How much information can you cram down an optical fiber?

A new cool result showed up in Science this week, implying that we may be able to increase the information-carrying capacity of fiber optics beyond what had been thought of as (material-dependent) fundamental limits.  To appreciate this, it's good to think a bit about the way optical fiber carries information right now, including the bits of this blog post to you.  (This sort of thing is discussed in the photonics chapter of my book, by the way.)

Information is passed through optical fibers in a way that isn't vastly different than AM radio.  A carrier frequency is chosen (corresponding to a free-space wavelength of light of around 1.55 microns, in the near-infrared) that just so happens to correspond to the frequency where the optical absorption of ultrapure SiO₂ glass is minimized.   Light at that frequency is generated by a diode laser, and the intensity of that light is modulated at high speed (say 10 GHz or 40 GHz), to encode the 1s and 0s of digital information.  If you look at the power vs. frequency for the modulated signal, you get something like what is shown in the figure - the central carrier frequency, with sidebands offset by the modulation frequency.   The faster the modulation, the farther apart the sidebands.   In current practice, a number of carrier frequencies (colors) are used, all close to the minimum in the fiber absorption, and the carriers are offset enough that the sidebands from modulation don't run into each other.  Since the glass is very nearly a linear medium, we can generally use superposition nicely and have those different colors all in there without them affecting each other (much).

So, if you want to improve data carrying capacity (including signal-to-noise), what can you do?  You could imagine packing in as many channels as possible, modulated as fast as possible to avoid cross-channel interference, and cranking up the laser power so that the signal size is big.  One problem, though, is that while the ultrapure silica glass is really good stuff, it's not perfectly linear, and it has dispersion:  The propagation speed of different colors is slightly different, and it's affected by the intensity of the different colors.  This tends to limit the total amount of power you can put in without the signals degrading each other (that is, channel A effectively acts like a phase and amplitude noise source for channel B).  What the UCSD researchers have apparently figured out is, if you start with the different channels coherently synced, then the way the channels couple to each other is mathematically nicely determined, and can be de-convolved later on, essentially cutting down on the effective interference.  This could boost total information carrying capacity by quite a bit - very neat. 

What is quantum coherence?

Often when people write about the "weirdness" of quantum mechanics, they talk about the difference between the interesting, often counter-intuitive properties of matter at the microscopic level (single electrons or single atoms) and the response of matter at the macroscopic level.  That is, they point out how on the one hand we can have quantum interference physics where electrons (or atoms or small molecules) seem to act like waves that are, in some sense, in multiple places at once; but on the other hand we can't seem to make a baseball act like this, or have a cat act like it's in a superposition of being both alive and dead.  Somehow, as system size (whatever that means) increases, matter acts more like classical physics would suggest, and quantum effects (except in very particular situations) become negligibly small.  How does that work, exactly?   

Rather than comparing the properties of one atom vs. 10²⁵ atoms, we can gain some insights by thinking about one electron "by itself" vs. one electron in a more complicated environment.   We learn in high school chemistry that we need quantum mechanics to understand how electrons arrange themselves in single atoms. The 1s orbital of a hydrogen atom is a puffy spherical shape; the 2p orbitals look like two-lobed blobs that just touch at the position of the proton; the higher d and f orbitals look even more complicated.  Later on, if you actually take quantum mechanics, you learn that these shapes are basically standing waves - the spatial state of the electron is described by a (complex, in the sense of complex numbers) wavefunction \(\psi(\mathbf{r})\) that obeys the Schroedinger equation, and if you have the electron feeling the spherically symmetric \(1/r\) attractive potential from the proton, then there are certain discrete allowed shapes for \(\psi(\mathbf{r})\).  These funny shapes are the result of "self interference", in the same way that the allowed vibrational modes of a drumhead are the result of self-interfering (and thus standing) waves of the drumhead.

In quantum mechanics, we also learn that, if you were able to do some measurement that tries to locate the electron (e.g., you decide to shoot gamma rays at the atom to do some scattering experiment to deduce where the electron is), and you looked at a big ensemble of such identically prepared atoms, each measurement would give you a different result for the location.  However, if you asked, what is the probability of finding the electron in some small region around a location \(\mathbf{r}\), the answer is \(|\psi(\mathbf{r})|^2\).  The wavefunction gives you the complex amplitude for finding the particle in a location, and the probability of that outcome of a measurement is proportional to the magnitude squared of that amplitude.  The complex nature of the quantum amplitudes, combined with the idea that you have to square amplitudes to get probabilities, is where quantum interference effects originate.   

This is all well and good, but when you worry about the electrons flowing in your house wiring, or even your computer or mobile device, you basically never worry about these quantum interference effects.  Why not?

The answer is rooted in the idea of quantum coherence, in this case of the spatial state of the electron.  Think of the electron as a wave with some wavelength and some particular phase - some arrangement of peaks and troughs that passes through zero at spatially periodic locations (say at x = 0, 1, 2, 3.... nanometers in some coordinate system).   If an electron propagates along in vacuum, this just continues ad infinitum.

If an electron scatters off some static obstacle, that can reset where the zeros are (say, now at x = 0.2, 1.2, 2.2, .... nm after the scattering).  A given static obstacle would always shift those zeros the same way.   Interference between waves (summing the complex wave amplitudes and squaring to find the probabilities) with a well-defined phase difference is what gives the fringes seen in the famous two-slit experiment linked above.

