Friday, September 28, 2007

Working on the Compact Muon Solenoid

It sounds like the end of the six weeks is coming up, so I thought this week I’d cut you guys a break and share with you some of what it’s like to work at CERN as a grad student. In a way, all of these physics puzzles are a little misleading, because they really have nothing to do with what professional physicists actually “do”. At the edges of particle physics things are fairly ragged, and nobody’s making up nifty little problems because nobody knows quite how things work yet. Instead, a typical day for me will consist of coding at a computer, or working with hardware and circuits, or occasionally sitting through seven hours of meetings. (As I write this, I’m in a meeting about something called “level 1 trigger efficiencies”, which is exactly as exciting as it sounds.)

To take a small step back, I work at a detector called the Compact Muon Solenoid. If you remember my earlier post, the Large Hadron Collider is responsible for accelerating protons up to almost the speed of light and then colliding them together, and at the actual collision points we stick detectors to see what comes out. At startup, there will be two detectors: CMS, and at almost the opposite end of the ring, ATLAS, which earns my award for worst acronym ever (“A Toroidal LHC ApparaTus”). Anyway, these two detectors are both designed to discover new physics, and there’s a (usually) friendly rivalry between the two.

Okay, so CMS is a detector, but maybe you’d like to know what it actually looks like. Here’s a picture of (part of) the thing. (I can't show you the whole thing because it's not fully constructed yet.)

When it's done, it'll all be one giant machine, and yet it’s packed unbelievably densely with sensitive electronics. You can’t really get a great sense of scale from the picture, but this thing is 15 meters tall. That number rolled off me the first time I heard it, and maybe it isn’t impressing you much either, but when you’re standing in front of a piece of equipment that’s almost six stories high it hits you that the pictures don’t entirely do it justice.

The whole thing weighs 12,500 metric tons, which is a lot even for the volume. The reason it’s so dense is a component called the electromagnetic calorimeter, which is made up of 80,000 crystals of something called lead tungstate. Believe it or not, this stuff is 98% lead, an opaque metal, and yet it’s completely transparent. Seriously. Here’s a picture:

Yup. If you pick one up, it feels like lead, and if you bang two together they make a metallic ringing (and people will get mad at you, because they're very expensive). In total, they weigh about as much as 24 adult African elephants, but they’re supported by carbon fiber structures about 0.4 millimeters thick.

Everything about CMS is epic, but in my opinion nothing is more impressive than the rate of data flow: at the speed the protons are going, they’ll circle the LHC 40 million times per second. Each time they pass there will be about 25 collisions, so we’re looking at about a billion “events” per second. The amount of data stored for each event is about 1 MB, so the data is pouring in at a rate of a million GB per second. (I used GB in case any of you have a 100 GB hardrive on your computers; this thing could fill up ten thousand of those every second.) In fact, most of this stuff is useless and gets weeded out immediately, but about 500 Gbits/s is actually transferred through the “event builder”. Just to put this in perspective, this is equal to the total amount of data exchanged by the entire world’s telecom networks. I'm counting data from every phone conversation, every file download, every email and every internet video viewed on the entire planet.

CMS is cool, but I don’t really see it very often. For one thing, it’s 100 meters underground, and I don’t like working where there are no windows. For another, it’s in a town called Cessy (in France), and I typically work in my office in Meyrin, Switzerland. In fact, if it’s a nice day out, I’ll sometimes take my laptop to an outdoor table near the cafeteria because they’ve got good coffee.

One of the things I love about CERN is how easy it is to run into famous or important people. This week is CMS week, which mostly means lots of meetings, but it also means people from all over the world fly in to Geneva. Just sitting in the CERN cafeteria, you can see Nobel laureates, highly cited researchers, and world experts on pretty much anything that has to do with physics or hardware or computing. Yesterday a bunch of grad students and postdocs got together for a game of ultimate frisbee and the Deputy Physics Director for CMS skipped out of a meeting to play with us. He was much better than us, too, in spite of being forty years older.

I haven’t really talked much about what exactly I do, in part because I didn’t want this blog entry to be too long, but if enough people are interested I could talk a little about my research. Some of it’s a bit technical and wouldn’t be interesting to you guys, but I have to deliver a “preliminary defense” in mid-December, and I’d guess that kind of thing would resonate with anyone who has to write a senior thesis at the end of the year. Anyway, if you’re interested let me know.

Tuesday, September 18, 2007

The twin "paradox"

Okay, so I promised last week that I’d try to clear up the confusion about Alice and Bob. Alice says time is running normally on Earth, but is slowed down on Bob’s spaceship. Meanwhile, Bob is claiming that time is running normally on his spaceship, and it’s on Earth that time is slowed down. Which one is right? You’re not going to like it, but it turns out they’re both right.

What gives? Well, let’s be a little clearer about what we’re saying. To know that time is moving slow, you’d have to check the time difference between two separate events. Suppose Alice and Bob agree that right when they pass each other, they’ll both hold up big digital stopwatches, and reset them to 0 just as they go by. Then they’ll simply watch each other through high powered binoculars and compare how long it takes for each of their stopwatches to get to 1 minute. Presumably, someone’s watch is going to reach 1 minute first.

