Caustics

There are many sublime examples of physics in everyday life that I have come to appreciate. Given that it is summer I will talk about something that you are likely to see, but perhaps you can see it with new light soon.

I am simply going to talk about light rays, shadows, and shimmering in your pool. Watch the video. Notice the brightening of light into little wavering filaments (at about 40 seconds notice the nice filamentary structure of closed loops). The waves in the water's surface are bending the incoming light just like your glasses, a telescope, or a magnifying glass and focusing this diffuse incoming light into the bright areas and lines which you observe. The bright areas shimmer according the to shape of the surface of the water as waves perturb that smooth surface. The pattern of light can then be traced to the waves in the water and then to source of light. In theory there is a direct mathematical mapping to the light rays and the water waves. The places on the lensing plane (in this case the surface of the water) which cause a critical increase in brightness on the imaging plane (in this case the side of a pool) are known as caustics (and would roughly map out the crests of the tiny waves in the pool). In astronomy these shimmering lights rays in a pool are a great analogy for the physics underling some observed phenomena.

Gravitational lenses are a bonanza of science and beautiful images tied together. One of the more famous examples of gravitational lensing is Abell 2218 which is an entire galaxy cluster lensing the background field of galaxies.

At first glance I would not say that the similarities between this image and lights in your pool are particularity striking, but the redeeming factor here is the mathematics. It turns out that the math that describes the critical paths that a given photon will travel from the distant background galaxies through the massive gravitational pull of the foreground lensing cluster uses caustics. Imagine riding a photon from one of the distant galaxies relatively unimpeded until you finally interact with the gravitational field of a cluster of galaxies and then you continue to travel again relatively unimpeded until you are observed as a strongly lensed photon. This is exactly what a photon does as it enters the pool. It starts off at some light source, travels unimpeded, hits the surface of the water where it may be bent to some extreme at a caustic, and then it travels relatively unimpeded again until it is observed.

Large scale structure is another aesthetically pleasing astronomical example that takes cues from the dancing lights in your pool. We can start exploring this strange similarity by looking in a strange place: the millennium run. It is a massive simulation astronomers created to examine the evolution of matter in the universe and the result has a clear visual and physical analogy to the filaments of light seen above. In the image below we see a slice through a three-dimensional dark matter distribution showing the structure of the cosmic-web.

The ripples of dark matter evident in the image were seeded by quantum fluctuations during the period of inflation just after the big bang. These minuscule primordial fluctuations expanded with inflation and continued to grow under the influence of gravity. While galaxies individually remain extremely complex statistically the universe has turned out to be simple and has followed closely to astrophysicist's linear predictions on scales greater than about 100 Mpc (that is a mega parsec which equals 1000 parsecs and that is about 2/3 of the way up our cosmic distance scale). We can examine statistics from our data to show that Fourier components of the density field are random, independent in phase, and are nearly scale invariant in power spectrum just as the theory predicts. If that didn't make any sense, don't worry because all you need to observe is that the theory and simulations display similar patterns to actual data that has been taken of galaxies, such as the image below from SDSS.

This image from the SDSS survey shows the distribution of galaxies we actually observe. Each dot represents a galaxy. Notice that their are voids and over densities in filaments and there is a preferred void and filament size. Galaxies merely cluster and form on top of the gravity dominating scaffold of dark matter; although this image and the millennium run are displaying two fundamentally different types of matter they look similar (and although they seem totally unrelated they also look just like the pool). The physics behind these patterns and the imprints seen in the Cosmic Microwave Background are known as acoustic peaks. They are literally oscillations of energy in the early universe and like an instrument's string that has been plucked the modes which resonate can tell us about the object resonating (also, the astute listener that the music accompaniment to the video is Johann Sebastian Bach's Cello Suite #1 in G major and this is no coincide). This may sound like all smoke and mirrors, but these acoustic peaks have been seen in the 2dFGRS and the SDSS. So if this all went over your head just realize that the striking part of all of this is that the patterns from astronomy match the patterns of light seen in any pool!

There is even more science you can think about in the pool this summer. Notice that the focused light on the sides or bottom of the pool is directly related to the current shape of the water's surface between where the light is being focused and the source of light. The really crazy thing to think about is this: there is roughly a certain size of focused light ray that is most common, meaning there is a certain size of wave disturbance in the pool that is most common, meaning that... Often the light rays form loopy circles of sort, but notice that the loops of light are not several meters in diameter nor are the less than a few centimeters in diameter. Nature has chosen a preferential size scale for these loops of light, just as it has chosen a preferential size scale for galaxy clusters! Why is this? Well, we could go through the looking glass here, but maybe it is time to let you just think it out on your own or relax by the pool.