If an electron scatters off some dynamic obstacle (this could be another electron, or some other degree of freedom whose state can be, in turn, altered by the electron), then the phase of the electron wave can be shifted in a more complicated way.  For example, maybe the scatterer ends up in state S1, and that corresponds to the electron wave having zeros at x=0.2, 1.2, 2.2, .....; maybe the scatterer ends up in state S2, and that goes with the electron wave having zeros at x=0.3, 1.3, 2.3, ....  If the electron loses energy to the scatterer, then the spacing between the zeros can change (x=0.2, 1.3, 2.4, ....).  If we don't keep track of the quantum state of the scatterer as well, and we only look at the electron, it looks like the electron's phase is no longer well-defined after the scattering event.  That means if we try to do an interference measurement with that electron, the interference effects are comparatively suppressed.

In your house wiring, there are many many allowed states for the conduction electrons that are close by in energy, and there are many many dynamical things (other electrons, lattice vibrations) that can scatter the electrons.  The consequence of this is that the phase of the electron's wavefunction only remains well defined for a really short time, like 10^-15 seconds.    Conversely, in a single hydrogen atom, the electron has no states available close in energy, and in the absence of some really invasive probe, doesn't have any dynamical things off which to scatter.

I'll try to write more about this soon, and may come back to make a figure or two to illustrate this post.

Brief news items

In the wake of travel, I wanted to point readers to a few things that might have been missed:

• Physics Today asks "Has science 'taken a turn towards darkness'?"  I tend to think that the physical sciences and engineering are inherently less problematic (because of the ability of others to try to reproduce results in a controlled environment) than biology/medicine (incredibly complex and therefore difficult or impractical to do controlled experimentation) or the social sciences.  
• Likewise, Physics Today's Steven Corneliussen also asks, "Could the evolution of theoretical physics harm public trust in science?"  This gets at the extremely worrying (to me) tendency of some high energy/cosmology theorists these days to decry that the inability to test their ideas is really not a big deal, and that we shouldn't be so hung up on the idea of falsifiability. 
• Ice spikes are cool.
• Anshul Kogar and Ethan Brown have started a new condensed matter blog!  The more the merrier, definitely.
• My book is available for download right now in kindle form, with hard copies available in the UK in a few days and in the US next month.

Molecular electronics: 40+ years

More than 40 years ago, this paper was published, articulating clearly from a physical chemistry point of view the possibility that it might be possible to make a nontrivial electronic device (a rectifier, or diode) out of a single small molecule (a "donor"-bridge-"acceptor" structure, analogous to a pn junction - see this figure, from that paper).  Since then, there has been a great deal of interest in "molecular electronics".  This week I am at this conference in Israel, celebrating both this anniversary and the 70th birthday of Mark Ratner, the tremendous theoretical physical chemist who coauthored that paper and has maintained an infectious level of enthusiasm about this and all related topics.

The progress of the field has been interesting.  In the late '90s through about 2002, there was enormous enthusiasm, with some practitioners making rather wild statements about where things were going.  It turned out that this hype was largely over-the-top - some early measurements proved to be very poorly reproducible and/or incorrectly interpreted; being able to synthesize 10²² identical "components" in a beaker is great, but if each one has to be bonded with atomic precision to get reproducible responses that's less awesome; getting molecular devices to have genuinely useful electronic properties was harder than it looked, with some fundamental limitations;  Hendrik Schoen was a fraud and his actions tainted the field; DARPA killed their Moletronics program, etc.    That's roughly when I entered the field.  Timing is everything.

Even with all these issues, these systems have proven to be a great proving ground for testing our understanding of a fair bit of physics and chemistry - how should we think about charge transport through small quantum systems?  How important are quantum effects, electron-electron interactions, electron-vibrational interactions?   How does dissipation really work at these scales?  Do we really understand how to compute molecular levels/gaps in free space and on surfaces with quantitative accuracy?  Can we properly treat open quantum systems, where particles and energy flow in and out?  What about time-dependent cases, relevant when experiments involve pump/probe optical approaches?  Even though we are (in my opinion) very unlikely to use single- or few-molecule devices in technologies, we are absolutely headed toward molecular-scale (countably few atom) silicon devices, and a lot of this physics is relevant there.  Similarly, the energetic and electronic structure issues involved are critically important to understanding catalysis, surface chemistry, organic photovoltaics, etc.

What does a molecule sound like?

We all learn in high school chemistry or earlier that atoms can bind together to form molecules, and like a "highly sophisticated interlocking brick system", those atoms like to bind in particular geometrical arrangements.  Later we learn that those bonds are dynamic things, with the atoms vibrating and wiggling like masses connected by springs, though here the (nonlinear) spring constants are set by the detailed quantum mechanical arrangement of electrons.  Like any connected set of masses and springs, or like a guitar string or tuning form, molecules have "normal modes" of vibration.  Because the vibrations involve the movement of charge, either altering how positive and negative charge are spatially separated (dipole active modes) or how the charge would be able to respond to an electric field (roughly speaking, Raman active modes), these vibrations can be excited by light.  This is the basis for the whole field of vibrational spectroscopy.  Each molecule has a particular, distinct set of vibrations, like a musical chord.

Because the atoms involved are quite light (one carbon atom has a mass of 2\(\times\)10^-26 kg) and the effective springs are rather stiff, the vibrations are typically at frequencies of around 10¹³ Hz and higher - that's 10 billion times higher than the frequency of a typical acoustic frequency (1 kHz).  Still, suppose we shifted the frequencies down to the acoustic range, using a conversion of 1 cm^-1 (a convenient unit of frequency for molecular spectroscopists) \(\rightarrow\) 1 Hz.  What would molecules sound like?  As an example, I looked at the (surface enhanced) Raman spectrum of a small molecule, pMA. The Raman spectrum is from this  paper (Fig. 3a), and I took the three most dominant vibrational modes, added the pitches with the appropriate amplitude, and this is the result (mp3 - embedding audio in blogger is annoying).

I thought I was being clever in doing this, only to realize that, as usual, someone else had this same idea, beat me to it, and implemented it in a very cool way.  You should really check that out.

