mspringer | September 30, 2008In physics, you come up with an idea, formulate it mathematically, find the theory's predictions about the real world, and test those predictions by experiment. This works because God is subtle, but not malicious (to borrow Einstein's words). In more concrete language, the laws of physics fit well together and make sense as a coherent, testable experimental whole.
Mathematical truths are not so easily verifiable. Because mathematics in some sense encompasses a much wider spectrum of possibilities, experimental tests can't cover all the needed ground in most cases. The laws of physics are…
mspringer | September 29, 2008Update: I seriously feel guilty for writing politics in a physics blog. I personally sometimes get annoyed at reading politics on other non-political blogs, and I imagine you do too. That's why I happily encourage you not to read anything I write tagged with politics unless you like that sort of thing. The election's only a month or so off. I promise after that the politics will be few and far between, and until then I'll still try to keep it to only an occasional thing.
The bailout is dead. As congressional acts often do, it may come back to life at a later date. But for the moment, it…
mspringer | September 29, 2008#7 - Erwin Schrodinger
Schroedinger, Erwin! Professor of physics! Wrote daring equations! Confounded his critics!
That's the first couple of lines of Cecil Adams' brilliant epic poem about Schrodinger's cat. Why does Schrodinger deserve an epic poem? Because he's the 7th greatest physicist, that's why.
Schrodinger was born in Austria in 1877. Looking back we can see that such a placement is a bit ominous, but war has rarely prevented science from moving forward. Quite the opposite, usually. He achieved his habilitation in 1914, and spent the next four years as an artillary officer. It…
mspringer | September 27, 2008Due to some homework which is taking longer than anticipated, today's Sunday Function will have to be a bit quick. It's no less interesting for that.
Define a function Q(n) on the natural numbers, such that Q(n) = 1 for a prime number and Q(n) = 0 for a composite number. In other words, it's just a function that checks to see if a number is prime or not. If you were trying to evaluate this function by hand, you could do so by manually dividing n by all the numbers less than n to see if anything divided evenly. Actually this would be very inefficient, you only have to divide by the prime…
mspringer | September 27, 2008The debate? Didn't watch it. I'm keeping my "not watching the debates this year" record spotless. Not because I don't want to keep myself informed but because modern TV debate formats don't let anyone do anything but go for the best soundbites, zingers, and gotchas. That said I'll probably read the transcript, but I can't bear to actually waste the time to sit through watching it live. I'd personally like candidates to debate Lincoln-Douglas style including cross-examination, unmoderated except for a guy with a timer. That I would watch. Anyway, both sides seem to be more or less…
mspringer | September 26, 2008Mean-spirited reactionary politics below the fold. If you're a kind-hearted liberal here for the physics, you might want to skip this post, have a nice tea instead, and calmly meditate on Obama's recent rise in the polls.
I've had several conversations with people over the past few days about the cause of the current financial crisis. One common refrain is that deregulation regulation pushed though by heartless free marketers is the cause. "Ok", I ask them, "what regulation specifically?" And I generally don't get an answer. The reason is that the crisis is due to loans not being repaid…
mspringer | September 26, 2008The Terminator?
Which headline do you think would sell more papers?
INTELLIGENT ROBOTS KILL 20,000, NO SIGN OF STOPPING
or
AUTO FATALITIES DECLINE 50%
In a nutshell, this is the PR problem of technology. Technological progress is taken for granted, and technological problems are trumpeted to the skies. In this case, I'm pessimistic about the chances of autonomous cars. Here's an article for Motor Trend which isn't really about the safety of robot cars, but which takes the following shot anyway:
"Driving will be safer," say the experts. "Computers will ensure that smart cars always maintain…
mspringer | September 25, 2008We're holding a rock, and we drop it. What happens?
There's lots of methods for treating this problem. We've done it with Newton's laws of force, and we've done that in more than one way. We've done the Lagrangian formulation in terms of minimizing the classical action. I don't think we've done the quantum mechanical propagator yet, but we'll get to it. Today we'll do the Hamiltonian formulation.
Like the Lagrangian, it's a formulation of mechanics that's based on the relationships between energy, momentum, and position. Define a quantity H called the Hamiltonian, and set it equal to…
mspringer | September 24, 2008#8 - Paul Dirac
Dirac was a physicist of incredible brilliance even by the standards of the great physicists. You can't turn a corner in quantum physics without bumping into something he discovered.
Solve the ubiquitous and vitally important quantum harmonic oscillator problem using the wave equation method and you'll get a complicated and not especially enlightening differential equation and its solution. Solve it using the elegant and clear operator method and you'll have taken a first step into a larger and richer view of the quantum world. Dirac was the first one to notice that this…
mspringer | September 23, 2008Hey, I just wanted to draw some attention to this great post of Chad's about femtosecond lasers and laser bandwidth in physics and chemistry. Those lasers are near and dear to my heart, as they're one of the main focuses of my research group.
