## Thursday, September 17, 2009

### Just How Pretty/Ugly Is The Standard Model?

Sorry this post contains equations.  (I had treat myself and make such a post at some point.)

The standard model is the creative name physicists have given to the theory that successfully unites the three forces: electromagnetic, strong and weak forces with all of the known particles but fails to explain gravity.  Excluding gravity, the standard model seems to explain everything we know about the universe with a few modern exceptions such as dark energy and dark matter.

Now, how beautiful is this theory?  In modern physics, theories are derived from "actions".  (Later I will post on why this is.)  When you "extremize" an action, it gives you equations that tell you what exactly your theory is.

For example, here is the entire action for general relativity:

When you "extremize" this action you get everything we know about general relativity. (And hence gravity).  The Einstein equations from such this action become: (Details here.)

This may not be apparent, but all of general relativity follows from such elegant looking equations.  Ah, so beautiful.

Another example is the action that gives rise to Maxwell's Equations, and thus all of electricity and magnetism: (The integral of this quantity is the action)

Here are the Maxwell Equations, derived from the above action, in all their symmetrical glory:

Now let's look at the Action for the standard model.  The action is the integral of this beast: (Click to See.)

Let's just say all of the equations that come from this is just too much.

There you go.  That image contains all the physics we know about the entire universe minus gravity. And now you all know how beautiful/ugly, the standard model is. :)

1. I vote ugly. Besides, I thought the answer to the Universe was 42.

2. As beautiful as Einstein's equations are, nothing will ever top Maxwell for beauty. They are just fantastic. (Although I love the Lagrangian formulation of mechanics as well - call me a Romantic)

3. My rule of thumb is that if you can't fit it on a t-shirt or a mug, it's not concise enough to be considered an elegant theory.

And Clark, I have to agree that Maxwell takes the cake in a beauty contest, but my second place vote goes to the Navier-Stokes equations. They're the black sheep of the physics community because they are practical as opposed to exact, but there is something very elegant about them.

4. Hey, I love fluid mechanics (although I'm sure over the years I've forgotten too much to keep up anymore). Throw in a bit of E&M and you get plasma physics!

While it's so idealized to be nearly meaningless, I have a soft spot for both the Ideal Gas Law and the Schrödinger Equation. (For some reason the Dirac version never did it for me)