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Posts Tagged ‘student life’

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The doorway to the registrar’s office where the final thesis check takes place

I took an entire month between defending my thesis and depositing it with the grad school. During that month, I mostly revised my thesis, but also I took care of a bunch of logistical things I had been putting off until after the defense: subletting the apartment, selling the car, engaging movers, starting to pack… and of course putting comments into the thesis from the committee. I wrote back to my (now current) new boss who said we should chat again after I “come up for air” (which is a pretty accurate way of describing it). I went grocery shopping, and for the first time in months it was fun to walk around the store imagining and planning the things I could make in my kitchen. I had spare creative energy again!

Partly I needed a full month to revise the thesis because I was making changes to the analysis within the thesis right up to the day before I defended, and I changed the wording on the concluding sentences literally 20 minutes before I presented. I didn’t have time to polish the writing because the analysis was changing so much. The professor who gave me the most detailed comments was justifiably annoyed that he didn’t have sufficient time to read the whole dissertation before the defense. It worked out in the end, because the time he needed to finish reading was a time when I didn’t want to think about my thesis in any way. I even left town and visited friends in Chicago, just to break up the routine that had become so stressful. There’s nothing quite as nice as waking up to a cooked breakfast when you’ve forgotten that cooked breakfasts are an option.

There were still thesis revisions to implement. Some major comments reflected the fact that, while some chapters had been edited within a peer group, no one had read it cover-to-cover until after the defense. The professor who had the most detailed comments wrote a 12-page email detailing his suggestions, many of which were word substitutions and thus easy to implement. Apparently I have some tics in my formal writing style.

I use slightly too many (~1.2) semicolons per page of text; this reflects my inclination to use compound sentences but also avoid parentheses in formal writing. As my high school teacher, Perryman, taught me: if you have to use parentheses you’re not being confidently declarative, and if you ever want to use nested parentheses in a formal setting, figure out what you really want to say and just say it! (subtext: or figure out why you don’t want to say it, and don’t say it. No amount of parenthesis can make a statement disappear.) Anyway, I’d rather have too many semicolons than too many parentheses; I’d rather be seen as too formal than too tentative. It’s the same argument, to me, that I’d rather wear too much black than too much pink. So, many of the semicolons stayed in despite the comments. Somehow, in the thesis haze, I didn’t think of the option of many simple single-clause sentences. Single-clause sentences are hard.

I also used the word “setup” over 100 times as a catch-all word to encompass all of the following: apparatus, configuration, software, procedure, hypothesis. I hadn’t noticed that, and I have no good reason for it, so now my thesis doesn’t use the word “setup” at all. I think. And if it does, it’s too late to change it now!

And of course there was the matter of completing the concluding paragraph so it matched the conclusion I presented in my defense seminar. That took some work. I also tried to produce some numbers to complete the description of my analysis in more detail than I needed for the defense seminar, just for archival completeness. But by the time I had fixed everything else, it was only a few hours until my deposit margin-check appointment (and also 2:30am), so I gave up on getting those numbers.

The deposit appointment was all of 5 minutes long, but marked the line between “almost done” and “DONE!!!”. The reviewing administrator realized this. She shook my hand three times in those 5 minutes. When it was done, I went outside and there were birds singing. I bought celebratory coffee and a new Wisconsin shirt. And then started packing up my apartment for the movers arriving the next morning.

During that month of re-entering society,  I had some weird conversations which reminded me how isolated I had been during the thesis. A friend who used to work in our office had started her own business, but I’d only had time to ask her about it once or perhaps twice. When we had a bit of time to catch up more, I asked how it had been during the last few months, and she replied that it had been a year. A year. It just went by and I didn’t notice, without the regular office interactions.

I’d gotten into a grove of watching a couple episodes each night of long-running TV shows with emotionally predictable episodic plot lines. Star Trek and various murder mysteries were big. The last series was “House, MD” with Hugh Laurie. By coincidence, when I defended my thesis and my stress level starting deflating, I was almost exactly at the point in the series where they ran out of mysteries from the original book it was based on, and started going more into a soap-opera style character drama. By the time I wasn’t interested in the soap opera aspects anymore, it was time to start reengaging with my real-life friends.

