# How many hours does it take to get the basic gist of string theory

## Main Question or Discussion Point

Say you have a rudimentary grasp of classical physics and calculus. How many hours of study does it take before you can start to understand string theory. I'm not talking about how many hours does it take before you can actually make a contribution to the field, rather how long does it take before you can understand what others have discovered and how they've discovered it. Of course, a lot of it depends on your talent but still just give me a ball park figure.

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Demystifier
Gold Member
I've started to understand string theory by reading the book
B. Zwiebach, A First Course in String Theory

How, many hours did it take? I don't know, but let me try to estimate it. The book has about 550 pages. If I can digest 5 pages per hour, it takes 110 hours for the book. If I study the book 4 hours per day, it takes about 4 weeks to digest the book. So in 4 weeks, I was able to say: Now I understand the basics of string theory. Sounds encouraging, doesn't it?

But of course, to digest 5 pages per hour, you have to have a good knowledge of theoretical physics in advance. If you know how much time you need for a page, you can easily calculate how much time do YOU need for the book.

I mean how much time does it take to get the background knowledge. The knowledge you need before you can read it. This assumes you have a rudimentary knowledge of classical physics and calculus.

Demystifier
Gold Member
I mean how much time does it take to get the background knowledge. The knowledge you need before you can read it. This assumes you have a rudimentary knowledge of classical physics and calculus.
Ah, I see.
Well, you need to learn some basics of

- special relativity
- classical waves and partial differential equations
- classical electrodynamics
- general relativity
- quantum mechanics
- quantum field theory

preferably but not necessary in that order. If you want a book that contains the basics of all this at one place, together with required math, and followed by a review of string theory, I recommend
R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe (1100 pages)

Fredrik
Staff Emeritus
Gold Member
This may give some clues... http://abstrusegoose.com/272. Remember to keep clicking on the comic for subsequent steps ;-)
That was pretty good. Steps 1-3 and 6 describe exactly my experience after buying Zwiebach's book about ten years ago. I already knew the basics of QM and SR, so I bought a bunch of QFT books (I already knew some QFT as well), and then decided I need to know SR and QM much better. I still haven't read those QFT books, but I'm really good at SR and QM. (I have improved my knowledge in several other areas too, including linear algebra, abstract algebra, topology, measure and integration theory, functional analysis, differential geometry, Lie groups, quantum logic and general relativity).

The final frame in the comic was pretty bad though. Nerds don't watch Jersey shore. We watch a lot of garbage, but not that kind of garbage.

Frederik, nice post. Has the journey been hard or just time consuming?

Fredrik
Staff Emeritus
Gold Member
Frederik, nice post. Has the journey been hard or just time consuming?
None of these topics are easy, but you know that already. Topology, integration theory, and worst of all, functional analysis, are topics that I found really hard. I don't know how many times I've decided that this time I'm going to make it all the way to the spectral theorem, only to put it aside weeks later after only making a little bit of progress. (I'm making very detailed notes of the stuff I've covered, so it takes a lot more time than it would otherwise).

Anyway, my goal isn't to understand string theory anymore, or even QFT. It's to have a very thorough understanding of the mathematical foundations of all theories of physics up to and including quantum field theories without interactions, general relativity and the classical version of Yang-Mills theory. I'm not interested in the "how to calculate" aspects of physics, I only care about definitions and theorems.

I suspect that string theorists don't need a lot of functional analysis, at least not the ones who are working at the level of rigor that's considered appropriate for theoretical physics. This sort of stuff is probably only needed for the rigorous stuff. So if I had preferred to make it all the way to string theory rather than to dive into the rigorous stuff, I could probably have had a decent understanding of it by now.

Demystifier
Gold Member
I suspect that string theorists don't need a lot of functional analysis, at least not the ones who are working at the level of rigor that's considered appropriate for theoretical physics.
That's quite true. In fact, contrary to a common myth, most research in string theory does NOT demand a very rigorous mathematics at all. It does not mean that the math in string theory is easy, just that it is not more rigorous than, e.g., math in quantum field theory or general relativity.