Let’s tell the story from Alice’s point of view. Right as Bob zooms by, she sees him set his watch to 0, and she does the same. Of course, time is moving slow on his spaceship, so for every second that ticks by on her watch, only half a second goes by on his. Finally, her watch reaches one minute exactly, and looking through the binoculars, she observes triumphantly that his watch only shows 30 seconds.*** (See "Optional note" below.) Now, how to prove to Bob that her watch got to 1 minute first? Simple! She’ll just take a picture of her stopwatch and sent it to him in a light signal. Except she quickly realizes that there’s a problem. The light races away from her at the speed c, but Bob’s spaceship is going pretty close to that speed anyway, so the light is only catching up very slowly. In fact, the ship is going so fast that the light signal ends up taking 3 whole minutes to get to him! By the time her picture gets to him, his watch (which is running at half speed), shows 2 minutes have elapsed, and he incorrectly thinks it’s her watch that’s running at half speed!

That’s not how Bob would tell the story at all. He agrees that as the Earth went shooting by they both set their watches, but since it’s the Earth that’s moving, Alice’s watch is only running at half speed. He’s looking through his binoculars, and he observes that right when his watch reads 2 minutes, hers only reads 1. In fact, just to prove it, she takes a picture and sends it to him! Of course, he’s not moving at all, so the light reaches him very quickly (since, of course, it’s traveling at the speed c while he’s completely stationary), and confirms what he already knew: that it’s Alice’s watch that’s running at half speed.

Okay, so that didn’t work out quite the way Alice planned. Note that she’s perfectly willing to admit that when her picture reached Bob, his watch showed 2 minutes, she just says it’s because the picture took so long to catch up to him. The culprit is the second postulate of relativity, which says that light travels at the speed c according to all observers. They both agreed on how fast the signal was moving; what they couldn’t agree on was how fast Bob was moving.

But Alice is quite clever, and she’s got another idea. Forget about sending messages; that’s too complicated. Instead, she gets her good friend Cassie to stand one light-minute away with a stopwatch of her own. Then when Bob goes by Alice, all three of them will start their watches at the same time, and when Bob’s spaceship gets to Cassie she can just hold up the stopwatch and show him it displays a longer time than his, proving his watch is running slow. What happens this time?

Well, no doubt about it, as Bob zooms by Cassie, her stopwatch shows 1 minute, and Bob’s only shows 30 seconds. Does that mean that Bob’s watch really is the one that’s running slow? Not at all! I claimed that Alice and Cassie started their watches at the same time. Put another way, I claimed they started their watches simultaneously. But of course, we already know that two events that are simultaneous in one frame are not in another! So Alice and Cassie may say they’ve started their watches at the same time, but according to Bob, Cassie made a rookie mistake and started her watch too early, which is the only reason her watch shows more time than his does.

Okay, well, if you’re anything like me, just these two examples won’t convince you that there’s not a legitimate time paradox here. I’ve just covered two possible ways you might show there’s a contradiction, and in both cases there’s a slippery way out. But maybe you’re not satisfied; it sure feels like there’s a problem somewhere. If you’re not yet convinced, I’d be interested to hear your take on the so-called “twin paradox”, which goes like this:

On her 21st birthday, an astronaut takes off in a spaceship at near the speed of light. After 5 years have elapsed on her watch, she turns around and heads back at the same speed to rejoin her twin brother, who stayed at home. The traveling twin has aged 10 years (5 years out, 5 years back), so she arrives at home just in time to celebrate her 31st birthday. However, as viewed from Earth, her clock has been running slow, so her twin brother will now be much older than she is!

But what happens when you try to tell this story from the point of view of the traveling twin? She sees the Earth fly off at near the speed of light, turn around after 5 years, and return. From her point of view, it would seem, she’s at rest, whereas her brother is in motion, and hence it is he who should be younger at the reunion. So which one is really younger when they meet up, and why? For the answer you’ll have to wait until next week, but in the meantime you can entertain yourselves with these questions.

*** Optional note: I’m being very slightly dishonest here, because I didn’t mention that Alice has to account for the travel time of light. What Alice would actually see, looking through the binoculars, is that Bob’s clock would read less than 30 seconds, and she’d have to figure out that at that moment his clock actually read 30 seconds, but the light hadn’t reached her yet. I left it out because I didn’t want the story to be any more confusing than it had to be. If this is too much, just forget about it; it doesn’t make any difference to the story. As long as you’re reading, though, let me remind you that Bob’s clock really is running slow (in the reference frame of the Earth), and it’s not just a trick of observation.

Tuesday, September 11, 2007

Time dilation

By the way, as a quick note, I should probably mention that simultaneity, and all the other consequences of special relativity, are not a matter of one observer or another “getting it wrong”. When I say that event B comes before A according to one observer, but another observer says that A comes before B, it’s not that one of them has made a mistake. In the first observer’s frame, B really does come before A, and in the other observer’s frame, it really doesn’t. It’s weird.

