mspringer | August 29, 2008I really loathe politics, and have mostly tried to avoid writing about it. But finally something interesting has happened, and it's worth a brief comment.
In physics we like to talk about symmetry. Conservation laws and symmetry are intimately related, and you can learn a lot about one by studying the other. One of the more interesting examples of this is parity. Parity basically means reversing left and right - if you do an experiment and then rebuild the entire thing backwards, everything happens as you'd expect. If you take a picture of a physical process and flip the picture in…
mspringer | August 29, 2008Top 10 lists are silly. But they're fun, which is why there's so many of them. In a week or two, I'm going to start a brief biographical series with a little bit of information on the lives and works of the great physicists.
The top 3 are obvious (Well, to me anyway). The top 5 - I think I have a decent idea what my opinions are. The top 10? Things start to get kind of fuzzy. There's a few dozen people who could make a pretty good case for being considered among the truly great physicists. But these lists are as much about who's not in them as who is. And heck, maybe we'll even make…
mspringer | August 28, 2008
Nine dayes they fell; confounded Chaos roard,And felt tenfold confusion in thir fallThrough his wilde Anarchie, so huge a routIncumberd him with ruin: Hell at lastYawning receavd them whole, and on them clos'd,Hell thir fit habitation fraught with fireUnquenchable, the house of woe and paine.- Milton, Paradise Lost
The biblical description of Satan's fall is sparse. Like lightning, says Luke's gospel. Milton's poetry fleshes this out with his typically beautiful and dramatic imagery. A fall of nine days into Hell.
Maybe it's just me, but the physicist in me is immediately curious at this…
mspringer | August 27, 2008Physics professors have this annoying habit. They'll present a problem to be solved, figure out how to describe it in mathematical terms, and declare that the physics is done and the rest is just math.
Well yeah, but that's kind of like drawing a blueprint for a house and then declaring to your trainee workers that the construction itself is a trivial exercise. At risk of sounding like Barbie, math is hard. Sometimes professors are particular drill instructors and they'll do the physics part of the problem for you, leaving you to only practice the math.
But math is the language of physics…
mspringer | August 26, 2008We all know what the formula for kinetic energy is. Take the mass, multiply by the velocity squared, divide by two. In 1905, Einstein raised his hand and said that we're not quite right. In fact the actual expression for kinetic energy is
where c is the speed of light and
That doesn't look much like our old formula:
Not a c in sight. Obviously this is going to make a big difference where v is close to c. When that happens, gamma gets huge. Arbitrarily huge - that's one of the things that makes it impossible to accelerate to the speed of light. You'd have to add infinite kinetic…
mspringer | August 25, 2008This is one of those times when being a non-anonymous blogger is a little inconvenient. Nonetheless, I think I can make things a little vague and change a few names and I'll be ok.
As I mentioned a couple of days ago, I'm taking two classes. I thought nothing of it when I signed up for them; they're the natural next classes I'm supposed to take. One of these classes is taught by a professor who has a reputation of being... well, we'll just say teaching is not his natural gift. But so what? I've had difficult classes with non-ideal professors before.
On the other hand, over the summer I'…
mspringer | August 24, 2008If you're a regular reader of this site, you might remember a post about this fascinating specimen from the collection of unusual functions. I'm only showing it on the interval [-1,1] for reasons that will become apparent, but outside that region the growth tapers off rapidly and the function approaches 1 for large negative and large positive x.
It's continuous once you define the point at the origin, and it has continuous derivatives of all orders. Nevertheless, if you try to find the power series about the origin, you see that every term in the series is 0. You can try offsetting the…
mspringer | August 23, 2008Don't think I've forgotten about the falling electron question from a while back. Short version: an accelerating charge radiates. So if you let an electron fall in a gravitational field, it should radiate. But a person (or detector) falling along beside it does not perceive the electron as accelerating and so the electron shouldn't radiate in their frame. How to reconcile the perspectives?
I didn't know. Still don't. I got back to the university and asked a few grad student friends of mine. One had an interesting argument involving vacuum polarizability that the electron will radiate…
mspringer | August 22, 2008Congratulations to all the Olympic athletes who have competed thus far, especially Michael Phelps, Nastia Liukin, and Shawn Johnson. Gymnastic events are all great to watch, and I don't think you could find a more colorful analyst than Bela Karolyi. The balance beam is probably the most classic and thrilling gymnastic event - the Summer Olympics equivalent of figure skating - but the men's high bar and women's uneven bars are just absolutely jaw-dropping. It looks like magic.
Now the track meets take center stage. My younger brother ran track in high school, and he tells me the track…
mspringer | August 21, 2008You can break the laws of your local jurisdiction. It might not be a good idea, but if you want to drive 60 in a 45, you can. You'll pay a hefty fine if you get caught, but you'll still have been able to do it.
There's no penalties for breaking the laws of physics because you can't break the laws of physics. On the other hand, technicalities in both legislative and physical laws can sometimes allow you do to things you wouldn't expect. Take this one:
You can't go faster than the speed of light.
