This is the last english paper I will ever write - read it if you dare...
p.s. I was about to exceed the page limit so it kind of suck towards the end. I didn't get to go into as much depth as i would have liked.
Peter McNeill
Allegra Blake
English 201 TR 3:30
19 Apr. 06
Abstract
Amidst an incredible amount of recent scientific advancement, physicists have been aware of a devastating problem in modern physical theory. The two fundamental theories used to describe the universe both claim that the other in incorrect. This problem is solved by a process of unification, or the combining of the four fundamental forces into one conceptual framework. The theory that has come to provide such a framework is known as superstring theory. String theory makes a number of seemingly outrageous claims about the universe in which we live, sometimes even making the most obscure science fiction seem tame. The theory states that all matter is composed of tiny, oscillating loops of energy called strings. It continues to predict eleven spatial dimensions, enormous multi-dimensional membranes, and parallel universes. Unable to be tested experimentally, many scientists criticize string theory saying that it is not science, but philosophy.
Peter McNeill
Allegra Blake
English 201 TR 3:30
19 Apr. 06
Superstring Theory
For the last half century, physicists have been quietly aware of, as physicist Brian Green puts it, “a dark cloud looming over a distant horizon” (“Elegant” 3). Modern physics rests on two pillars, that is, two profound theories that describe matter and interactions at their most fundamental levels. Both of these theories have been rigorously and experimentally tested over many years and predict observations literally without failure. The problem lies in that both of these theories claim that the other one is incorrect. How can two theories, both seemingly correct and describing the same universe, be mutually exclusive? This problem bothered Albert Einstein immensely, although he understood the problem in a slightly different sense than physicists do today. It bothered him so much that he spent the last two decades of his life at his home in Princeton, New Jersey feverishly attempting to find a single “unified field theory.” This equation, or set of equations, would describe the universe in its entirety within one, breathtakingly elegant framework. Sadly, Einstein passed away before accomplishing his goal (Greene 62). Such a theory, a “theory of everything”, has become the holy grail of modern theoretical physics. Excitingly, many physicists today believe that Einstein’s dream may be realized by a relatively new theory, called superstring theory. Superstring theory, or string theory for short, takes an entirely different perspective than its preceding theories when describing the universe. The theory suggests a world stranger than science fiction, composed of tiny pieces of string, mysterious membranes, and eleven dimensions. Although many physicists believe string theory borders the realm of philosophy, others believe that it possesses the depth to describe the entire universe. This feat is achieved by string theory’s ability to unify both of the fundamental physical theories in a single framework.
Unification has been one of the most common words used to describe the goals of physics over the last century. All the physical theories, the theories to which we attribute all of our astonishing scientific and technological breakthroughs, seem to be converging on one, elusive idea. This idea, termed a unified field theory, is the ultimate goal of modern physics. This unification fad dates back to Isaac Newton in the 1600s (Hawking 17).
Born in 1642, Sir Isaac Newton is regarded today as one of the most influential theorists in the history of science. During his career Newton was interested in light and optics, as well as forces and motion. He is generally accredited with the development of calculus, a form of math which he required to describe his observations. Perhaps his greatest contribution to physics is his famous theory of gravity (“Brief” 5). As the story goes, Isaac was sitting under a tree one day when he noticed an apple fall to the ground. This started within him a brainstorm that would change the world forever. He postulated that the force pulling the apple to the ground was actually the same force that kept the heavenly bodies in orbit. He was able to describe this force, which he called gravity, mathematically and accurately predict observations associated with the force. With the fall of an apple, Newton had unified heavenly orbits and falling objects within a single force (“Brief” 6). His equations are so accurate that they are still used today. In 1969, using no more than Newton’s equations, the United States plotted the course of a rocket that landed people on the moon. Despite the enormous success of his equations, Newton harbored an embarrassing secret. Although his theory of gravitation very accurately describes the strength of gravity, it does not address the mechanism by which gravity actually works. This would remain a mystery for 250 years (“Fabric” 8).
