How hard is string theory exactly?

[petergreat]

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?

 

[Spinnor]

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?

 

[petergreat]

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.

 

[arivero]

Given the number of papers published, I'd say it is a pretty easy topic.

 

[element4]

I've even heard of people saying it's getting too hard for humans, much like quantum mechanics is too hard for cats.

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.

 

[Kevin_Axion]

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.

 

[petergreat]

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.

 

[smoit]

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.

 

[Demystifier]

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

 

[humanino]

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

The difficulty refers to M-theory, which is as of today undefined.

 

[MathematicalPhysicist]

The difficulty refers to M-theory, which is as of today undefined.

At least it has an attractive name to lure in the innocent youngsters.

 

[humanino]

At least it has an attractive name to lure in the innocent youngsters.

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.

 

[MathematicalPhysicist]

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.

Maybe the name doesn't, but the popular books and popular tv show sure do.

 

[haushofer]

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

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.

 

[Kevin_Axion]

SUSY actually makes things much easier to solve, so I've heard.

 

[Demystifier]

SUSY actually makes things much easier to solve, so I've heard.

Yes, but only when it describes a theoretical world with unbroken SUSY, which is NOT our world.

 

[Demystifier]

The difficulty refers to M-theory, which is as of today undefined.

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.

 

[dkotschessaa]

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.

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

 

[dkotschessaa]

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

 

[humanino]

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.

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.

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.

IMHO, one of the reasons M-theory is so difficult is that it is a non-perturbative problem.

SUSY actually makes things much easier to solve, so I've heard.

Yes, but only when it describes a theoretical world with unbroken SUSY, which is NOT our world.

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.

 

[Demystifier]

IMHO, one of the reasons M-theory is so difficult is that it is a non-perturbative problem.

QCD at low energies is also a non-perturbative problem, but it is much less difficult than M-theory because we still have a well-defined QCD action, so we know what exactly IS the problem. The problem with M-theory is that we don't even know what exactly is the 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.

My point is the following. It is usually simpler to solve a theory with more symmetry. For example, QCD with a chiral symmetry (with all masses put to zero) is simpler than true QCD. Unbroken SUSY is another example. However, it is at best questionable how much such oversimplified theories really help to understand the true stuff.

 

[Demystifier]

There is also a big difference between first and second superstring revolution.

After the first revolution, physicists were able say: Good, now we understand the theory much better.

But after the second revolution, they could rather say: Now we see that there is much more to understand than meets the eye.

 

[Kracatoan]

String "Theory" is a complex topic, made more complex by that fact that is is more of a pseudo-science than proper physics - It can't be tested and doesn't make any unique predictions. Rather than try to understand string theory right now, stand back, and see if anything is actually achieved by it. Only then will it be worth the bother investigating it.

I reccomend reading Lee Smolin's "The Trouble with Physics" for a more detailed critical analysis of string theory.

 

[crackjack]

There is enough room (by way of hitherto-unused, modern geometrical tools, in addition to undiscovered physics itself) in string theory to do it as "hard" as you would like to do it. While some might find generating creative physical principles hard, others find understanding and applying math tools to be hard.

 

[humanino]

Rather than try to understand string theory

And do YOU claim to really have studied and understood string theory, or do you simply repeat what Smolin said ?

 

[Kracatoan]

And do YOU claim to really have studied and understood string theory, or do you simply repeat what Smolin said ?

No. Naturally I've spent most of my time as a Physicist reading as much around the topic as I can, and seeing as String Theory is the in thing at the moment, I've read extensively on the topic. It was just that reading Smolin's book provided a refreshing view of string theory, not as a theory which is currently favoured, but instead as a mathematical curiosity, a view which has been mirrored by pretty much everyone I've talked to at Cambridge and Imperial. However, not everything Smolin says is sensible and and I do disagree with him on many counts, such as DSR, but that's that.

 

[humanino]

Well, thank you for your honesty and perspective. Since you mention UK institutions, I would be interested to hear the update of Penrose's opinion on string theory. There has been tremendous attention paid to the twistor formalism ever since Witten's 2003 article. This approach is essentially a revival of S-matrix method. It has provided very concrete calculation for QCD backgrounds at the LHC, and this is independent of whether string theory is realized at a fundamental level. Simply, playing with string theory (say as a toy model if you want), we discovered new methods to go beyond Feynman's perturbative calculations.

I imagine you have also heard of high-T superconductors. Another example where string theory provides calculations, which makes it interesting and achieving important results, while not proving to be "fundamental" in the "popular" sense.

 

[Kracatoan]

That approach, to me, does seem to be the right one. Not accepting the theory completely, but instead using its mathematics, techniques and essentials to further our current model.

 

[marcus]

That approach, to me, does seem to be the right one. Not accepting the theory completely, but instead using its mathematics, techniques and essentials to further our current model.

