Hi, from newcomer J. interested in string/M

[marcus]

This greeting from a newcomer was posted out of place (in bibliography) so I copy here, to give J. his own thread. Please welcome.

Hi everyone, I most likely do not belong here at all, but I wanted to ask a few questions. This topic seems very heated and I am liking physics a lot right now. I am a freshman in college and I am studying math my guts out because String theory, and other proposed GUT theories require the craziest math I know of. Is the "math path" on the superstringhtheory website accurate? I am basing my studies off of that, although I don't know any other math than that anyways haha. Is it possible to learn any technical information about string theory with the mathematics level of multivariable calculus? I assume no, but if so please let me know.

I am currently in multivariable calculus class, while studying differential equations, linear algebra, and I am walking into a Classical Mechanics and graduate differential equations (that class I understand much less than the others but I try to pick up on a few things. For example, they went over lp norms and I researched that, I am sad to realize that I only know of one space - Euclidean space. I cannot wait to try to imagine the others.)

Thanks.

My comment: Jonny the core message here may actually belong in the "Academic guidance" forum up near the top of PF main menu. I will copy and highlight what I think is the gist, in case anyone wants to respond. Good luck with your courses this semester!

==quote what I think is the main message==
I am a freshman in college and I am studying math my guts out because String theory, and other proposed GUT theories require the craziest math I know of. Is the "math path" on the superstringhtheory website accurate? I am basing my studies off of that, although I don't know any other math than that anyways haha. Is it possible to learn any technical information about string theory with the mathematics level of multivariable calculus? I assume no, but if so please let me know.

I am currently in multivariable calculus class, while studying differential equations, linear algebra, and I am walking into a Classical Mechanics and graduate differential equations (that class I understand much less than the others but I try to pick up on a few things. For example, they went over lp norms and I researched that, ...
==endquote==

 

[Jonnyb42]

Thanks marcus, I apologize for the misplaced post.
I didn't realize that topic was for news

 

[Kevin_Axion]

The page is quite accurate if you're referencing to this: http://superstringtheory.com/math/index.html. The only formality I think you haven't considered is that Mathematics is the core and abstract Physics concepts grow from its soil. Therefore it is necessary to take Physics classes or gain a thorough understanding of Relativity, Quantum Mechanics- Quantum Field Theory and of course Particle Physics which derives from Quantum Field Theory beyond the aspects of Mathematics.

 

[crackjack]

Barton Zwiebach's string book should be quite readable in the near future.

 

[mitchell porter]

I would go further than Kevin and say that the fastest route to understanding string theory is to grasp its picture of the physical world. All the mathematics then becomes a technology for implementing that picture in calculations. But you can understand the picture before you understand the mathematics.

So if I was designing a fast-track string curriculum on those lines, I might start with Feynman's sum-over-histories version of quantum mechanics, e.g. as explained in his book "QED". Then I'd go over the mathematics of this - perturbation theory, quantum fields, the S-matrix. Once that was understood, you could then go to string perturbation theory as a sum over worldsheet histories, and the way that infinite-time scattering of strings gets mapped to Riemann surfaces. We'd digress to explain supersymmetry, sketch the five superstring theories of the 1980s as they are described in section 1.1 of hep-th/9802051, and then we'd be ready for branes, dualities, and M theory.

I suppose there are quite a few other topics, not mentioned above, which we'd have to cover along the way. :-)

 

[humanino]

The website program is a few years of study I think. You may want to check Hatfield's book "quantum field theory of point particles and strings". It takes the reader from quantum mechanics to string theory, strict minimum, but has the advantage of displaying as full calculations as reasonable. Zwiebach's book is also excellent, it will give you more of string but less quantum field theory, so it might be a second step.

 

[Kevin_Axion]

Most definitely the Standard Model, hence Quantum Field Theory, Yang-Mills Gauge Theories and the Gauge Structure of Particle Interactions: SU(3)xSU(2)xU(1). These topics aren't easily comprehended by students and even professors alike and it is essential to have an understanding of this to understand what exactly Superstring Theory does. Many of the ideas and fascinating concepts in Superstring Theory have to do with these Gauge Groups mostly in AdS/CFT or more generally Gauge/Gravity Duality.

 

[Jonnyb42]

Wow, I love all the replies! I will definitely take the advice, and I am interested in Zwiebach's book, thanks again.

I have one question, if possible to answer in a way I can understand;

Why do I hear string theory cannot be proven a true theory of everything or not?

Can't you just take some values and consider them 0, or limit to infinity, etc. and see if it boils down to classical mechanics, showing that classical mechanics is indeed an approximation of a bigger theory, and the same done for quantum and relativity?

 

[mitchell porter]

Why do I hear string theory cannot be proven a true theory of everything or not?

Can't you just take some values and consider them 0, or limit to infinity, etc. and see if it boils down to classical mechanics, showing that classical mechanics is indeed an approximation of a bigger theory, and the same done for quantum and relativity?

String theory does contain all those limits. But to match experiment, it has to match all the observed particles and forces, and their observed properties and interactions. We actually know the right limits to take, too (low energies and long distances - low compared to the big bang, long compared to the string). So it may sound simple - string theory tells us what strings there are, how they move and interact, and then we can just do the math and see if it looks like the real world.

But here's the punchline: How the strings move depends on which space they move through. You already know there can be spaces other than Euclidean space. In fact, there's an infinity of different types of spaces that the strings might be in. So to match reality, we have to guess the space first. And there are a lot of choices.

 

[Kevin_Axion]

About 10^1000 now I believe.

 

[crackjack]

String theory is a framework - just like QM or QFT. To apply it, it has to be fed the right parameters and the results matched with known data (Just like how SU3xSU2xU1 can be seen as one parameter of QFT. When people talk of zillions of vacua, it is akin to talking about all possible QFT vacua with all possible parameters).

But the results of the kind of string theories (ie. string framework + parameters) that one is referring to, when he talks of strings being out of experimental reach, will only lead us to SUSY GUT energy scales. What this SUSY GUT is and how it is broken down to our standard model is an equally hot work in progress (which also involves cosmology). But, as of now, our experiments are only scratching the surface of 'theories beyond the standard model' (SUSY, GUT etc). So, we need to be doubly lucky in order to match the results of above string theories to the standard model data that we currently have.

Also know that there are also groups working on low energy string scales - with scales as low as QCD, for example.