The sky above us is more complicated than it looks. As the sun moves across the sky, it creates a complicated pattern of polarized light. The Vikings could even use this phenomenon to navigate (so do bees, for the record). Are you gonna say they're wrong?
The Clear Blue Sky
The blue sky is the result of scattered light. The atmosphere itself, and particles in it, scatter the blue wavelengths of light coming from the sun. As sunlight moves through the atmosphere, the blue light hits particles which send it everywhere, including showering down on us. This is why we see radiant blue light when we look upward.
Not all light is scattered in the same way. The blue sky is the result of what we call Rayleigh Scattering. Not only does Rayleigh Scattering single out the shorter wavelengths of light—- making our sky blue instead of red or orange — it scatters light in pretty much all directions, which is why the sky is uniformly blue instead of blue in patches.
Rayleigh Scattering not the only game in town. If you look into the sky you can also see Mie Scattering; the difference is Mie Scattering isn't picky about wavelength. It scatters all wavelengths of light, which combine to form white light. However, Mie Scattering is picky about direction; it tends to scatter light forward, in the direction the light was traveling in the first place. Mie Scattering is one of the reasons why the sky near the sun appears whitish instead of blue.
The Rayleigh Scattered Beam of Light
There is a peculiar consequence of Rayleigh Scattering: it slightly polarizes the light from the entire sky. The pattern of polarization depends on the position of the sun, as the scattered light we see is polarized depending on the direction the light was traveling before it was scattered.
Scattering is less random than its name makes it sound. To understand the way light is polarized through Rayleigh Scattering, look at the picture above. When light, as a wave, travels in a certain direction, the "wave" part of it vibrates perpendicular to the direction it's traveling. Imagine little circular buzz-saw blades cutting into your computer at the edge of every one of those "light rays" emanating from the sun. The waves would be vibrating back and forth from one edge of that circle to the other. It could be vibrating directly "out" of the plane of your screen, or it could be vibrating up and down along the plane of your screen, or any direction in between. Just as long as the direction of the ray of light,and the direction of the vibration of the light form a T shape.
When the light hits an atom in the atmosphere, the electrons in that atom vibrate in the same direction as the light is vibrating. The electrons then shoot off their own photons, their own rays of light. There's a catch, though — they don't shoot out those rays in the direction they are vibrating. So if an electron is vibrating up and down, it can only send a beam light to the sides. If an electron is vibrating side to side, it can only send a beam of light traveling upwards and downwards.
Those newly sent-out beams of light are vibrating in the same direction as their originating electrons were. This is what causes the light we see on the ground to be slightly polarized. If a person is standing on the ground, they are only seeing the beams of light that are traveling downwards toward them. And if the beams of light are traveling downwards toward that person, the light has to be vibrating side to side. Only the light that's polarized in a certain direction can get down to us on the ground.
Let's put it another way. Let's say a beam of light is traveling across the sky, parallel to the ground. One person is standing on the ground directly under it, and the other is standing on a mountain top exactly at the beam of light's level. The light hits a particle in the atmosphere, and the electron on the particle vibrates. Let's say it vibrates horizontally (and we have a literal horizon to compare it to). The person on the ground looks up and sees a vibrating electron - an electron moving back and forth. Presently, the person on the ground sees a beam of light coming towards them, vibrating the same way that the electron was vibrating.
The person standing on the hill doesn't see the electron vibrate at all. The electron is vibrating directly in line with their line of sight, so its path would look only like a point — or like a person taking a step directly towards you and a step back. Because the electron can't emit a beam of light in the same direction it vibrates, the light emitted would never reach them.
If the direction of the vibration were reversed, and the beam of light were to vibrate vertically, the situation would be reversed. The person on the ground would see neither the vibration of the electron nor the beam of light, and the person on the mountain would. The point is, if light is traveling down from the atmosphere to us here on the ground, it has been slightly polarized. There are certain directions that it simply cannot be vibrating.
The Rayleigh Sky
So what does a sky that has been polarized look like? Depends on where the sun is. The position of the sun will determine which way the rays of light travel (with respect to people on the ground), and so will affect the pattern of polarization. The ultra-sophisticated diagram above shows what the sky looks like when the sun is as its zenith. The light in the sky is polarized in little tangents to the circle of the sun.
Meanwhile, this color diagram shows what the sky looks like when the sun is at one edge of the sky (either at sunset or sunrise). Picture the sun as one of the black half-circles at the edge of the diagram. The direction of the bands of color show roughly the direction of the polarization of the light across the sky. In the dark blue and purple spots, the light is barely polarized, whereas in the red and yellow spots the light is strongly polarized.
If you want a rough understanding of how the sky is polarized, just imagine those tangential lines forming circles around the sun. As you get farther away from the sun they slowly straighten. Get even farther away from the sun and they start bending the other away.
You might also want to go outside and play with a polarizing filter. If you have a pair of glare-proof sunglasses, they have polarized lenses that block out horizontally polarized light. Go outside one day, point them at the sky, and turn them. You'll see the sky get brighter or darker depending on their orientation.
Navigation Like Bees and Vikings
When you are hoisting your sunglasses towards the sky, consider yourself a mighty viking, or an even more mighty bee. Supposedly both bees and Vikings can navigate by looking at the polarization of the sky. Bees came by the ability naturally, while the Vikings needed a little help. The Vikings supposedly had a stone that they could lift towards the sky, when the sun was partially obscured by clouds, which could be rotated to show the polarization of the light and the position of the sun.
I doubt they could use it when the sky was entirely obscured by clouds, because clouds scramble the polarized light from the sky. This leads to one of my favorite natural phenomena, even though I have yet to see it in person. Sometimes, when you look in a pond or a stream towards sunset, you will see clouds. Turn around and look at the sky, and you will see no clouds. Are these the ghosts of drowned clouds staring up at you from the depths?
No! The light from the sunset is vertically polarized. Ponds, lakes, rivers, and other horizontal shiny things are horizontal polarizers. When vertically polarized light from the sky hits a surface that only lets horizontally polarized light through, all the light is choked off. If the light has gone through clouds, it is truly scrambled and no longer vertically polarized. This works for even very faint clouds that we can't see when we look towards the sky because the sun washes them out. So when the light from those clouds hits the pond, much of it is reflected, and we see a cloud in the pond that we can't see in the sky.
In conclusion, having a polarized sky is neat.