String Field Theory

1. Jul 3, 2008

Englishman

I know about string theory, but have heard that string theory is part of the bigger scheme of string field theory, which I think is part of the bigger scheme of M-theory, which is part of the bigger scheme of the Grand Unified Theory. Are my speculations correct, and how long will the Grand Unified Theory take to be completed?

2. Jul 3, 2008

Coin

Hopefully someone who knows more than I do can take a crack at this, but i'll do my best:

• I don't know what string field theory is.

• M-Theory is a generalization of string theory. Exactly in what way it's generalized is often a little bit vague but the primary differences seem to be that M-Theory is 11-dimensional whereas superstring theory is 10-dimensional, and string theory contains only strings (vibrating 1-dimensional objects) whereas M-theory also contains "branes" (vibrating 2-dimensional, 3-dimensional, 4-dimensional and so on objects). (I've heard it claimed that all of M-Theory can be derived from formulating supergravity in 11 dimensions but how exactly this works confuses me.)

The problem with M-Theory is that nobody knows what it is. They basically have a description of what M-Theory looks like but they've never fully formulated it. However there are very strong reasons to believe a theory that fits the M-Theory description exists. The neat thing about M-theory is that we know that if we find M-Theory, all of the old string theories will exist inside of it-- as I understand it there are several different types of traditional string theory, and M-Theory can "act like" any of these different string theories depending on how you configure your branes. In other words string theories are really just special cases of M-theory.

• String theory is not a Grand Unified Theory.

"Grand Unified Theory" is a very specific term referring to any theory that includes the idea that the fundamental forces all merge into a single force at a high enough energy scale.

A big thing in modern physics is to describe forces using their symmetry groups. Theories that do this are called "gauge theories" or "yang-mills theories". A long time ago people figured out that if you do this, you can describe the electromagnetic and weak-nuclear forces as really the same force-- the electromagnetic and weak-nuclear forces share a single big symmetry group, but the symmetry is broken so that it looks like two asymmetrical forces. The standard model of particle physics depends on this idea and the Large Hadron Collider is expected to test whether it is true.

Once people realized this, they started wondering if they could repeat the trick, and combine the electromagnetic, weak-nuclear, and strong forces into one single huge symmetry group. Theories that do this are called "Grand Unified Theories". This was a big deal in the 70s and 80s. However although the idea is really neat, it turned out to have a lot of problems. "GUT"s predict a lot of weird things, like magnetic monopoles and proton decay, that don't exist in nature. It is no longer widely expected that the true theory of everything will be a GUT.

Both M-Theory and vanilla string theory are unification theories in the sense that they explain all four fundamental forces (including gravity) using a single underlying fundamental process (the string). But they are not really Grand Unified Theories because they do not suggest that all of these forces share a single yang-mills symmetry group, or that they merge at high energies. Wikipedia's page on GUTs describes string and m- theory as "Not quite GUTs".

Wikipedia does suggest that you could accurately describe string and m- theory as "Unified Field Theories".

3. Jul 3, 2008

Englishman

I know string theory and M-theory are not the Grand Unified Theory. And the Grand Unified Theory I was talking about is not just any Grand Unified Theory; it is the one that will unify General Relativity and Quantum Mechanics.

4. Jul 3, 2008

nrqed

What Coin was explaining was that the term "Grand Unified Theory" is generally NOT used to talk about the unification of GR and quantum mechanics!

GUT refer to unifying the other three forces (weak, Strong and E&M) of nature as a single force.

"Unifying GR and quantum mechanics" as you say is just what people call finding a theory of quantum gravity, which does not involve "unification" of the forces. The word "unification" usually refers to uifying *forces*.

String theory does more than all of that...it offers a way to quantize gravity AND to unify all the forces of nature and this is sometimes referred as a "TOE", a theory of everything.

5. Jul 3, 2008

nrqed

String field theory is conceptually quite unrelated to M-theory.

String theory is usually written as a first quantized theory (with all states "on the mass-shell"). Strinf field theory is a second quantized formulation of string theory, the equivalent of the quantum field theories of E&M, QCD, etc. Have you done any quantum field theory? If not, this is a very technical point to explain. In a nutshell, string field theory is a more general formlaism to do calculations in string theory. It's more of a technique than a new theory.

