STRING THEORY: The Super Unified Theory
                                                                                                                    By John Urgo

Strings can sing.  So you can think of the world around us as a symphony of strings vibrating in different frequencies.
                                                                                                                        Jim Gates, University of Maryland

     The power of string theory lies in the potential it his to unify two fields of physics that have been at odds for several decades--quantum mechanics and general relativity.  As a result, string theory has been hailed by some as a “theory of everything,” an ultimate unifier that will be the one grand theory that explains how every bit of matter and every pulse of energy in the universe came into being and why each has the properties it has.  This new, as yet unproven theory, quite understandably has many skeptics and it remains to be seen if it will live up to its potential as the "super unified theory."

     String theory is so exciting to physicists because it is a very promising solution to a puzzle that has been plaguing them for the last eighty years.  If the puzzle can be solved, physicists say they will have achieved a virtually complete understanding of the nature of existence.

     The puzzle is that the two greatest theories of modern physics-general relativity and quantum mechanics-give what seem to be conflicting explanations of gravity.  These theories are well established in the scientific world, causing their irreconcilable differences to be even more plaguing.  Albert Einstein’s general theory of relativity and quantum mechanical theory, which began with Einstein and was developed further by many others through the 1920s, have both been verified in countless experiments.  Both are embodied by mathematical formulas that can be used to predict natural phenomena.  “In fact,” says Jim Gates, “every experiment ever done to test relativity has given positive results.  The theory correctly predicts what happens in the real world.  And the same is true of quantum theory.  They’re both firmly established.  They work, and there’s no way to escape that fact.”  General relativity and quantum mechanics are the finest achievements of human understanding of the fundamental nature of matter and energy.  Their seemingly contradictory statements about gravity, however, show that something is lacking in our understanding of one of the most basic and observable forces of our everyday lives.

     Quantum theory is a very successful framework for describing three of the four fundamental forces in the standard model .  Quantum theory portrays forces as fields transmitted by particles called quanta.  The strong force holds the atomic nucleus together.  Carried out by gluons, the strong force binds protons in the nucleus and is the source of the sun’s energy and thermonuclear explosions.  The weak force governs radioactive processes within the nucleus of the atom and is carried by W-bosons.  The two forces that we are able to perceive in the everyday world are gravity and electromagnetism.  Electromagnetism, carried by photons moving through space, binds electrons to atomic nuclei and thus is responsible for all chemical reactions.  Electromagnetism also makes electrons jump from atom to atom in a wire, producing electricity.  In recent decades, physicists have unified electromagnetism and the weak force into one electroweak theory, describing a process in the early universe through which one force could have broken down to yield these two forces.  Physicists believe that all four forces are present day remnants of one original force that existed at the time of the Big Bang.  As the universe expanded and cooled, this one force eventually changed into the other four forms that we recognize today.

     Physicists have been less successful using quantum theory to describe the force of gravity.  According to quantum theory, gravity must be like the other forces in that it must be carried by special force carrying particles, called gravitons, which move back and forth between particles of matter.  The problem is that no one has ever found a graviton.  However, based on the strength of the mathematical equations that predict them, scientists have faith that they exist.

     The conflict is that general relativity also describes gravity, not as a force mitigated by sub-atomic particles, but as kind of an illusion created by the curvature of space.  The basic idea is that mass curves space in an infinite number of directions, which causes the force of gravity.  This phenomena reaches in all directions from anything that has mass and causes things with less mass to be attracted to things of greater mass, as if they were rolling across rubber sheets curved by the more massive objects.  Though this theory is hard to visualize, the mathematics of relativity theory passes every test in the real world that says that this must be what gravity is.

     Thus, the two sets of mathematical equations describing gravity in both quantum theory and relativity theory are diametrically opposed.  Physicists see this as a problem because they have learned to have faith in mathematics. They have discovered that the universe is unfailingly mathematical.  The only way to reconcile the two theories, physicists say, is to find some overarching theory such that both relativity’s gravity and quantum theory’s gravity can be derived from it.  This is where string theory comes in.

     Since its quiet beginnings in the 1960s, string theory has flared and faded through a first “superstring revolution” in the mid-1980s to a second revolution a decade later.  In recent months, a new wave of discoveries and enthusiasm has begun what many have hailed as the third revolution that may lead toward the day when all the laws of creation will be explained on the same terms.

     String theory first arose in the late 1960s as an ill-fated attempt to understand the strong force.  Some physicists took this failure as a sign that quantum field theory ought to be scrapped and replaced with a whole new vision.  What emerged was the possibility that particles were really different notes produced by vibrating strings.  This is the major deviation that string theory has from the ways physicists used to think.  Until now, physicists have treated everything as a point particle, an infinitesimal, dimensionless dot.  One big problem in dealing with the infinitesimally small particles of quantum theory is that they cause mathematical absurdities to pop up in the equations.  String theory, by contrast, says the smallest particles are not dimensionless points but one-dimensional strings.  They are on the scale of 10^-33 centimeters long and to our instruments look like points.  An attractive feature of string theory is that if sizeless particles are replaced by little strings, the infinities go away.