A few days after I moved away from Madison, when I was staying with my parents, I picked up my high school routine of reading the local paper over breakfast, starting with the comics, then local editorials. I found (or rather, my dad found) myself criticizing the writing from the point of view of a dissertator. It takes more than a few days to get out of thesis-writing mode. The little nagging conscience doesn’t go away, still telling me that the difference between ok writing and great writing is important, more so now than at any point so far in my career. For the last edits of a PhD, it might be important to criticize at that level of detail. But for a local paper, pretty much anything is useful to the community.

At lunch Saturday in a little restaurant in the medieval part of the Italian village of Assergi, I found the antidote. When I can’t read any of the articles and posters on the walls, when I can’t carry on a conversation with more than 3-word sentences, it doesn’t matter anymore if the paragraphs have a clear and concise topic sentence. I need simple text. I’m happy if I can understand the general meaning. The humility of starting over again with Italian is the antidote for the anxiety of a thesis. It’s ok to look like a fool in some ways, because I am a certified non-fool in one small part of physics.

It’s not perfect of course: there’s still a lot of anxiety inherent in living in a country without speaking the language (well enough to get by without english-speaking help). I’ll write more about the cultural transition in another post, since I have so many posts to catch up on from while I was in the thesis-hole, and this post is definitely long enough. But for now, the thesis is over.

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Graduating, part 1: The Defense

Tuesday, November 25th, 2014

It’s been a crazy 3 weeks since I officially finished my PhD. I’m in the transition from being a grad student slowly approaching insanity to a postdoc who has everything figured out, and it’s a rocky transition.

DSC_0738The end of the PhD at Wisconsin has two steps. The first is the defense, which is a formal presentation of my research to the professors and committee, our colleagues, and very few friends and family. The second is actually turning the completed dissertation to the grad school, with the accompanying “margin check” appointment with the grad school. In between, the professors can send me comments about the thesis. I’ve heard so many stories of different universities setting up the end of a degree differently, it’s pretty much not worth going into the details. If you or someone you know is going through this process, you don’t need a comparison of how it works at different schools, you just need a lot of support and coping mechanisms. All the coping mechanisms you can think of, you need them. It’s ok, it’s a limited time, don’t feel guilty, just get through it. There is an end, and you will reach it.

The days surrounding the defense were planned out fairly carefully, including a practice talk with my colleagues, again with my parents (who visited for the defense), and delivery burritos. I ordered coffee and doughnuts for the defense from the places where you get those, and I realized why such an important day has such a surprisingly small variety of foods: because deviating from the traditional food is so very far down my list of priorities when there’s the physics to think about, and the committee, and the writing. The doughnuts just aren’t worth messing with. Plus, the traditional place to get doughnuts is already really good.

We even upheld a tradition the night before the defense. It’s not really a tradition per se, but I’ve seen it once and performed it once, so that makes it a tradition. If you find it useful, you can call it an even stronger tradition! We played an entire soundtrack and sung along, with laptops open working on defense slides. When my friend was defending, we watched “Chicago” the musical, and I was a little hoarse the next day. When I was defending, we listened to Leonard Bernstein’s version of Voltaire’s “Candide,” which has some wonderful wordplay and beautiful writing for choruses. The closing message was the comforting thought that it’s not going to be perfect, but life will go on.

“We’re neither wise nor pure nor good, we’ll do the best we know. We’ll build our house, and chop our wood, and make our garden grow.”

Hearing that at the apex of thesis stress, I think it will always make me cry. By contrast, there’s also a scene in Candide depicting the absurd juxtaposition of a fun-filled fair centered around a religious inquisition and hanging. Every time someone said they were looking forward to seeing my defense, I thought of this hanging-festival scene. I wonder if Pangloss had to provide his own doughnuts.

The defense itself went about as I expected it would. The arguments I presented had been polished over the last year, the slides over the last couple weeks, and the wording over a few days. My outfit was chosen well in advance to be comfortable, professional, and otherwise unremarkable (and keep my hair out my way). The seminar itself was scheduled for the time when we usually have lab group meetings, so the audience was the regular lab group albeit with a higher attendance-efficiency factor. The committee members were all present, even though one had to switch to a 6am flight into Madison to avoid impending flight cancellations. The questions from the committee mostly focused on understanding the implications of my results for other IceCube results, which I took to mean that my own work was presented well enough to not need further explanation.