Anecdote 3: The postdoc job talk and the Nobel laureate

Back when I was finishing up my doctoral work, I made a trip to New Jersey to interview in two places for possible postdoc positions.  As you might imagine, this was both exciting and nerve-wracking.  My first stop was Princeton, my old undergrad stomping grounds, where I was trying to compete for a prestigious named fellowship, and from there I was headed north to Bell Labs the following day. 

As I've mentioned previously, my graduate work was on the low temperature properties of glasses, which share certain universal properties (temperature dependences of the thermal conductivity, specific heat, speed of sound, and dielectric response, to name a few) that are very distinct from those of crystals.  These parameters were all described remarkably well by the "two-level system" (TLS) model (the original paper - sorry for the paywall that even my own university library won't cover) dreamed up in 1971 by Phil Anderson, Bert Halperin, and Chandra Varma.  Anderson, a Nobel laureate for his many contributions to condensed matter physics (including Anderson localization, the Anderson model, and the Anderson-Higgs mechanism) was widely known for his paean to condensed matter physics and for being a curmudgeon.  He was (and still is) at Princeton, and while he'd known my thesis adviser for years, I was still pretty nervous about presenting my thesis work (experiments that essentially poked at the residual inadequacies of the original TLS model trying to understand why it worked so darn well) to him.

My visit was the standard format - in addition to showing me around the lab and talking with me about what projects I'd likely be doing, my host (who would've been my postdoc boss if I'd ended up going there) had thoughtfully arranged a few 1-on-1 meetings for me with a couple of other postdocs and a couple of faculty members, including Anderson.  My meeting with Anderson was right before lunch, and after I got over my nerves we had what felt to me like a pretty good discussion, and he seemed interested in what I was going to present.  My talk was scheduled for 1:00pm, right after lunch, always a tricky time.  I was speaking in one of the small classrooms in the basement of Jadwin Hall (right next to the room where I'd had undergrad quantum seven years earlier).  I was all set to go, with my binder full of transparencies - this was in the awkward period when we used computers to print transparencies, but good laptops + projectors were rare.   Anderson came in and sat down pointedly in the second row.  By my third slide, he was sound asleep.  By my fifth slide, he was noticeably snoring, though that didn't last too long.  He did revive and ask me a solid question at the end of the talk, which had gone fine.  In hindsight, I realize that my work, while solid and interesting, was in an area pretty far from the trendiest topics of the day, and therefore it was going to be an uphill battle to capture enthusiasm.  At least I'd survived, and the talk the next day up at Murray Hill was better received.

Fun with fluids: Hydraulic jump

We usually think of shock waves as exotic - something that happens when a huge explosion goes off, or when a supersonic plane flies by.  A shock in a gas is a relatively abrupt boundary between relatively cold gas moving faster than the speed of sound in the gas (that is, with a Mach number \(M \equiv v/c_{s} > 1\), where \(c_{s}\) is the sound speed and \(v\) is the speed of the gas) and warmer gas moving slower than sound (\(M < 1\)).  A shock that moves on its own relative to a stationary environment is a shock wave, while one that remains fixed in place relative to its surroundings is a "standing shock".   The details of the gas motion within the shock itself are very complicated, but the constraints of mass and momentum conservation make it possible to understand a lot about the relationship between upstream and downstream gas conditions even without knowing the nitty gritty.

  

It turns out that you have very likely seen a fluid analog of a standing shock in your sink!   Run the tap so that a stream of water hits the flat bottom of a typical kitchen sink.  You will see a disk-shaped region with a radius of a few cm (depending on flow rate) where the water is fast-moving but thin, surrounded by a turbulent ring, outside of which the water layer is thicker but slower-moving.   This is called a hydraulic jump.   The fast-moving water has a speed \(v\) greater than the speed of gravity-driven ripples in a thin fluid layer, \(\sqrt{g h}\), where \(g\) is the gravitational acceleration and \(h\) is the fluid depth.  The Froude number \(Fr \equiv v/\sqrt{gh}\) is greater than one on the fast-moving side of the jump, and less than one on the slow moving side.  Like the gas shock case, the boundary is a mess, but mass and momentum conservation can let you calculate the flow speed and fluid depth downstream if you know the flow speed and fluid depth upstream.   

The receding floodwaters in my neighborhood Tuesday provided me with a great example of a hydraulic jump, shown in the brief video clip above.  I still think it's cool that you can see an analog of a sonic boom in your sink, or in a nearby street if you're unlucky.

Storms are powerful heat engines!

Storms are incredibly powerful (on human scales) heat engines - driven by the sun, the fluxes of mass and energy are simply enormous.  To see just how big, let's take a look at the big thunderstorm system that flooded large parts of the city of Houston last night (hence why I'm blogging and unable to get to campus until the waters recede).   A large storm system dumped about 20 cm of rain (!) over a land area of approximately 4000 km² between 10:00pm and about 4:00am.   That's 8 x 10¹¹ kg of water!

The bottom of the rain clouds was maybe 0.5 km above ground level.  That's a lower bound on how far all that rain had to fall.  Using \(g \approx \)10 m/s², that's about 4 x 10¹⁵ J of energy, deposited in about 20000 sec, for an average power delivered of 2 x 10¹¹ Watts, as much as 100 municipal-scale power stations.   That doesn't even account for the energy contained in the wind and the lightning discharges.

Remember, this is all being driven by the sun, through temperature differences that are at most 20 K.  Thermodynamics tells us that the most efficient this process could possibly be is something like 1 - (300 K/320 K) = 1/16.  That means that the total energy involved had to be at least 6.4 x 10¹⁶ J = about 18 billion kW-h, and that's only one part of a big storm system.  This is why engineering the weather is a non-starter!

