and what we call the corresponding radiation:

"Electromagnetic-Spectrum" by Victor Blacus. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Electromagnetic-Spectrum.svg#/media/File:Electromagnetic-Spectrum.svg
As you can see, there is only a small range of wavelengths that we can see, namely the one marked as 'visible light'. Now, a beam of light of a fixed wavelength is called monochromatic light, and indeed it has a fixed color (if it is within the visible range). What is important to understand, however, is that light around us is virtually never of a single wavelength - instead, it has contributions of varying intensity at all possible wavelengths. The intensity of the light as a function of its wavelength is what is called the spectrum. Color is almost the same thing, but it requires in addition a brain to recognize the spectrum and give it the color-label. For color is certainly in the eye of the beholder, and the way two identical spectra are recognized differs among different animals, and even among different people. Here, I won't be discussing the human eye; instead, let's just assume a generic observer that registers equally well light of wavelengths from 400nm to 700nm, see image above (nm stands for nanometer, which is one billionth of a meter). Anything outside of this spectral range is, in our discussion here, irrelevant. In other words, the following two light sources appear to be of the same color to a human, since they have the exact same intensity vs. wavelength dependence in the spectral range that we register.
In short, the color of a beam of light is determined by the contributions of the various colors - or wavelengths - that make it up. In the example above, the intensity is the strongest in the blue region, and so we would probably register both of the spectra as blue-ish. However, in general, all the contributions mix up - proportionally to their intensity - to determine the final color. Much like in an artist’s palette, or in primary school art lessons.

Now, the range of wavelengths that our eyes detect is not at all arbitrary. This is what the spectrum associated to sunlight reaching the Earth looks like:
"Solar spectrum en" by Nick84. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Solar_spectrum_en.svg#/media/File:Solar_spectrum_en.svg
Our eyes have naturally evolved to detect light in the range in which there is the most of it! If it’s not clear why, I’d have to explain natural selection to you, and that’s well beyond this post. But sunlight brings me to the next point: so far we only discussed color in relation to the spectrum of a beam of light. With this in mind, the color of objects is naturally determined by the light coming from them. However, since most objects around us don’t emit light on their own - at least not in the visible range - color is implicitly also determined by the spectrum of the light illuminating them. In other words, if we were to illuminate any object with monochromatic blue light, it would appear either blue or black, or something in between - because no other hue can mix up in the spectrum. Thus, in a sense, we should call the 'true' color of an object the one we see after illumination with light of equal intensity at all wavelengths, otherwise known as white light. Sunlight is to a good approximation white light, see image above.

Finally, I come to the main point. What determines the color of an object once we fix the observer (an average human) and we fix the illumination (white light)? Both of these factors are important, but they are extrinsic to the object itself. There must also be some intrinsic property that gives an object its hue. Indeed, its physical and/or chemical structure determine its optical features, and more specifically - the absorption, reflection, and transmission properties. These are related to a wide variety of phenomena and can be incredibly complex to study and predict, but here we take them for granted for illustrative purposes. The important point is that there are several possible outcomes for light hitting an object, and the interplay between those determines its color. Namely, light can be transmitted, reflected, scattered, or absorbed, and normally all of those happen simultaneously - to a various extent.
It is in principle possible that the object itself emits some light, which adds to or even dominates its color. However, as mentioned earlier, the color of the vast majority of everyday stuff is determined by the four properties illustrated above, and not by emission. Actually, all objects around us, including ourselves, do emit electromagnetic radiation, but the intensity is peaked in the infra-red, making it invisible to us. The peak of the emission spectrum is determined by the temperature of the object. This is why incandescent light-bulbs, for example, in which the wire becomes much hotter than room temperature, do emit light at wavelengths that we see. But, again, we neglect emission in our discussion, and focus on illumination. Here are several basic examples of colors and how they arise from the interplay of transmission, reflection, scattering, and absorption. Black bodies absorb most of the incident light:

And white things scatter most of the light back.
Here, a distinction should be made between scattering and reflection. When the reflection dominates, the object is still technically white. However, we would be more prone to calling this object a mirror, because we'd be more used to seeing the exact same color of light that hits it. Still, if you think about looking at a mirror from far away when it's in the sunlight, it looks like a bright white object. The difference is that the reflected light is directional, and thus far stronger in the reflection direction than the scattered light, which goes everywhere. Have a look at this Vsauce video for further insight into the color of mirrors.
Finally, when there is mostly transmission, the object appears translucent because we see the light coming from behind rather than the illuminating light. 
To make matters more complex still, color depends on the interplay between these four phenomena not just in general, but at every wavelength within the visible range. Thus, for example, an object could be mostly absorbing at all wavelengths apart from blue light, which gets mostly scattered. Such an object would appear blue.
And, as for white objects above, if the blue light were mostly reflected rather than scattered, the color would be brighter, glossier blue, with some reflections of nearby objects appearing (in blue). Think car paint.

These qualitative consideration give a lot of intuition about color. So, while we are at it, why not answer the age-old mystery: why is the sky blue? In fact, it's not really - or rather, it can take on various colors, blue being just one of them. The first important note is that the sky is actually mostly translucent (assuming no clouds). When you look at the Sun, you see it (right?), and when you look back at Earth from space, you see it. Furthermore, the Sun looks white (technically kinda yellow-ish because the spectrum is not exactly white light), and around the Sun the sky looks white, too. It doesn't look blue, because we're mostly seeing the light coming directly from our star.
You can have a quick look to make sure that's the case, but, needless to say (I hope), please be careful with burning your retinas out.  
Apart from that, the sky is indeed blue when we look away from the Sun, at the light that is scattered by the constituent particles of our atmosphere. Now, it turns out that light of a given wavelength gets scattered stronger the lower the wavelength. This means that light in the blue-violet part of the spectrum gets scattered the most (in the visible range). And that's why we see a blue color when we look away from the Sun.
Of course, that's not the full story. We also all know that the sky appears red at sunset and sunrise. The explanation is pretty much the same, only now sunlight travels a long distance through the atmosphere. Since red is on the long-wavelength part of the spectrum, the red component of the light is the last to scatter out before reaching us. Thus, now, when looking directly at the sun, it appears red-ish, as does the region around it.
On the other hand, if we look away from our star, the sky is still blue-ish, or white-ish, or just getting dark, because most of the light gets scattered away before reaching us.
All this constitutes the well understood, and maybe boring, part of the story. When physiology and psychology kick in, it gets much, much messier, as color perception gets very subjective. Note for example that language shapes the way we perceive colors. Blue is a particularly weird color, and believe it or not there's evidence that you might not know that the sky was blue had you not heard that all your life. But, at least when it comes to Physics, you now know why it should be somewhat blue-ish. Apart from the cases when it's white-ish or red-ish... 

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