It surprised me, in retrospect, how quickly the whole process went. The preparation took so long, but the defense itself went so quickly. From watching other people’s defenses, I knew to expect a few key moments: an introduction from my advisor, handshakes from many people at the end of the public session, the moment of walking out from the closed session to friends waiting in the hallway, and finally the first committee member coming out smiling to tell me they decided to pass me. I knew to look for these moments, and they went by so much faster in my own defense than I remember from my friends. Even though it went by so quickly, it still makes a difference having friends waiting in the hallway.

People asked me if it was a weight off my shoulders when I finally defended my thesis. It was, in a way, but even more it felt like cement shoes off my feet. Towards the end of the process, for the last year or so, a central part of myself felt professionally qualified, happy, and competent. I tried desperately to make that the main part. But until the PhD was finished, that part wasn’t the exterior truth. When I finished, I felt like the qualifications I had on paper matched how qualified I felt about myself. I’m still not an expert on many things, but I do know the dirty details of IceCube software and programing. I have my little corner of expertise, and no one can take that away. Degrees are different from job qualifications that way: if you stop working towards a PhD several years in, it doesn’t count as a fractional part of a degree; it’s just quitting. But if you work at almost any other job for a few years, you can more or less call it a few years of experience. A month before my defense, part of me knew I was so so so close to being done, but that didn’t mean I could take a break.

And now, I can take a break.

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Why pure research?

Thursday, October 2nd, 2014

With my first post on Quantum Diaries I will not address a technical topic; instead, I would like to talk about the act (or art) of “studying” itself. In particular, why do we care about fundamental research, pure knowledge without any practical purpose or immediate application?

A. Flexner in 1939 authored a contribution to Harper’s Magazine (issue 179) named “The usefulness of useless knowledge”. He opens the discussion with an interesting question: “Is it not a curios fact that in a world steeped in irrational hatreds which threaten civilization itself, men and women – old and young – detach themselves wholly or partly from the angry current of daily life to devote themselves to the cultivation of beauty, to the extension of knowledge […] ?”

Nowadays this interrogative is still present, and probably the need for a satisfactory answer is even stronger.

From a pragmatic point of view, we can argue that there are many important applications and spin-offs of theoretical investigations into the deep structure of Nature that did not arise immediately after the scientific discoveries. This is, for example, the case of QED and antimatter, the theories for which date back to the 1920s and are nowadays exploited in hospitals for imaging purposes (like in PET, positron emission tomography). The most important discoveries affecting our everyday life, from electricity to the energy bounded in the atom, came from completely pure and theoretical studies: electricity and magnetism, summarized in Maxwell’s equations, and quantum mechanics are shining examples.

It may seem that it is just a matter of time: “Wait enough, and something useful will eventually pop out of these abstract studies!” True. But that would not be the most important answer. To me this is: “Pure research is important because it generates knowledge and education”. It is our own contribution to the understanding of Nature, a short but important step in a marvelous challenge set up by the human mind.

Personally, I find that research into the yet unknown aspects of Nature responds to some partly conscious and partly unconscious desires. Intellectual achievements provide a genuine ‘spiritual’ satisfaction, peculiar to the art of studying. For sake of truth I must say that there are also a lot of dark sides: frustration, stress, graduate-depression effects, geographical and economic instability and so on. But leaving for a while all these troubles aside, I think I am pretty lucky in doing this job.

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Books, the source of my knowledge

During difficult times from the economic point of view, it is legitimate to ask also “Why spend a lot of money on expensive experiments like the Large Hadron Collider?” or “Why fund abstract research in labs and universities instead of investing in more socially useful studies?”

We could answer by stressing again the fact that many of the best innovations came from the fuzziest studies. But in my mind the ultimate answer, once for all, relies in the power of generating culture, and education through its diffusion. Everything occurs within our possibilities and limitations. A willingness to learn, a passion for teaching, blackboards, books and (super)computers: these are our tools.

Citing again Flexner’s paper: “The mere fact spiritual and intellectual freedoms bring satisfaction to an individual soul bent upon its own purification and elevation is all the justification that they need. […] A poem, a symphony, a painting, a mathematical truth, a new scientific fact, all bear in themselves all the justification that universities, colleges and institutes of research need or require.”

