The Superstring Theory: A New Beginning?
One of the major paradoxes in the physics of elementary particles is the conflict that arises between Einstein's theory of relativity and quantum mechanics. Eisntein's theory of relativity relates the forces of gravity to the structure of space and time. Quantum mechanics deals primarily with atomic and subatomic particles.
Quantum theories were formulated to help in the understanding of the three of the four known forces of the universe. The four forces are the Strong Force, the Weak Force, Electromagnetic Force, and Gravity.
Gravity, according to Einstein, does not unite with the basic ideas of quantum mechanics. Two ways to unite the two theories would be to restructure quantum mechanics to deal with scales of extremely small distances or to throw away the idea that space and time are a continuous set of points.
Until the theories of superstrings the mathematics used in particle physics dealt primarily with points as the basic structure of all things. Yet, point like structures created mathematical results that made no sense at high energy or temperatures.
Point like structures also made it impossible to combine gravity with the three other forces of the universe. Superstring theory introduces an alternative to point like structures, string-like loops of energy that open up a whole new realm of the physical universe we live in along with the production of a new an exciting look at mathematics.
Some critics argue that superstrings would be too small, almost at the same scale as an atom compared to the size of our galaxy, and at this scale it would be incredibly unlikely to find proof of superstrings in the next thousand years, or of the extra dimensions where the superstrings would lie.
How Did This Theory Evolve?
All theories begin with an evolution of an idea that begins to change its shape and find a new home within another theory.
The superstring theory came from theories that were direct results of the paradox of particle physics and the search for a grand unifying theory that would include all the forces of the universe.
In the late 1960's the dual-resonance model was formed that observed particles subjected to the Strong Force, or Hadrons. There were no theories in the 1960's that dealt with the behaviour of interacting Hadrons having a large spin.
Gabriele Veneziano, at CERN, created a formula that described Hadrons as strings. Veneziano explained that the harmonics of string vibrations corresponded to the vibrations of ineracting Hadrons. He stated that these strings bound together the quarks that make up the proton, the neutron, and other hadrons. The dual-model developed into the spinning-string theory, which was the birth father of all supersymmetric theories.
Both of the earlier theories were scarred by the fact that the states of the lowest energy of the string would have to be Tachyons, or particles that moved faster than the speed of light. These particles needed to be massless spin-1 and spin-2 particles. These particles could not be Hadrons.
None of the theories mentioned above tackled the issue of where gravity fits in with the other forces of the universe. Supergravity was a combination of Einstein's theory of gravity with supersymmetry, and created a graviton with a spin of 3/2, and needed 11-dimensions.
In 1976 it was suggested that the spinning-string theory could be made supersymmetric. The three theories that stand at the foundation of the Superstring theory prior to the inclusion of gravity were, quantum chromodynamics, and quantum electrodynamics, and the Weak Nuclear Force combined with the theory of quantum electrodynamics to create the electroweak theory.
The above-mentioned theories were combined to form the supersymmetric standard model, and this model led to the "Unified Theory" and supergravity. When the concept of shadow matter in our universe was combined with the "Unified Theory" and supergravity the superstring theory was formulated.
This superstring theory had 6 compact dimensions and 4 ordinary dimensions. After compactification, which will be described later, a flat 10-dimensional superstring theory was produced.
The Language of the Superstring Theory
The superstring theory states that the elementary particles are strings, or the elementary particles are understood as different modes of a single string.
So the fundamental quanta that are present in the universe are as infinite as the many excited states of the string.
The "Super" in superstrings refers to the symmetry that strings possess and their ability to combine the four forces in the universe. These theoritical strings would be 10^35 meters long and 10^20 times smaller that the diameter of a proton. Superstrings need more than three dimensions to exist.
The current Superstring theory requires 10-dimensions. If modern physics have found evidence for four dimensions, the question arises about where the other 6-dimensions are hiding. The idea of compactification states that the extra 6-dimensions are curled up into what are called Calabi-Yau manifolds.
The size of the Calabia-Yau manifold is approximately the same as the length of the string.
Einstein's theory of gravity places the four major dimensions into a continuum called the space-time continuum. The influence of gravitational force is determined by the curvature of this space-time continuum.
A spherical time-space continuum works with a series of cylindrical strings yet does not correspond with point like particles. The strings in the superstring theory will contract, in lower temperatures like 3 Kelvin, or the temperature of the Universe, and behave similar to point-like particles.
In Einstein's theory of gravity a gravitational field is defined at every point in a space-time continuum. In the Superstring Theory there is a similar field that depens on the configuration of the string, this is called the string field. A string field is realted to a new kind of geometry that examines all the possible configurations of a string.
To help obtain a clearer view of this new geometry it is necessary to look at Feynman's method of summing over histories. When any particle moves it will try to move through all the possible paths from its initial state to final state. The probability of each path tends to lean towards the path of lower action.
