A. A path with a detour
If you look at many artists' renderings of Albert Einstein, you are likely to find some that depict Einstein with some representation of the universe as a whole, or black holes, or other objects in deep space. Because many such pictures exist, we may, somewhat unconsciously, associate Einstein with the dark nighttime sky.
This is a quite reasonable association, since Einstein's theories of space and time deal with the universe as a whole and with certain astrophysical phenomena. All the same, one of Einstein's early papers was directly related to certain features of the daytime sky: why it is blue (an obvious feature), and why its blue light waves vibrate more strongly in certain directions than others (a less obvious feature, but one readily observed with polarizing sunglasses). This paper was about the more general topic of how light is dispersed by certain types of liquids and gases. Since the atmosphere is one such gas, Einstein noted that his findings might explain why the atmosphere looks blue in daylight.
The old question of what makes the sky blue is something that many people besides Einstein have helped to answer. Some landmarks on a path towards the answer were found in the late 19th century by Lord Rayleigh (John William Strutt), near the turn of the 20th century by Marian von Smoluchowski and Albert Einstein, and in the mid-20th century by Bruno H. Zimm. The path outlined by these landmarks was not a direct one. Smoluchowski, studying the more general question of how liquids and gases disperse light, discovered something that Einstein soon saw was a way to circumvent an obstacle along the path Lord Rayleigh had blazed. Later, Zimm succeeded in going straight through the obstacle using concepts developed after Rayleigh's time.
It turns out that the light from the daytime sky is shaped by two key physical processes. First, when a light wave from the sun runs into an air molecule, it will scatter off the molecule in different directions, with the scattered wave being more intense in some directions and less intense in others. Second, light waves scattered from different molecules will interfere, either reinforcing each other if their side-to-side vibrations are mostly in step, or diminishing each other if their vibrations are mostly out of step. As a result, the light we see from different parts of the sky will vary in brightness, shades of blue, and even polarization (vibration direction). Similar processes occur in any gas or liquid whose molecules scatter light.
Rayleigh's contribution was a thorough analysis of light-wave scattering, and some insight into wave interference. Since light waves are ripples of electric and magnetic force fields, the laws governing the force fields can be used to deduce how light waves are reshaped by objects, such as molecules, that obstruct their path. Rayleigh was able to work out how strongly a single molecule would scatter light in each possible direction. The effect of wave interference proved a bigger obstacle to Rayleigh. For most scattering directions, whether the light waves from different molecules are in step or out of step with each other depends on where the molecules are in relation to each other. Rayleigh's assumption was that the molecules are randomly distributed, with no particular pattern, and that the waves scattered from any two molecules are therefore equally likely to be completely in step, completely out of step, or any possible condition in between. Based on this assumption, he arrived at formulas relating the scattered light's intensity to the scattering direction and to the wavelength and intensity of the original waves.
Rayleigh's formulas proved accurate enough to show what gases did to light, but not liquids. Rayleigh himself recognized that in liquids and solids, the molecules are not so randomly distributed. In gases, the molecules are very far apart, so every molecule has a wide range of possible locations no matter where all its neighbors are. In liquids and solids, the molecules are close together, so the possible locations for a molecule are quite limited by where its neighbors are-the molecules' distribution is less random. Rayleigh lacked a ready mathematical method of dealing with this kind of limited randomness. Once such methods had been discovered, about a half-century later, Zimm used them to show a way to make further progress along Rayleigh's path.
Before these methods were found, Einstein saw a different way to look at the question. Instead of thinking in terms of how light waves scattered from individual molecules and then reinforced or cancelled each other, Einstein considered how light was affected by entire volumes of gas or liquid much larger than a single molecule, treating each volume as a unit. (.....continued)