Last but not least, it is remarkable to think about how many people from different parts of the world may have met and collaborated while questing together after knowledge. This may seem a drop in the ocean, but research daily contributes in generating a culture of peace and cooperation among people with different cultural backgrounds. And that is for sure one of the more important practical spin-offs.

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It’s Saturday, so I’m at the coffee shop working on my thesis again. It’s become a tradition over the last year that I meet a writer friend each week, we catch up, have something to drink, and sit down for a few hours of good-quality writing time.

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The work desk at the coffee shop: laptop, steamed pork bun, and rosebud latte.

We’ve gotten to know the coffee shop really well over the course of this year. It’s pretty new in the neighborhood, but dark and hidden enough that business is slow, and we don’t feel bad keeping a table for several hours. We have our favorite menu items, but we’ve tried most everything by now. Some mornings, the owner’s family comes in, and the kids watch cartoons at another table.

I work on my thesis mostly, or sometimes I’ll work on analysis that spills over from the week, or I’ll check on some scheduled jobs running on the computing cluster.

My friend Jason writes short stories, works on revising his novel (magical realism in ancient Egypt in the reign of Rameses XI), or drafts posts for his blog about the puzzles of the British constitution. We trade tips on how to organize notes and citations, and how to stay motivated. So I’ve been hearing a lot about the cultural difference between academic work in the humanities and the sciences. One of the big differences is the level of citation that’s expected.

As a particle physicist, when I write a paper it’s very clear which experiment I’m writing about. I only write about one experiment at a time, and I typically focus on a very small topic. Because of that, I’ve learned that the standard for making new claims is that you usually make one new claim per paper, and it’s highlighted in the abstract, introduction, and conclusion with a clear phrase like “the new contribution of this work is…” It’s easy to separate which work you claim as your own and which work is from others, because anything outside “the new contribution of this work” belongs to others. A single citation for each external experiment should suffice.

For academic work in history, the standard is much different: the writing itself is much closer to the original research. As a start, you’ll need a citation for each quote, going to sources that are as primary as you can get your hands on. The stranger idea for me is that you also need a citation for each and every idea of analysis that someone else has come up with, and that a statement without a citation is automatically claimed as original work. This shows up in the difference between Jason’s posts about modern constitutional issues and historical ones: the historical ones have huge source lists, while the modern ones are content with a few hyperlinks.

In both cases, things that are “common knowledge” doesn’t need to be cited, like the fact that TeV cosmic rays exist (they do) or the year that Elizabeth I ascended the throne (1558).

There’s a difference in the number of citations between modern physics research and history research. Is that because of the timing (historical versus modern) or the subject matter? Do they have different amounts of common knowledge? For modern topics in physics and in history, the sources are available online, so a hyperlink is a perfect reference, even in formal post. By that standard, all Quantum Diaries posts should be ok with the hyperlink citation model. But even in those cases, Jason puts footnoted citations to modern articles in the JSTOR database, and uses more citations overall.

Another cool aspect of our coffee shop is that the music is sometimes ridiculous, and it interrupts my thoughts if I get stuck in some esoteric bog. There’s an oddly large sample of German covers of 30s and 40s showtunes. You haven’t lived until you’ve heard “The Lady is a Tramp” in German while calculating oscillation probabilities. I’m kidding. Mostly.

Jason has shown me a different way of handling citations, and I’ve taught him some of the basics of HTML, so now his citations can appear as hyperlinks to the references list!

As habits go, I’m proud of this social coffee shop habit. I default to getting stuff done, even if I’m feeling slightly off or uninspired.  The social reward of hanging out makes up for the slight activation energy of getting off my couch, and once I’m out of the house, it’s always easier to focus.  I miss prime Farmers’ Market time, but I could go before we meet. The friendship has been a wonderful supportive certainty over the last year, plus I get some perspective on my field compared to others.