What is band theory? (car analogy)

One of the commenters on my previous post asked how I could explain band theory to a nonscientist, an artist in particular.  Here's a shot.  By necessity, when trying to give an explanation that avoids math almost completely, I'm forced to lean heavily on analogy, which means sacrificing accuracy to some degree.  Still, I think this is a useful exercise - it certainly makes me think hard about what I consider to be the important elements of a concept.  (This must be what Randall Munroe had to do many times for his upcoming book!  If you haven't read his first one, what have you been waiting for?)

The electronic properties of many crystalline materials are well described by "band theory".  At its heart, band theory comes down to three important ideas that I'll explain more in a minute:  Electrons in solids can only have certain states (to be defined below); those states are determined by the arrangement of the atoms in the solid; and each state can only hold two electrons, no more.   To describe this, I'm going to have to mix metaphors a bit, but bear with me.

In a very American mode, we're going to picture the electronic states as individual lanes in a verrrrrry wide, multi-lane highway.  Each lane has a different speed limit (each state has a particular kinetic energy), with the slowest traffic off to the driver's right (in this US-centric analogy) and speed limits increasing progressively to the driver's left.   Each lane can only hold at most two cars (each state can only hold two electrons, one of each kind of "spin").   Here's where the analogy becomes more of a reach:  Not all speed limits (electron kinetic energies) are allowed.  Speeds in adjacent lanes are separated by a small amount (energy level spacings are set by the size of the crystal), and some lanes are missing altogether (some energies are outright forbidden, determined by the type and arrangement of atoms in the crystal).  So, there are "bands" of lanes, separated from each other by "gaps".

Now we start adding cars to the highway with the restriction that cars can only drive at the speed limit of their lane, and (in an un-American twist) the drivers want to go the minimum possible speed.  This is going to tell us the "ground state", the slowest/lowest energy configuration of the system.  The first two cars (electrons) go into the slowest lanes waaaaay over on the driver's right.  The next two cars go into the second-slowest lane, and so forth.  We keep adding in cars (electrons) until we run out of inventory (until we have kept track of all of the electrons).  The more cars we put in, the faster the top speed of the fastest cars!

Cars can only merge into lanes that are open (or only partly occupied).  If the last car added ends up in a lane in the middle of a band of lanes, so that it can easily merge into an adjacent unoccupied lane, this situation corresponds to a material that is a metal.  If the last car ends up right against the guard rail of a band of lanes, so that there just is no adjacent lane to the driver's left available, then this situation corresponds to a "band insulator".   (If the gap to the next band of lanes is large, we call such materials "insulators"; if it's not too big, we call those materials "semiconductors".)

One point that even this very imperfect analogy can highlight:  The speed of the fastest cars (electrons) in a block of copper is actually about 0.5% of the speed of light (!), or more than 6,000,000 kph.  For metals with even more electrons, the fastest movers can be going so quickly that relativistic effects become important!

This was a very rough cut.  I'll try to return to this later, with other ways of thinking about it.

Book recommendations: Stuff Matters and The Disappearing Spoon

I've lamented the lack of good popularizations of condensed matter/solid state physics.  I do, however, have recommendations for two relatively recent books about materials and chemistry, which is pretty close.

The Disappearing Spoon, by Sam Kean, is a fun, engaging stroll across the periodic table, exploring the properties of the various chemical elements through the usually fascinating, sometimes funny, occasionally macabre histories of their discoveries and uses.  The title references joke spoons made from gallium that would melt (and fall to the bottom of the cup) when used to stir tea.  The tone is light and anecdotal, and the history is obscure enough that you haven't heard all the stories before.  Very fun.

Stuff Matters, by Mark Miodownik, is similar in spirit, though not quite so historical and containing more physics and materials science.  The author is a materials scientist who happens to be a gifted author and popularizer as well.  He's done a BBC three-episode series about materials (available here), another BBC series about modern technologies, and a TED lesson about why glass is transparent.

A matter of gravity

Gravity remains an enduring challenge in physics.  Newton had the insight that he could understand many phenomena (e.g., the falling of an apple, the orbit of Halley's comet) if the gravitational interaction between two objects is an attractive force proportional to the product of the objects' masses, and inversely proportional to the square of the distance between them ( \(F = - G M_{1}M_{2}/r^{2}\) ), and acts along the line between the objects.  The constant of proportionality, \(G\), is Newton's gravitational constant.   About 225 years later, Einstein had the insight that in more generality one should think of gravity as actually distorting space-time; what looks like a force is really a case of freely falling objects moving in the (locally) straightest trajectories that they can.  (Obligatory rubber sheet analogy here.)  In that theory, general relativity (GR), Newton's constant \(G\) again appears as a constant of proportionality that basically sets the scale for the amount of space-time distortion produced by a certain amount of stress-energy (rather than just good old-fashioned mass).  GR has been very successful so far, though we have reasons to believe that it is the classical limit of some still unknown quantum theory of gravity.  Whatever that quantum theory is, \(G\) must still show up to set the scale for the gravitational interaction.

It makes sense that we would like to know the numerical value of \(G\) as accurately and precisely as possible - seems like the first thing you'd like to understand, right?  The challenge is, as I've explained before, gravity is actually an incredibly weak force.  To measure it well in absolute numbers, you need an apparatus that can measure small forces while not being influenced by other, faaaaaar stronger forces like electromagnetism, and you need to do something like measure the force (or the counter-force that you need to apply to null out the gravitational force) as a function of different configurations of test masses (such as tungsten spheres). 

