### Issue 41 / January - March 2003

### Understanding String Theory

### Dr. Ibrahim B. Syed

Cosmology is the study of the universe's birth and evolution. The Standard Model of Cosmology, a widely accepted modern theory, states that some 15 billion years ago the universe emerged from the Big Bang, an enormously energetic singular event that spewed forth all space and all matter. The universe's temperature at 10-43 seconds after the Big Bang, the so-called Planck time, is estimated to have been 1032K, or some 10 trillion 10 trillion times hotter than the sun's interior. (1) In the first few picoseconds after the Big Bang, the universe expanded and cooled. About a hundredth-thousandth of a second after the Big Bang, it was cool enough (10 trillion K) to produce protons and neutrons. About 300,000 years after Big Bang, electrically neutral atoms formed. A billion years later, 100 billion galaxies and 100 billion stars (like our sun) were formed in each galaxy, and ultimately planets began to emerge.

Modern theories of creation are built upon quantum theory and Einstein's theory of gravity. The question is what happened before the Big Bang? Einstein's equations break down at the enormously small distances and large energies found at the universe's origin. At distances 10-33cm, quantum effects take over from Einstein's theory. For questions involving the beginning of time, one must invoke the ten-dimensional theory. The Big Bang probably originated in the breakdown of the original ten-dimensional universe into a four- and six-dimensional universe. Therefore, the history of the Big Bang represents the breakup of previously unified symmetries, and the split universe was no longer symmetrical. Six dimensions have curled up.

Quantum physics abolishes time close to the Big Bang. How did the universe come into existence? Why does time vanish in the black hole? Did time exist before the universe came into being? These questions and realities point to the existence of a Creator.

Unfortunately, quantum theory and Einstein's theory of gravity are mutually incompatible. In this new millennium, superstring theory, or simply string theory, resolves this tension. Three particle theorists (Yoichiro Nambu, Leonard Susskind, and Holger Nielsen) independently realized that the dual theories developed in 1968 to describe the particle spectrum also describe the quantum mechanics of an oscillating string. This marks the official birth of string theory in 1970, according to which the marriage of the laws of the large and the small is not only happy but also inevitable. Brian Greene writes in his The Elegant Universe: String theory has the inherent capability to show that all of the astonishing happenings in the universeâ€from the frenzied dance of subatomic quarks (components of protons or neutrons) to the stately dance of orbiting binary stars, from the primordial fireball of the big bang to the majestic whirl of celestial galaxiesâ€are reflections of one grand physical principle, one master equation.**Fundamental forces**

During the past hundred years, physicists have proven the existence of four fundamental forces in nature: Gravitational force, electromagnetic force, the weak force, and the strong force. Gravity, the most familiar force, keeps Earth revolving around the sun and our feet planted firmly on the ground. Electromagnetic force, the next most familiar force, is the driving force for such things as lights, TVs, computers, and telephones.

The strong nuclear and weak nuclear forces are less familiar, because they operate in the atom's nucleus. The strong force (mediated by gluons) keeps quarks glued together inside protons and neutrons, and keeps protons and neutrons tightly crammed together inside atomic nuclei. The weak force (mediated by W and Z particles) determines the radioactive decay of such radioactive materials as uranium, plutonium, and tritium.

Gravitational force is mediated by graviton (the concept of graviton was introduced in 1974), photons for the electromagnetic force (a photon is the smallest EM force or the smallest packet of energy for light). In Einstein's day, the strong and weak forces were unknown. For 30 years Einstein sought to unify the two distinct forces of gravity and electromagnetism.**String theory**

Matter is composed of atoms, which in turn are made of nucleons (protons and neutrons in the nucleus) and electrons orbiting around the nucleus. Nucleons are made of three quarks each. Quarks are made of string. According to the standard model of particle physics, the universe's elementary constituents are point-like ingredients with no internal structure. However, this standard model cannot be a complete theory, for it does not include gravity. But according to string theory, atomic and subatomic particles are not point-like; rather, they consist of tiny one-dimensional filaments somewhat like infinitely thin rubber bands. Physicists call these vibrating, oscillating, and dancing filaments strings.

