Blog Index
This past Monday was the culmination of three weeks' worth of frenzied studying, learning everything I could about gravitational waves. Rather a tall order, since I never took a course in general relativity to begin with, but I digress. Once I'd given my 20-minute, no-notes talk, and braved the following 60-plus minute question period, all that was left was to wait.
Yesterday the faculty met to decide everyone's fate, and shortly thereafter came the news -- I passed my special oral qualifying exam! It was a real relief, since I didn't know whether I'd passed (I didn't ace it the same way I aced the written quals). Thus, all the hurdles are behind me, and nothing stands between me and doing my thesis research. The pizza and beer were well-earned!
It's exciting that things are basically in my own hands from here on out. I have the opportunity to really take charge, stay focused, and get my research done and thesis written in as few years as possible. I hope I can prove up to the challenge!
ScienceAfter 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!
I just got the email from Prof. Majetich. Turns out there is room for me in the nanoparticles group! It's a real change in direction for me, but I can't help but be utterly fascinated by the things. I'm going to be working on the Spin-NIRT data storage project. I get to figure out how to get nanoparticle monolayers to write to media, which apparently is quite hard. And in the process I will understand electricity and magnetism -- understand them, you see -- down to the very core of my being.
I have mixed feelings about having given my final two recitations for the semester today. On the one hand, I'm relieved not to have to wake up before 7 in the morning just to get to school on time. On the other, I'm sure going to miss my kids! I ended up with two great groups this year with whom I could scarcely be happier. And my teaching today between morning and afternoon could scarcely be more different.
The morning section was subpar, to put it politely. I felt like I didn't enlighten them, and the fact that I forgot my textbook at school last night really showed through in my relative lack of preparation. It went alright, overall, but I didn't do nearly enough examples and I didn't explain what I taught particularly well.
The highlight of the morning section was definitely another transcendental experience. A rather bright student (whom I'll not name here) asked me a question about something I'd explained. While I was answering the question as best I could, I looked at him to find that he had fallen asleep while I was answering his own question. I asked him at the end whether the answer was satisfactory, and there was a noticeable pause before he jerked awake again and told me I had. Just as I was turning to write something else on the board, I heard his voice again.
"Um... could you repeat that last bit?"
I struggled mightily to suppress my knowing smile as I indulged his request. Fortunately, as a student, I know from experience that falling asleep does not imply a lack of interest. Still, I don't think that'll be topped any time soon!
By the time my afternoon section rolled around, I had definitely learned from my mistakes. I spoke clearly, gave good examples, and tied things up nicely at the end. As I began to hand back what homework remained, I received something I certainly never expected.
Applause.
Several of my students actually applauded my work as a TA as I finished. It was kind and affirming -- definitely an excellent start to my career as an educator! I know I still have a very long way to go, and have a lot of improving to do, both in terms of knowledge and technique. Still, it was a kinder compliment than I could have hoped for.
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)
Humour
Personal
School
So today I handed out my midterm evaluations to my students. In theory, this gives them a chance to offer constructive feedback, allowing me to adjust my style accordingly to serve them better. This ended up being the case for the vast majority of students, and they really gave me a lot to go on when considering how to improve my teaching. However, the best feedback ever cannot reasonably be placed in that category. Good thing these forms are anonymous, eh? :)
Also I'd like to apologize to everyone I owe an email to. It turns out that grad school is hard -- in fact, it's very hard and it keeps me busy all the time. Rest assured, though, that I haven't forgotten you! I hope after these next few weeks pass (round 2 of midterms is upon me) I can turn my attention to correspondence once more.