M theory is a more general theory than string theory and is described by Coin in his reply.

6. Jul 3, 2008

humanino

It is worth mentioning that some people argue, quantum gravity requires GUT on physical grounds.

By the same token, it was well known before QCD that a correct theory of hadrons will require to get rid of the renormalization procedures.

7. Jul 3, 2008

Englishman

Well, I have read Richard Wolfson's book, Simply Einstein: Relativity Demystified, and it says that the "unification" of general relativity and quantum mechanics is the Grand Unified Theory, and that it would be called the Theory of Everything.

8. Jul 3, 2008

nrqed

• The entire post is quite good. Just one small correction: it's not that M theory should be "derivable" from M theory. It's the opposite. 11D supergravity is the low energy limit of M theory.

9. Jul 3, 2008

nrqed

In a popular book it is possible that he might have used the term "quantum mechanics" in a different way than what is used in research. I have seen some popular treatment using "quantum mechanics" to actually refer to the quantization of all the other three forces. But if you talk to anyone doing reserach in the field they would probably not use that language. But fair enough.

and again, GUT can be used to mean different things but people in the field usually mean what Coin wrote: putting all the fields of the Standard Model in one gauge group like SU(5) or SO(10).

Again, it's a question of semantics. Coin and I are simply using more the language of the people doing research in the field but I can see how a popular book may cut corners and use a much less careful language.

10. Jul 3, 2008

humanino

Also, nobody serious about his understanding of general relativity refers to Einstein's writing as authority. Weinberg for instance claims that a decent student understand it better than Einstein himself (sitting on the shoulders of giants concept...) Not even to mention that he had no clue about M-theory...

11. Jul 3, 2008

Englishman

I see. You are saying that, perhaps, in an attempt to write for the masses, that Richard Wolfson has used language somewhat inconsistent with the actual language used in the field?

12. Jul 3, 2008

nrqed

Yes. If you ask researchers in the field to list some GUT theories, they would not give you theories including gravity, they would describe the sort of thinsg Coin talked about in his post. And if you would ask if a theory marrying GR and quantum mechanics is a theory of everything, they would almost certainly tell you "no, because the other three forces are not included". For example, "loop quantum gravity" is an approach to quantizing gravity (so marrying gravity and GR) but it does not deal with the other three forces so it's not considered a theory of everything.

13. Jul 3, 2008

happyprof

I think a read of Lisa Randall's "Warped Passages" might give you some unifying thought. Things are changing so rapidly and, in some circles, the spiritual and scientific thoughts are getting mixed up (or are they?). for the longest time we have relied upon our most historically important tools: Socration, Platonic and Aristotelean logics. I think to find out anything more than neat models every few days or so, we will have to find a new way, or new ways, of thinking. I don't know what it/they are.

14. Jul 3, 2008

Englishman

Okay.

15. Jul 4, 2008

Demystifier

String field theory is a rather conservative attempt to derive string theory from something more fundamental. It does not seem very successfull, except for open bosonic strings.
(By contrast, M-theory is a much more radical attempt to derive string theory from something more fundamental.)
See e.g.
http://xxx.lanl.gov/abs/hep-th/9411028
especially Sec. 4.

16. Jul 4, 2008

Coin

Hm, thanks, that makes a lot more sense I think!

This is very interesting, can you vaguely explain the grounds for this argument?

I have to admit I'd actually never heard of any attempt to couple quantum gravity to a GUT. Actually the only GUT I've ever heard of to include an attempt at incorporating gravity is Garret Lisi's "long shot" E8 theory that got all that random press last year.

17. Jul 4, 2008

humanino

The idea is that new physics occurs at a given scale. You expect new physics for EW-strong unification at a scale below quantum gravity. Therefore, attempting to quantize gravity before knowing what happens at all may be doomed to fail.

The second part of my post was to indicate that one should take such simple "physical" intuitive argument with caution. I find the argument deceptively simple.