# string theory

String theory is an important theory in modern physics, largely developed by Ed Witten, in
which the fundamental particles in nature are thought of as the musical
notes or excitation modes of elementary strings. These strings have the
shortest meaningful length, known as the Planck
length (equal to about 10^{-33} centimeter), but no thickness, and for
the theory to make sense, the universe must have nine space dimensions and
one time dimension, for a total of ten dimensions. This idea of a ten-dimensional
universe was first mooted in the Kaluza-Klein
theory. We're familiar with time and three of the space dimensions:
the other six together are known as Calabi-Yau
spaces.

In string theory, as in a stringed instrument, the string must be stretched
under tension in order to become excited. This tension is fantastically
high – equivalent to a loading of about 10^{39} tons. String
theories are classified according to whether or not the strings are required
to be closed loops, and whether or not the particle spectrum includes fermions.
In order to include fermions in string theory, there must be a special kind
of symmetry called supersymmetry, which
means that for every boson (a particle, of
integral spin, that transmits a force) there is a corresponding fermion
(a particle, of half-integral spin, that makes up matter). So supersymmetry
relates the particles that transmit forces to the particles that make up
matter. Supersymmetric partners to currently known particles have not been
observed in particle experiments, but theorists believe this is because
supersymmetric particles are too massive to be detected using present-day
high-energy accelerators. Particle accelerators
could be on the verge of finding evidence for high energy supersymmetry
in the next decade. Evidence for supersymmetry at high energy would be compelling
evidence that string theory was a good mathematical model for nature at
the smallest distance scales.

In string theory, all of the properties of elementary particles – charge, mass, spin, etc – come from the vibration of the string. The easiest to see is mass. The more frenetic the vibration, the more energy. And since mass and energy are the same thing, higher mass comes from greater vibration.

## Gravity and the development of string theory

One of the major outcomes of work on the electroweak unification was the so-called Standard Model of particle physics, which neatly describes all the elementary particles in nature and the forces between them – with one notable exception. It includes six different types of lepton, or lightweight particle, six different types of quark, and the exchange particles for the weak, strong and electromagnetic interactions. It also calls upon an enigmatic new particle, the Higgs boson, named after its inventor, Peter Higgs of the University of Manchester (England), which, although not yet detected, is expected to play an important role in fixing the masses of all the other particles in the scheme. The Standard Model has agreed well, so far, with experimental data collected using particle accelerators. Yet physicists aren't completely happy with it. For one thing, it leaves too many arbitrary properties undecided – important values that simply have to be stuck into the Model ad hoc. For another, it has no place for gravity.

How then to get gravity into the scheme? A clue to this emerged while researchers were working on the quantum field theory of the strong force. Along the way, they came up with a wonderfully creative explanation for the observed relationship between the mass and spin of hadrons. Called string theory, it treats particles as specific vibrations or excitations of very, very small lengths of a peculiar kind of string. In the end, quantum chromodynamics (QCD) proved to be a better theory for hadrons. Yet string theory wasn't consigned to the trashcan of ideas that had passed their sell-by date. It made one extremely interesting prediction: the existence of a particle – a certain excitation of string – with a rest mass of zero and an intrinsic spin of two units. Theorists had long known that there ought to be such a particle. It was none other than the hypothetical exchange particle of gravitation – the graviton.

With this discovery, that one of the essential vibrational modes of string corresponded to the graviton, string theorists realized they had a bigger fish to fry than trying to explain the ins and outs of hadrons. Their notions of elemental quivering threads might, it seemed, bear directly on the much sought-after quantum theory of gravity – and not just because the graviton is predicted by string theory. You can stick a graviton into quantum field theory by hand if you like, but it won't do you any good because you'll be blown away by infinities. Particle interactions happen at single points in spacetime, so that the distance between interacting particles is zero. In the case of gravitons, the mathematics behaves so badly at zero distance that the answers come out as gobbledygook. String theory gets around this problem because the interacting entities aren't points but lengths, which collide over a small but finite distance. As a result, the math doesn't self-destruct and the answers make sense.

## Vibrating strings

To get the hang of string theory, think of a guitar string that's been tuned by stretching it between the head and the bridge. Depending on how the string is plucked and how tense it is, different musical notes are created. These notes can be thought of as excitation modes of the guitar string under tension. Similarly, in string theory, the elementary particles observed in particle accelerators correspond to the notes or excitation modes of elementary strings. One mode of vibration makes the string appear as an electron, another as a photon, and so on.

In string theory, as in guitar playing, the string has to be under tension
in order to become excited. A big difference is that the strings in string
theory aren't tied down to anything but instead are floating in spacetime.
Even so, they're under tension – by an amount that depends, roughly
speaking, on one over the square of the string's length. Now, if string
theory is to work as a theory of quantum gravity, then the average length
of a string has to be in the ballpark of the distance over which the quantization
of spacetime – the granularity of space and time – becomes noticeable.
This outrageously tiny distance, known as the Planck length, is about 10^{-33} centimeter, or one billion trillion trillionth of a centimeter. So much
tinier is it than anything that current or planned particle physics technology
can hope to be able to see that string theorists have to look for craftier,
more indirect ways to test their ideas.

