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Understanding String Theory
Ibrahim B. Syed,
Ph. D. Human beings
throughout history have been passionately searching answers for the origin of
the universe, from our ancestors to modern day cosmologists. Cosmology is the
study of the birth and evolution of the universe. The modern theory called the
Standard Model of Cosmology states that some 15 billion years ago, the universe
emerged from a big bang (enormously energetic singular event) which spewed forth
all of space and all of matter. The temperature of the universe at 10^ -43
seconds after the big band, the so-called Planck time, is estimated to be 10^32
Kelvin or some 10trillion 10 trillion times hotter than the interior of the Sun.
As time passed, the universe expanded and cooled. About a hundredth-thousandth
of a second after the big bang, it was cool enough (10 trillion Kelvin) to
produce protons and neutrons. As time passed electrically neutral atoms formed.
A billion years later 100 billion galaxies and 100 billion stars (our sun is a
star) in each galaxy, and ultimately planets began to emerge. Modern physics rests
on two foundational pillars: Einstein's general theory of relativity, which
provides an understanding of the large scale structures in the universe: stars,
galaxies, clusters of galaxies, and expanse of the universe itself. The other is
quantum mechanics, which provides understanding of the universe on the smallest
of scales: molecules, atoms, and the subatomic particles like electrons and
quarks. The two theories are mutually incompatible. In this new millennium
superstring theory or simply string theory resolves the tension between general
relativity and quantum mechanics. According to string theory, the marriage of
the laws of the large and the small is not only happy but also inevitable.
String theory has the inherent capability to show that all of the astonishing
happenings in the universe-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 galaxies-- are reflections of one grand physical principle, one master
equation. 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 is the most familiar of the forces, being responsible for
keeping our planet earth around the sun as well as keeping our feet firmly
planted on earth. Electromagnetic force is the next most familiar of the four.
It is the driving force for lights, TVs, computers, telephones. The strong
nuclear and weak nuclear forces are less familiar because they operate in the
nucleus of the atom. The strong force is responsible for keeping quarks "glued"
together inside of protons and neutrons and keeping protons and neutrons tightly
crammed together inside atomic nuclei. The weak force is responsible for the
radioactive decay of radioactive materials such as uranium, plutonium, and
tritium. At the microscopic level all the forces have an associated particle or
the smallest packet of the force. Photons for the electromagnetic force,
graviton for the gravitational force, weak gauge bosons (W and Z particles) for
the weak force and gluons (strong glue holding atomic nuclei together) for the
strong nuclear force. 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 3 quarks each. Quarks are made of string. According to the standard model of particle physics the elementary constituents of the universe are pointlike ingredients with no internal structure. However, the standard model cannot be complete or final theory because it does not include gravity. But according to string theory, atomic particles and subatomic particles are not pointlike, but instead consists of a tiny one-dimensional filaments somewhat like infinitely thin rubber bands, vibrating oscillating, dancing filament that physicists have named a string. Unlike an ordinary piece of string, which is itself composed of molecules and atoms, the strings of string theory are alleged to lie deeply within the heart of matter and they are so small-on average they are about as long the Planck length (10^ -33 cm-about a hundred billion billion (10^20) times smaller than an atomic nucleus) and they appear pointlike even when examined with our most powerful equipment. String theory offers a far fuller and more satisfying explanation than is found in the standard model. In Einstein's day, the strong and the weak forces were not discovered, but he found the two distinct forces-gravity and electromagnetism-deeply troubling. For thirty years he was in search of a unified field theory that he hoped would that these two forces are really manifestations of one grand underlying principle. String theory is showing the harmonious union of general relativity and quantum mechanics. Its ability to ameliorate the hostilities
between the gravitational force and quantum mechanics is a major success. In
this new millennium, the excitement in the physics community is that string
theory may provide the answer for the unified theory of the all the four forces
and all matter. For this reason string theory is sometimes described as possibly
being the "theory of everything" (T.O.E.). String theory proclaims that the
observed particle properties (mass, charge, spin) are a reflection of the
various ways in which a string can vibrate. Just as the strings on a piano or
violin have resonant frequencies at which they prefer to vibrate-the same holds
true for the loops of string theory. Each of the preferred patterns of vibration