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Welcome to Thesisland

Tuesday, July 22nd, 2014

When I joined Quantum Diaries, I did so with trepidation: while it was an exciting opportunity, I was worried that all I could write about was the process of writing a thesis and looking for postdoc jobs. I ended up telling the site admin exactly that: I only had time to work on a thesis and job hunt. I thought I was turning down the offer. But the reply I got was along the lines of “It’s great to know what topics you’ll write about! When can we expect a post?”. So, despite the fact that this is a very different topic from any recent QD posts, I’m starting a series about the process of writing a physics PhD thesis. Welcome.

The main thesis editing desk: laptop, external monitor keyboard mouse; coffee, water; notes; and lots of encouragement.

The main thesis editing desk: laptop, external monitor keyboard mouse; coffee, water; notes; and lots of encouragement.

There are as many approaches to writing a PhD thesis as there are PhDs, but they can be broadly described along a spectrum.

On one end is the “constant documentation” approach: spend some fixed fraction of your time on documenting every project you work on. In this approach, the writing phase is completely integrated with the research work, and it’s easy to remember the things you’re writing about. There is a big disadvantage: it’s really easy to write too much, to spend too much time writing and not enough doing, or otherwise un-balance your time. If you keep a constant fraction of your schedule dedicated to writing, and that fraction is (in retrospect) too big, you’ve lost a lot of time. But you have documented everything, which everyone who comes after will be grateful for. If they ever see your work.

The other end of the spectrum is the “write like hell” approach (that is, write as fast as you can), where all the research is completed and approved before writing starts. This has the advantage that if you (and your committee) decide you’ve written enough, you immediately get a PhD! The disadvantage is that if you have to write about old projects, you’ll probably have forgotten a lot. So this approach typically leads to shorter theses.

These two extremes were first described to me (see the effect of thesis writing? It’s making my blog voice go all weird and passive) by two professors who were in grad school together and still work together. Each took one approach, and they both did fine, but the “constant documentation” thesis was at least twice (or was it three times?) as long as the “write like hell” thesis.

Somewhere between those extremes is the funny phenomenon of the “staple thesis”: a thesis primarily composed of all the papers you wrote in grad school, stapled together. A few of my friends have done this, but it’s not common in my research group because our collaboration is so large. I’ll discuss that in more detail later.

I’m going for something in the middle: as soon as I saw a light at the end of the tunnel, I wanted to start writing, so I downloaded the UW latex template for PhD theses and started filling it in. It’s been about 14 months since then, with huge variations in the writing/research balance. To help balance between the two approaches, I’ve found it helpful to keep at least some notes about all the physics I do, but nothing too polished: it’s always easier to start from some notes, however minimal, than to start from nothing.

When I started writing, there were lots of topics available that needed some discussion: history and theory, my detector, all the calibration work I did for my master’s project–I could have gone full-time writing at that point and had plenty to do. But my main research project wasn’t done yet. So for me, it’s not just a matter of balancing “doing” with “documenting”; it’s also a question of balancing old documentation with current documentation. I’ve almost, *almost* finished writing the parts that don’t depend on my work from the last year or so. In the meantime, I’m still finishing the last bits of analysis work.

It’s all a very long process. How many readers are looking towards writing a thesis later on? How many have gone through this and found a method that served them well? If it was fast and relatively low-stress, would you tell me about it?

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Particles of the Day

Tuesday, November 20th, 2012
My copy of the 2012 PDG booklet

My copy of the 2012 PDG booklet

Last week, I got my copy of the 2012 Particle Data Group Review of Particle Physics booklet — which, along with its heavy, 1000-page full-length counterpart, we simply call “the PDG.” My very first copy, during my first months at CERN in the summer of 2003, is a vivid memory for me. Here was a book with almost everything you want to know, about every particle ever discovered! It was like the book of dinosaurs I had when I was a kid, and I read it in exactly the same way: flipping to a random page and reading a few facts about, say, the charged kaon.

My new copy of the PDG has inspired me to adapt this fun for non-experts. So each day, I’ll feature a new particle on Twitter; I’m @sethzenz, and the hashtag will be #ParticleOfTheDay. Since starting last week, I’ve featured the B0s meson, the pion, the kaon, the electron, and the Higgs.