In the early 1900s, Albert Einstein pondered the behavior of light. At age twenty six, Einstein discovered that the speed of light is a cosmological speed limit, that is, nothing can exceed the speed of light. This directly conflicted with Newton’s laws, which said that gravity acts instantaneously over any distance. Brian Green describes this conflict well using a hypothetical situation. Suppose that the sun disappeared one day instantly and without warning. Newton’s laws say that the planets would instantaneously leave their orbits and hurtle off into space (“Elegant” 65). But if nothing can exceed the speed of light, how can gravity? Einstein struggled with this problem for nearly ten years. Eventually, he began thinking of space and time in a revolutionary new way. Instead of looking at the three spatial dimensions and the dimension of time as being separate and unrelated, he combined them into a single entity which he called space-time. Einstein postulated that the fabric of space-time is able to stretch and warp due to mass. The warping of space-time due to mass, said Einstein, is what we know as gravity. This basic idea can be visualized by placing a basket ball on a taut blanket. The weight of the basketball causes it to sink into the blanket, warping the blanket’s once flat surface (“Elegant” 69). Einstein’s new theory of gravity, which he called general relativity, uses this concept to solve the discrepancy between his and Newton’s theories. Albert’s new theory states that the planets remain in orbit because they are following the contours of space-time warped by the mass of the sun. Returning to our hypothetical situation, relativity says that the disappearance of the sun would cause a wave in space-time, much like a wave in the ocean, which would travel at exactly the speed of light. This being so, we would not be affected by the suns sudden absence for about eight minutes, the time that it takes light to reach earth from the sun. This new theory established Einstein as one of the world’s greatest scientists (“Nutshell” 4).
Although pleased with his success, Einstein was not finished. He was still unsatisfied with the fact that the universe required several theories to describe it. Einstein felt that uniting his own general relativity, a theory of gravity, with James Clerk Maxwell’s theory of electromagnetism would be the next step (“Elegant” 88).
Maxwell had united electricity and magnetism only fifty years earlier. He realized that the two forces were related by a simple observation. Whenever a stream of charged particles flows, they produce a magnetic field. This can be seen by holding a compass during a thunderstorm. When lightning strikes nearby, you will notice that your compass needle begins to spin, reacting to the magnetic field produced by the charged electrons. With this in mind, Maxwell wrote down a set of four equations that united electricity and magnetism within a single force, just like Newton before him did with gravity (“Brief” 19).
Einstein felt that uniting general relativity with electromagnetism would yield a theory able to describe the entire universe, a goal shared by superstring theory. However, to his frustration, Albert found that the extreme difference in the strength of the forces outweighed their similarities. Although we tend to think of gravity as a powerful force, in reality, it is actually quite feeble (Gribbin 108). The muscles in your arm are able to overcome the pull of gravity of the entire earth exerted on an apple when you raise it to your mouth. Additionally, if you were to jump off of high ledge, the force of electromagnetism would easily overcome gravity and prevent you from crashing though the ground. The atoms in your body, as well as the atoms composing the ground, all have valence shell electrons with a net negative charge. The electromagnetic repulsion of the like charges is the force that prevents you from sinking into the ground in the previous example. It turns out that electromagnetism is actually some million billion billion billion billion (10^42) times stronger than gravity! This difference in strength prevented Einstein from unifying the two forces (“Elegant” 12).
Although Einstein’s relativity described things on a large scale very precisely, his equations broke down when addressing the microscopic world. Relativity’s equations perfectly described things that were large in size and mass such as planets, galaxies, or the universe as a whole. However, his equations couldn’t be used to describe things that are very small and have tiny masses such as atoms, electrons, and quarks. In the 1920s, a team of physicists headed by Niels Bohr solved this problem with their theory of quantum mechanics. This theory was just as successful in describing the microscopic world as relativity was in describing the macro world. What they found was that the “quantum” world is very different from the macro world. In the world of atoms and quarks, everything is ruled by probability. This is in direct contrast to the world that we experience in which everything is orderly and predictable. The best you can do in the quantum world is predict the probability of one outcome or another (Gribbin 46). All concepts such as left and right, up and down, even before and after break down on quantum scales. Quantum mechanics also predicts strange things such as that if you can not certainly say what will happen, then all possibilities must happen. It also says, in a concept called quantum tunneling, that if you walk directly into a wall, there is a calculable probability that you will simply pass through it unscathed. The probability of this occurring at the macro scale is so small, however, that you would need to do this for nearly an eternity for it to occur (“Elegant” 115). Einstein found quantum mechanics to be quite distasteful. He hated the idea that the universe is not predictable, a feeling he often expressed saying “God, does not roll dice” (“Nutshell” 26). Empirical evidence suggests that Einstein was wrong. Quantum physics has yet to provide one prediction that isn’t realized by observation (“Nutshell” 27).
