Built on Facts

I am a huge fan of the environment. I’m not a huge Al Gore fan. Human beings are part of the environment as well, and the default setting of Gore and many other bureaucratic environmentalists seems to be “Do as I say, not as I do, follow my rules, pay new taxes, and generally try to be as much of a peasant as possible.” Ok, it’s not a fair caricature but often climate change policy ends up looking pretty costly to the average Joe. Like me.

But the earth is an incredible place, and I want to see it stay that way. We’re obligated to take care of it. How can these often conflicting priorities of environmental care and comfortable civilization be reconciled?

Science.

If we can screw things up by accident we can surely fix them with intention. Take CO2 emission, for instance. About half of it comes from fossil fueled power plants and petroleum powered cars. Every day automotive technology brings electric vehicles closer to practicality. There’s also cellulosic ethanol and hydrogen as real possibilities to replace fossil fuel as well. Those all require varying amounts of electrical energy to generate though, and replacing gasoline with coal-generated electricity is a limited improvement at best. We need a better solution for electricity generation. Renewables are often mentioned as a possibility, and indeed they are almost certainly part of the solution. But their flaws as large-scale base-load power are well documented and unlikely to be overcome.

You know where I’m going with this. Snap the bonds on an octane molecule and you get about 5eV per molecule. Crack open a uranium nucleus and you get about 200,000,000eV per atom. There’s lots of energy in nuclear power, and in modern reactors meltdowns are effectively impossible.

The Wall Street Journal has an interesting article about this.

All over the world, nuclear power is making a comeback. British Prime Minister Gordon Brown has just commissioned eight new reactors, and says there’s “no upper limit” to the number Britain will build in the future. German Chancellor Angela Merkel has challenged her country’s program to phase out 17 nuclear reactors by 2020, saying it will be impossible to deal with climate change without them. China and India are building nuclear power plants; France and Russia, both of whom have embraced the technology, are fiercely competing to sell them the hardware.

And just last month John McCain called for the construction of 45 new reactors by 2030. Barack Obama is less enthusiastic about nuclear energy, but he seems to be moving toward tacit approval.

The article is written in a business newspaper, and so it largely focuses on the business hurdles to setting up reactors in the US. They’re extremely expensive with regard to start-up capital, and few businesses are willing to risk that kind of money when lawsuits might potentially derail the entire project. But why are there so many lawsuits and hurdles in the first place? The answer is decades of unexamined fear, made easy by the fact that cheap coal and oil meant nuclear power could be comfortably kept at arm’s length. The solution to that problem is education. Both business interests and environmentalist groups can find common cause here; a public which is informed enough to make good decisions about nuclear energy is a public that is that much closer to a fossil-fuel-free future.

What’s the benefits? There’s cheap fuel not purchased from terrorist-sponsoring foreign governments. There’s reduced air pollution. There’s lessened global warming. There’s less need for large-scale coal mining. There’s abundant energy for the technological requirements of the future.

Ladies and gentlemen, let’s give it a shot.

In Episode 82 of the best applied science show on TV, the Mythbusters looked at some myths involving snow. The basic idea of science is that if you have a question about nature, you set up an experiment and find out the answer for yourself. The Mythbusters do this with verve and alacrity. Occasionally they take some gentle chiding from professional scientists for not doing “real” science with mathematical rigor and constant retesting, but I think that’s a bit of a red herring. Mythbusting is every bit real science, it’s just not academic-style science. Professional scientists are working on difficult unsolved problems by definition, and so those kinds of problems have to be attacked much more carefully because if they were easy they wouldn’t be unsolved. “Will your tongue freeze to a cold pipe like in A Christmas Story?” is a scientific question with a scientific answer, but not one that needs hardcore academic methods to address.

However in this particular episode, they did manage to run head-on into a type of problem that Mythbusting methods aren’t well equipped to handle. It’s a problem with a low signal-to-noise ratio.

Signal-to-noise ratios are in concept like looking for one person you know in a large crowd. While you’d easily be able to pick out your friend in a room with just a few people, a stadium full of people might mean you’ll be looking for a while. The signal (your friend) is small in comparison to the noise (the crowd). The only solution is to do a better experiment (maybe call him on the loudspeaker) or run your original experiment longer.

The Mythbusters question was whether an avalanche could be triggered by a loud noise, such as yodeling. Adam and Jamie tried to create avalanches by using noise, and tested their sonic efforts against more traditional methods like explosives, machine guns, and air cannons. There was limited success with any of those, and no success at all with the yodeling.

