#FridayPhysicsFun: what *is* that bright thing? 
Everybody has seen light caustics since they are everywhere: reflections and refractions in glasses and cups, the net pattern cast by sunlit waves on walls and boats, rainbows & halos.
Caustics happen when a lot of light rays get bundled together. The term caustic comes from the Greek word kaustos for "burnt" - the concentrated light at the focal point of a magnifying glass is hot. en.wikipedia.org/wiki/Caustic_(…
Once you start noticing caustics you will see them nearly everywhere. But why do they show those cusps? They come from all sorts of unrelated optical phenomena, after all.
Caustics are envelope curves, curves that at each point is tangent to at least one of the family of light rays. Since the rays from nearby points have to be close and nearly parallel they pile up, making them bright. en.wikipedia.org/wiki/Caustic_(…
There is a fairly deep reason for the cusps: they are singularities of the envelope manifold. That is, everywhere else the manifold looks like a smooth curve when viewed close, but here and there it has sharp corners or self-crossings.
en.wikipedia.org/wiki/Cusp_(sin…
en.wikipedia.org/wiki/Cusp_(sin…
Singularity theory classifies such singularities. Of particular interest are stable singularities: when you change the system (e.g. the light & position of glass and table) they don't change qualitatively, just move slightly. en.wikipedia.org/wiki/Singulari…
Work by Whitney, Hironaka, Thom, and Arnold found that there are rather few possible types of stable singularities when you have few dimensions. So the type of caustic you get tends to be constrained to cusps, swallowtails and a few others. iopscience.iop.org/article/10.108…
Thom and Zeeman's work is known as Catastrophe Theory and hyped itself to death in the 1970s by claiming to solve all sorts of grand questions. Still, it got depicted in Salvador Dali's last painting. en.wikipedia.org/wiki/The_Swall…
In any case, caustics show up a lot. Including in gravity. Evenly distributed dark matter flowing past a heavy object could form caustics that may lead to gravitational lensing. arxiv.org/abs/astro-ph/0…
When galaxies merge, stars can form shells that are basically envelopes where the surface is the turnaround radius for the stellar orbits: caustics on a galactic scale. apod.nasa.gov/apod/ap110726.…
In fact, the cosmic web of galaxies and dark matter is in a sense a set of caustics caused by matter flowing together due to gravity: arxiv.org/abs/1703.09598
We are living *in* a caustic.
We are living *in* a caustic.