I'm revisiting this because of a couple (1, 2) of interesting papers that came out recently.  As I'd said in that 2010 post, the challenge in measuring \(G\) is so difficult that different groups have obtained nominally high precision measurements (precise out to the fourth decimal place, such as \(G = 6.6730 \pm 0.00029 \times 10^{-11}\) Nm²/kg²) that are mutually inconsistent with each other.  See this plot (Fig. 1 from arxiv:1505.01774).  The various symbols correspond to different published measurements of \(G\) over the last 35 years (!).  The distressing thing is that there does not seem to be much sign of convergence.  The recent papers are looking to see whether there is actually some periodicity to the results (as hinted by the sinusoid on the plot).  To be clear:  The authors are not suggesting that \(G\) really varies with a several year period - rather, they're exploring the possibility that there might be some unknown systematic effect that is skewing the results of some or all of the various measurement approaches.  As both teams of authors say, the best solution would be to come up with a very clean experimental scheme and run it, undisturbed, continuously for years at a time.  That's not easy or cheap.  It's important to note that this is what real, careful measurement science looks like, not some of the stuff that has made web headlines lately.

People you should've heard about: John Bardeen

If you ask the average person to name a physicist, chances are they'll mention Einstein, Hawking, and possibly Sheldon Cooper.  Maybe Richard Feynman, Brian Greene or (*sigh*) Michio Kaku.  I'd like to have an occasional series of posts pointing out people that should be well-known, but for some reason are not.  High up on that list:  John Bardeen, who is the only person one of only two people to win two Nobel prizes in the same field.

Bardeen, like many of his contemporaries, followed what would now be considered a meandering, unconventional trajectory into physics, starting out as an undergrad engineer at Wisconsin, working as a geophysicist, enrolling as a math grad student at Princeton, and eventually doing a doctoral thesis with Wigner worrying about electron-electron interactions in metals (resulting in these two papers about how much energy it takes to remove an electron from a metal, and how that can be strongly affected by the very last layer of atoms at the surface - in the 1980s this would be called "surface science" and now it would be called "nanoscience").

Bardeen was a quiet, brilliant person.  After WWII (during which he worked for the Navy), he went to Bell Labs, where he worked with Walter Brattain to invent the point contact transistor (and much more disagreeably with William Shockley), explaining the critical importance of "surface states" (special levels for the electrons in a semiconductor that exist at the surface, where the periodic potential of the lattice is terminated).  Shockley is viewed in hindsight as famously unpleasant as a co-worker/boss - Bardeen left Bell Labs in large part because of this and ended up at Illinois, where seven years later he worked with Bob Schrieffer and Leon Cooper to produce the brilliant BCS theory of superconductivity, earning his second Nobel.  (Shockley's borderline abusive management style is also responsible for the creation of modern Silicon Valley, but that's another story.)

During and after this period, Bardeen helped build the physics department of UIUC into a condensed matter physics powerhouse, a position it continues to hold.  He was very interested in the theory of charge density waves (special states where the electrons in a solid spontaneously take on a spatially periodic density), though according to Lillian Hoddeson's excellent book (see here, too) he had lost the intellectual flexibility of his youth by this time.  

Bardeen contributed greatly to our understanding and advancement of two whole classes of technologies that have reshaped the world (transistors and superconductors).  He was not a flamboyant personality like Feynman (after all, he was from the Midwest :-) ), and he was not a self-promoter (like Feynman), but he absolutely deserves greater notoriety and appreciation from the general public.

Bad science, bad science journalism: the EmDrive

No, NASA has not discovered warp drive.  There is a huge amount of media attention (here, here, here, for examples of relatively mainstream media) being given to a claim that a NASA team has successfully tested a gadget called the EmDrive.  The claim is that one can take a conical microwave resonator (picture the cavity that is your microwave oven, only shaped like a truncated cone rather than a rectangular box), fire up microwaves to drive the resonant modes, and the cone will experience a steady thrust in one direction (the direction of the fat end of the cavity).  There are multiple alleged explanations for this, ranging from botched thinking about special relativity to really bizarre word-salad about virtual particles, the quantum vacuum, and "warp fields".

Let me explain why this is bad science, terrible science journalism, and highly problematic.

First, the science.  Our theory of electricity and magnetism is arguably the best understood, most precisely tested theory we have, both in its classical limit (the limit relevant for your microwave oven) and in its quantum limit (the limit relevant for things like calculating the magnetic moment of the electron, something that we can do to more than 14 decimal places!  According to that theory, a closed microwave resonator does not generate thrust (surprise surprise).  Given over 100 years of tests of classical E&M, it's going to take more than one poorly documented experiment, not published, to convince scientists that something exotic is going on.  Extraordinary claims require extraordinary evidence, and this just isn't it.  Moreover, claims that exotic quantum vacuum effects or "warp fields" are somehow relevant here are just on their face absurd!  The energy densities, the materials involved, none of this couples to exotic quantum vacuum physics any more than my microwave oven does.  This is like arguing that by accelerating a simple dielectric like a piece of plastic, I should see electron-positron pair production and warped spacetime.  It's nonsense.

What would it take to convince me?  How about a thoroughly documented experiment done by someone with credibility in precision measurement, for a start.

As for science journalism:  The number of outlets who uncritically pass along something like this is appalling.  What's worse, they distort it even more - the third link up top not only claims that this is a reactionless drive, but that it will allow faster-than-light travel.  What the hell?  (Yes, I know that the Daily Fail is third-rate fish-wrap.)  I fully expect to see a CNN story about this, and it will be terrible.  This will propagate in the media for several days, and they will portray it as some underdog inventors showing that the Scientific Establishment is wrong, or they'll present this as an actual scientific controversy, when in fact the burden is all on the experimenters to show that their work (which flies in the face of decades of contrary evidence) is right.  Hey, IFLS:  You should be ashamed of yourselves for your coverage of this.  Good grief - I thought part of your message was that people should, I don't know, think critically!

