An Introduction to String Theory

This post is prompted by a question from Daniel, one of my former students. He said he's been reading a bit about string theory lately and wondered whether there is any connection between string theory and cosmology. This is a very tough subject, but I'll try to give it a shot! I'll start off with a little bit of background on what we mean by "string theory" in this post, and then follow up later with how it connects to the physics of the universe as a whole.

The Background: Why String Theory?

One of the goals of physics research is to figure out the fundamental structure of matter. Most people are familiar with the idea that ordinary matter is made up of particles like protons, neutrons, and electrons. Go a little deeper and you find out that protons and neutrons are made up of even more fundamental particles called quarks. Decades of experimental research (largely using high-energy particle accelerators like Fermilab) have been used to build a theoretical model for the structure of matter, which goes by the very snazzy title of the "Standard Model".

The Standard Model is a theory that describes all the types of particles we know to exist, as well as the ways that they an interact. For example, electrons are fundamental particles that are described in the Standard Model. Their interactions with each other through the electric force are also encapsulated in the theory. The Standard Model has been fantastically successful, in that it is capable of predicting how particles will behave to very high accuracy. At the same time, this powerful theory is frustrating to physicists because we know it is still incomplete.

The biggest way that the Standard Model is incomplete is that it leaves out the force of gravity. It just doesn't work to stuff a description of gravitational forces into the mathematics of the Standard Model. On the one hand, gravity is so weak between individual particles that we can completely leave it out of the theory and still have a highly accurate model for describing how individual particles will interact. But on the other hand, if we want our fundamental theory to mathematically describe all the behavior of matter, how can we possibly leave out something as obvious as gravity?

Another way that the Standard Model is incomplete is that we suspect it's "missing" some fundamental particles. For example, we believe that the explanation for a number of weird phenomena in the universe is that there's some new particle out there that we're calling Dark Matter. We know Dark Matter can't be made up of any of the particles in the Standard Model, so clearly the Standard Model doesn't describe the complete picture.

(Just for your curiosity, if you want to know what it looks like to write down an equation that describes all the particles and their interactions, one version the Standard Model equation has been typed up an posted in pdf form here. Yikes!)

What is String Theory?

String theory is one postulated theory to replace the Standard Model (actually, there are many versions of string theory, so it's not strictly "one" theory).  So far, we don't have evidence that string theory is correct, and a lot of physicists remain skeptical about it.  String theory is a highly mathematical model that allows gravity to be described in the same framework as everything else we know about the behavior of matter.  In order to do this, it plays fast and loose with the fundamental nature of space-time, with some exotic consequences.  In particular, string theory requires the existence of many extra "spatial dimensions".  It also requires the existence of a bunch of additional particles that we have never seen, and one of these as-yet-unknown particles might explain Dark Matter.  Basically, these "requirements" for the existence of extra dimensions and extra particles are results of the mathematics:  if the equations of string theory are true, then they must exist.

In string theory, all of the "fundamental" particles of the Standard Model (and also any new exotic fundamental particles we haven't discovered yet) actually have an even more fundamental common structure.   All of these things we call "particles" are pictured as being vibrating "strings".  The strings are the true fundamental constituents of all matter.  Depending on how the strings are vibrating, they behave like particles with different properties (e.g. an electron, or a quark).  Even the force of gravity can be understood in terms of vibrating strings.  In particular, the strings associated with gravity vibrate and wiggle beyond our ordinary three-dimensional space into a bunch of extra spatial dimensions.

Extra Dimensions? 

One idea people seem to find especially intriguing from string theory is the notion that there are "extra dimensions" to space.  I've noticed that this concept often gets confused in people's minds with the idea of "multiple universes", so let me see if I can help you to distinguish these ideas.

The extra dimensions in string theory are difficult to talk about because they defy visualization by our human brains.  Let's start by imagining a line drawn across a piece of paper.  A line is something that you would describe mathematically as a "one-dimensional" object.  This means that you can represent every position on the line using a single number, perhaps the distance from the edge of the paper.  The whole piece of paper itself is a "two-dimensional" object:  to specify a particular position on the piece of paper, you need to provide two numbers, like the distance from the top and the distance from the left edge.  Another way of thinking of this is that if you were confined to a piece of paper, your motion would be limited to being in the up-down direction, the left-right direction, or some combination of these. Ordinary space that we live in has three dimensions:  we can move in the up-down direction, the left-right direction, and a third "in-out" direction.

In string theory, there are extra "directions" for the motion of strings, that aren't visible to us.  They exist everywhere, and if you were a string you could have access to them in addition to the regular three dimensions in which we ordinarily move around.  But, that's a really different idea than a "different universe".

More on String Theory

A good place to start to learn more is the PBS website associated with the program The Elegant Universe.  Check it out here.