How to Understand String Theory

Thanks to an endless string of books, magazine articles, and NOVA specials, string theory has gradually seeped down from the abstruse realms of higher mathematics to the common horde. As difficult as it is to master, though, this theory rests on some basic assumptions that can be understood by pretty much anybody with a high-school science education. Here’s an introduction to string-theory basics, so you can impress guests at your next cocktail party.

Difficulty: Moderate

Instructions

1. Think very, very small. For most of the 20th century, physicists were accustomed to thinking of protons, electrons and the the like as “point particles”—that is, idealized points of zero dimension. String theory postulates that these elementary particles are actually manifestations of string-like (and hence at least one-dimensional) entities that are trillions and trillions of times smaller.

2. Imagine these tiny strings vibrating. The near-infinitesimal strings at the heart of string theory are constantly “vibrating” or “oscillating,” and the frequency of these vibrations (or oscillations) produces all the known particles and fields of modern physics: not only elementary particles like electrons and quarks, but force carriers like gravitons (which mediate the gravitational field) and photons (particles of light).

3. Picture a bunch of extra dimensions. Here’s where string theory becomes especially controversial: The math doesn't work unless there are six (or possibly more) spacial dimensions over and above the familiar length, breadth and height of our three-dimensional universe. These extra dimensions are supposedly curled up into a vanishingly small size, which is why we don’t experience them directly.

4. Direct tests of the theory are still a long way away. As a rule, probing down to smaller and smaller size scales requires larger and larger amounts of energy. Since the fundamental components of string theory are so incredibly small, resolving structure on the string level would require galactic levels of energy—meaning that certain aspects of this theory may never be experimentally verified.

5. String theory isn’t the only game in town. Despite all the hoopla it's generated, there are many prominent physicists who think string theory is a dead end (and has been oversold by the researchers involved). The most prominent competing theory is something called “loop quantum gravity,” which some scientists find attractive because it avoids all those extra dimensions and may be experimentally verifiable.

[ucbboy]

on 11/5/2009 Math topics:
- Single variable calculus is the bread and butter of physics. Try the book by Stewart for methods and the book by Apostol for theory.
- Multivariable calculus is used to account for the fact that we live in more than one dimension and might want to consider functions of multiple variables. For methods, Williamson and Trotter. For theory, Hubbard and Hubbard.
- Linear algebra is the natural language of quantum mechanics. For an intro (college freshman level) book, try Bretscher. For more advanced stuff, I like the book by Olver.
- Ordinary differential equations are ubiquitous in physics. For ways to sole them, try the book by Boyce and Diprima. For more theoretical accounts, try Agrawal, Coddington, or Ince.
- Partial differential equations are the extension of ODEs to functions of many variables and are the language in which most equations of physics are written...

[ucbboy]

on 11/5/2009 A few points need to be made here. Firstly, my understanding is that as yet there is no "complete derivation of string theory". That is, there is no fundamental equation or set of equations, such as Newton's law in classical mechanics, the Schrodinger equation in quantum mechanics, or Einstein's field equations in general relativity, which governs the behavior of these so-called strings. Whereas the aforementioned fields have their basics more or less worked out, string theory is currently just a collection of mathematical concepts and techniques which lacks an overarching foundation. Even if there were a complete equation governing the behavior of strings, it's usually the case in physics that writing down an equation is much, much easier than solving it. For instance, in quantum mechanics it is easy to write down the Schrodinger equation; indeed, one could provide a "derivatio...

[tangerines]

on 7/1/2009 What I'd really like to know is how to understand the math that derives string theory. If anyone can list a sequence of textbooks that I'd need to master in order to go through the complete derivation of string theory, that would be greatly appreciated. The layman's explanation just doesn't quench my intellectual thirst.