And just so you have some original content, here's the Crazy Matt Opinion Of The Day: I like the Seinfeld Microsoft ads. They don't make me want to buy Windows, and they're not very dramatic or even interesting. I like them because they have Bill Gates doing the robot and reading a programming manual as a little kid's bedtime story. I like the idea…
mspringer | September 23, 2008How about a quick little circular motion exercise, since that's what I'm teaching in my recitation at the moment? We know the force equals mass time acceleration, so how about we put the force of gravity on the right side and the force required for uniform circular motion on the left:
And we'll solve that for the velocity:
That's the velocity you need to reach in order to attain circular orbit at a distance r above the earth's center. M is the mass of the Earth (or whatever you happen to be orbiting, and m is the mass of the thing in orbit. Of course m cancels anyway. But what if we…
mspringer | September 22, 2008Richard Feynman once said of large numbers that "astronomical" was no longer the best adjective. "Economical" was. There are more dollars in the national debt than there are miles in a lightyear.
Today we're getting a some exposure to one of those numbers: $700 billion. It's the size of the bailout of the various failing banks. People like to trot out the Iraq war (if I may link to an anti-war site so you can be sure the cost is not biased downward) when discussing how federal money could be better spent, so let me do the same thing. The five years of the Iraq war have cost more than $…
mspringer | September 22, 2008Several places in the Bible, there's long lists of genealogies. The first chapter of Matthew, for instance, looks pretty much like this: ...and Asa begat Josaphat; and Josaphat begat Joram; and Joram begat Ozias; and Ozias begat Joatham; and Joatham begat Achaz; and Achaz begat Ezekias... and so on. There's a point to it. Ancestry and tribal lineage were a big deal to ancient peoples, and lists of genealogy were how people kept track of ancestry.
Extreme talent in the sciences is rarely hereditary. Great physicists tend to be extreme outliers and regression to the mean tends to reduce…
mspringer | September 21, 2008In our tour of the zoo of functions we've been spending time in the snake pit. These are the pathological functions of pure math, and are generally but not always useless in physics and pretty much everything else. But they're very cool to look at! We'll eventually get back to the useful domesticated farm animals of the functions but we're in no hurry. Here's the next snake and its picture:
It looks like a double-valued function, a straight line under a parabola. but it's not. If x is rational, f(x) is just the square of x. Otherwise, it's 0. So f(π) = 0, but f(3) = 9.
It's loosely…
mspringer | September 20, 2008Has anyone checked out ScienceBlogs' new election site, A Vote for Science? It's nominally about science issues in the presidential and congressional elections, but of course in practice it's a pretty standard near-self-parody of the ultraviolet end of the political spectrum. Well, I've got an account there as well. Haven't used it yet, but I think I probably will at some point. My own nutty borderline minarchist politics will be decidedly in the minority, but it's no fun if everyone agrees with you anyway.
Moving on, a couple of links. Here is Dr. Frank Close of Oxford University…
mspringer | September 19, 2008#9 - J.J. Thomson
The entire edifice of chemistry is a theme and variation on the study of the properties of atomic electrons. Tremendous sections of physics, from solid state to quantum optics to AMO and beyond hings almost entirely on electron behavior. Astrophysics, spectroscopy, and large chunks of high energy physics rely on the understanding of the electron. And those are just the leading edge of what the electron means to modern science. More than anyone else, we owe J.J. Thomson for what we know about the electron.
No one knew for sure that there was any such thing as an electron…
mspringer | September 18, 2008#10: Wolfgang Pauli
Wolfgang Pauli was once asked to critique a paper of questionable merit. As he is said to have put it, "This is not right. It is not even wrong." It was a good and concise statement of what physics requires - not merely interesting ideas, but ones that are both grounded in experimental reality and theoretical rigor. Ideas which don't do both are not even wrong. There's even a a physics book in the popular press today titled after Pauli's quote, making the titular claim about string theory.
But of course snappy quotes won't get a scientist on the top ten list. Pauli…
mspringer | September 17, 2008No, I'm not dead or anything. There was no post this morning because I was absolutely bushed and bone tired. Homework, classes, teaching, and research over the last two days were ridiculous. The rest of the week looks not to be so bad. Funny how the whole "work" part of school never makes it into those films in the college-frat-party genre. I mean come on, I did my undergrad at LSU. They're a legendary party school. If those films have any relation to reality I think I'd have seen it. Now there was no shortage of parties and booze, but if there was anyone who tried to relive Animal…
mspringer | September 16, 2008Yesterday some of my fellow students and I had this homework assignment which, long story short, amounted to doing some changes of variables. One part of the problem in particular was not very transparent until we realized we were missing a factor of a Jacobian.
"I'm just going to write 'The Jacobian enters in a natural way' and present the conclusion as an accomplished fact.", one of my friends said. Obviously it didn't enter in anything approaching like a natural way, but if there's one thing hard science books and papers like to do, it's talk about hard stuff like it was easy. In that…
mspringer | September 15, 2008Remember the post a while back where we tried to come up with a list of the 10 greatest physicists? I've been thinking and rearranging and I think I've come up with a list I'm reasonably happy with. There are quite a few great physicists I'm not happy at all about having to leave out, but 10 is a small number and no matter which ten are picked there's at least ten more who have some good cause to feel left out. The criteria is the importance of their contribution to physics, not just their raw brilliance.
To make up for those left out, I'm including a number of unordered Honorable Mentions…