     Physicists say these short strings vibrate at different frequencies, much like a guitar string, producing various tones.  The differing vibrations of these sub-atomic strings show up in scientific instruments as protons, neutrons, photons, and other fundamental particles.  For example, a proton can be thought of as three vibrating strings, one for each quark.  The different combinations of the vibrations of the strings produce the different properties of the proton, such as charge, mass, and spin.  Furthermore, if you give each string a characteristic way to vibrate and calculate the properties of those vibrations with the same formulas developed for describing the vibrations of strings in musical instruments, string theory will give you good mathematical descriptions of all known fundamental particles of matter and energy.  Even better, string theory effectively includes gravitons as one of the fundamental particles.  Researches studying string theory have found a particle similar to the graviton, arising from the vibrations of the strings. The famous mathematical inconsistency that for decades made it impossible to incorporate quantum gravity with the other fundamental forces of the standard model is absent in string theory. It is almost as if gravity needs strings in order to exist.

     Strings can be open or closed, sweeping out a worldsheet through space-time.  A closed string has periodic boundary conditions while an open string has an endpoint free to move about.  Strings interact by splitting and joining.  The vibrational modes of strings can be characterized by various quantum numbers, such as mass, spin, etc.  This means that each mode carries a set of quantum numbers that correspond to a distinct type of particle, as described above.  Thus, all fundamental particles can be described by one object, a string.

     The hardest pill to swallow concerning string theory is that it makes mathematical sense only if the universe has 26 dimensions.  When an early version of string theory emerged in the 1970s, it was realized that one could only believe the equations if the strings were vibrating in a space of 26 dimensions.  This is 22 more than the four space-time dimensions that we are in contact with in our everyday existence.  Mathematically, it is trivial to add dimensions, but it is only plausible to claim 26 dimensions if it is asserted that 22 of them are hidden from our perception.  This is where the idea of compactification plays a major role.

     Compactification means the “curling up” of extra dimensions of the strings to a very small size.  To curl up two dimensions, for example, take a doughnut and begin squeezing it down to a circular wire with an unobservably small cross section.  Then squeeze the wire loop down to a point.  The wire thus appears one-dimensional and the point appears to have zero dimensions.

Compactifying a doughnut into a circular wire
J.M. Pierre/University of California at Santa Barbara

     In 1984, four Princeton University physicists found a way to make string theory work in a 10-dimensional world, having compactified the other 16 dimensions, curling them up so that they no longer played a role in the everyday world.  Later, it was discovered that of all the possible ways to compactify a string into 10-dimensions, only five were mathematically sturdy.  Physicists continued to toil with compactification until in the mid 1990s they realized that the five ways to hide the extra dimensions were closely related.  The five 10-dimensional string theories were found to be just different views of a single underlying 11-dimensional theory, called M theory.  All of the five theories could be connected by “dualities,” mathematical relationships describing the same physics.

     As the varying string theories began to funnel into one, physicists realized that their equations spoke of a world made not just from strings but also from membranous things called p-branes, with the p standing for the number of dimensions.  Especially important to M theory is a special type called a D-brane.  In 1995, Dr. Joseph Polchinsky of the University of Santa Barbara showed that D-branes, which come in as many as nine dimensions, described surfaces on which strings can end.  D-branes are now seen as entities at least as fundamental as strings and they may even be the fundamental objects from which strings and everything else is made.

     Recently, a theory by Dr. Juan Maldacena of Harvard University, has been the source of much excitement.  Maldacena used D-branes to construct a quantum field theory in the ordinary four space-time dimensions.  He also used D-branes to build a 10-dimensional string theory (with five of the dimensions compactified).  By their nature, string theories include gravity.  Thus Maldacena was able to show that quantum theory, string theory, and gravity were all intimately related.

    An interesting aspect of Maldacena’s new theory is the notion that the universe is holographic.  In laser holography, a three dimensional object is projected onto a two-dimensional plane.  In the Maldacena model, the four-dimensional field theory can be thought of as a holographic projection of the five dimensional string theory (the other five dimensions having been compactified).  “In a holographic universe,” says George Johnson, “the information about everything in a volume of space would be displayed somehow on its surface.” The implications of this notion are only beginning to unfold.

    So is string theory the final answer, the super-unified theory that solves the discrepancy between relativity and quantum theory and explains all the forces of nature in the same terms?  Understandably, there is much skepticism in the scientific world.  The main problem is that no theory can be considered valid until it has produced predictions that can be tested.  Up to now, string theory has been entirely conceptual, as there have been no means of testing it.

    In principle, an extremely powerful particle accelerator could test string theory, but such a machine would have to be a million billion times more powerful than the Superconducting Super Collider that was to be built in Texas before Congress killed its funding.  A new accelerator, the Large Hadron Collider, being built in Europe, may offer some means of testing string theory, but not for several years.  String theory predicts that the electroweak force, the strong force, and gravity have the same strength at 10^19 GeV, so the accelerator would have to be very powerful, to say the least.  Even so, a direct testing of string theory seems impossible and this has led many scientists to claim that string theory is mere speculation and does not deserve the lofty term theory.  For all the conceptual revolutions in string theory, many physicists maintain that there is little to show but a lot of beautiful mathematics.

    “We’ve made an enormous amount of progress in the last few years”, says Dr. Steven Giddings of the University of Santa Barbara, “but now we realize the greater depth of our ignorance."