This post marks 3000 essays, short thoughts and link collections authored by yours truly. I’ve hosted carnivals, particpated in many.I’ve had, and am currently engaged in, great conversation(s) and have profited greatly and hope to continue in days to come. I’ve never however started a meme. So this is my attempt at that.
The 20th century gave us much that was not beautiful such as the Killing Fields, Auschwitz, Holodomor, Stalingrad, and that list continues much too far. However, every age has beauty to claim as its own. Doestoevsky claimed that “beauty would save the world.” In this vein it seems imperative that we remark and remember beauty that is in our midst.
This particular meme invites the partipants to name five things of transcendent beauty that were discovered or created in the last 100 years. Name them, explain why you find it beautiful and then instead of tagging N others to pass it along, if you read this and think beauty important … take it up!
- Emmy Noether‘s theorem linking symmetry and conservation. I’m going to explain more about that in detail below the fold.
- The SR-71 Blackbird, art, engineering, and sheer power built to fly mach 3.
- Michele Bartoli’s ride to victory in Liege-Bastogne-Liege in 1997, dueling at the end against two teammates ranked #1 and #2 in the world and beating both.
- J.R.R. Tolkein’s Lord Of the Rings trilogy and Peter Jackson’s portrayal of the same.
- Donald Knuth’s program TeX.
Emmy Noether in 1915 showed that any continuous symmetry implies that the conjugate variable is conserved. 19th century Physics developed by a host of mathematical physicists established a powerful mathemetical tools for describing classical mechanical systems in a formal way. In that system, there is a notion of conjugate variables. For example, position and momentum, angular momentum and angular position, energy and time are all examples of conjugate variables. Ms Noether proved that when one is a symmetry, the other is conserved.
In practice this means, because the “laws of physics” are unchanged under translations in space (that is the laws describing motion are the same here and 10 feet to the left or right) that momentum must be conserved. Because those laws are the same now and tomorrow … energy is conserved. But … Ms Noether’s theorem wider implications, in gauge theories.
Gauge theories can be seens in part in this way. Imagine for a moment, at each point in space, placing a small circle. If one were to write a simple equation describing a field moving through that space, one might imagine that geometrically speaking exactly how one puts coordinates on those circles from point to point shouldn’t matter at all. The constraints on the field theory that implies … yield Maxwell’s equations describing how electricty and magnetism behave. Ms Noether’s theorem leads to charge conservation of currents in this space (and quantization of field vibrations in the “small” circle yields quantization of charge).
Just to put some modern physics in perspective, the more complicated quark and gluon interactions are found by replacing the circle with a more complicated space.
In short, Ms Noether’s theorem was a fundamental driving force behind the ongoing geometrization of physics throughout the 20th century.