I often hear people talk about string theory being the hardest branch of theoretical physics, and require a PhD to even understand the basics. I've even heard of people saying it's getting too hard for humans, much like quantum mechanics is too hard for cats. So to put things into perspective, how hard is it really? Is it any harder than pure math? Is it any harder than other branches of mathematical physics, such as general relativity, fluid dynamics, or statistical mechanics, all of which have unsolved mathematical problems? And is it any harder than understanding the literature on high Tc superconductors which is another great unsolved problem in physics besides quantum gravity?
http://www.superstringtheory.com/math/index.html http://www.superstringtheory.com/math/math2.html http://www.superstringtheory.com/math/math3.html What subject is harder to learn and then make a contribution to?
Yes, this is a daunting list to look at, and no one would doubt it's very hard to contribute anything to string theory. However, requiring extensive knowledge of mathematics is also true for someone who wants to work on pure mathematics. I hear that different branches of modern mathematics are incredibly inter-connected. Can someone with knowledge about math departments clarify the situation? Is it harder to understand modern string theory than to understand some specialized field in modern mathematics, such as algebraic number theory or whatever? Is it harder than "rigorous mathematical physics" (which is not pursued by large number of people), such as constructive quantum field theory? I'd be glad if someone can make some comparisons and put things into perspective.
So addition of integers is easy for cats? :) In my opinion, it is a complete myth that string theory is "the hardest branch of theoretical physics". For example, there is not a single subject in the links provided by Spinnor that isn't used by Condensed Matter theorists (here the theories have to agree with experiments too, which complicates everything even more). And the comparison with pure math doesn't make sense either. Most good theoretical physicists could contribute to pure math provided they had spend as much time studying math as mathematicians. And vice versa. In order to get better answers, I think you need to provide a quantitative measure of how hard a subject is.
It's arbitrary to ask what is the most difficult subject, it based on the perspective and skills of oneself. Similar to the experimental/theoretical argument, where many think theory is far more strenuous. We all have our merits and shortcomings that are cohesive to certain areas of research.
About experiment / theory argument, I would say making important experimental discoveries is as hard as making important theoretical discoveries, but the entry barrier is lower. Just look at how many undergrads help out in the labs. In fact, once you get to the professional level, you're competing with people who have devoted a large part of their life to understanding the subject. It's hard to make truly groundbreaking contribution to any field. So my impression is that when people talk about a subject, e.g. string theory, being hard, what they're really saying is that the entry barrier is high.
Even after one masters all the background subjects and jumps over the entry barrier, the situation one often faces in doing ST research is that in many instances it's hard to make progress because the math one needs to use has not yet been developed by the mathematicians. For example, for purely computational reasons, most of the Calabi Yau examples that string phenomenologists use in various constructions are so-called toric varieties. However, this is only a tiny fraction of possible CYs, it's just that people don't have the mathematical tools to explore those other possibilities. The situation with the 4d compactifications of M-theory on G2 holonomy manifolds is even more extreme in that sense because there is no equivalent of Yau's theorem and one cannot use the power of complex geometry. So if you work in this area you literally have to discover the relevant math tools in order to proceed.
The alleged incredible difficulty of string theory is a myth. The truth is that most theoretical physicists can understand the basics of string theory. Just get the book B. Zwiebach, A First Course in String Theory
I do not think the name was coined to attract anybody. Witten coined the name because he did not like the simplicity suggested by "membrane". When he (they) stumbled upon those dualities, I think he (they) realized quickly that they would not need a fancy name to attract attention. By the same token, I do not imagine that "monstrous moonshine" was coined to attract attention.
Of course, but just check how big that book is. The basics are not that difficult, and I would say that almost every physicist who has a bachelor in physics should be able to understand the book of Zwiebach if he/she would try enough. The hard part is superstringtheory and beyond and the mathematical details of it, but also the physical principles of these complex ideas. That's why Zwiebach's book is so good; it's very physical.
M-theory is difficult, but NOT due to a difficult mathematics. Instead, it is difficult because no one really knows what this theory is about. :tongue2:
Is string theory still as "hot" in Academia as the popular books and TV documentaries (Such as the Elegant Universe) make it out to be? The Elegant Universe (Nova special) all but suggested that practically everybody who was going to school for physics was studying string theory. Really? Brian Greene comes across as something of a sham-wow salesman in that documentary and makes it hard for me to take him seriously. -DaveKA
Oh and of course you can buy "String Theory for Dummies" at Amazon now. (He says cynically as he secretly plans to buy it in the near future) -DaveKA
Brian Greene is certainly too enthusiastic for my personal taste. In my opinion, there are better popular accounts, such as Randall's. This being said, we should keep our minds open. String theory is still the most active and fruitful merely in terms of number of articles written, which simply reflects a number of researchers. Just have a look on arXiv for yourself. IMHO, one of the reasons M-theory is so difficult is that it is a non-perturbative problem. How is that helpful ? Say, if you take Zee's last edition, you fill find clearly that one mainstream point of view is that it does not matter so much whether SUSY is realized in Nature or not. There are many papers which are not concerned by this question. People study N=4 YM because it is a playground in which we may be able to get insights and improve our handling of even scalar fields.