of a string in string theory appears as a particle whose mass and force charges
are determined by the string's oscillatory pattern. The electron is a string
vibrating one way; the up-quark is a string vibrating another way. Particles
like photons, weak gauge bosons, and gluons are yet other resonant patterns of
string vibration. There is even a mode describing the graviton which is the
particle carrying the force of gravity. Particle properties in string theory are
the manifestations of one and the same physical feature: the resonant patterns
of vibration-the music so to speak- of fundamental loops of string. The same
idea applies to the forces of nature as well. Hence everything, all matter and
all forces, is unified under the microscopic string oscillations- the "notes"
that strings can play. EXTRA DIMENSIONS: It is taken for granted that our universe has three spatial (length, width and height) dimensions. In formulating the general theory of relativity Einstein showed time is another dimension. According to general relativity space and time communicate the gravitational force through their curvature. Special theory of relativity is Einstein's laws of space and time in the absence of gravity. In 1919 Theodor Kaluza, a Polish mathematician suggested that the universe might have more than the three spatial dimensions. For example, a garden hose viewed from a long distance looks like a one-dimensional object. When magnified (when looked closely), a second dimension-one that is in the shape of a circle and is curled around the house-becomes visible. The direction along the length of the hose is long, extended, and easily visible. The direction circling around the thickness of the hose is short, "curled up," and harder to see. Hence spatial dimensions are of two types. They can be large, extended, and therefore directly evident, or they can be small, curled up, and much more difficult to detect. In the case of the garden hose, the "curled-up" dimension encircling the thickness of the hose is detected either going closer the hose or using a pair of binoculars from a distance. If the garden hose is as thin as a hair or a capillary, then its curled-up dimension is more difficult to detect. Kaluza proposed that the spatial fabric of the universe might possess more than three dimensions of everyday experience. He showed by having four spatial dimensions, Einstein's general relativity and Maxwell's electromagnetic theory can be unified into a single theory. In 1926 Oskar Klein, a Swedish mathematician showed that the spatial fabric of our universe may have both extended(the three spatial dimensions of everyday experience) and curled-up dimensions. The additional dimensions in the universe are tightly curled up into a tiny space- a space so tiny that it has so far eluded detection by even our most advanced experimental equipment. The equations of
string theory show that the universe has nine space dimensions and one time
dimension. Why is it that three space and one time dimensions are large and
extended while all of the others are tiny and curled up? At present there is no
answer to this question. 1 dimension of time + 9 dimensions (6 hidden and 3 known) of space = 10 dimensions Supersymmetry Symmetry is a property of a physical system that does not change when the system is transformed in some manner. For example, a sphere is rotationally symmetrical since its appearance does not change if it is rotated. Supersymmetry (mathematical transformation) is a symmetry principle that relates the properties of particles with 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" which experiences these forces. Bosons can occupy the same space, and have integral spin (0,1, ….), while fermions cannot occupy the same space and have half-integral spin ( 1/2, 3/2, ….). Bosons are particles that transmit forces such as photons, gravitons, W, Z, particles, mesons and gluons. Many bosons can occupy the same state at the same time. Fermions( matter) such as electrons, muons, tau, protons, neutrons, quarks, neutrinos, can occupy a given state at a given time, and this is why fermions are the particles that make up matter. This is the reason why solids cannot pass through one another. This explains why we cannot walk through walls--- the inability of fermions(matter) to share the same space they way bosons (forces) can. Supersymmetry is the principle that treats all particles of the same mass as different varieties of the same superparticle. Supersymmetry means an equal matching between bosons(particles that transmit forces) and fermions (particles that make up matter). A supersymmetric string theory is called a superstring theory. The original string theory only described particles that were bosons, hence Bosonic String Theory. It did not describe Fermions. So quarks and electrons, for instance, were not included in Bosonic String Theory. By introducing Supersymmetry to Bosonic String Theory, a new theory is obtained that describes both the forces and the matter which make up the Universe. This is the theory of superstrings. Five string theories developed depending on whether the string is a closed string (loop) or open, like a hair. 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 Mother of all theories or Mystery, Magic, or Matrix.
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