I mention this because sooner or later one of you is going to read a bad relativity book, and it’s going to say something about one observer not accounting for the travel time of light, or something. But that has nothing to do with relativity. If I take a measurement of something, I have to be clever enough to subtract out any effect due to the signal taking time to reach me. Actually, if I’m really clever, I’ll get a bunch of low-ranking grad students and space them at intervals with a stopwatch and a ruler so they can just write down measurements and bring them back to me. It’s like when you see lightning and then later you hear the thunder, you might incorrectly believe that they didn’t come from the same source, because you didn’t account for their different travel times. But this isn’t relativity, this is just making a mistake.

Anyway, the weirdness this week is about time dilation. Simply put, time dilation says this:

In a moving frame, time runs slow.

How much slower? That’s the subject of this week’s question. (By the way, if you happen to get stuck, you can always write me a comment; I’m happy to help.)

Let’s say Bob hops on a spaceship that goes rocketing by the Earth at near the speed of light. Just as he passes by, Alice peeks in the window. If right at that moment Bob is, I dunno, say playing a game of pool, then Alice sees it as though it were happening in slow motion. If Bob jumps the cueball, it seems to float slowly through the air; if he sinks a ball, it drifts gently downwards to the bottom of the pocket; and a blast break doesn’t look nearly as impressive when Bob’s traveling at 90% of the speed of light.

Of course, if you ask Bob about all this, he’ll say he’s just moving at normal speed. As far as he’s concerned, his spaceship is completely stationary, and it’s the Earth that’s rocketing by in the other direction. Hmm…

With any luck, at least a couple of you are scratching your heads at this point. I just told you that time runs slow in a moving frame, so Bob is moving slow according to Alice because Bob is moving with respect to her. But by the same argument, Alice must be moving slow according to Bob, because in Bob’s reference frame (the spaceship) it’s Alice who’s doing the moving.

So what’s the deal? Common sense says that if Bob looks slow to Alice, then Alice must look fast to Bob, right? If they both pull out stop watches and start them just as they pass by, whose watch reaches one minute first? Is it possible that one of them is wrong? If so, which one? I’ll try to unstick this one for you next week, but in the meantime, if you have any opinions or guesses, leave me a comment. (Christos, if you’re reading this blog, you’re not allowed to give away the answer.)

Problem on time dilation:

Monday, September 3, 2007

Special Relativity

The plan for the next few weeks is to start with Einstein’s special theory of relativity. (It’s “special” because it only deals with things that aren’t accelerating; if you want acceleration, you’re looking for the general theory of relativity, but I would advise you not to go looking for it anytime soon.) Special relativity is a good place to start because you already have all the math you need, namely algebra and trig. Plus it was figured out before all the other stuff I’ll talk about in this blog, and some of the other stuff is based on it.

The whole theory comes from just two postulates:

1. Principle of relativity: The laws of physics are the same in all inertial (non-accelerating) reference frames.
2. Universal speed of light c: The speed of light in vacuum c (about 300 000 m/s) is the same for all inertial observers, regardless of the motion of the source.

The first postulate has actually been around for hundreds of years, but it probably deserves a little explanation. As far as we’re concerned, it means this: if you’re moving along without speeding up or slowing down, you can never really prove that you’re moving at all. After all, how would you prove it? You’d have to do some sort of physics experiment, and according to postulate 1 you’ll get the same result as if you weren’t moving. If you see me walking down the street you could say I’m moving while the ground stays still, but it’s just as fair to say I’m staying in one place while the ground moves underneath me. Like what happens on a treadmill, for example.

The upshot is that you can pick any (non-accelerating) reference frame you like and decide it’s stationary. If someone else picks a reference frame that’s moving relative to yours and claims that’s the one that’s stationary, that’s cool too. Neither one of you is wrong; you’re just describing the same thing two different ways. If I walk into a wall, it doesn’t matter whether you think I’m moving forward or the wall is moving backward, the physics when I hit it stays the same.

Okay, so hopefully you believe me about the principle of relativity. It’s the universal speed of light which ought to really upset you. You certainly wouldn’t believe me if I’d said that the speed of a bowling ball is the same for all observers, regardless of their relative motion. If I’m on a train going 60 mph and I roll a bowling ball at 5 mph down the corridor, then the ball’s total speed relative to the ground is “obviously” 65 mph—the speed of the bowling ball (A) with respect to the ground (C) is equal to the speed of the ball (A) relative to the train (B) plus the speed of the train (B) relative to the ground (C). Our common sense tells us that this should work for any three objects A, B, and C. But according to postulate 2, if instead I send a light signal down the corridor, its speed is c relative to the train and c relative to the ground!

Impossible? When I was a kid I sure thought so. In fact, I was absolutely convinced there was a logical paradox there, and I’d spend days coming up with thought experiments that would give contradictory results. But, infuriatingly, each time there was some clever way out so that you could just barely avoid a contradiction. As it turns out, there really isn’t any paradox at all, but special relativity does require you to change dramatically how you look at space and time.

There are three major consequences to special relativity. We’ll work out the first one this week and I’ll give you a little problem, and we’ll save the last two for next week. If I can direct your attention here, we’ll get started:
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