I found a really promising book on Amazon the other day. It looks very relevant to my research, reasonably priced -- a perfect addition to my wish list, given the current status of our family budget!

On adding it to the wish list, I was greeted with a rather bewildering sight...

I suppose nanomaterials research, being a more advanced subject, tends to attract researchers from a more advanced stage in life. It's not inconceivable that some of them might have kids, for whom they also shop at Amazon. Or maybe they just really like animated films.

Either way, it's a pretty funny connection.

0 Comments

After weeks of continuous and unvarying disappointment in the results of my samples, I got a very pleasant surprise. The TEM came back from a recent batch, and the results are stunning. A beautifully monodisperse monolayer of particles, with long range ordering. It's the kind of monolayer picture I could present at a conference. And most surprising of all, I didn't even use the Langmuir trough! Nope -- it's just a single drop applied by pipet to a TEM grid.

All my best TEM pics are available in the TEM album. Unfortunately I never wrote the code to link directly to an individual image, so you'll have to hunt around. Should be pretty obvious which one it is, though, and the rest of the pictures are pretty too. Note the scale bar in the bottom left, which tells you about the size!

0 Comments

So we're down to two more assignments, period, for the semester, and one of them is due today. We're doing relativity in E&M, and it's been a real treat. For the first time, I feel like I'm getting a really solid foundation in this most beautiful of subjects, and the index gymnastics of Minkowski space tensor analysis is even starting to feel natural to me!

The first problem was to find the general Lorentz transformation for constant velocity in an arbitrary direction. I knew it had to reduce to the simple (quasi)block-diagonal form for velocity along one of the axes, and I was hoping for some kind of beautiful symmetry. My plan of attack hinged on realizing that regular rotations are Lorentz transformations, too!

So the idea is this: if the velocity vector makes a polar angle theta with the z-axis, and if its projection on the xy-plane makes an azimuthal angle phi with the x-axis, then we do a rotation about the z-axis by an angle phi, then rotate about the new y-axis by an angle theta. (The point of this is to line up the z-axis with the velocity vector.) Now we know how to do a Lorentz transformation along one of the axes; it's really easy! So we do that along our new z-axis, and then we make the inverse of the (composite) rotation we did to align our z-axis (which puts us back into the old coordinates).

Any symmetry I could have hoped for, I got. The first thing that jumped out at me was that when all was said and done, there was not the slightest clue in the final matrix that it was the z-axis I had chosen to align. (This is necessary for it to be correct, of course, but still very aesthetically pleasing!) Even better was when I subtracted off the identity matrix: the space-space components all had the same factor of (gamma - 1), and they all paired up perfectly: the xy-component had the product of the x- and y-projections of the velocity, same for the yz-component, the xx-component, etc. Simply beautiful!

The second problem was a more practical one: given that 2/3 of charged pions are observed to survive a distance 30 metres from a collision site (in a particle accelerator), and given the half-life of pions in their own rest frame, what is the energy of the pions in the collision? It wasn't particularly difficult, but it was a fun problem, particularly because if you use lab time instead of proper time, you'll come to the (erroneous) conclusion that they're zipping along faster than light. :)

The third problem was the hardest to do, but the easiest to explain to a general audience. Essentially, it's a more practical realization of the famous twin paradox. Usually, the twin paradox goes something like this: suppose of two twins on Earth, one leaves on a spaceship and travels near the speed of light for 20-odd years, and returns to Earth. How much time will have passed on Earth during that journey? (Answer: a lot more!) But if any reference frame is as good as any other, then the twin on the spaceship can surely claim to have been stationary while the Earth moved far away and then back, right? Well, the difference lies in acceleration: in order to get to the speed of light in the first place, the spaceship must accelerate, which is an effect that can be detected on the ship but not on Earth. Remember, not all reference frames are created equal, just all inertial reference frames.

But that's still a bit sketchy, becuase when the spaceship turns around, going from near the speed of light one way to near the speed of light the other way is a huge amount of acceleration, and our spacefaring twin has much bigger worries than a now-long-dead sibling. Jackson poses a more satisfying question: let the spaceship accelerate instead constantly, for 5 years, at a rate equal to the gravitational acceleration near the Earth's surface. (This will make the ride much more comfortable!) For the next 5 years it decelerates at the same rate, then turns around and does the same thing. 20 years total, from the spaceship's reference frame. How many years have passed on Earth in the intervening time?

Three hundred thirty-eight.

That's right, 338 years pass on Earth during that spaceship's trip. And believe me, that answer was not easy (for me) to come by! Consider this: the acceleration is constant in the spaceship's own reference frame. But it's speed in its own reference frame -- i.e., its speed with respect to itself -- is always zero by definition! Trying to figure out how it can be always increasing yet always zero is just one conceptual hurdle that had to be cleared. Really, all the difficulties stem from the fact that the velocity isn't constant: acceleration complicates things in special relativity.

I feel like I'm learning a lot in this class, and this semester overall. Now, time for exams and then Christmas break! (When I'll finally be able to respond to emails again... :P)

0 Comments

Good food, great discussion, and all of it free. It boggles the mind that more didn't attend!

We had a Pugwash meeting this evening on the topic of the ID/evolution debate, and what we as scientists can do to promote good science. Pugwash is named after Pugwash, Nova Scotia, where many eminent scientists first met in the middle of the last century to discuss the ethical implications of their work and their responsibilities to society at large.

There didn't actually seem to be any ID supporters in the crowd. The organizer tried to play Devil's advocate at first, but didn't have much to work with. We discussed the arguments for and against ID at first, then moved on to discussing why it doesn't belong in the science classroom and what we can do about it.

The main point that I took away from it was that more critical thinking skills are needed in schools in general, because good science is difficult enough to distinguish from bad science as it is. We can (and should) address the ID issue directly, but ultimately that's only a band-aid solution. It doesn't do any good for students to accept evolutionary theory just because teacher told them so: we must teach them how to think, and not what to think.

I sat next to a guy who was very strongly atheistic. Most of us didn't have a problem with ID being taught in, say, Philosophy class, but he was vigorously opposed to any form it might take, referring to it several times as a "dangerous idea". Funny, that's what fundamentalists usually say about atheism! Ultimately, I see the people who declare religion and science incompatible, no matter which they advocate, as flip sides of the same coin. As a religious person and a scientist, I strongly disagree with the both of 'em.

There was one person who was there from the beginning, and was relatively quiet compared to the rest of us. He made a comment about the compatibility of religion and science, and how they complement each other. Right on! He left soon after. I wish we would have heard more of what he had to say; there might have been some insights we missed out on.

Ah well. Now that I'm well fed (a bit too much so, perhaps) and home, I haven't really got any excuse not to prepare tomorrow's recitation.

7 Comments

Apparently when I use my hairdryer in the bathroom, the lights get dimmer. Now call me crazy, but isn't that slightly suggestive of a poor job of wiring? Makes for a fun electronics question, though: is the plug in series or parallel with the lights? Answer: it's in serial, and it shouldn't be.

Further experimentation reveals that the two switches (one for the main light, and one for the shower light and fan) are wired up in parallel, since neither affects the other. What a funny oversight with the plugs!

2 Comments