That point of view appeals as highly reasonable. I can see string mathematics being applied usefully in various directions, at various scales, even if not providing a fundamental unifying theory.

It is also possible that interesting math will grow out of LQG. See for example:
http://arxiv.org/abs/1010.1939
Feynman rules for 2-complexes (spinfoams)
Group field theory techniques (including the idea of a graph Hilbert space)
Spin networks (an earlier idea of Penrose but developed in this context)

Also the general idea of a quantum theoretical presentation of geometry, and of constructing quantum field theory not on a pre-established classical spacetime geometry but on the corresponding quantum geometry---the mathematical gains from addressing this problem (while not so widely recognized) could also be significant.

 

[elfboy]

it is unimaginably difficult...to put it succinctly

 

[scottbekerham]

It's very difficult due to the huge amount of knowledge you have to master in order to make any interesting contribution to the field and the physics is also inherently very difficult so it's difficult on both physics and math side. However , If you want to know what's string theory is all about . You can pick the book "string theory demystified " or a somewhat more advanced book " String theory and M theory" ,You can understand things in those books which gives an impression that it's not difficult at all

 

[haushofer]

It's very difficult due to the huge amount of knowledge you have to master in order to make any interesting contribution to the field and the physics is also inherently very difficult so it's difficult on both physics and math side. However , If you want to know what's string theory is all about . You can pick the book "string theory demystified " or a somewhat more advanced book " String theory and M theory" ,You can understand things in those books which gives an impression that it's not difficult at all

That's not really strange. A lot of stuff is not explained in these books. Especially "String theory and M theory" by Becker^2 and Schwarz, which after some chapters is more like an encyclopedic overview than a pedagogic explanation. I've never understood why people like this book as an introduction.

 

[Demystifier]

Especially "String theory and M theory" by Becker^2 and Schwarz, which after some chapters is more like an encyclopedic overview than a pedagogic explanation.

I definitely agree with that description.

I've never understood why people like this book as an introduction.

Neither did I, but several possible explanations come to my mind:
- Because they are much more CLEVER than me and you.
- Because they want to LOOK much more clever than they really are.
- Because by "introduction" they actually MEAN "encyclopedic overview".

By the way, as a more advanced textbook on string theory I like:
M. Kaku, Introduction to Superstrings and M-theory
But for some reason, mainstream string theorists don't like this book at all.

 

[QGravity]

in my opinion String Theory is really a hard subject (either considering it physically sensible or just a mathematical curiosity) because the amount of material one must know to learn and pursue the subject. just look at the contents of the "Quantum Fields and Strings - a Course for Mathematicians". if you want to learn the subject, my suggestions are as follows:

1) you must master (really doesn't mean that you must know everything, just the basics) the QFT especially the path integral and BRST methods for quantization of gauge theories; for this see Zee's "Quantum Field theory in a Nutshell" or Srednicki's "Quantum Field Theory" (for path integrals, Srednicki's book treated BRST also) and "Aspects of BRST Quantization" or "Quantization of Gauge Systems" (for BRST Methods);
2) you must master in 2-D conformal field theory, for this the first 6 chapters of Di francesco et al "Conformal Field Theory" is sufficient;
3) you must master General Relativity, for this see Schutz "A First Course in General Relativity" or Hartels's "Gravity : an Introduction to Einstein's General Relativity";
4) the relevant mathematics (just for start) is topology, differential geometry, complex geometry, some algebraic topology; the relevant parts of Nakahara's "Topology, Geometry and Physics" are excellent. acquaintance with group theory and representation of groups is mandatory. familiarity with differential and complex geometry of Riemann Surfaces is helpful.

for Books I recommend the followings:
1) "a First Course in String Theory" by B.Zwibach (there is no need for the above mentioned prerequisite); in my opinion a "must read" to know the basics! Excellent at pedagogical style!
2) "Lectures on String Theory" or its update "Basic Concepts of String Theory" by D.Lust & S.Theisen & R.Blumenhagen(required CFT is thoroughly explained); an excellent book to start with; without exercise
4) "The Superstring Theory" by three authorities of the field M.Green, J.Schwarz and Ed.Witten; its start with dual resonance models which is not treated in any other books. in my opinion "required reading" despite of 25 years has been passed sice its publication. mathematical parts, written by Ed.Witten, are excellent; a great second book; without exercise;
3) "Introduction to Strings and Branes" by P.West, a new book with nice presentation of spinors and the role of lie algebras in string theory; a good second book; without exercise
4) "String theory in a Nutshel" by E.Kritsis, a good second book with exercise!
5) "String theory and M-theory : an Introduction" by K&M Becker and J.Schwarz, as our friends stated this book is encyclopedic in some parts and need to be suppelmented by another math or physics book, a good second book with exercises;
6) "Vol.01 - Bosonic String Theory" and "Vol.02 - Superstring Theory & Beyond" by J.Polchinski, a very nice but at the same time hard book which in my opinion in "required reading". Polchinski is a master of QFT and String theory and founder of D-Branes, and its insights are very helpful, a good second or third book with good exercises!
7) "D-Branes" by C.Johanson: a good book on advanced topics such as Quiver gauge theories, Holographic Renormalization group and etc, a third or forth reading without exercise
8) "Gravity & Strings" by T.Ortín; an advanced text that assumes you know string theory, very good on "the stringy gravity"

