Compactification in String Theory Part I: Motivation

A new attempt to reinvigorate the blog!

Yes, I am aware that I already have two physics related threads that have started and ended at “Part I” (false vacua and string theory). However, I’m really motivated by the introductory explanations. I promise to come back and finish the other ones real soon. But for a while, I’d like to talk about compactification.

A word about the word…I’ve had at least two scientist friends laugh when I’ve said “compactification”. Also, the text editor I’m typing this in thinks its a misspelling. Apparently in all other science fields, the correct word for taking big things and making them small is “compaction”. 

Well, we string theorists are just a little bit cooler then you “real scientists.”  We’re not taking some obsidian and making it smaller (like my roommate, the geologist, and one of the laughers), we’re making goddamned extra dimensions smaller. You read right, the extra dimensions.

For casual, non-specialist readers (if there are any left) the first few posts will be an introduction–an attempt to explain WHY we need to “make the dimensions smaller,” what that means, and why its so hard. I hope to follow up much later with more technical issues and a few comments of my own very small research in this subject. At the very least, you will be able to read pretentious, unfunny Woody Allen short stories and chuckle with smugness.

Ok, so let’s get on with it.

We know a lot about what happens when we collide two particles. We have a “standard model” of particle physics, and it is astoundingly precise. However, we have no real idea bout how to take these techniques that have been so successful and apply them to gravity. Gravity’s a real mystery.  If you try to do the simplest thing, it just doesn’t make any sense, the theory is beset with infinities all over the place. This problem is often known as “the quantization of gravity”.

Now, in some sense, the quantization of gravity is an extremely academic (and masturbatory [that's now 2 blog posts, 1 powerpoint presentation!]) problem. We would only be able to measure the effects of such quantization if we were able to get our particle accelerators up to an extremely high energy, WAY higher than the energy we are currently able to reach (and I mean way higher, like 10^15 times what we can reach now).

Nevertheless, people don’t do theoretical particle physics for it’s usefulness, and it’s a rather nagging problem. There should be some way to quantize gravity.

It turns out there’s at least one, and it’s called string theory. Instead of the fundamental objects being “particles” they are tiny vibrating strings (full disclosure: not entirely true, but that’s another discussion). 

Now, some very smart people in the 70’s wrote down string theory, and realized that it solved the problem of quantizing gravity. And it was good. 

At the first pass, one might try to write down string theory in flat space; it’s solvable (at least perturbatively) and valid as long as your not in the vicinity of some black hole or something. 

However, after playing with the theory for a little bit, you realize something–it only seems to make sense if it is a theory in 10 spacetime dimensions (1 time + 9 space)! 

This is clearly a problem and immediately in contradiction with experimental evidence–we only “see” four dimensions (3 space, 1 time). But if you’re only nominally clever, you realize there’s a way out–redefine your theory so that there are six dimensions that are “really small.”

Sounds simple enough. But we’ve actually created quite a problem; when we had ten flat and big dimensions, we could compute things with string theory. As we’ll soon see, computing things becomes extremely hard once we make some of the dimensions really small….

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3 responses to “Compactification in String Theory Part I: Motivation

  1. Butbut.. compactification isn’t “taking something big and making it small”. It’s taking something noncompact and making it compact!

  2. Well someone’s being a bit of a nitpicker! Of course your right, but “taking something big and making it smaller” is how one might describe compactification to a layman.

    It probably works better than “taking something whose open coverings do not necessarily have finite subcoverings and making it so”.

  3. …enjoyed reading this entry, very engaging and intriguing. It got me looking up Calabi-Yau manifolds on Wikipedia.

    So W. defines ‘compatification’ in physics as “curling up of extra dimensions” versus in mathematics, “enlarging of topological space to make it compact”. If this were left to a chemist’s guess, I would’ve said that it sounds like something that involves a mortar and pestle.

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