String theory takes its name from this point of view. Unlike an ordinary piece of string, which itself is composed of molecules and atoms, the strings of string theory are alleged to lie deeply within the heart of matter. They are so smallâ€on average about as long the Planck length (10-33 cm, or about 100 billion billion [1020] times smaller than an atomic nucleus)â€that they appear point-like even when examined with our most powerful equipment. String theory offers a far fuller and more satisfying explanation than that of the standard model.

Moreover, this theory shows the harmonious union of general relativity and quantum mechanicsâ€a major success. In this new millennium, the excitement in the physics community is that string theory may provide the unified theory of all four forces and all matter. For this reason, string theory sometimes is described as possibly being the theory of everything.

String theory proclaims that the observed particle properties (i.e., mass, charge, and spin) are reflections of a string's various vibrations. Each preferred pattern of a string's vibration in string theory appears as a particle whose mass and force charges are determined by the string's oscillatory pattern. All fundamental particles can be described as resonant patterns of these string vibrations. There is even a mode describing the graviton. The same idea applies to the forces of nature as well. Hence everything, all matter and all forces, is unified under the microscopic string oscillationsâ€the notes that strings can play. **Extra Dimensions**

Our universe has three spatial dimensions: length, width, and height. In formulating the general theory of relativity, Einstein showed that time is another dimension. According to the general theory of relativity, space and time communicate the gravitational force through their curvature. The special theory of relativity is Einstein's law of space and time in the absence of gravity.

In 1919, the mathematician Theodor Kaluza unified Maxwell's electromagnetism and Einstein's theory of general relativity by adding a fifth dimension. Thus Kaluza was the one who suggested that the universe might have more than three spatial dimensions.

For example, a garden hose viewed from a long distance looks like a one-dimensional object. When looked at closely, a second dimension, one shaped like a circle and curled around the hose, becomes visible. The direction along the hose's length is long, extended, and easily visible. The direction circling around its thickness is short, curled up, and harder to see. Hence spatial dimensions are of two types: large, extended, and therefore directly evident, or small, curled up, and far harder to detect. As for the garden hose, the curled-up dimension encircling its thickness is detected either moving closer to the hose or using a pair of binoculars from a distance. If the hose is as thin as a hair or a capillary, its curled-up dimension is more difficult to detect.

In 1926, the mathematician Oskar Klein applied Kaluza's theory to quantum theory, which is used in modern string theory. Klein showed that our universe's spatial fabric may have both extended (the three spatial dimensions of daily experience) and curled-up dimensions. The universe's additional dimensions are tightly curled up into a tiny space, a space so tiny that it has so far eluded detection. These extra dimensions are believed to be minuscule, somewhere between 10-35 meters and 0.3 millimeters in size.

The equations of string theory show that the universe has nine space dimensions and one time dimension. At present, no one knows why the three space and one time dimensions are large and extended, while all of the others are tiny and curled up. **Supersymmetry**

Symmetry is a physical system property that does not change when the system is transformed. For example, a sphere is rotationally symmetrical, since its appearance does not change if it is rotated.

In 1971, supersymmetry was invented in two contexts at once: in ordinary particle field theory and as a consequence of introducing fermions into string theory. It holds the promise of resolving many problems in particle theory, but requires equal numbers of fermions and bosons. Thus, it cannot be an exact symmetry of Nature.

Supersymmetry, a mathematical transformation, is a symmetry principle that relates a particle's properties of a whole number amount (integer) of spin (bosons) to those with half a whole (half-integer or odd) number amount of spin (fermions). Bosons tend to be the mediators of fundamental forces, while fermions make up the matter experiencing these forces. Bosons can occupy the same space and have an integral spin (0,1, .), while fermions cannot occupy the same space and have a half-integral spin ( 1/2, 3/2,.). Bosons transmit such forces as photons, gravitons, W and Z particles, mesons, and gluons. Many bosons can occupy the same state at the same time. Fermions (e.g., electrons, muons, tau, protons, neutrons, quarks, and neutrinos) cannot share a given state at a given time with other fermions. The fact that fermions make up matter explains why we cannot walk through walls: the inability of fermions (matter) to share the same space the way bosons (particles of force or energy) can.

