String Theory: Symmetry in Multiple Dimensions

Author:  Pattanayak Vikram
Institution:  Biochemistry and Biophysics
Date:  September 2005

Two theories currently shape the world of physics: quantum mechanical theory, which involves small particles, and gravitational theory, which involves large particles. Physicists and mathematicians are currently trying to unify the two theories into an all-encompassing quantum theory, called string theory, that can account for the four main forces: gravity, electromagnetism, the strong force and the weak force (1).

A theory of particle physics, the Standard Theory, seeks to unify the latter three, while string theory goes one step farther: trying to also incorporate a quantum theory of gravity. Theoretical calculations on the currently-favored string theory postulate that the strong and weak forces come together at temperatures that are eighteen orders of magnitude above what physicists can currently experiment with using particle accelerators (2). This property of string theory makes it hard to confirm through the use of experimental physics.

String theory attempts to explain the universe in terms of tiny, vibrating, "strings" that represent the fundamental particles postulated by the Standard Theory of particle physics: bosons, which are force-carrying particles like photons, and muons, particles that make up matter such as the electron (3). These vibrating strings are quantum mechanical entities that can exist in different states. They can be closed or open-ended and can have different modes of vibration, similar to how a guitar string can vibrate differently depending on how and where you pluck it. The different vibrational states of the strings correspond to the particles. To account for these strings, a theory called superstring theory postulates that space and time exist in ten dimensions. Six of the ten dimensions are compactified: they are curled up on themselves on very small scales (on the order of 10-33 cm) (1,4). The other four consist of what we traditionally think of as space (the three spatial dimensions) and time. However, while superstring theory is a good start, it fails to explain cosmological observations, leaving mathematicians and theoretical physicists searching for a new postulate.

The current prevailing string theory, called M-Theory (5), came after what scientists refer to as the "second superstring revolution." It proposes an eleven-dimensional space that consists of objects with multiple dimensions called p-branes. One type of p-brane is the d-brane, which can be related to the end points of the strings. Another string theory postulates a twenty-six dimensional space (3). Yet another seeks to use a five-dimensional space to describe the universe. The mathematical principles and equations associated with these theories are all extremely complex and difficult for the average undergraduate to understand.

However, the essence of string theory is easier to understand. Theoretical physicists are still searching for the proper theory to unify gravity and quantum mechanics, and leading experts in the field believe it will take many more years and many different incarnations to get there. If and when it is discovered, string theory will most likely include symmetry, indicating that all times and spatial locations are described by the same fundamental physical principles (6). It could also involve extra dimensions of space that form a compact space (7), a property that the theories proposed so far (superstring theory, M-theory, etc.) have used.

Experimental evidence will be important in confirming string theory. The super-symmetry involved in the theory postulates that the vibrations that correspond to the fundamental particles come in pairs that differ in their spin properties. The Standard Theory also predicts these partner particles, which have not been experimentally found yet. There is hope that they will be found when a new high-energy particle accelerator, the Large Hadron Collider, opens in Geneva, Switzerland in 2010 (6).

Other researchers are looking to black holes for experimental evidence for string theory. Scientists have postulated the existence of theoretical black holes, called gedanken black holes, which are composed of d-branes. One property of d-branes is that their electromagnetic repulsion and gravitational attraction cancel each other out, allowing researchers to combine them into larger objects, some of which are reminiscent of black holes (2). Both string theory and the theory of general relativity agree when appropriate boundary constraints are applied to these systems, giving physicists hope that they are closer to being able to verify string theory by experiment. Black holes mostly involve gravitational force, and according to Maldacena's conjecture, "a quantum theory with gravity and strings in a given space is completely equivalent to an ordinary quantum system without gravity that lives on the boundary of that space" (2). Black holes constitute these ordinary quantum systems, and while they have not provided any breakthroughs on the nature of string theory, they do represent a real-life system that can be studied to give clues about string theory (2).

Over the past thirty years, string theory has seen many forms. When it reaches its final form, physicists expect it to include symmetry and multiple dimensions, while it might not look like anything yet proposed. Since string theory can only be empirically confirmed at high energies that are many orders of magnitude above what we can currently probe experimentally, it has been tested only theoretically. If it holds up experimentally as well, physics finally will have a theory to describe all particles, including (and replacing) the currently unrelated quantum mechanical and general relativity theories.

Suggested Reading

1. D. Kestenbaum. "Practical Tests for an 'Untestable' Theory of Everything?" (1998) Science 281, 758-9.

2. G. Taubes. "String Theorists Find a Rosetta Stone." (1999) Science 285, 512-7.

3. Schwarz, Patricia. Home page. 14 Nov. 2001.

4. G. Gibbons. "Brane-Worlds." Science 287 (2000), 49-50.

5. E. Witten. "Overview of K-theory applied to strings." (2001) International Journal of Modern Physics A 16, 693-706.

6. B. Greene. The Elegant Universe. Vintage Books: New York, 1999.

7. J. H. Schwarz. "The Future of String Theory." (2001) Journal of Mathematical Physics 42, 2889-2895.