You wouldn’t really expect there to be. To start an avalanche, the snow pack has to be very close to slipping slipping. All it takes is a push to get it going. Usually the push has to be something significant - one of Jamie’s bombs, or an unlucky skier. Sounds waves are very, very weak and so that snow would have to be absolutely right on the barest possible threshold before avalanche in order for a sound wave to get it started. It stands to reason that snowy mountains balanced that finely will be few and far between.  But it’s very probably not impossible.

Things that seemingly stand to reason have been wrong before though, so we’re caught in a quandry. The Mythbusters can stand with the data and declare the myth busted. Or they can make a judgment contrary to data and declare it plausible on the basis of physical principles and reports from the field. Neither is very palatable. The dillemma was only given a very brief discussion at the end; Adam insisted that the myth was busted because in the final analysis the show must defer to data. Jamie agreed to an extent, but also thought that the myth needed to be revisited.

I agree. This is one of those situations where the rigorous academic science method of taking lots more data would have come in handy. If you deal 100 hands of poker, you might conclude that the royal flush is a myth, but in reality you just haven’t played enough hands yet. Instead of just “confirmed”, “plausible”, and “busted”, maybe there should be an “inconclusive” for those times where a one-hour show just isn’t enough time to adequately do the experiment.

Yesterday I completely forgot to mention the anniversary of the most amazing thing humanity has ever done.  July 20, 1969, Neil Armstrong, Buzz Aldrin, and Michael Collins successfully completed our first steps onto another world.  Though I was born long after their success, I am in absolute awe of them and those who helped make the mission possible.  They are an inspiration to me, and will be inspiring future generations forever.  Let’s do some classical mechanics in their honor:

This a cute trick that I first saw in my undergrad classical mechanics class. You grad students and above will already know it, but hey, everyone has to start somewhere.

Let’s say you have some force which is a function of position. A gravitational potential, for example. You have some initial velocity and you’d like to know how velocity varies as a function of distance. Say you want to find the maximum height of a projectile shot directly upwards, or similar. You’re not worried directly about velocity as a function of time. Odds are the equation you’re given is the equation for force, and thus the equation for acceleration up to a factor of 1/mass.

Hmm. There’s time involved in that, and if possible maybe getting rid of it will shed some light on whatever our problem happens to be. How about the chain rule, which we learned in calculus?

Does that help any? Yes, it does! The last term dx/dt is just the velocity v, and so we have

Now there’s a version of Newton’s second law you may not have seen before. No time dependence at all, not directly. And that can make it quite useful for various forces F which depend on v but not t directly, chiefly through rearranging into the integral

For an example of throwing a rock in a gravitational potential F = -mg, (taking g positive) we get

With initial and final positions and velocities subscripted appropriately. Performing the integrations and canceling m gives

Now we might as well solve for the final position so the equation is a little more useful

You could set the final velocity and initial position to 0 if you wanted to find the maximum height attained by a rock thrown upward if you wanted, and you’d get exactly the usual result.

“So Matt, this is probably the third time you’ve treated the falling rock with some different weird method. What gives? Isn’t 1/2 g t² good enough?” Yes it is, but the rock is just an example which I’m using precisely because we know what should happen and thus we can verify that we’re not misunderstanding the new method. There’s plenty of problems where this method will give you a pretty easy solution where using the time dependence directly would be much harder. In fact I’m going to treat that rock at least two more ways; we haven’t yet done the classical Hamiltonian formulation or the quantum mechanical propagator.

Professional carpenters have a lot of tools in their workshops for a reason. Physicists learn a lot of math for precisely the same reason.

This is the graph of the Bessel function of order 0, along with its asymptotic approximation for large x. You can see that the convergence is quite fast. The Bessel function is important in many problems in physics, from solutions of the Helmholtz equation in cylindrical coordinates (as in a vibrating drumhead) to many quantum mechanical systems.

In non-physics news, I saw The Dark Knight this weekend. Oh holy carp. Previously it was perfectly true to say that there were comic book movies which were legitimately good film - Spider Man 2, Sin City, a few others. There weren’t any that were actual Great Films, though. The Dark Knight rises to that level. I can’t speak highly enough of it. It makes the Batman Begins look like sunshine and bunnies.

For some light weekend posting, here’s the latest xkcd. It’s a pretty funny commentary on the state of academic discourse in literary fields. Remember the Sokal affair? That’s what happens when you build a discipline on something other than facts.