Why is this problematic?  It's an issue because people don't trust science, in part because they end up reading uncritical bull like this and come away thinking that science is either a dodge, a scam, or entirely a matter of opinion, when in fact it's an approach to thinking critically about the world that has made possible all of modern technology and medicine.

Anecdote 2: Life in a lab - the Demon Liquefier From Hell

I know this will come as a shock to many of you (ahem), but when I was a kid I watched a lot of Star Trek reruns.  Even in middle school one story-telling trope that seemed phony to me was the way Scotty (and Kirk) could tell just from the sound and feel of the ship whether something was wrong with the engines or environmental controls.   Years later, as a grad student in the Osheroff lab, I realized that this was actually one of the more realistic bits of writing and characterization in the show.

Our lab focused on ultralow temperature physics.  We ran experiments using dilution refrigerators (also see here), and these each required multiple vacuum pumps running continuously (in our case, each fridge needed a helium-leak-tight, sealed, mechanical "roughing" pump, a big conventional mechanical pump (for the "1K pot"), and a large diffusion pump as a "booster").   The mechanical pumps were housed in a cabinet in a room one floor below the main lab, and even with that kind of distance and insulation they provided a continuous background hum to the room.  That basement room also contained our group's helium liquefier, an ancient beast of a machine (a twin is shown here) that took in recycled helium gas from our experiments, cooled it by using pistons to drive a big flywheel, and then liquefied it by squirting it through a tiny, cold orifice.  The liquefier provided something between a wheeze and a heartbeat to the lab, a steady state "pachooka pachooka" sound with a repetition period of around one second when it was working well.  The muffled version of this noise also permeated the lab.  After being in the group for a few months, I understood completely where Scotty was coming from.  It was deeply disturbing to walk into the lab and realize that something, somewhere was amiss because the sound or extremely subtle floor vibrations felt "off".  

The liquefier (officially the Demon Liquefier From Hell [DLFH], or The Liquef--ker) was a formative part of our lab's grad school experience.  Running the system, which predated any serious automated controls, required some amount of fiddling in the best of times, interpreting half a dozen cryptic gauges ("inches of water" as a pressure unit?  Really?), with the only useful diagnostic being whether the liquid level in the big helium storage dewar is increasing or not.  A period preventative maintenance every few months meant replacing press-fit bearings, cleaning amazingly stinky phenolic parts, and worrying that we would bend a cam "wrist" and be out hundreds of dollars for a spare as well as having the system be down for a week.  Even before helium prices rose dramatically, recycling helium was a good idea if you could do it.   One of the most depressing calculations you could do as a student in our lab, as you were listening to the intake purifier blow moisture like a sad sneeze and wondering why the hell the DLFH wasn't making liquid, was to compare the cost of your time, recycled helium, and externally purchased helium, and realize that it was clearly financially smart for your adviser to use you to maintain the system.

The DLFH was certainly educational.  I learned a lot about engines and big mechanical systems.  I learned that it is only marginally cheaper to build a heavy crate and ship via an express carrier than it is just to buy a plane ticket for a 130 kg flywheel.  I learned what it feels like to take a jolt of 208 V (not recommended) and that yelped curses from that room could still be heard up in the lab.  To this day I still reflexively shudder a bit when I hear that "pachooka" sound when I visit a place with a similar gadget.  

Anecdote 1: The Qual

A key aspect of a good graduate education is realizing, more than ever, that to be competitive you'll have to raise your game.

My cohort of physics grad students arrived at Stanford in a sunny, dry September of 1993, and we were an interesting bunch.  Four out of the twenty of us were Russian (or from the recently former Soviet Union), and for this story it's important to understand that these folks were incredibly well-prepared in terms of academic physics training.  Growing up in the Soviet system, they basically decided for you when you were something like 14 years old if you were going to be trained as a physicist.  We all got together at a mixer in a crummy graduate apartment, and I still remember a bunch of us standing around the drinks table, chatting about our undergrad schools and what we'd studied.  One person had been a kicker for the Northwestern football team!  One person had been into rock climbing and had done a fun summer program at Los Alamos.  Then one of the Russians said that he'd studied conformal field theory.  For fun.  Kind of set the stage a bit.

At the time the department had a "qualifying exam" that was one of a series of tasks students had to complete in order to (eventually) receive doctoral candidacy.  In this case, the qual was a two-day, six hours each day, written exam with a total of eight problems, basically on advanced Stanford-level undergrad material, administered early in the fall quarter.  Two of the questions were "general physics", meant to test your ability to think on the fly and reason quantitatively as a physicist - these tended to be hard, since they didn't really seem like the kinds of questions you're usually asked in a standard undergrad physics class.  As I later learned from serving as the student rep on the department's qual committee, the point of the test was not to act as a filter to weed out weak students, or some kind of check on admissions.  The intent, at least for the 30% of the faculty who really thought this was a good idea, was that this was an assessment tool.  For example, if you passed overall but did badly on the quantum question, you would be strongly encouraged to think about taking (or grading) the undergrad quantum course.  You had two tries to pass the written exam, and if you were well prepared, you were strongly encouraged to give it a shot as soon as you got started in the program - why wait?  A strong showing on the qual could also ease the process of finding a rotation slot with a would-be thesis adviser.  Still, like any formal exam when the stakes are high, the process was fraught with tension.