Supersymmetry treats all particles of the same mass as different varieties of the same superparticle. This means that there is an equal matching between bosons and fermions. A supersymmetric string theory is called a superstring theory. The original string theory only described bosons, and hence became known as bosonic string theory (BST). Thus it did not describe fermions or, for example, include quarks and electrons.

Introducing supersymmetry to BST engendered a new theory that describes both the forces and the matter making up the universe: the theory of superstrings. String theorists have shown that all string theories are different aspects of a string theory that has not 10 but 11 spatial dimensions. This was called M-theory. The M might stand for the mother of all theories or mystery, magic, matrix, or membrane. The last two refer to mathematical techniques used in science. There is no space or time in M Theory. Furthermore, our space-time is not four-dimensional after all. M theory unites the four forces of nature (e.g., gravity, quantum mechanics, strong force, and weak force) and, remarkably, is a mathematical and geometrical theory. It is attractive because it can explain gravity and an atom's inside at the same time and thus resolve the contradiction between current theories. **Summary and Conclusions**

String theory gives a theoretical description of elementary particles and treats them as one-dimensional curves (strings). Traditional models of interactions between elementary particles are based on quantum field theory, which treats particles as dimensionless points. Theoretical physicists have not developed a workable theory of gravitation that is consistent with quantum mechanics' principles.

However, treating elementary particles as strings permits the derivation of a quantum theory that encompasses all four forces. Superstring theory, a combination of string theory and supersymmetry, treats particles as very short (10-33 cm along its single dimension, which is 1020 smaller than a proton's diameter) closed strings (string loops). All of the masses, charges, and other properties of elementary particles result from the vibration of these superstrings at different frequencies. The complex mathematical basis of superstrings involves 10 dimensions: 9 spatial dimensions, 6 of which are invisible, and time. Since superstring theory provides a unified description of all elementary particles and fundamental forces, it is sometimes called the theory of everything.

Some major unsolved problems of string theory are how to condense, 10 dimensions to 6 (spatial) plus 4 (space and time) dimensions, and what is happening at distances smaller than 10-33 cm. In addition, the experimental verification of the existence of strings in the near future poses quite a challenge. Since they are thought to be less than a billionth of a billionth the size of an atom, we cannot use current technology to detect them directly. An indirect test, however, will be carried out within the next decade or so by the Large Hadron Collider, a huge atom smasher being built by CERN (European Organization for Nuclear Research, located in Geneva, Switzerland). There also is an urgent need to develop new mathematics in areas of Riemann surfaces, algebraic geometry, singular geometries, number theory, and other related fields. *Footnotes*

1 K stands for Kelvin, a measurement of degree relating to, conforming to, or having a thermometric scale on which the unit of measurement equals the centigrade degree and according to which absolute zero is 0A , the equivalent of â€œ273.16A C.**References**

Adams, Steve. A Theory of Everything. New Scientist 161 (20 Feb. 1999).

Arkani-Hamed, Nima et al. The Universe's Unseen Dimensions. Scientific American 283 (Aug. 2000): 62-69.

Davies, P. C. W. and Julian Brown, Eds. Superstrings: A Theory of Everything? Cambridge, UK and New York: Cambridge University Press, 1988.

Duff, Michael J. The Theory Formerly Known as Strings. Scientific American 278, (Feb. 1998): 64-69.

Green, Michael M., John H. Schwarz, and Edward Witten. Superstring Theory. 2 vols. Cambridge, UK and New York: Cambridge University Press, 1987.

Greene, Brian. The Elegant Universe. New York: W. W. Norton, 1999.

Gribbin, John R. The Search for Superstrings, Symmetry, and the Theory of Everything. Boston: Little, Brown Co., 1998.

Kaku, Michio. Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension. New York: Oxford University Press, 1994.

Mukhi, Sunil. The Theory of Strings: An Introduction. Current Science 77 (25 Dec. 1999): 1624-34.

Peat, David F. Superstring and the Search for the Theory of Everything. Chicago: Contemporary Books, 1988.

Polchinski, Joseph G. String Theory. 2 vols. Cambridge, UK and New York: Cambridge University Press, 1998.