Clear enough, until the lawyer chimes in. "What," he says with a raised eyebrow, "do you mean…
mspringer | August 20, 2008
This is Zhang Juanjuan, immediately after applying an impulse to an arrow. Impulse is something which gets less airtime than work in freshman physics, but it's nonetheless very important. It's sort of momentum's version of work.
You'll remember from Monday that there are two main things to keep in mind about work.
1. Work is defined as force through a distance
2. Work equivalent to the change in energy
You can think of impulse the same way.
1. Impulse is defined as a force thorough a time
2. Impulse is equivalent to the change in momentum
Crucially, impulse is a vector and work is not.…
mspringer | August 19, 2008This is more technology than strictly physical science, but I'm professionally interested in laser physics. My own area is mainly attosecond pulses at modest average power, still, the applications of broader laser technology are always instructive.
Boeing has been working on laser weapons technology for a while now. I've written about it before, mainly from the perspective of battlefield anti-missile and anti-mortar defense. Anti-personnel use is possible but generally impractical. A bullet is just as effective and several orders of magnitude cheaper. There's possible advantages with…
mspringer | August 18, 2008
This is Liao Hui, not doing any work. He did work to get the weight over his head, but despite the tremendous force he's applying to this 348 kilogram [Update: Thanks to commenter Ducklike for correcting this to 158 kg] weight he's not doing any work in this picture. The weight is stationary.
Work in physics is a term of art meaning force through a distance. The reason for that definition of work is that this definition coincides perfectly with the energy transferred in the process. Work results in a change in energy. When Liao Hui did work to move the weight to its highest position,…
mspringer | August 17, 2008You all know what the natural log function looks like. Take the number 1, divide it by the natural log, and then find the antiderivative of that function. You'll get the logarithmic integral function. It looks like this:
Sometimes the lower limit of the integral is changed to 2 instead of 0, in order to get rid of that singularity at the origin. But we're only interested in the behavior at large x so it doesn't matter either way.
It turns out that if you count all the prime numbers up to one million, the answer will be approximately li(1000000). This is helpful because it's a lot…
mspringer | August 16, 2008Greg Laden responds to the recent change in policy allowing teachers with concealed carry permits to carry in one particular public high school in north Texas should they so choose. If only the teachers had guns.... (Texans = Morons). Here's CNN's original story.
The school is a 30-minute drive from the nearest police station, and the board decided that it was better to have somebody armed than waiting so long for the police to respond. Greg does not think this is a good idea, to put it mildly. Neither do most of his commenters. I have another perspective.
Every public college in Utah…
mspringer | August 16, 2008A quick Olympic question: How would a native of China pronounce the j in Beijing? All the commentators pronounce it like the J in the French je suis, but I've heard that in China the pronunciation would be closer to the J in jingle. I have no idea if this is true, and I'm not at the university now so I can't just ask one of my Chinese friends. Anyone know?
Now how about some short items from around the web, which I particularly enjoyed.
Here's Swans on Tea and our own Chad Orzel on the (lack of) menace of radioactive bananas and granite countertops.
Here's Cocktail Party Physics on the age…
mspringer | August 15, 2008What's the temperature inside a microwave oven?
I've seen some thermodynamics textbooks start off with a preliminary definition of temperature that amounts to "The temperature is what a thermometer says it is", since temperature is really a concept that fundamentally is derived from energy and entropy. So the books like to discuss those at length before talking about the real definition of temperature despite the fact that temperature is what people are accustomed to seeing.
So let's put a thermometer in the microwave. If it's a mercury thermometer it will probably rocket up to off-scale…
mspringer | August 14, 2008I think it's time for a good old practice problem. This is a pretty basic one, which you might encounter as a freshman physics major. The general concept of dealing with inelastic collisions is one that you never escape, and from special relativity to quantum mechanics this type of thing keeps appearing in new contexts. This particular problem is from an old GRE practice exam, but I think solving it is kosher since it's not original to them and you can't copyright facts.
In a nonrelativistic, one-dimensional collision, a particle of mass 2m collides with a particle of mass m at rest. If…
mspringer | August 13, 2008MarkCC on Good Math, Bad Math has been posting lately on encryption and privacy. As usual, technology has increased the number of ways the government can read your mail, but it has also increased the ways you can hide your communications as well. Modern open-source encryption is very secure and all other things being equal it's much harder for the government to read encrypted email than it is for the government to open an envelope old-style. To read encrypted email, realistically the government is going to have to surreptitiously bug your computer and get your password, which (for the…
mspringer | August 13, 2008In quantum mechanics, particles like electrons can be observed in one of two spin states: up or down. The theory, however, doesn't require the state to be completely determined before we look at it. Any given electron doesn't have to be in one of those spin eigenstates; it can be in a superposition of spin up and spin down. It's like Schroedinger's cat being in a superposition of alive and dead, but less dramatic. For instance, a particular electron may be in a state which has a probability of 60% of being in an up state and 40% of being in the down state. Once measured it will…