Please explain "string theory" to me.

Factual Questions
1

I have, at best , a layman’s knowledge of string theory. I would love an explaination of it’s most fundamental aspects. The “proofs” about 5+ dimensions, and the apparent contradictions of today’s laws of physics are of the most interest to me. Also, how does this fit with the unified field theeory, or is it just an expansion of that?

Lest anyone be confused…“I know Nusssing!!” /Klink

2

Check out Brian Greene’s book, “The Elegant Universe” - it covers all the subjects you mentioned very well in layman’s terms. He just released a new book too, but I can’t remember the title.

3

whoa! trippy! I had the same question about this the other day. I think I was flipping through channels and caught something on PBS talking about String Theory.

Wikipedia - String Theory

4

I just spent the last two academic quarters trying to understand Polchinski, so let me give this a shot.

  1. Why does string theory require a larger number of dimensions than we actually see? It’s due to something called an “anomaly.” If we have a classical theory and we try to construct a quantum theory that corresponds to it, we often find that certain symmetries of the classical theory aren’t preserved in the quantum theory; such a symmetry is called an “anomalous symmetry” or an “anomaly” for short. In the case of string theory, the symmetry in question is Lorentz invariance, which is the symmetry that special and general relativity are based on, so physicists are loath to work with theories that don’t have it (SR and GR are pretty well established.) One can easily write down classical theories of strings moving in space which have Lorentz symmetry; but when one tries to construct the quantum theory corresponding to this, one finds that Lorentz symmetry is only preserved if spacetime has a certain number of dimensions (ten dimensions for the most “realistic” string theories out there.)

The problem with this, of course, is that the Universe we observe is most emphactically not ten-dimensional. String theorists explain this by postulating that the other six dimensions are “compactified”, which means (roughly speaking) that there’s only a finite distance you can go in any one of these extra six directions before you end up back where you started. (For example, if you’re confined to the surface of the Earth, there’s only so far you can get from the North Pole.) The exact shape of these extra six dimensions is still not established, though; there are thousands of plausible choices that we know of and probably even more that we don’t.

  1. What’s the relation between unified theories and string theory? When most physicists talk about a “Grand Unified Theory” (GUT), they mean a theory that unifies three of the four fundamental forces in the Universe, namely the electromagnetic force and the two nuclear forces. String theory goes one step further and tries to describe all four fundamental forces (the three above plus gravity) in one unified theory. It’s an interesting fact, though, that if you want your string theory to resemble a GUT, your choice of the shape of the extra six dimensions (see above) is pretty constrained, and trying to get a shape that makes string theory look like the real world (with the forces we already know about) is one of the more intensely-examined projects in string theory these days.

Hope this helps. Feel free to ask further questions & I’ll try to answer them as best I can.

5

The PBS show on string theory was… The Elegant Universe, hosted by Brian Greene.

No coincidence there. His book The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory is still the book of choice for those wanting to learn more about the topic.

You cannot, with all due respect to the wonderful explainers here on the Dope, you cannot hope to understand the whys and whats about string theory or even the basic need for a theory that goes beyond general relativity and quantum mechanics from a couple of paragraphs on a message board. Even a whole well-written book by a working physicist filled with wonderful analogies will be a tough struggle for the non-scientific reader. Greene’s book does it better than any other.

And his new book, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, is just as mind-boggling.

BTW, it was Sgt. Schultz whose tagline was “I know nuzthing.” If you can’t get sitcoms, you’re going to have a real tough slog through string theory. :smiley:

6

here

7

IIRC, what we do know is that the fiber must be a six-dimensional (thus making ten in toto) compact Kahler Calabi-Yau manifold with certain gauged symmetries. It’s actually pretty restrictive compared with just a compact 6-manifold.

8

<highfalutin mathematical physics>
Yup, but there are still several thousand known Calabi-Yau manifolds, and it’s not even known if the number of topologically distinct Calabi-Yaus three-folds (i.e., three complex dimensions) is finite. And the restriction to CYMs comes from the desire to preserve supersymmetry below the compactification scale — but supersymmetry is far from proven. (Or disproven, granted. We’ll see what happens in five years when the LHC turns on.)

That said, it’s true that the Calabi-Yau restriction is a fairly large one, and if you restrict attention to CYMs that actually give rise to reasonable phenomenology (e.g., three generations of quarks & leptons) there aren’t that many known CYMs. If you’re interested in finding out more, you can read this PDF which I wrote as a final project for the aforementioned string theory course.

Oh, and a nitpick: a Calabi-Yau manifold is just a Ricci-flat Kähler manifold, so saying a “Kähler Calabi-Yau manifold” is redundant.
</highfalutin mathematical physics>

9

Thanks. It’s interesting how in a department and with an advisor who used to be relatively known for strings theory that I’ve never gotten quite the straight answer (“dope”, if you will) on C-Y.

10

That was Schultz. :slight_smile:

Schu-u-u-u-ultz! /Klink
Klink, you’re an idiot. /Gen. Burkhalter

11

One reason physicists started looking into string theories in the first place is an attempt to get rid of the infinities that result when you try to do physics on infinity small point particles, in a space-time that can be an arbitrarily infinitely small space. By being strings, particles have a minimum size, so does space-time. This keeps the force on two particles that get too close from rising to infinity*, and it keeps the quantum fluctuations in space-time from getting out of control.

*Most forces fall off at an inverse square, so that something twice as far away is 4 times weaker. Likewise, something twice as close feels a force 4 times higher, assuming equal total forces. If you reduce the distance to 0, the force rises to infinity. Adding a minimum distance means the distance can never be 0.