Random 3am Thoughts

I typed this up pretty late last night, but I guess I never hit ‘post’. So…

• I just finished a 20-page lab report on using the Mössbauer effect to study the isomer shift and hyperfine splitting of ⁵⁷Fe, and I must say, it’s an incredible experiment. You move a thin foil of isotopically-enriched absorber (e.g. stainless steel/Fe metal) at extremely, extremely non-relativistic speeds of several millimeters per second relative to a ⁵⁷Co source. You record the number of 14.4keV gamma-rays detected. You analyze the heck out of your data. And somewhere along the way, somehow, you figure out how to deduce the magnitude of these splittings (sometimes as small as ~10^-9eV), among other things, from this mess of data. It works like magic, and apparently other people think so too (with applications from testing GR to looking at car exhaust/hemoglobin to the Mars Rover).

• Speaking of physics lab, I’ve just realized something: although classes, talks, homework, et cetera are fun (for very broad definitions of fun in some cases), I find that I’m happiest either when I’m actually doing an experiment, or trying to dissect my data. There’s this thrill involved with trying to learn something new about a system by playing with it, probing it, trying to force it to reveal its secrets in a systematic and careful manner; and either actually learning something new about it, or more commonly finding out why your approach is flawed. But debugging an experiment or trying to find a nugget of signal in a sea of noise can be fun, too. It’s like being a detective (cliché, I know, but it’s true). I really love experimental science, and I’m lucky because all of the experiments I get to do for this modern physics lab class are really beautiful. I’ve learned a ton from this class - and not just physics, too, but things like statistics, or more methodological things like really thinking things through and being careful and systematic. Which is perhaps why this post (via Chad Orzel) pissed me off, although I have better things to do than rant about it.

• And speaking of things of a curricular nature, I really, really hate in-class midterms for upper-level classes (the ones that you actually have to think deeply about). It just doesn’t make sense to compress the thought process involved in solving problem sets (an intense process of deep thought, trial, error, et cetera spread out over a week) into an hour-long block, and I find that when faced with such a situation, I’m so scared of screwing up that, well, I screw up. If I were in charge, I’d give really, really hard take-home midterms, or something of that sort, I think.

• I recently ordered a poster-size version of the ‘map of science’ (from here for $10), featured in Nature several months ago. I’ve always had the desire to map out the sciences, particularly the ones I’m interested in. It always struck me as a kid how throughout the history of science, hot new fields always seemed to emerge by drawing connections between fields that otherwise hadn’t been connected, and if you had a map of it all, identifying places to draw new connections would be a breeze. I’m not sure if I think quite so simplistically anymore, but I still agree with the general philosophy to a certain extent. That being said, the people who constructed this ‘map’ of science did a lot of work, and it shows: the only way to actually read the thing is by squinting.

Atomic Spectroscopy

I’m doing an ‘experiments in modern physics’ lab this semester. The structure of the course is simple: we do 4 labs chosen from a tantalizing list of many, complete with a report and an APS-style talk. I decided to do my first experiment on atomic spectroscopy: measuring energy level splittings using optical resonators, and I figured I’d write a post on it (well, paraphrase my report) because it may be interesting to a non-scientific audience. So, this post only has a few equations and is mainly an overview of the basic concepts involved.

(For those interested in the details, here’s the executive summary: the experiment was basically to use Fabry-Perot and Michelson interferometers to characterize the spectral lines of atomic sodium and hydrogen/deuterium, and measure the spectral splitting of the sodium 3p_3/2→3s_1/2 / 3p_1/2→3s_1/2 D line and the hydrogen/deuterium 3s→3p H-α transition due to spin-orbit coupling and isotope mass differences, respectively. The H/D splitting measurement also allows one to deduce the proton/deuteron mass ratio by playing around with the numbers a bit. Note that the picture on the left is a photo of slightly split sodium fringes from a Fabry-Perot interferometer, from [1] - click Read on… and scroll to the bottom for the references.)

In this post I’ll briefly review the historical context of this experiment, go over the basic physics responsible for the spectral splittings and the physics behind the experimental tools, and outline the experiment itself.

Ideas in Condensed Matter Physics

Doug Natelson has a post soliciting suggestions for the most powerful idea in condensed matter physics, putting out the Hohenberg-Kohn-Sham theorem/method underlying DFT as being a good candidate. Others have suggested Bloch’s theorem, Anderson’s paper on localization, Laughlin’s paper on the Fractional Quantum Hall Effect, Onsager’s solution of the 2D Ising model, Landau’s papers on Fermi liquids, BCS theory, “and whatever the most appropriate Bethe ansatz paper is”.

I need to learn way more condensed matter physics in order to say anything constructive, although I do feel that another on the list could be Philip Anderson’s “More is Different: Broken symmetry and the nature of the hierarchichal structure of science“, which arguably set the tone for the principle (paradigm?) of emergence in complex systems (and perhaps unwillingly led to a good deal of philosophy and/or pseudoscience, too). Perhaps one of the most-quoted passages from the paper - that I’ve seen, at any rate - is the following:

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe… The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts.

Anyway, the post reminded me of a paper I came across a long time ago in Rev. Mod. Phys. by W. Kohn (of Hohenberg-Kohn-Sham, as mentioned above) in 1999 that basically attempts to document the evolution of condensed matter physics. Here’s an excerpt:

It is perhaps interesting to look at the history of condensed matter physics from the viewpoint of T. S. Kuhn… [who] sees scientific history as a succession of (1) periods of ‘‘normal’’ science, governed by serviceable scientific paradigms, followed by (2) transitional, troubled periods in which existing paradigms are found to be seriously wanting, which in turn lead to (3) ‘‘scientific revolutions,’’ i.e., the establishment of new paradigms, which may or may not be accompanied by the rejection of the old ones.

Such a linear view seems applicable to the whole field of CMP for some of the broadest revolutions, which directly or indirectly affected a large fraction of the field:

• x-ray diagnostics yielding crystal structures (1910s);
• achievement of low temperatures allowing the observation of calmed condensed matter (1900s);
• quantum mechanics, (1920s);
• the band-structure paradigm (1920s, 1930s);
• nuclear and electron spin magnetic-resonance diagnostics (1940s and 50s);
• neutron elastic and inelastic diagnostics (1950s);
• many-body electron theories (beginning in the 1930s, with major revolutionary steps in the 1950s and 60s);
• electronic computer-assisted theory and experiments (1960s-);
• soft matter (1960s-);
• and nanoscience (1980s-).

I like it - clearly this is very broad, but it’s a very good summary of how the field has evolved into what it is today.