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.

The Gravitas Project: Supercomputer Simulations Recast as Art

This is a short video showing simulations of what would happen if you put several identical galaxies together in space and allowed them to collide according to the equations of gravity.  It takes a scientific tool (supercomputer simulations of galaxy collisions) and uses it to create beautiful patterns that are impossible to find in nature.  Astrophysicist John Dubinski is responsible for the simulations, and he works with musician John Kameel Farah to set the images to original music.  

Real galaxy collisions, when multiple galaxies crash together, merging or passing through one another, are some of the most spectacular and seemingly violent events we can see with telescopes.  In one sense they truly are violent, making a surprising and often beautiful mess out of what were once orderly spiral or elliptical collections of stars.  However, not much actually "collides" in a galaxy collision.  Rather, the stars and other materials just get rearranged in reaction to the changing gravitational fields.  The collisions also take place very slowly.  All of the telescope images of galaxy collisions in the universe are essentially static snapshots; we are unable to watch them evolve because of our limited human timescales.

To study the physics of galaxy collisions, we therefore turn to computer simulations.  The basic idea to these simulations is to make three-dimensional numerical models of imaginary galaxies, and then to set them on a collision course.  The computer programs use the mathematical equations describing gravity to figure out how the system will evolve over time.  These simulations are a key part of the scientific effort to better understand how galaxies grew, merged, and interacted over the history of the universe.

The process of "visualizing" the simulations is a secondary step:  the simulation output consists of vast amounts of numerical data, recording the position of every individual "particle" in the simulation at every simulated time.  You can take these simulations and represent them visually, though, and the results are some of the most awe-inspiring movies you will ever see.

Dubinski, recognizing this, has created a series of stunning animations based on his simulations, which you can find here.  While it does not model anything that truly happens in nature, the animation I posted above still teaches some interesting lessons about, as Dubinski puts it, "the emergence of chaos".  It's also  just really pretty.

Dark Matter, Gravity, and Wine Glasses

Dark Matter is a mystery substance that virtually all physicists believe to exist, even though we don't know what it is.  Our best guess is that it is some form of yet-unknown fundamental particle, which interacts through gravity but neither emits nor absorbs light.  Since direct searches for the mystery Dark Matter particle have been making news lately, I thought I'd start this blog by reviewing some of the best indirect evidence we have that Dark Matter exists.  There are, by now, lots of independent lines of evidence that point to the presence of large amounts of invisible ("dark") matter in the universe, but this post will concentrate on my favorite:  gravitational lenses.

Introducing Galaxy Cluster Abell 1689

When astrophysicists look at an image like this one from the Hubble Space Telescope, they interpret the image using what they know about physics:  the nature of matter, the behavior of light, and the mathematical equations describing the force of gravity.  In this image, the fuzzy yellowish blobs are all galaxies, in a grouping known as a "galaxy cluster".  Each galaxy is, like our Milky Way, composed of around one-hundred billion stars (!!!).   Even though these galaxies are remote, the stuff they are made of is no different from what makes up our own galaxy.  The glowing stars in each galaxy are mostly made of the ordinary chemical elements hydrogen and helium, with a few other chemical elements mixed in.

All of the chemical elements we find around us (or in distant stars and galaxies) are what we might call "ordinary matter".  Ordinary matter is ultimately made up of just a few basic fundamental particles:  protons, neutrons, and electrons.   Two properties of "ordinary matter" are important for this discussion.  First of all, all ordinary matter has mass, which also means that it exerts a gravitational pull on other stuff that has mass.  The earth, for example, is made up of ordinary matter with enough mass that its gravity keeps us firmly anchored on the ground. Second, all ordinary matter is capable of emitting and absorbing light (electromagnetic radiation).   Even though some forms of ordinary matter (like the gasses that make up the air) appear to be invisible to our eyes, they all still absorb or emit some form of electromagnetic radiation, perhaps just not in the frequencies that our eyes can detect.  Telescopes that are sensitive to other forms of electromagnetic radiation like x-rays, radio waves, or infrared light can be used in addition to those sensitive to visible light, in order to study the ordinary matter that exists in the universe.  Using the Hubble picture above, we can measure how much light is emitted by the ordinary matter in the galaxy cluster Abell 1689.  We can then apply what we know about the physics of stars and dust and gas to make some rough estimates of how much mass there is in the glowing yellow galaxies. This means we can calculate the strength of the gravitational field that we expect to be associated with this collection of objects.