## Varieties of string theory

String theories come in various forms. All of these assume that the basic
stuff of creation are tiny wriggling strings. However, if the theory deals
with only *closed* loops of string, like Spaghetti Hoops, then it's
limited to describing bosons – the force-carrying particles –
and so is called **bosonic string theory**. The first string theory
to be developed was of this type. If **open** strings, like strands
of ordinary spaghetti, are allowed into the theoretical picture then these
provide a description of fermions, or particles of matter. But a very interesting
thing happens when string theory is extended in this way to let in fermions.
It demands that there must be a special kind of symmetry in the particle
world, know as supersymmetry. In this expanded masterplan of things, there's
a corresponding fermion for every boson. In other words, supersymmetry relates
the particles that transmit forces to the particles that make up matter.
A supersymmetric string theory is called, not surprisingly, a superstring
theory.

Theorists uncovered three different string theories that were mathematically consistent and therefore made good sense. Two of these were bosonic, the other of the superstring ilk. But in order to make any of them work, they had to resort to a strategy first employed by Kaluza and Klein in the days when Einstein first started wandering down his blind unification alley: they had to call upon higher dimensions, rolled up so small that they're way below the threshold of detection. The bosonic string theories needed an awesome 26 dimensions (25 of space plus one of time) in order to work properly, which seemed a bit of a stretch even for scientists who enjoyed some wayout sci-fi in their off-hours. Compared with this, the mere ten dimensions of spacetime required by superstring theory seemed positively modest. Six of the ten would have to be curled up, or "compactified," to leave visible the four normal spacetime dimensions (three of space plus one of time). But these compactified dimensions, far from being an embarrassment to be swept under the cosmic carpet and forgotten about, come in very handy if string theory is to aspire to become a theory of everything: motion in them can be used to explain the values taken by important constants in nature, such as the charge on the electron.

Combining the best features of bosonic and superstring theory has led to
two other consistent schemes known as heterotic string theories. So, there
are five viable string theories in all, which, if we're hoping to arrive
at the one true TOE, is a tad too many. Fortunately, it's beginning to look
as if the quintet of finalists for the Miss Universe Theory competition
is really the same contestant dressed up in five different costumes. This
supersymmetric mistress of disguise has been given the rather enigmatic
name *M-theory*.

Some say that the M is for Mother of All Theories. Others that it stands for Magic or Mystery. But, although no one seems to know for sure, there may be a more prosaic reason for this particular choice of initial.

Before string theory rose to scientific superstardom, the most popular unified theory in town was supergravity, which was basically supersymmetry plus gravity without the string. Like any respectable quantum gravity candidate it boasted a surfeit of spacetime dimensions – in this case, eleven (the compactified ones all wrapped up neatly on an itty-bitty 7-dimensional sphere). Unfortunately, it had to be abandoned because of the problems mentioned earlier involving point particles and string.

But along came M-theory. Still under development, it carries the hopes of many that it will combine the various flavors of string theory soup into one single, satisfying broth. The cost of this in conceptual terms is the addition of a single dimension: M-theory is 11-dimensional but with the unusual trait that it can appear 10-dimensional at some points in its space of parameters. Supergravity rides again – but this time with strings attached.

And the M in M-theory? We omitted to say earlier that while strings, with their one-dimensional extension, are the fundamental objects in string theory, they're not the only objects allowed. String theory can accommodate multidimensional entities, called branes, with anywhere from zero (points) to nine spatial dimensions. A brane with an unspecified number, p, of dimensions is called a p-brane. In M-theory, with its extra dimension, the fundamental object is an M-brane, which resembles a sheet or membrane. Like a drinking straw seen at a distance, the membranes would look like strings since the eleventh dimension is compactified into a small circle. Membranes, M-branes, M-theory. Hmmm ...

## End in sight?

Building a theory of everything is one thing, testing it quite another.
The physical conditions that have to prevail for the four forces of nature
to be unified into a single force haven't existed since the universe was
about 10^{-43} seconds (one ten million trillion trillion trillionth
of a second) old. There's not the remotest chance of recreating that kind
of environment in the lab any time soon, if ever. But what physicists can
do is look for other clues that their unification scheme is on the right
track.

We saw above that supersymmetry predicts there are supersymmetric fermion partners of all the force-carrying bosons. The supersymmetric partner of the graviton, for example, is a spin 3/2 particle that, like all its supersymmetry cousins is expected to be very massive – maybe a thousand times more massive than a proton. This high mass has put the creation of such particles beyond the reach of accelerators thus far. But that may be about to change. A new generation of more powerful instruments, including the Large Hadron Collider (LHC) at the European CERN facility near Geneva, Switzerland, is about to come on line capable of exploring the energy domain in which the new particles might be found. Evidence for supersymmetry at high energy would be compelling evidence that string theory was a good mathematical model for nature at the smallest distance scales.

In some ways, the invention of string theory was premature – its physical concepts running ahead of the mathematical techniques needed to describe them. One of the architect's of string theory in its modern form, Edward Witten of the Institute for Advanced Study in Princeton (where Einstein spent his latter days), has said:

By rights, twentieth century physicists shouldn't have had the privilege of studying this theory. What should have happened, by rights, is that the correct mathematical structures should have been developed in the 21st or 22nd century, and then finally physicists should have invented string theory as a physical theory that is made possible by those structures... [T]hen the first physicists working with string theory would have known what they were doing, just like Einstein knew what he was doing when he invented general relativity.

There are other theories of quantum gravity besides string theory. One of the leading rivals is called loop quantum gravity, founded in the late 1980s by Abhay Ashtekar of Penn State University, Carlo Rovelli of the Center for Theoretical Physics in Marseille, France, and Lee Smolin of Harvard. Its strategy is to focus on quantizing the spacetime of general relativity without getting involved in trying to unify gravity with the three other forces. Smolin, however, has suggested that string theory and loop quantum gravity might eventually be reconciled as different aspects of the same underlying theory.