How long can I keep this up? That is, how many particles are there? Well, that depends on how you count. The Standard Model has 3 charged leptons, 3 neutrinos, 6 quarks, the photon, and the W, Z, and Higgs bosons. But then there’s all the antiparticles. Dark matter candidates. The graviton. I could even argue for taking 8 days covering all the gluon colors! (Don’t worry, I won’t.) But most of all, there’s all the composite particles — those that are made from a combination of quarks. There are a very large number of those, and there will always be more to find too, because you can always add more energy to the same combination of quarks.

The point isn’t to be systematic. I might go back and be more specific. I might repeat. What I really want to do is find a particle each day that’s in the news or I can say something interesting about.

Flipping at random through a book of particles turns out not to be the best way to learn particle physics; ultimately, I needed to learn the principles by which those particles are organized. But it is an interesting way to tell the story of particle physics: its history and how it’s done today. After all, the particles do come out of accelerators in a random jumble; it’s our job to organize them.

Have an idea for the Particle of the Day, and what to say about it? Let me know!

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Zombies at CERN!

Tuesday, October 30th, 2012

Some friends of colleagues of mine made a zombie movie here at CERN. It looks pretty neat, and will be available for free soon online, so here’s the trailer:

Now, then. There are some things I should probably clarify:

1. This film has not been authorized or endorsed by CERN.

2. The Higgs boson obviously cannot turn people into zombies. Never mind the biology, it’s enough to know that the Higgs decays instantaneously into more ordinary particles, and never leaves the detector. If any LHC collisions could make zombies, the earth would already be filled with zombies created when ultra high-energy cosmic rays hit the atmosphere.

3. Zombies do not really exist, and they will not eat your brains. Really. I promise.

4. The LHC cannot be operated when anyone is in one its tunnels or experimental caverns. The safety systems that prevent this are quite a bit more sophisticated than the trailer seems to imply.

5. The tunnels in the film aren’t the LHC tunnels — which are continuously being used for science rather than cinematography — but they do appear to be real steam tunnels from some of the buildings here at CERN. Rather interesting and spooky, but maybe not as polished and high-tech as you were expecting.

In conclusion: it’s always fun to see zombies in cool places, especially in your own back yard. I look forward to the movie coming out. For more information, you can look at decayfilm.com, facebook.com/decayfilm, or twitter.com/decayfilm

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More Multitasking

Friday, April 13th, 2012

I fell out of practice at multitasking at the end of grad school. For the final six months, almost all of my work went into finalizing how to present my analysis results. There were two versions of the presentation: the paper and my thesis, but the general direction of work was all the same. The previous tasks I had worked on, geared toward keeping ATLAS running, were all long since “done,” at least as far as I was concerned.

Starting a postdoc means a sudden change of gears, with more multitasking than ever before. I’ve started many new projects from scratch at the same time, and because I’m new to CMS, every one of those tasks involves tools and procedures that I don’t know. It’s easy to lose track of some of those tasks at any given time, or simply to want to focus on one thing until I understand it, but the job doesn’t work that way. Being succesful as a postdoc will mean significant contributions to the running and understanding of the detector and significant contributions to keeping my group’s analysis running and starting a new analysis (sub)channel of my own. None can be dropped, and most of the things I’m doing have deadlines in the next few months.

So I’m having to remember and improve my multitasking skills, quickly. Step one is bringing this post to a close, and asking you to wish me luck, and getting back to work!

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Look Mom No Nabla’s!

Monday, August 8th, 2011

From time to time I find myself looking back at my class notes from my undergraduate studies, just to brush up on a topic or two (usually when I am taking the graduate class on the subject matter). And I’ve begun to notice a trend while comparing my undergraduate and graduate notes. I’ve gotten lazier.

That is, the notation I use to describe mathematics has gotten simpler. I think the reason for this is because there has been simply more material to write down, and less time for me to do it. I’ve seen professors at least double (sometimes triple) my age move faster with a white board marker then I can move on a treadmill. I have a tough time keeping up. So to keep up with them (aside from nagging them to slow down) I’ve started adopting a shorthand notation.

But unlike the late Dr. Feynman, I’ve not come up with my own short hand notation [1]. Instead I’ve just tried to incorporate what’s known as four-vector notation.

Four Vectors

Four vector notation is the notation of choice for quantum field theory. It allows a great simplification in how much you have to write (once you know the rules).