Richard P. Feynman called the summing of the probability of a particle's path the summing over histories of the particles. When looking at the summing over histories of a closed string the sum includes all the possible connected surfaces.
This surface at any given time can stretch, twist, deform into a cylinder, or a cylinder with moving tentacles located throughout. These tentacles can move to form a new string, or a new string and a new closed string.
The actions of the tentacles on a cylinder prove that the strings interact with space.
There are two kinds of strings, the first being open strings. Open strings have endpoints, conserved charges, and form massless spin-1 guage particles, not including the graviton.
The second type of string is the closed string that either form new open strings or remain closed. The closed strings are massless spin-2 particles, including the graviton.
The concept of closed strings led to the closed string theory. The closed string theory defines the string as heterotic. The entire heterotic string carries the charges of Yang-Mills forces. As a string moves it sweeps out over a 2-dimensional surface in space-time. The string moves in a manner that minimizes its action.
The action is proportional to the area swept. The area swept over is called the world line, and the world sheet covers a surface of minimum area. All vibrations of the string on the world sheet are perindicular to its surface.
Possible sources of evidence to support superstrings are Feynam's diagrams. Some believe that Feynman's diagrams describe all the summed over histories of world sheets. The diagram is a topographical equivalent to a torus, or the surface of a doughnut.
The vibrations of the strings are determined by the tension of the string. The strings vibrate like a stringed instrument and include harmonic modes of vibration. The energy-differences between superstring quanta are multiples of the string's tension. The tension of the string is about 10^19 GeV squared, or 10^39 tons.
This leads string theorists to believe that the frequencies of the modes of the strings are separated by gaps or loops. These loops can be compared to rubber bands whose tension depends on the temperature of the enviroment.
Since superstring theory includes gravity the string tension must be closely related to Planck's constant.
Some Arguments For and Against
Like all theories the superstring theory is constantly under suspicion and many critics have good reason to think the theory has no basis in reality. This side of the coin should not be overlooked.
The Weak Force is responsible for radioactive decay such as beta-decay. The Weak Force has been found to be chiral, or its effects have mirror-image counterparts that do not exist in nature.
Quantum Mechanics cannot support chirality of the Weak Force without violating conservation laws like the law of the conservation of electric charge. This is called the Chiral Anomaly.
In order to support chirality there needs to be an odd number of dimensions. With an odd number of dimensions, an odd number of reflections would be created leaving one to be left-handed.
Superstring Theory has nine spatial dimensions. Earlier it was stated that the superstrings take up 10-dimensions. This is still true, since based on the dynamics of a one-dimensional object the string at one given time will have nine spatial dimensions.
The Heisenberg Uncertainty Principle states that the more precise the spatial measurement the less precise the energy or momentum can be measured. At distances of 10^-15 meters the uncertainties of energy are called energy fluctuations. These energy fluctuations are called virtual particles.
These virtual particles form and then annihilate themselves. At distances of less than 10^-35 meters, the energy fluctuations become enormous. According to the theory of general relativity virtual black holes form.
The energy of the above mentioned fluctuations are 10^19 GeV, this is Planck's energy, and this distance is Planck's distance. The calculations at Planck's energy and Planck's distance according to quantum mechanics give results that make no sense.
Superstring theory changes the assumptions of general relativity at short distances, since the curved space-time is extended into the infinite confirmations of a string.
On the other hand, Superstrings at low energy would have an extra quark in the 27-multiplet of the charge of -1/3. This extra quark should be detectable by the decay of this quark into a conventional quark, or one lepton and one quark. This detectable decay could be experimentally validated. Yet, experimentation has not been able to confirm this decay.
Furthermore, the question arises about the number of dimensions in our universe. SOme argue that a universe with too many dimensions could not hold atoms, or planetary orbit's stable. So how many is too many dimensions?
An even number of dimensions causes wave signals to reverberate, and an odd number would not. An odd number of dimensions would cause a considerable amount of distortion in the wave signal. It seems that three dimension waves propagate in a sharp undisturbed fashion. There are more than three dimensions described by Einsteins theory of relativity, but there may not be much room for too many more.
Last, most of the physics of superstrings at energies above 10^19 GeV, is not even remotely close to accelerator physics. This point alone leads most critics to believe that the imagination behind the Superstring Theory will never have a chance to become reality in our lifetimes.
Barrow JD. 1994. The Origin of the Universe. New York. Harper-Collins Publishers Inc.
Borner G. 1992. The Early Universe: Facts and Fiction. 2nd ed. Berlin. Springer Verlag.
Green MB. Sept 1986. Superstrings. Scientific American. 255:3:48-53
Horgan J. Nov. 1991. The Pied Piper of Superstrings Profile: Edward Witten. Scientific American 265:5:42-47
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