Which is too bad. Literature and its study are beautiful things, but you can twist anything into anything if it will get you notoriety as a transgressive deconstructionist or whatever. It’s too bad such things have been in vogue for so long. After all, a sufficiently clever person can make Moby Dick a metaphor about marriage!

I am sick. Sore throat, sinus congestion, muscle soreness, all the hallmarks of what I hope is just the common cold.

Barring more serious failures of the body itself, illness is usually caused by bacteria trying to eat you, or viruses trying to program you to stop all that pesky “life” business and get to the real work or producing more viruses.

If they haven’t developed antibiotic resistance, bacteria are usually more or less killable. They’re living things, so if you saturate them with enough chemicals which interfere with their metabolism you can kill them or at least stop them from reproducing. Viruses are trickier. They’re not alive, at least not in any usual sense of the word. They’re little DNA or RNA carrying packages which simply latch onto your cells and make them do the work of making new viruses. With no metabolism to disrupt, there’s not really any good way to kill them chemically. You can shred them to little bitty disassociated pieces with something like bleach, but this is not a viable treatment for viruses already in residence in your body. Interferon is better, but generally not even remotely approaching a cure.

Here, straight from the Wikipedia article, is a picture of an adenovirus.  Two, actually:

You might notice it’s a very regular geometric shape. This particular bundle of viral joy is an icosahedron, itself made up of roughly spherical globs of protein capsids which form the external structure. Hit it with a tiny tiny hammer and it will vibrate just like anything else, from bells to wine glasses to the Tacoma Narrows Bridge. What laymen usually call natural or resonant frequencies of an object are usually called normal modes, eigenmodes, or something similar by physicists.

Dump enough energy into an object vibrating at resonance and you may well be able to shake it apart. It happened to that bridge at Tacoma, and it happens to wine glasses in science demonstrations all the time. Here, for instance.

You can’t do this to a virus with sound. The resonant frequency of a virus is way, way too high to even think about trying to use sound. But how about light? Its frequency can be pretty much as high as we want. The trick would be to figure out just what the resonant frequencies of the virus particles were. You can’t literally hit one with a hammer to see how it vibrates and so the only remaining option is to do the hardcore computational physics to calculate the normal modes from scratch.  For a bumpy system where atomic-level resolution is important this is very, very difficult.

Eric Dykeman and Otto Sankey have developed a pretty good system for doing this, published in PRL 100, 028101 (2008).  They’ve successfully determined the normal modes for several viruses, and that’s the first step to selectively vibrating them to pieces with lasers.  There’s a lot of technical difficulties to be overcome, and it may never become a practical reality.

But as I sit here with a box of tissues and a bottle of Day-Quil, here’s hoping it does.

We now know the physics, which is: this is the quantum mechanics of the sequence of symmetry operations to create mass out of light by compressing charge.
- Dan Winter, Public Speaker on Sacred Geometry

Wait, what?  Beats me, I haven’t got the foggiest idea what he’s talking about. Well actually that’s not quite true. He’s stringing together physics words which sound to physicists just like lorem ipsum sounds to classics scholars. And I don’t know what Sacred Geometry is supposed to be either, but it doesn’t sound promising. I found this particular gem of not-physics via StumbleUpon as part of a trailer for a documentary by an outfit calling itself Covert Garage, which aims to “lift the lid on underground energy inventions”.

Well. In theory this could be a fine undertaking. There’s lots of hobbyists who have built vehicles which run on vegetable oil, or batteries, or which are brutally optimized for highest possible fuel efficiency, and many other creative, clever, and legitimate ideas which may well have real applications for the future.

The trailer seems not to be about any of that. It’s about a guy named Joe, who has built a device called the Joe Cell which they don’t quite come out and say is a free energy machine. There’s the perfunctory soundbite from a dour-looking professor saying the device can’t possibly work, followed by a cut to a shot of the device working. “Working”, anyway. “If it’s so easy to build one of these machines, why aren’t hundreds of people doing it?”, he reasonably asks - followed by a cut to hundreds of pages of Google results of people doing it. “Doing it”, anyway.

