Will the String Theory Tie Them All Together?

firaq:

Thanks for your comments. No, I am not a string theorist. I am a civil engineer. My knowledge of string theory is based on popular physics books, some of them written by professional physicists. I am usually careful in stating facts as accurately as is possible for a civil engineer and sometimes supprt such statements with appropriate references. (Engineers are notorious for approximations but not fabrications. I had a German Professor who taught us Theory of Structures and Strength of Materials. He used to say that 2+2 is never 4 for engineeres; it`s either 3.99999999 or 4.00000001). By the way the perturbative methods are also approximate.

1. Regarding the collision of branes, you are correct; I alluded to the work of Steinhardt et al but I may not be wrong in assuming that Ed. Witten also supported this line of thought. Things are still in a state of flux in the field of string theory. My knowledge is by no means up-to-date or comprehensive; it`s however derived from the facts published by the physicists.

2. Vafa`s theory is said to be based on ten dimensions of space and two of time. The concept of two dimensional time is an `oddity` and not very popular with majority of the physicists. Vafa`s theory is still a tentative idea. I can come up with a reference in support of two dimensional time; I learned it from published material.

Wishing you well,

Mohammad Gill

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Gill sahib, Are you a string theorist? Or does your knowledge of string theory come from reading popular articles?

And a couple of minor points...

1) You say that the big bang in string theory is a collision of branes. You are probably referring to a recent idea of Steinhard, Ovrut, Turok and Khoury, named the ekpyrotic universe. Its an interesting idea, but by absolutely no means is it accepted in string theory. In fact there are serious problems with it and it would be fair to say that as it stands now, it is discredited. There is a lot of work these days to understand inflation within string theory, and this is completely independent of the brane collision idea.

2) F-theory, proposed by Vafa is not really thought of as a 12 dimensional theory but just a special compactification of Type IIB string theory. That is how the theory is defined. If there is a theory with 12 large dimensions (lorentz invariant directions), no one has found it.

tobateksingh:

Yes, you’ve a general idea of the uncertainty principle but you need to brush it up. Then you will be able to understand the vacuum energy by reading a suitable popular book on quantum mechanics.

Irfanahmad:

It is similar to series solution but with a difference. Each of the succeeding terms in a perturbation series is multiplied with the increasing powers of a perturbation parameter which is always less than one. The leading term is multiplied by e^0 (=1) where e=perturbation parameter, the second term is multiplied by e^1, the third term by e^2, so on and so forth. In this way all the succeeding terms become progressively smaller and smaller and the series is convergent.

Sometimes, if some other term grows large exponentially after a certain stage, it means trouble (problem). There are ways to handle such situations although they may not always be very satisfactory. In the perturbation solutions in Quantum Mechanics, infinities started appearing invariably. Richard Feynman’s renormalization method provided a way to handle this irksome situation. Many however believe that this is an ad hoc kind of solution and not very satisfactory one. The string theory is believed to provide a better solution.

Mohammad Gill

Tobateksingh,
You know my formal physics education is even flimsier than yours :)

Gill,
So perturbation methods are something akin to series solutions where we discard the higher order terms because their contribution diminshes and also oscillates around 0 so that it converges towards a finite value?

Irfan.

Sir,

Okay, that does help.
I do remember the uncertainty principle from school - the idea was that there is a limit to the precision of our measurements. The more you know about the velocity of a particle, the less you know about its direction. Am I correct?
So, could you now connect the dots between vacua, unique vacua and perturbative solutions and the implications for TOE`s?

Thanks,
Aman

Dear tobateksingh:

I had written a post to explain `perturbative solution` but lost it by punching a wrong button before posting it. Let me write a new version because I hadn`t saved the older version. I had written it directly on the computer without preparing a draft.

I hope plancherel does not mind my giving you this explaination because you had asked him for it (He was the one who mentioned perturbative solution and the vacuua). In my first version, I had mentioned that I`ld give the explaination on perturbative method only because explaination of the `vacuum energy concept` (if that is what plancherel implied) is a little more complex withot discussing Heisenberg`s Uncertainty Principle. This is one reason that I avoid introducing the patent technological terms while writing on science topics in popular vein.

Much of physics is in terms of `ordinary` and `partial` differential equations. There are linear differential equations which are relatively easier to solve and there are non-linear differential equations which are very hard to solve. One of the very strong approximate methods of solving the non-linear equations is by the method of perturbation. The original non-linear equation is written in terms of a series of linear equations. Usually the first linear equation (the leading term of the perturbation series) provides a very good approximation. Each of the succeeding terms of the series is progressively smaller than the preceding term.

Exact solution of a given non-linear equation, if it can be found, will be non-perturbative solution. Quantum Mechanics is generally in terms of non-linear partial differential equations. Hope, this explaination will be useful. I have tried to keep it as simple as I could manage. At the same time, I`m not really an expert although I had the occasion of using perturbation method in some of my own work.

Mohammad Gill

Dear plancherel,

Could you explain what non-pertubatively means?
And what do vacua have to do with a TOE?

I just like to catch up from time to time with these discussions, and lacking any formal training in physics, I was wondering if you could do some translations there?

It is quite unlikely that string theory will be able to achieve all that is mentioned in the conclusions. It has been clear for some time now that the theory has no unique vacuum (representing something similar to our universe) instead it has billions upon billions of consistent vacua even non-perturbatively. This fact alone reduces the predictive power of the theory. The fact that it seems to be a consistent theory of quantum gravity is a major reason why so many people are working on it (since nobody understands what string theory really is non-perturbatively it is hoped that once it is understood everything will work out ok). However, string theory is not the only theory which claims to be consistent with quantum mechanics and general relativity. The other approach known as ``loop quantum gravity`` also has many strong points, but certainly not ``sexy`` enough for people to pay attention.

Will the String Theory Tie Them All Together?
I hope so.