Monday, November 03, 2008

Statistical physics

This fall I'm teaching Statistical and Thermal Physics, a senior (in the most common Rice physics curriculum, anyway) undergraduate course, and once again I'm struck by the power and profundity of the material. Rather like quantum, stat mech can be a difficult course to teach and to take; from the student perspective, you're learning a new vocabulary, a new physical intuition, and some new mathematical tools. Some of the concepts are rather slippery and may be difficult to absorb at a first hearing. Still, the subject matter is some of the best intellectual content in physics: you learn about some of the reasons for the "demise" of classical physics (the Ultraviolet Catastrophe; the heat capacity problem), major foundational issues (macroscopic irreversibility and the arrow of time; the precise issue where quantum mechanics and general relativity are at odds (or, as I like to call it, "Ultraviolet Catastrophe II: Electric Boogaloo")), and the meat of some of the hottest topics in current physics (Fermi gases and their properties; Bose Einstein condensation). Beyond all that you also get practical, useful topics like thermodynamic cycles, how engines and refrigerators work, chemical equilibria, and an intro to phase transitions. Someone should write a popular book about some of this, along the lines of Feynman's QED. If only there were enough hours in the day (and my nano book was further along). Anyway, I bring this up because over time I'm thinking about doing a series of blog posts at a popular level about some of these topics. We'll see how it goes.

7 comments:

Uncle Al said...

Entropy arises from extrinsic observables. Conservation of angular momentum (Feynman's sprinkler) is an absolute arrow of time. Detected anisotropic vacuum plus Noether's theorem uncreates the conserved current.

The Equivalence Principle is not tested against opposite parity mass distributions. A parity Eötvös experiment contrasts quartz single crystal solid spheres in space groups P3(1)21 (dextral atomic helices) and P3(2)21 (sinistral). Massed sector chiral vacuum is a prize worth winning.

Massimo aka Okham said...

Doug did you ever check out Feynman's book on path integrals regarding the appearance of hbar in Stat Mech ? I still find it illuminating...

Anonymous said...

Uncle Al reminds me of those Precogs from "Minority Report."

Yeah, Stat mech was my favorite class so far. I never took it as an undergrad, so I took an undergrad stat mech class in grad school and loved it. Wish I had time for the graduate version.

Paul said...

What exactly is the issue at hand with Ultraviolet Catastrophe II?

Doug Natelson said...

Paul - Here's how I present it. The traditional UV catastrophe arises if we treat each EM mode of a cavity as a classical harmonic oscillator and then use equipartition. That would say that there is kT worth of energy in every mode, all the way up to arbitrarily high frequencies (down to arbitrarily short wavelengths), for a cavity in equilibrium at temperature T. Clearly, since we're not continuously bathed in gamma rays while sitting in our offices, this is not correct.

By using the correct form for the partition function for EM radiation (that is, treat each EM mode of a cavity as a quantum harmonic oscillator rather than a classical harmonic oscillator), we arrive at the Planck blackbody spectrum, vanquishing the traditional ultraviolet catastrophe. Because kT is actually much smaller than the quantum of energy for the really high energy EM modes, those modes are never excited.

Now, according to quantum mechanics, each mode (still going up to arbitrarily high frequencies) contains 1/2 \hbar \omega worth of zero-point energy, independent of the temperature. In ordinary quantum, that's fine - we can define our zero of energy to be that ground state value, and only worry about differences from there. The problem is, general relativity says that you can't arbitrarily define your energy scale: an absolute energy density of zero corresponds to flat spacetime. So, the 1/2 \hbar \omega integrated over all possible frequencies \omega predicts an enormous vacuum energy density, even if you cut off the integral at the Planck scale. That's the second UV catastrophe, by my terminology. We know that those zero-point fluctuations of the EM field exist, since they lead to things like the Lamb shift in the spectrum of hydrogen. However, we also know that for some reason the energy density from those fluctuations doesn't strongly curve spacetime. One (IMO reasonably appealing) argument for supersymmetry is that the superpartners of the photon actually contribute -1/2 \hbar \omega for each mode, naturally canceling out the photon contributions. Imperfect cancellation (due to broken supersymmetry?) could be an explanation for "dark energy".

R said...

Doug,

What book are you using? I have looked for a good undergraduate Stat Mech book and I haven't found a great one yet.

No doubt Stat Mech is the most interesting basic course in physics. You can do anything with it!

DanM said...

"The Equivalence Principle is not tested against opposite parity mass distributions. A parity Eötvös experiment contrasts quartz single crystal solid spheres in space groups P3(1)21 (dextral atomic helices) and P3(2)21 (sinistral). Massed sector chiral vacuum is a prize worth winning."

I swear I heard somebody utter this precise set of words on Battlestar Galactica. I think it was one of the hybrids, ya know, those babes in bathing suits sitting in puddles of ooze on the toaster's ships.