But that could just be a marketing tactic to drum up interest. There’s also a shot of a man talking to a gathering of the enthusiasts of this device. He offered $5000 to anyone who was willing to bring in their purportedly water-powered cars to his mechanic to be examined. There were no takers. This is followed by a shot of the inventor explaining the conspiracy to shut him down.  That’s more promising, as it’s a pretty good look into the mindset of many free-energy types.  As such I couldn’t hazard a guess about the view the documentary takes, credulous or incredulous. Actually I think the ideal would just be to let the cameras roll and let the intrinsic… colorfulness of the people involved speak for itself.

As for my opinion, it’s true that there are plenty of unexplained things left in physics.  Macroscopic room-temperature electrical phenomena aren’t among those things. The device doesn’t and can’t work. Noether’s Theorem guarantees that even the unexplained things in physics can’t generate free energy as long as the laws of nature don’t change with time. As far as we have ever seen, they don’t.

But never let it be said that I’m not willing to keep an open mind. The Joe Cell is small, and it is supposed to produce enough power to run a car. That makes it an absolutely ideal candidate for the Built on Facts Protocol for testing free energy. I’m not holding my breath that Joe will rush to apply.

I believe I originally planned the Georgia trip post for Monday, and then pushed it back to Tuesday. Here it is Wednesday and I’ve finally written the darn thing. C’est la vie.

Where to start? Last Thursday morning I drove from College Station to Houston where my flight was departing. There’s an airport in College Station but it was considerably more expensive to fly out from there for some reason, so Houston Hobby it was. I’ve mentioned before that we grad students are not rich, and if all that math training is good for anything it’s good for minimizing whatever the financial equivalent of the classical action is.

An unfortunate lightning and hailstorm knocked Atlanta’s Hartsfield-Jackson airport offline for a few hours, and so we landed at some tiny airport in Columbus for two hours before taking off again and arriving in Atlanta. Met up with some friends and wandered around downtown for a few hours and attempted to see the aquarium and the Coke Museum. Both were closed by that time - apparently Atlanta is not one of those cities that never sleep. So we had fun walking through Underground Atlanta, at which we were pretty solidly a minority. Lots of Obama shirts and such. I don’t think this is just stereotypes being expressed; later on we spent some time in blazingly white Cumming, GA and didn’t see a single McCain sticker. While it’s perfectly possible he simply appeals more to people who don’t actively participate in politics, there does seem to be an enthusiasm gap. This observation is built on anecdote, not facts, so take it for what it’s worth - not much.

Of course the reason I was in Georgia in the first place was to see my girlfriend’s sister’s wedding. The ceremony was held at the lodge in Amicalola Falls State Park, which is a really lovely place with a 700-foot waterfall. There’s a trail leading from the lodge to the base of the falls. Despite the fact that the downhill climb is in theory a perfectly natural energy-favorable process, it’s surprisingly strenuous. The uphill climb was much worse and revealed that I am in fact in tremendous need of some endurance-building exercise. The staggering amount of reception food I ate a few hours earlier probably didn’t help. Let’s see, my weight times 700 feet is about… a whopping 36 (food) calories. Oh good grief. Well, I guess the fact that the human body is not nearly 100% efficient means I actually burned a lot more than that. That’s what I’ll tell myself anyway. All in all though, it was a great experience. The wedding went without a hitch (other than the intentional one), and not only did it not have a faulty unity candle, they actually kept the dramatic moment where they inquire if anyone had a reason that the marriage should not take place. No one did. The groom and his father are both applied scientists - petroleum engineers to be specific - and we had some great conversations about the future of oil and other energy sources. We’re all big nuclear fans. As my wedding attendance goes, this was certainly one of my favorites.

The next day I arrived at the Atlanta airport at 10 AM, with my flight scheduled for departure at noon. My flight had been overbooked and I was put on standby. While I understand the efficiency rationale behind overbooking, the fact of the matter is that I paid for a seat on a certain flight and it’s frankly rather irritating that some airlines (AirTran in this case) are willing to say “Oops, it seems we’re not going to give you the service you paid good money for, despite the fact that we’d wouldn’t refund in a million years if you failed to show up for your flight.” As it was, more inclement weather delayed the arrival of our plane at our gate until about 4 PM. It would have been more tolerable to just tell us that, but instead they pushed back the estimated departure time by about 45 minutes every 45 minutes. Then with no explanation, the plane sat at the gate for another two hours while different flight crews meandered on and off. Finally at 6 we were in the air, as apparently enough people had missed their connecting flights and given up to try their luck at a later flight so that I managed to wrangle a seat on the flight for which I actually bought a ticket. To top it off, roughly 75 minutes elapsed between landing and the first luggage appearing at the baggage claim carousel. It was a rough day.

