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Issue 3, December 2001
String Theory: Symmetry in Multiple Dimensions
Vikram Pattanayak
Biochemistry and Biophysics, University of Pennsylvania
pattanayak@jyi.org
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. http://www.superstringtheory.com
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.
Journal of Young
Investigators. 2001. Volume Five.
Copyright © 2001 by AUTHOR'S NAME and JYI. All rights reserved.
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