Gravity and the Warping of Space-Time

According to Einstein's theory of General Relativity, the attractive force of gravity is actually caused by the fact that massive objects warp space and time.  In areas where there are very large objects, space itself is literally bent out of shape.  This causes objects to "fall in" to areas where there is a lot of mass, appearing to be attracted through the force we call gravity.  The usual visual metaphor for this is the picture of a bowling ball on a trampoline:  marbles placed on the trampoline will fall toward the bowling ball because of how it has warped the surface.

(Image taken from a blog posting from Discovery Magazine, by Clifford Johnson, in 2005)

The one trick in applying this metaphor, though, is that you have to remember that a trampoline surface is essentially a two-dimensional sheet.  When we talk about gravity, what's happening is that matter is warping three-dimensional space (plus time, too), which is not as easy to picture in your head.

A "Gravitational Lens"

Let's go back to that Hubble image, and zoom in on a particularly interesting feature:
 

(Image credit:   NASA, N. Benitez (JHU), T. Broadhurst (The Hebrew University), H. Ford (JHU), M. Clampin(STScI), G. Hartig (STScI), G. Illingworth (UCO/Lick Observatory), the ACS Science Team and ESA.  Downloaded from HubbleSite.)

What exactly are those "arcs" that stream through the picture?  They are a very cool side effect of the warping of space-time in Einstein's picture of gravity.  Essentially, in areas where there is a lot of mass, the path taken by light follows the curvature of space.  It's as if the light is being "bent" around an object that is extremely massive. The arcs we see here are images of even more distant galaxies (far behind the cluster of yellowish galaxies that make up most of the picture).  The intense gravitational field of the galaxy cluster in the foreground has bent the light and created bizarre arc-like patterns out of the light from the distant galaxies.

The bending of light around areas where gravity is very strong has been observed many times, and it's one of the main ways that Einstein's theory was experimentally demonstrated to be correct.   This bending of light is not entirely unlike how light gets bent when it goes through common lenses like the ones in your eyeglasses or in your camera.  Hence, this phenomenon is known as "gravitational lensing".  In fact, a common glass lens that imitates the gravitational lensing seen by Hubble is the bottom of an ordinary wine glass:

Here, you can see some coffee beans being "lensed" by the bottom of a wine glass from my cabinet.   Notice how the glass bends the light in such a way to create arc-like images of the coffee beans, much like the arc-like images of distant galaxies in the Hubble picture.  Here, the glass in the wine glass is bending the light, but there it's the warping of space by a very large amount of mass.  And that brings us back to the idea of Dark Matter.

Evidence for Dark Matter from Gravitational Lensing

The phenomenon of gravitational lensing by itself is just cool and weird. It's also informative.  The patterns created by a strong gravitational lens like this galaxy cluster can be used to calculate to what degree the space in the vicinity of the cluster is warped, which is the same thing as figuring out how much mass is there.  The more mass there is, the greater the warping of space, and the more the light will be bent by the "gravitational lens".   When we do this calculation, we find that the particular cluster Abell 1689 is really whoppingly amazingly massive:  something on the scale of 1,000,000,000,000,000 times the mass of our Sun (as first reported here)!  However, there is no way that the visible "ordinary matter" in this cluster of galaxies could possibly have that much mass.  There's just not enough stuff there to account for it.

This is just one of the lines of argumentation that leads to the idea of Dark Matter.  In galaxy clusters that act like gravitational lenses, we know for certain that much more mass is present than the amount of visible, ordinary matter would lead us to believe.  The way that we explain this is by postulating that there is some kind of "dark" (invisible) matter present surrounding all of the galaxies in the cluster.  It is massive and warps space the way ordinary matter does, but it doesn't absorb or emit light.  We can't see it, but we know it's there because of its gravitational effect.  Most of the cosmological lines of evidence for the existence of Dark Matter involve observing its gravitational effects.  This just happens to be my personal favorite line of evidence.

The next time you're sipping a glass of wine, play around a little bit with the lensing effects you can create.  It's fun to compare this simple demonstration with the other-worldly images of gravitational lenses collected by Hubble Space Telescope.  Individual galaxies with a lot of mass (also mostly believed to be in the form of Dark Matter) also act as lenses, and some cool pictures can be found here and here. 

For more on the topic of gravitational lensing, check out local physicist Evalyn Gates' new book, Einstein's Telescope, which is in bookstores now.