You don’t want to read about it, and at this point I’m done thinking about it.

To make up for the appalling lack of science in this post, and to continue the theme of woeful sorrow over the air transportation industry, here’s Michael Benson in the Washington Post with a proposal for the International Space Station: move it out of low Earth orbit and use it as a large spacecraft. It’s actually possible, and at any rate couldn’t be any more of a waste than it is now, draining funds that could be used for robotic science missions or (my counter-science-cultural preference) more dramatic and groundbreaking human spaceflight. Strap an ion engine on to the thing and let ‘er rip. It’s worth looking at the idea, anyway.

Yesterday in my recitation section I went through the chapter on electromagnetic induction, covering Faraday’s law and the displacement current term in Ampere’s law before assigning a quiz. Though this quiz really doesn’t need those concepts, it was a good opportunity to break out my all-time favorite Intro E&M quiz question.

Consider two parallel wires of infinite length, separated by a distance r, each with a uniform positive charge density λ. Both wires are moving in the same direction with velocity v, also parallel to the wires. If the electrical repulsion is exactly balanced by the magnetic attraction caused by the current, what is v?

I’ll assume you know how to get the electric field of a long wire. It’s

And the force felt by a length l of the other wire is thus

Which is a little awkward because l is infinite, but the force per length is a fine thing to use:

Ok, that’s that for the electrical repulsion. The magnetic field of a current-carrying wire is

Doing the same sort of jazz as above to find the force per length, we get

Now we need to figure out what the current is. Current is (charge/time) which is the same thing as (charge/length)*(length/time). And that is just the charge density times the velocity. We get as our final expression for the magnetic force per length:

Since the magnetic force must exactly cancel with the electric force, we have

Solve for v and you finally get the answer

Gasp! It’s the speed of light. The goal of the quiz is of course to show in dramatic fashion that the speed of light is naturally a consequence of the very same equations we’ve been using to characterize mundane charged particles and wires. When I first saw this problem as an undergrad it felt like an epiphany. Yes of course you can show that Maxwell’s equations satisfy the wave equation, but it’s quite another thing to see light metaphorically blaze forth from a problem with nothing to do with light at all.

Lurking in the background is some even deeper physics. After all, in velocity regimes less than c the electrical repulsion will be partially canceled by the magnetic attraction and thus the acceleration of the wires apart from each other will not be as fast. But in a frame of reference moving along with the wires, there’s no velocity at all and thus there’s no magnetic field at all. The wires should accelerate apart at full speed in that frame. Einstein ended up dramatically dispatching this discrepancy when he wrote the relativistic versions of Maxwell’s equations. Turns out (simplifying, and making a long story short) that in fact relativistic effects resolve the difficulty. The premise of the question - that the electric and magnetic effects completely cancel - is not actually realizable.

The question has some real depth, and it’s not too often you have the opportunity to do that in a question that a Physics 208 student can be legitimately expected to do. So I’m always looking forward to being able to assign this particular problem!

Well. I had planned to write the story of my weekend in Atlanta watching a wedding, but a whopping six hour delay at the Hartsfield-Jackson Atlanta International Airport meant I didn’t get back home in time to write up much here to make the Monday morning post. With any luck I should have that written up for you by Tuesday morning. Suffice it to say that there was lots of delicious wedding food, Mr. W and Miss S became Mr. and Mrs. W, and since Mr. W and his father are petroleum engineers and many of their friends are engineers as well, there was plenty of good sciency conversation even though most of the crowd wasn’t particularly science-inclined.

And even though the six hour delay at the airport was extremely frustrating and nerve wracking (did I mention the flight was oversold and I ended up on standby?), I at least had plenty of time to read some of M. Scully’s excellent Quantum Optics textbook.  There’s a particularly interesting discussion on whether the photon has a wavefunction, which explores some interesting territory and consequences that I haven’t read much about previously.  The short answer is “not really”, but it’s a more subtle point than you might initially expect.

So as you read this, I’m probably off teaching the undergrads about Faraday’s law.  And I have a doozy of a quiz for them.  Here’s hoping they pay attention!

And finally, andy.s gets 10 bonus points (1:1 exchange rate with Whose Line Is It Anyway points) for correctly solving the other quiz problem a few posts down.  Good job!  He also makes me feel guilty for not having spent the time to figure out how to put LaTeX on this server despite it having been on my list of things to do for several weeks now.  I promise I’ll get around to it eventually!