Let’s start with a simple example. Four vector notation allows me to describe a point in space-time (with respect to some reference frame), take the point:

(ct, x, y, z)

I can write this as:

Well that’s not astonishing in the least bit, I could have just as well labeled the point P.

Let’s take a second example. I can combine a scalar and a vector together in four-vector notation. For instance, if I wanted to describe a particle’s energy and it’s momentum (again, with respect to some reference frame) I could use a four-vector:

We can even go a bit more abstract and use four-vectors as mathematical operators:

Here we have a partial derivative with respect to time and the “del” operator (sometimes referred to as a nabla).

Now suppose I wanted to multiply two four-vectors, how would I do this? The product of two arbitrary four-vectors goes like this:

Notice how A and B have either a super-script or a sub-script in the above equations. In one case we have a contra-variant four-vector (super-script); and in the other we have a co-variant four-vector (sub-script).  However, their components are always labeled with super-scripts.  Notice how the product of four-vectors A & B is described by a “dot-product like” operation in which their respective components are multiplied together; but the last three are assigned a minus sign.

In fact I can only ever take the product of a contra-variant with a co-variant (nothing else); but the order in which one comes first doesn’t matter, their product is left invariant. I should also point out the name of the game is “summation over repeated index.” This means if I toss a third four-vector into the mix, if it has a different index (sub- or super-script) it’s ignored:

Notice how A & B have index μ and C has index ν. The μ is the “repeated” index, and the four-vector product acts between A & B. I realize this isn’t a true summation because there is a minus sign involved, but that’s just what the process is referred as.

Maxwell’s Equations – The Lazy Way

Now let’s dive into a serious example to really show the power of four-vector notation. And let’s go outside the realm of quantum field theory, instead let’s take Maxwell’s Equations:

With these four equations-and appropriate boundary conditions-I can describe all phenomenon in classical electrodynamics (I chosen to work in Heaviside-Lorentz units as opposed to the standard SI system, this causes the pesky μ’s & ε‘s to drop out. Remember I’m lazy!!).

These are four coupled first order differential equations that relate two vector fields (electric & magnetic). But from the theory of classical electrodynamics I can write these two vector fields as originating from a scalar and a vector potential (note, I did not say potential energy, which is very different from potential):

With this I can actually express Maxwell’s four first order equations as two second order equations:

Of course this is an awful mess when you look at it. Why on earth would anyone want to do this!? There are so many more terms and derivatives all over the place.

But, in physics there is something known as the “Lorentz Condition,” sometimes also called the Lorentz Gauge [2], which says:

(When I put this into Heaviside-Lorentz units the με again drop away).

Which simplifies the above two equations rather nicely:

Now this is truly enticing, these equations are almost identical! Suppose I made a set of four-vectors:

Notice how the last two are mathematical operators, one is a co-variant and the other is a contra-variant. They are just begging to be multiplied, so let’s do just that:

This is actually a new mathematical operator known as the d’Alembertian Operator, its usually represented by a square, but I don’t know the LaTeX command to make that. =(

But, with this set of four-vectors and the two equations above I can write mankind’s sum knowledge of all electromagnetic theory in one line:

Let’s pause on this for a moment.  I think this is really an astonishing miracle that physicists over the years have figured out how to write so much information about the natural world in such a small space (one line)!  Some of you might remember the Standard Model Lagrangian, which is conveniently written on a coffee mug should you forget.  That coffee mug contains A LOT of information, but it definitely cannot  fit on one line, at least with my handwriting (maybe someone someday will come up with some ingenious notation of their own?!).

But, just like that four vector notation has allowed physicists to simplify Maxwell’s Equations (all four of them) in a single concise statement. Talk about saving space on your final exam’s equation sheet! So hopefully you’ve come to appreciate the power of four-vector notation.

Until Next Time,

-Brian

 

References

[1] Richard Feynman routinely used his own notation for trigonometric functions, logarithms and other common functions in mathematics, he did this because it was simpler & faster for him to write in such a fashion. For more details and other great stories, see Feynman’s own “Surely You’re Joking Mr. Feynman,” W. W. Norton & Company, Inc. 1985.

[2] See for instance D. J. Griffiths, “Introduction to Electrodynamics,” 2nd ed., Prentice-Hall, Inc., 1989.