Getting a really good qual exam together is very challenging, particularly if you want the problems to be solvable yet not be rehashed from books or other common sources.  This particular year, Bob Laughlin was chairing the qual committee, and he had lost patience with some of his colleagues and decided to put together much of the exam himself.   (Laughlin is a well-known, larger-than-life person who figures in a couple of other stories I may get around to telling.)  The previous year he'd written a question about heat capacity and thermal conductivity involving the cooking of a pot roast.  This problem was sufficiently infamous that he thought it would be funny to write another problem our year about pot roast (though he spelled it "potroast", prompting one Russian to ask, "Vot is this 'po-tro-ast'?").  He wrote a question spoofing "Brilliant Pebbles" (pdf!), a missile defense concept that he found completely ridiculous and impractical.  The exercise was about "brilliant pot roast", with the idea of de-orbiting 2 kg pieces of beef as kinetic kill weapons to take out missiles.   This included giving your opinion and a physics justification of whether the pot roast would splatter on the outside of the missile or punch a cartoonish pot roast-shaped hole through the missile.  He concluded the problem by saying "Don't worry if the numbers you find for this are absurd.  We'll just delete them and replace them with happier numbers.  This is called 'government science'."

We took the test in a big lecture room in one of the buildings ringing Stanford's main quad.   Chalkboards up front, lots of wood, afternoon sunlight slanting through narrow windows near the high ceiling.  The room had somewhat shallow tiered seating and long, curved tables rather than desks, so that everyone taking the exam (probably 30 people or so) could spread out and have plenty of room.   Stanford's honor code meant that the exam was unproctored, but Laughlin was sitting outside doing some reading, in case we had questions about the wording of the test.

Around 5 hours into day 1 (if I recall correctly), Laughlin came into the room, looking somewhat agitated.  "May I have your attention please?  It's been brought to my attention that there is a typographical mistake on the exam."

[groan from frustrated, tired students]

"On the time-dependent quantum problem, these two frequencies \( \omega_{0} \) and \( \omega \) are both supposed to be \( \omega_{0} \).  It may not be analytically solvable as written."

[angry muttering from bitter, aggravated students who had been wasting critical time on this]

"No," says a clear, Russian-accented voice from the back of the room, the same fellow who had studied conformal field theory, "Is difficult, but can be solved.  Have done."

[combination of disbelief, resignation, and semi-desperate laughter from the crowd]

Welcome to physics grad school.

Anecdotes from grad school and beyond

I've been thinking about what a more general audience likes to read in terms of science writing beyond descriptions of cool science.  Interesting personalities definitely have appeal.  Sure, he was a Nobel Laureate, but my guess is that much of Feyman's popularity originates from the fact that he really was a "curious character" and a great story-teller.  I'm not remotely in the same league, but in my scientific career, going back to grad school, I've been ridiculously fortunate to have had the chance to meet and interact with many interesting people.  Some of the stories might give a better slice-of-life feel for graduate science education and a scientific career than you'd get from The Big Bang Theory.  I'm going to start trying to write up some of these anecdotes - my apologies to friends who have heard some of these before....

Several items - SpaceX, dark matter, Dyson spheres, Bell Labs, and some condensed matter articles

There are a number of interesting physicsy science stories out there right now:

• SpaceX came very very close to successfully landing and recovering the first stage of their Falcon 9 rocket yesterday.  It goes almost without saying that they are doing this because they want to reuse the booster and want to avoid ruining the engines by having them end up in salt water.  I've seen a number of well-intentioned people online ask, why don't they just use a parachute, or set up a big net to catch it if it falls sideways, etc.  To answer the first question:  The booster is designed to be mechanically happy in compression, when the weight of the rocket is pushing down on the lower parts as it sits on the pad, and when the acceleration due to the engines is pushing it along its long axis.  Adding structure to make the booster strong in tension as well (as when it gets yanked on from above by parachute drogue lines) would be a major redesign and would add mass (that takes away from payload).  For the second question:  The nearly empty booster is basically a thin-walled metal tube.  If it's supported unevenly from the side, it will buckle under accelerations (like hitting a net).  Good luck to them!
• It would appear that there is observational evidence that dark matter might interact with itself through forces that are not just gravitational.  That would be very interesting indeed.  Many "simple" ideas about dark matter (say photinos) are not charged, so real dark-dark interactions beyond gravity could limit the candidates to consider.  I'm sure there will be papers on the high energy part of the arXiv within days claiming that string theory predicts exactly this, regardless of what "this" is.
• A Penn State group did a study based on WISE data, and concluded after surveying 100000 distant galaxies that there are only about 50 that seem to emit "too much" in the infrared relative to expectations.   Why look for this?  Well, if there were galaxy-spanning civilizations capable of stellar-scale engineering projects, and if they decided to use that capability to build Dyson spheres to try to capture more than 10% of the star-radiated power in the galaxy, and if those civilizations liked temperature ranges near ours, then you would expect to see an excess of infrared.  So.  Seems like galaxy-spanning civilizations that like to do massive building of Dyson spheres and similar structures are very rare.  I can't say that I'm surprised, but I am glad that creative people are doing searches like this.
• Alcatel-Lucent, including Bell Labs, is being purchased by Nokia.  If anyone knows what this means for Bell Labs research at the combined company, please feel free to post below.  
• One interesting article I noticed in Nature Physics (sorry for the paywall) shows remarkably nice, clean fractional quantum Hall effect (FQHE) physics in ZnMgO/ZnO heterostructures.  The FQHE tends to be "fragile" - the 2d electron system has to be in a material environment so clean and perfect that not only can an electron make many cyclotron orbits before it scatters off any impurities or defects, but that kind of disorder has to be weak compared to some finicky electron-electron interactions that are at milliKelvin scales.   The new data shows FQHE signatures at "filling fractions" (ratios of magnetic field to electron density) that correspond to some comparatively exotic collective states.  Neat.
• There is a special issue of Physica C coming out in honor of the remarkable (and very nice guy) Ted Geballe, a pioneer in superconductivity research.  I really don't like Elsevier as a publisher, so I am not going to link to their journal.  However, I will link to the arXiv versions of all the articles I've found from that issue:  "What Tc Tells", "Unconventional superconductivity in electron-doped layered metal nitride halides", "Superconductivity of magnesium diboride", "Superconducting doped topological materials", "Hole-doped cuprate high temperature superconductors", "Superconductivity in the elements, alloys, and simple compounds", "Epilogue:  Superconducting materials, past, present, and future", and "Superconducting materials classes:  Introduction and overview".  Good stuff by some of the big names in the field.