the two good critical books on String theory are:
1) "The Trouble with Physics" by L.Smolin;
2) "Not Even Wrong" by P.Woit

if you want to know just the basics, I think that "Superstringtheory.com" and Wikipedia Articles or just Zwibach's book are sufficient! the following books are also very valuable:

1) "The Birth of String Theory" by A.Cappelli
2) "D-Brane: Superstrings and New Perspective of Our World" by K.Hashimoto

you must know that these are just the beginning and more advanced topics such as Topological String Theory and the ones treated on the "Quantum Fields and Strings - a Course for Mathematicians", or mathematically oriented topics which are related to Field Theory and String Theory such as String topology, Quantum Cohomology and Gromov - Witten Theory and etc are much more subtle and complex!
all in all, String Theory is a fascinating subject that worth learning. I always wonder why when one goes from 0-D particles to 1-D strings gets such a tremendous amount of new mathematics and theoretical (not necessarily physical!) ideas!
Good Luck!

 

[Kazz]

It's as if we discovered time dilation, but without Einstein ever being born.

 

[negru]

in my opinion String Theory is really a hard subject (either considering it physically sensible or just a mathematical curiosity) because the amount of material one must know to learn and pursue the subject.

But this can be an issue with pretty much every single topic in physics. For example just in Classical Mechanics, with dynamical systems and whatnot, there's enough theory to keep anyone occupied for many many years. If you put together all the random research topics, problems or concepts in Classical Mechanics I'm fairly certain the volume will be comparable to all the random research topics and problems in QFT or string theory.

The point is you don't need to know more than 5% of string theory to do research, just like you don't need to know what a symplectic manifold is to do classical mechanics. I guess the difference is that most people can agree what the basics of CM are, but it's not yet clear for ST.

Knowing all string theory is like knowing all of History. Unpractical, unnecessary, most likely impossible.

 

[ImaLooser]

It's as if we discovered time dilation, but without Einstein ever being born.

Huh?

 

[Demystifier]

I agree with negru (and disagree with QGravity).

 

[scottbekerham]

I think (I don't know if it's true) that the most important skill one has to acquire in order to really understand strings is differential geometry and lie groups . Differential geometry is the basic tool to use as one deals with curved surfaces , branes and other geometric structures. Even gauge theory is best expressed using fibre bundles and connections . So you can't get far in string theory without differential geometry .What I want to know is :
Is it sufficient to understand differential geometry from a practical point of view (e.g. nakahara ) or should one learn the foundations of the subject (Which means absolute ragor) (e.g. read spivak textbooks on DG) in order to be able to apply these mathematical ideas in nonconventional and non-trivial way ?

 

[haushofer]

I would say that Nakahara is sometimes already to rigorous. Its treatment on Fibre Bundles and gauge theories is not really a revelation; I've never understood this fetish of some people with fibre bundles anyway.

So imho Nakahara suffices for most applications, unless you really want to do die-hard math. E.g., the proof that certain string theories are anomaly-free is rather involved, and I think that only reading Nakahara doesn't give a thorough understanding. On the other hand, I'm not sure how interesting that is unless you really want to be able to do the full calculation on your own.

 

[sshai45]

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.

So does this mean you can only be ready to compete after spending, say, 25-30 years (a "large part of your life") studying it?

 

[haushofer]

So does this mean you can only be ready to compete after spending, say, 25-30 years (a "large part of your life") studying it?

No, that's impossible. In that time the field already has involved in such a way that you should catch up again, creating some sort of Zeno paradox.

That's why people buy the book of Becker^2 Schwarz. It's horrible as a pedagogic introduction, but it gives a highly compressed overview of the field in less than 1000 pages. It allows people to get the overview which is needed to start research, even though it's more of a "knowing the jargon" than "understanding what's really going on".

One of the hard things about research in theoretisch physics, and string theory in particular, is that you have to find a midway between understanding and being able to contribute to the field. Most people, not being geniuses, will find the following: trying to understand too much does not allow you to contribute, and trying to dive into something very specific doesn't allow you to develop a broad overview and put your findings into the bigger picture. Which can become awkwardly exposed during questions if you give a talk :P