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My Crazy Semester: Thesis Writing

Monday, February 28th, 2011

Oops, I seem to have done things in the wrong order. The good news is that I have a job lined up for when I graduate. The… challenging… news is that I still have a few things to finish here in Berkeley: little things, like finalizing my analysis and writing my thesis! This has made for a rather busy semester, to say the least.

From the perspective of readers here, though, I’m not going anywhere fast. I will be switching universities, and (gasp!) switching experiments, but in neither case am I going far enough that I fall outside the subject of this blog. I didn’t mean “far enough” too literally, but the distances are about 2500 miles and 5.3 miles respectively.

This gives me lots to write about, so let me start with my thesis. It’s not that much fun. It has two parts: background stuff I have to look up, and describing my analysis in more detail. But it is, I have to admit, probably all wortwhile. The former part is all stuff that’s relevant to my work and I ought to be able to describe off the top of my head — and in fact, I usually can, but not with all the numbers and equations and details just right. The latter part is a good chance to really document what I did in my analysis, which is information that might not be public elsewhere. Maybe someone, someday, will want to look up what I did. Maybe I’ll look it up myself out of nostalgia. Once I get my thesis written at last, though, one thing I’m sure of: I won’t look at it again for a while. I’m already ready to move on!

While I’m working on that, here are some goodies from my thesis. The output of a helpful script I wrote:

Seth-Zenzs-MacBook-Pro:~ sethzenz$ python scripts/thesistimeleft.py

You have 75 days left to file your thesis!!!

It recalculates every day. I could make it send me automatic emails, if I really want to make myself nervous.

And here’s a bit of my (first draft) introduction, which tries to explain how my work fits into the overall context of the LHC program:

The Large Hadron Collider (LHC) was built to produce new particles and rare interactions at a high rate, but its first and foremost byproduct is sprays of low-energy hadrons. At its full design capacity, the LHC will cross proton bunches 31.6 million times per second at each interaction point, with an average of about 20 proton-proton collisions per crossing. Most of these collisions will be “soft” interactions, with relatively little energy exchanged and the outgoing hadrons having relatively little momentum perpendicular to the beam axis. These interactions are described in principle by Quantum Chromodynamics (QCD), the quantum field theory of the strong interactions. In practice, however, they are the most difficult to understand, because the theory becomes non-perturbative at low energies. Predictions can only be made via approximations and phenomenological models. This difficulty with low-energy strong interactions appears even in interactions that are initially well-described by perturbation theory. Outgoing high-energy quarks and gluons quickly “clothe” their strong color charge by evolving into jets of lower-energy hadrons, a process that again requires approximation and modelling.

The LHC’s general-purpose experiments, ATLAS and CMS, are equipped with multi-stage trigger systems that select against these common processes, for example by identifying leptons and missing energy produced in electroweak interactions. However, low-energy QCD still has a significant impact on the physics program in several areas. With so many collisions in each crossing, the most interesting collisions will have many low-energy collisions whose signals in the detector overlap with the objects of interest. In order for their effects to be subtracted, these features of these pileup collisions must be known quantitatively. The evolution of high-energy hadronic jets must also be well-understood. This is partially to account for their contribution as pileup events, but their energy must also be calibrated so they can be studied in their own right. Although even very high-energy jets are relatively common at the LHC, they can also serve as signatures of the decay of new particles.

The quantitative investigation of low-energy QCD is thus a foundational element of the LHC program, which will inform the studies and discoveries of the coming years. Initial low-energy QCD measurements have divided the problem between low-energy events and the study of higher-energy jet properties. In the former case, inclusive charged particle distributions are produced from events identified using a “minimum bias” trigger. In the latter case, higher-energy jets are triggered and studied using the calorimeter system built for the purpose.

This work focuses on the additional information to be gained in the case that the two issues are not-so easily factorized, by studying the emergence of low-energy jets from soft interactions. Particles are identified using the methods of the lowest-energy measurements, but grouped together into jets according to the algorithms used to study jets at higher energies. Low-momentum jets and their properties are measured using the ATLAS Inner Detector, the component of the ATLAS experiment that tracks charged particles, in events identified using the ATLAS Minimum Bias Trigger Scintilators.

That’s very unlikely to be final, but in any case that gives you a picture of the sort of thing I’m working on.

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