The Leidenfrost Effect, or how I didn't burn myself in the kitchen

The transfer of heat, the energy content of materials tied to the disorganized motion of their constituents, is big business.  A typical car engine is cooled by conducting heat to a flowing mixture of water and glycol, and that mixture is cooled by transferring that heat to gas molecules that get blown past a radiator by a fan.  Without this transfer of heat, your engine would overheat and fail.  Likewise, the processor in your desktop computer generates about 100 W of thermal power, and that's carried away by either a fancy heat-sink with air blown across it by a fan, or through a liquid cooling system if you have a really fancy gaming machine.

Heat transfer is described quantitatively by a couple of different parameters.  The simplest one to think about is the thermal conductivity \(\kappa_{T}\).  If you have a hunk of material with cross-sectional area \(A\) and length \(L\), and the temperature difference between the hot side and the cold side is \(\Delta T\), the thermal conductivity (units of W/m-K in SI) tells you the rate (\(\dot{q}\), units of Watts) at which thermal energy is transferred across the material:  \( \dot{q} = \kappa_{T} A \Delta T/L\).

Where things can get tricky is that \(\kappa_{T}\) isn't necessarily just some material-specific number - the transport of heat can depend on lots of details.  For example, you could have heat being transferred from the bottom of a hot pot into water that's boiling.  Some of the energy from the solid is going into the kinetic energy of the liquid water molecules; some of that energy is going into popping molecules from the liquid and into the gas phase.  The motion of the liquid and the vapor is complicated, and made all the more so because \(\kappa_{T}\) for the liquid is \(>> \kappa_{T}\) for the vapor.  (There is a generalized quantity, the heat transfer coefficient, that is defined similarly to \(\kappa_{T}\) but is meant to encompass all this sort of mess.)  If you think about \(\dot{q}\) as the variable you control (for example, by cranking up the knob on your gas burner), you can have different regimes, as shown in the graph to the right (from this nice wikipedia entry).  

At the highest heat flux, the water right next to the pan flashes into a layer of vapor, and because that vapor is a relatively poor thermal conductor, the liquid water remains relatively cool (that is, because \(\kappa_{T}\) is low, \(\Delta T\) is comparatively large for a fixed \(\dot{q}\)).    This regime is called film boiling, and you have seen it if you've ever watched a droplet of water skitter over a hot pan, or watched a blob of liquid nitrogen skate across a lab floor.  The fact that the liquid stays comparatively cool is called the Leidenfrost Effect.   This comparatively thermal insulating property of the vapor layer can be very dramatic, as shown in this Mythbusters video, where they show that having wet hands allows you to momentarily dip your hand in molten lead (!) without being injured. Note that this demo was most famously performed by Prof. Jearl Walker, author of the Flying Circus of Physics, former Amateur Scientist columnist for SciAm, and inheritor of the mantle of Halliday and Resnick.  The Leidenfrost Effect is also the reason that I did not actually burn my (wet) hand on the handle of a hot roasting pan last weekend.

This heat transfer example is actually a particular instance of a more general phenomenon.  When some property of a material (here \(\kappa_{T}\)) is dramatically dependent on the phase of that material (here liquid vs vapor), and that property can help determine dynamically which phase the material is in, you can get very rich behavior, including oscillations.  This can be seen in boiling liquids, as well as electronic systems with a phase change (pdf example with a metal-insulator transition, link to a review of examples with superconductor-normal metal transitions ).  

submerged due to grant deadline

Fear not, a new post is coming soon, but for now I'm trying to finish off a proposal.

America's "obsession with STEM education" is neither an obsession, nor is it dangerous

I'm late to the party about Fareed Zakaria's piece in the Washington Post titled "Why America's Obsession with STEM Education is Dangerous".  Zakaria is a smart guy, and I recognize that he has a book to sell, but this article is rhetorically frustrating:  He demolishes a serious straw man.  He wants people to be aware of the importance of a broad-based education, and he is apparently worried (or claiming to be for the sake of getting attention) that the US is culturally too focused on STEM and not enough on the other things, like creativity, the arts, and teaching people how to write well.

He is absolutely right that a broad-based education is generally a good idea, and that teaching people actual critical thinking and writing skills and an appreciation for things beyond math and science is also good.  However, I don't think you'll find any reasonable person advocating for purely technical educations with no cultural appreciation and ignoring teaching people how to communicate.   It's easy to demolish an argument that no one is making.  I could write 500 words about how it's crazy for people to drive themselves into crushing debt to get degrees that fail to teach them anything beyond rudimentary writing skills, but that would not be an assault on liberal education.

In two key respects, Zakaria has missed the boat.  First, while there is basically zero chance that we are going to abandon broad-based education in the US, it does seem like there is a far more real danger that we are trending away from science and rationality (c.f. vaccines, evolution, climate science).  Second, and here he was much closer to right, there is a danger in viewing absolutely all public investment in people (via education) and research purely in terms of short-term economic benefit - essentially eschewing basic research or basic education in favor purely of applied research and vocational training of obvious economic benefit to the country.   Frankly, there are people out there who truly do not believe in public education, period, and that's much scarier to me than an imagined attack on the value of the humanities as a component of an education.