String Theory

Written By: Wendell Krossa

Tthis is a clearer explanation of string theory (and its status) than any other I have read.

The String theory was supposed to provide a single, unified theory of matter.  Four decades later, the math keeps getting in the way.

Keith Devlin, National Post – Published: Thursday, December 07, 2006

Most people are familiar with the term “string theory.”  Perhaps they’ve read a magazine article or two describing how important it is, or they have an egghead relative who expounds on the subject at the dinner table.  But few people know what string theory really says. While a thorough mathematical explanation would go over the head of most non-specialists, the basics are easily summarized.

The first thing to understand about string theory is the original motivation for its formulation in the 1960s.  The theory solves an important problem associated with classical physics: the divide-by-zero problem.

If it were possible to zoom in ever more closely on the stuff everything in the universe is made of, including yourself, what would you eventually find?  For hundreds of years, the received wisdom has been that you could in principle keep narrowing down the focus indefinitely, approaching but not quite reaching the ultimate theoretical state of defined ultra-tiny “point masses.” There are known physical laws that prevent you ever actually carrying out such a procedure, but as a thought-experiment it serves well to explain the fundamental idea behind what is nowadays known as the “classical view” of matter.

The “everything is built up from point masses” idea leads to mathematical equations that have been shown to be extremely accurate in describing the universe and all the matter in it.  For example, it leads to Newton’s inverse square law of gravity, that the gravitational attraction between two bodies of masses M and N at distance r apart is proportional to (M x N)/r2

This law works fine for the kinds of distances that we encounter in our everyday lives, even if in that everyday life you are a NASA scientist sending spacecraft across the solar system.  But when the distance is very small, the answer you get for the gravitational force becomes extremely large, and if you try to use the equation to understand the behaviour of the universe a fraction of a second after the Big Bang, where r = 0, you get an infinite, and hence meaningless answer.

That’s a common problem when you have an equation with a variable in the denominator of a fraction: If you want to know what happens when that variable has the value zero, the formula breaks down.  In mathematical parlance, the formula has a “singularity” at zero.

Unfortunately for physicists, it’s not just the inverse square law of gravity that has a variable in a denominator.  It happens all the time in the equations physicists use to understand our world.  That means that those equations cannot be used to study matter on a very small scale.  And so the laws expressed by those equations do not actually apply on a small scale; something else is going on, but what?

This is where string theory comes in.  According to string theorists, there are no point masses. When you carry out the hypothetical zooming process, there comes a moment where what you discover is that everything is made up of tiny little strings, wriggling furiously like maggots in a jar.  The different wriggle rates are what give rise to the various fundamental particles that are the stuff of classical particle physics.  The strings are so tiny (around 0.00000000000000000000000000000000001 meters in length) that they are well below the level of detection, but because they have a definite length, not zero, you don’t get singularities in the equations.

The cost of eliminating the singularities is that we are faced with two new puzzles.  First, what are the strings made of?  The answer string theorists give is that they are not really made of anything; rather, they are tiny ripples in the very fabric of space-time.  That may strike many people as a bit of a stretch — and it is — but string theory, like classical particle physics, is essentially a mathematical theory, and mathematics does not require either point masses or tiny strings to be made of anything.

The second puzzle is that, to make the math work, the universe must have more than the three spatial dimensions (along with one time dimension) we are familiar with; it must have nine or more spatial dimensions.  The reason we don’t notice the extra dimensions, string theorists say, is that they are curled up into tight tubes that makes them invisible.  Think of a garden hose: from a distance it looks one-dimensional, like a line, but up close it can be seen to have a second dimension, curled up into a little circle.

Again, this might seem a stretch, but when string theory started out, the promise, and the hope, of a single mathematical theory of matter — just one set of equations — that avoided singularities and could help physicists understand the universe on every possible scale, from the very large to the very small, was so great that the new theory rapidly drew in some of the best physicists around.

The theory got a second boost in the 1990s, when four physicists at Princeton University, dubbed the Princeton String Quartet, showed that string theory could encompass all the forces of nature, which was something classical physics has been unable to achieve.  Since then, practically every new Ph.D. in fundamental physics has been a string theorist, and together they have written more than a thousand papers on the topic.  For a while, hopes were high that the physics community was on the verge of finding its long sought “theory of everything.”

But then the doubts began to emerge.  Instead of homing in on a single set of equations, the mathematics started to diverge in different directions, and there was no way of telling which, if any, was the right way.  And once the possibility of a single elegant solution was lost (string theorist Brian Green optimistically called his 1999 bestselling book about the subject The Elegant Universe), and physicists were left with a confusing plethora of alternative string theories, they had to face up to an uncomfortable aspect about string theory that they had hitherto managed to sweep under the carpet.

To be a scientific theory, the theoretical mathematics would have to generate predictions that could be tested in the laboratory.  The classical theory of matter, which is also mathematical, had met that test, and indeed passed it with flying colors. The classical equations are admittedly a bit of a mathematical ragbag, and you have to use one set of equations to study the universe on a large scale and another set to handle the small stuff, but the experiments agreed with the theoretical predictions to a degree of accuracy unprecedented in science.

Unfortunately, no one has succeeded in coming up with a string theory prediction and an associated experiment to test it. (The strings themselves, if such exist, are way too small to be detected.)  That means that what was once called the “string theory revolution” seems set to go down as a fascinating and dazzling episode in the history of mathematics, but will ultimately be rejected as a scientific theory.

But one should not judge the attempt by the outcome.  The very essence of science is to generate hypotheses, study them in depth, and ultimately test them for accuracy.  String theory was a bold attempt to understand the stuff we, and everything around us, are made of.  If it fails, and that now seems increasingly likely, because it is neither elegant nor can it be tested, that is simply a spur to try again.  That is how our scientific knowledge advances.


Dr Keith Devlin is a mathematician at Stanford University in California, the “Math Guy” on National Public Radio, and the author of many books, including The Math Instinct and The Math Gene, both written for a general audience.

National Post 2006

Wendell Krossa submitted