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I've heard that one of the cardinal rules for writing a good blog is to "stick to what you know". If you're an expert at something, write about that, skip the comments on things you're only starting to figure out. I've never adhered to that. Instead, I tend to write about whatever I'm thinking about, or whatever I'm learning about. I think the problem is that if you stick to topics you know everything about, it's boring to write out. It's more exciting for me to write about something I *don't* know much about and am just starting to think about... then I get lots of interesting comments that are educational for me.

You might think that, given that I spent from 2003 through 2009 in grad school for physics, I would have been learning a lot of physics and therefore would be writing about it a lot. Unfortunately, that's not true either. I didn't usually write anything about what I was learning about there because I knew it would likely take a whole book to explain instead of a single post. I did make a few posts toward the beginning of grad school, but by the end the topics were so esoteric I knew that the interested audience would be so small that it wasn't worth it.

Anyway, I said to myself at some point "that's sad, I should at least try to write about something interesting that I know a lot about, even if it's not what I'm immediately learning." I thought surely there was a balance somewhere that could be attained, and yet I never quite got around to figuring it out. Right toward the end of my degree, as I was writing my dissertation, I did decide that I wanted to write something about dimensional transmutation and quantum anomalies. But my priority was always writing the actual dissertation rather than my blog. So now, I've got a bit more free-time and can give it a shot. I should warn up front that the "balance" I've chosen here is to write about something deep and interesting that I have never *quite* fully understood (otherwise it would be too boring for me to write about) but I nevertheless feel like I have much more knowledge about it than the average person so I can count it as "good blogging behavior". Not sure how many parts this will be in or how well it will go over but here goes...

Theoretical physicists love to pick cool-sounding names for things, names like "Anti de Sitter space", "tachyon condensation", "zero point energy", "warp factor", "the eightfold way", or the names for the flavors of quarks, "up", "down", "strange", "charm", "truth", and "beauty"... or even sexually sounding names for things like "quivers" and "kinks"! Sadly, in most cases if the average person found out what these names actually stood for, they'd probably be very disappointed or bored. They all boil down to different sorts of mathematical relationships. (And no, "warp factor" as used in physics has nothing to do with the term "warp factor" used in the Star Trek world.) Give them a cool name and they get very excited, but show them the equation that it stands for and they're like "oh, just a bunch of greek symbols?" Of course, those mathematical structures do useful work in describing the universe we live in (or so we think) and many of them are very interesting in their own right. But they are still pretty different than what people expect when they hear the names. There is not always a perfect correlation between how cool the name for something sounds and how deep or interesting it really is if you understand the concept. But as I was writing my dissertation, two of the coolest-sounding names for things that I wrote about--"dimensional transmutation" and "quantum anomalies"--do happen to stand for really deep and important things in physics. And what's more, they are related! Indeed, dimensional transmutation is due to one particular kind of quantum anomaly, called the conformal anomaly. Granted, none of those terms mean what they probably sound like they mean, but the connections are still pretty neat. So this is what tempts me to try to write a more "accessible" explanation of them than the brief paragraph or so I dedicated to them in my dissertation. Really, when I look back it's some of the most interesting yet most difficult to understand stuff that I learned in graduate school. And connected to so many different interrelated topics that have bearing on all sorts of different things in quantum field theory and string theory.

I guess this "part 1" is turning out to be more of an introduction to my intended post about quantum anomalies, rather than the explanation itself. I guess I won't really start jumping into the meat of it until at least part 2. But I will give a little bit more of a teaser first. Quantum anomalies are a weird kind of effect that shows up in some quantum field theories. Dimensional transmutation is something that happens when a conformal anomaly, one type of anomaly, shows up. Quantum anomalies are also important in string theory. If you've ever heard anything about string theory, you've probably heard that it requires 10 spacetime dimensions rather than the usual 4 (3 space + 1 time) that are more traditionally assumed in physics. (If you heard 11, you're right also, but let's ignore the M-theory dimension for now.) So one of the first questions most people ask is "why 10? why not 20, or 50, or 300? where does the 10 come from?? And why can't you just have vibrating strings in the usual 4 dimensions, what's wrong with that?" Well, it turns out that the reason you need 10 dimensions rather than 4 or some other number is because of the conformal anomaly. So if you want to understand where the 10 comes from, you must first understand the conformal anomaly.

Comments

( 6 comments — Leave a comment )
(Deleted comment)
gaspaheangea
Jul. 11th, 2010 11:44 am (UTC)
speaking of Star Trek, there is something called "Cardassian cosmology".
vaelynphi
Jul. 11th, 2010 12:52 pm (UTC)
As long as it's not Kardashian Cosmology--I'd hate to see those people take over everything! (I'm not sure Kim's 'made of matter'!)
gaspaheangea
Jul. 12th, 2010 04:05 am (UTC)
That's what the Kardashev scale is for.
vaelynphi
Jul. 15th, 2010 02:34 pm (UTC)
Yes, but shouldn't it rationally be based on how much pleather we've covered the moon or Mars in? (Ever see Total Recall? Or, as I like to call it, Yuppie Moon Wars.)
vaelynphi
Jul. 11th, 2010 12:53 pm (UTC)
Indeed, I look forward to hearing about this in more detail; I was just yesterday tinkering with a GUT model and seeing what sorts of strange things come out of non-multiples-of-4 + 2.
( 6 comments — Leave a comment )

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