The distinction between a fluid's liquid and gaseous phases
breaks down at a certain temperature and pressure; when illuminated under
these conditions, the fluid looks milky white, like a common opal.
Einstein found how this relates to the reason the sky is blue.
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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)
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