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Demystifier
Gold Member
Just for the record, the book was published in 2004.

Fredrik
Staff Emeritus
Gold Member
Just for the record, the book was published in 2004.
Aha. Well it feels like at least ten years ago. I think what confused me is that I bought Kaku's book at least ten years ago (2nd ed., published in 1998). They're on the same shelf in my bookcase, both pretty much untouched.

atyy
Just for the record, the book was published in 2004.
8 ~ 10, just as string theory contains ~ standard model.

Demystifier
Gold Member
8 ~ 10, just as string theory contains ~ standard model.
Just as your sentence ~ makes sense grammatically and semantically.
Honestly, I needed ~ 30 seconds to understand what are you trying to say.

This may give some clues... http://abstrusegoose.com/272. Remember to keep clicking on the comic for subsequent steps ;-)
That captures it pretty well. So that's why the title of the thread should not refer to hours but to years.

ohwilleke
Gold Member
I would argue that you probably need the gist of at least four or five post-calculus mathematical topics usually taught in one semester college courses, although not always lumped together in the packages.

* Differential equations
* Linear algebra
* Applied analysis with a hodgepodge of tools such as tensors, spinsors, integration with Dirac Delta functions, and the calculus of variations and path integral evaluation
* Complex analysis
* Abstract algebra and
* Topology

(Most string theorists would have a taken an advanced real analysis course as well, but while necessary for rigorous work, to get the gist of the ideas this can probably be skipped almost entirely, as can higher level mathematical probability and statistics that is crucial for experimental work and careful calculation but can be dispensed with if you just want the gist of it.)

I would also argue that you need the gist of at least two or three upper division/early graduate school level physics courses introducing the subjects of:

* General relativity
* Quantum mechanics (probably a two semester set of courses to get sufficiency master of not just QED and Dirac's Equation, but also QCD and electroweak unification).
* An advanced mechanics class, even if its classical mechanics (e.g. three body problems), to develop a mastery of concepts like Hamiltonians and Lagrangians.

So, you need the gist of six to eight three or four semester credit college courses beyond your basic calculus and physics, which would be something on the order of 25 weeks of full time study if you took the courses themselves and passed them.

But, of course, you can get the gist of those subjects well enough to make some sense of published works and understand what string theorists are talking about without doing research and using the equations to make more than back of napkin calculations on your own with far less work. You could probably pick up all the physics you need to get the gist of it in the equivalent of the work that goes into a single three credit mid-level undergraduate survey course (perhaps 45 hours of real time). You could probably get the gist of all the math you need other than abstract algebra and some of the finer topological points in a similar amount of time or maybe even a hair less (call it 35 hours). But, while you don't need all of either a rigorous single semester course in either abstract algebra or topology to get the gist of string theory, you do need a quite a bit higher level of mastery of each of them to get even the gist of those concepts which are not very natural ones to someone with your level of mathematical and physics background, in part because they involve a lot of non-intuitive terminology. You probably need 20-30 hours of work to get enough of the gist of these topics to be useful. After that it would probably take an effort to read a few dozen academic articles and conference presentations in the area pretty carefully, at twenty minutes or so each to pick up on string theory specific conventions used in the field. So maybe that would take 15 hours.

So, overall, it probably takes 115-125 hours of study to get even the basic gist of string theory well enough to follow the main points made in a published string theory paper or conference presentation about string theory taking a position that you will trust the presenter or author to be correct in his or her technical mathematical manipulations but educating yourself enough so that you could understand and articulate the main conclusions of the presentation, the basic program of the reasoning used to get that result, and to have some sense of why someone might ever care about the questions asked in the first place.

Of course, with lower standards for the "gist" of that you want to achieve (e.g. simply to be able to say what string theory is as a program and its main subdivisions and most well know premises) you could probably master that in less than a week (i.e. less than forty hours) of browsing wikipedia articles and referring back to old textbooks and maybe reading a short quantum mechanic's treatment like Feynman's QED and skimming one or two popular book length treatments of string theory intended for educated laymen.