Light and the Age of the Universe - the Cosmic Microwave Background

Our main window to understanding the universe is light and the electromagnetic spectrum. Trapped here on earth, there is very little of the universe that we can actually touch and test with our own hands, but light provides an amazing tool. The Cosmic Microwave Background is perhaps on of the best methods we have of finding the age of the universe.

All objects that are in thermal equilibrium - that is, the matter and EM radiation in the objects are the same temperature - have what is known as a black body spectrum - EM radiation with properties that are a function of the temperature of that object only. That spectrum might be modified a little but atomic absorption and emission lines, but the fundamental black body spectrum will remain. The spectrum looks like the curves on this graph:

Each curve represents a black body emitter with a particular temperature, shown in Kelvin (roughly the temperature in degrees plus 273, where 0 is absolute zero). The Sun, indeed all stars have a black body spectrum. In the case of the sun, the surface, and black body temperature is about 6000K, so it looks not so dissimilar from the 5000K curve. You can see that the black body spectrum continues beyond the visible - indeed the IR part is what is responsible for heat from the sun. The earth has a black body spectrum of about 278K (5.5 Celsius), which peaks in the infra red.

So what does this have to do with the age of the universe? Well when the universe was a mere 400,000 years old, about 13.7 billion years ago, everything was very much closer together, though space was expanding rapidly, and so the universe was much hotter than it is now, so hot in fact that there were no atoms, there was just a sea or plasma of hydrogen and helium nuclei (and a bit of lithium) electrons, Electromagnetic radiation and other subatomic particles (earlier than this there weren't even nuclei, but that's earlier than we are interested in here). The universe was still too hot for the electrons to bind to the nuclei, and so photons were constantly being absorbed and re-emitted by the various charged particles that were around, and the universe was in a state of equilibrium between matter and radiation. This means there was a black body spectrum. Eventually, as the universe expanded electrons no longer had enough energy to constantly escape binding to the nuclei, and they finally bound, becoming hydrogen and helium atoms. There was still substantial interaction between matter and radiation, particularly in the form of scattering, such as Compton Scattering and Thompson Scattering. The universe continued to cool as it expanded further, and eventually cooled down to a temperature of about 4000K at which the scattering dropped off. The radiation at this point became decoupled from the matter in the universe, as the universe became transparent, though the shape of the spectrum remained imprinted on the light that passed on, and continued traveling through the universe.

In the intervening billions of years, space itself continued to stretch. Imagine drawing a wave on a balloon, and blowing up the balloon. You will see the wavelength becomes longer and longer. The same effect occurs to the radiation, but now the the very space of the universe is expanding, so photons that initially had a short wavelength, over time were stretched out so the wavelength was longer and longer, so long in fact, that the BB spectrum which peaked at 4000K now peaks at a temperature of just 2.725K - barely above absolute zero.

This temperature is the same in all directions, though there are tiny fluctuations, which resulted from small changes to the very uniform distribution of matter and energy in the early universe as we can see in the (Wilkinson Microwave Anisotropy Probe ) WMAP satellite image below. It is these tiny imperfections that seeded the collapse of the primordial matter into the stars and galaxies of the universe today.

By knowing the rate at which the universe is expanding, which we can measure from the red shift of other features of the universe such as distant stars, galaxies and quasars, and these initial temperatures (which we know from looking at hydrogen and helium in the lab) we can then deduce the age of the universe (in much the same way as we can determine how long a cup of water has been standing on a table for if we know it was boiling when it was put there)...

...13.7 billion years old.

The Science of Optics: Polarization of light, Water, Insects and 3D Cinema.

As mentioned earlier, light is a transverse wave, but as it is in 3D space (rather than on a surface like water) it can oscillate in any direction perpendicular to the direction of motion. The particular polarization depends on the relationship between the electric and magnetic field, but the simplest polarization is linear polarization - the light oscillates in a flat plane. When interacting with materials, it is often useful to be able to determine the relationship of the polarization to the material or angle of reflection. Here we will consider reflection from a mirror.

The light travels in the direction of the black line, and bounces off the mirror (the grey shape) - so the light takes a path that stays in the plane of the blue shape. The blue wave oscillates perpendicularly to the blue shape and is known as perpendicular or s-polarization. The red wave oscillates in the plane of the blue shape and is known as parallel or p-polarization. The light can also oscillate in any direction perpendicular to the direction of travel, and so some component of the light can be perpendicular, and some can be parallel.

This is very important in reflections, because different amounts of the perpendicular and parallel components can be reflected from a surface. The light that reflects from water at a shallow angle for example is almost all p-polarized light. That means if we take a polarizing sheet or polarized glasses (remember it has to be linear polarization - 3D glasses from cinemas are usually circularly polarized, so this won't work) and hold them in front of the reflection, we can cut out almost all of the reflected light and see into the water.

This image shows two photos of a puddle - one without a polarizer and one with a polarizer. The polarizer removes all of the light reflected from the surface, and so the reflection of the building disappears.

Interestingly, when locusts are swarming, they avoid areas of ground where there are large amounts of horizontally polarized light, because that means the light is reflected from water, meaning they avoid lakes and only land where there is food. You can read more about that here.

Some scattered light is also polarized, particularly light that is Rayleigh scattered. Rayleigh scattering occurs when the object that the light scatters from is very much smaller than the wavelength of light. Rayleigh scattering is stronger for shorter (bluer) wavelengths of light than for longer (redder) wavelengths. A good example of this is the scattering of sunlight that makes the sky blue.

As sunlight passes through the atmosphere, more of the blue light is scattered than the longer wavelengths, and so the sky appears blue. Just like the reflection from the water, this light is also partially polarized (though not totally, because of multiple reflections that can mess the polarizations up a bit). The polarization of the sky is in a direction that is tangental to a circle drawn around the sun.

As a result of this, insects which can detect the polarization of the light can tell where the sun is in the sky, even on cloudy days, and without being able to see the sun or shadows. Since this polarization follows the sun as it moves through the sky, this allows insects like bees to find the same patch of flowers even as the day goes on.

Circular Polarization and 3D Cinemas

So far I have described linear polarization, but light can also be circularly polarized. If we imagine some light traveling in the x direction, oscillating at an angle between the y and z direction, we can project its components in the y and z direction like this:

As we can see, they are in phase. This means they are doing the same thing i.e. they are both maximum at the same time, zero at the same time and minimum at the same time. But what happens if they are out of phase?

When we add them together, we can see that the electric field now rotates around the x-direction. This is known as circularly polarized light. The light can either spin clockwise as it moves, or counter-clockwise. Just like with the linear polarizer, we can have polarizers that let through only one circular polarization of light and block the other, and this is the technique that some 3D cinemas use - One lens blocks light that is clockwise polarized, and one lens blocks light that is counterclockwise polarized. This means that different images can be sent to each eye, and then your brain can make a 3D image from these.

Circular polarization is used rather than linear polarization, because if one image was projected using horizontally polarized light, and the other using vertically polarized light, the glasses would have to be perfectly oriented all the time, or you could keep picking up a bit of the wrong image in your eyes, making you see a double image (like you see if you take the glasses off). Circularly polarized light is not affected in this way. Note that only some 3D cinemas use this technique - others have switching glasses, that very rapidly block and unblock the eye, allowing your eye to see alternate images.