This exciting new theory quickly became the focus of mainstream physics. With everyone lining up to study the microscopic world using this incredible new tool, Einstein was left to continue his work alone. While probing the structure of an atom, two new forces were discovered (Feynman 43). These forces were named the strong and weak nuclear forces. The strong nuclear force is responsible for “gluing” the protons and neutrons in the nucleus of an atom together. The weak nuclear force allows neutrons to turn into protons giving off radiation in the process (Feynman 44). The strength of these new forces was realized in 1945 at the Trinity test site in the desert of New Mexico. On July 2, the first nuclear bomb was tested at this site. The bomb, a little over five feet across, exploded with the force of 20,000 tons of TNT. This bomb contained a 6kg sphere of plutonium. The reaction was initiated by breaking the bonds of the strong nuclear force, tearing the plutonium nuclei apart and releasing vast amounts of destructive energy. Remnants of the explosion can still be detected today by means of the weak nuclear force. The radiation at the test site is to this day about ten times greater than normal (“Nutshell” 13). Quantum mechanics easily incorporated both of these forces into its framework.
With the inclusion of the nuclear forces into quantum mechanics, all of the fundamental forces were covered by just two theories. One may think that it is not necessary to unite general relativity and quantum mechanics because we can already use one or the other to describe anything we encounter. This is mostly true, but not quite. In everyday life, one or the other is generally enough to describe what we experience. When we look at things that are very large, like stars or galaxies, relativity is all we need. When we look at things that are very small, quantum mechanics takes over. It is only in certain extreme circumstances that neither theory alone is adequate. One such circumstance lies within a black hole (“Essays” 105). With the entire mass of a star crushed into an infinitesimally small space, it is ambiguous as to which theory should be used. Do we use relativity because it is extremely massive, or quantum mechanics because it is tiny on distance scales? The answer is that you can not escape using both. This presents a huge problem, probably the biggest in modern physics. When the two theories are combined, the results simply don’t make sense (“Essays” 107). General relativity and quantum mechanics both claim that the other theory is incorrect. With Einstein’s death in 1955, this problem left physics split into two camps. Physicists either studied the microscopic world using quantum mechanics, or cosmology using general relativity. It seemed that neither camp would be able to offer a complete description of the universe without unification.
The cogs of fate began to turn in 1968 as Gabriele Veneziano searched for an equation that described the strong nuclear force. He stumbled upon a two hundred year old equation written by a Swiss mathematician named Leonard Euler that seemed to do the trick (“Fabric” 339). His discovery was published in a paper which was in turn read by Leonard Susskind, a physicist. Susskind played with Euler’s equations and came to realize that they described a particle that had internal structure. Upon further investigation, he found that the equations represented a string that could not only expand and contract, but also undulate, or “wiggle.” Confident that this discovery would promote him as Einstein’s successor, he quickly submitted a paper for publication. The paper’s reception was very disappointing. The panel reviewing the paper concluded that it wasn’t very good and probably shouldn’t be published (“Fabric” 340).
Meanwhile, the mainstream branches of physics had developed an exciting new tool, the atom smasher. The colossal devises were being used to collide and “smash” atoms into a shower of constituent, sub-atomic particles. New sub-atomic particles were being discovered at an alarming rate - about one a week. Soon, so many particles had been discovered that physicists were running out of letters in several different alphabets with which to name them. This new framework of particle physics made a startling but exciting prediction - that not only matter, but forces can be explained in terms of particles. Particles, called messenger particles, are exchanged to produce what we know as force. For example, the electromagnetic force is associated with a messenger particle called a photon (Feynman 130). Similar messenger particles were found for the strong and weak nuclear forces. Using particles, scientists were again feeling that unification was within their grasp. This new model of particle physics was given the name of the Standard Model by physicist Stephen Weinberg. The Standard Model, however, still failed to include gravity (Feynman 132). The theory did make other exciting advances. Experiments showed that if we were to rewind time back to the extremely hot conditions just after the big bang, the electromagnetic force and the weak nuclear force would “melt” together into a single force known as the electroweak force. Although it is still yet to be proven, physicists also believe that if the clock was rewound further still, that the strong nuclear force would follow suit creating one superforce. Thus, the Standard Model allows us to describe all three forces in one language within quantum mechanics (“Fabric” 264). That is, it provides us with an understanding of how all three forces operate on a sub-atomic level.
As previously stated, string theory was completely overshadowed by the new Standard Model. The proponents of early string theory were tormented by a theory riddled with problems. The theory predicted strange things such as particles that travel faster than the speed of light, now known as tachyons (Magueijo 77). It also predicted ten spatial dimensions which were obviously more than existed. Lastly, it predicted a massless particle not seen in experiments. Despite all of these flaws, John Schwarz worked through the 1970s to solve the predicament of the massless particle and various math anomalies. He attempted things like changing the number of dimensions from ten to four, and eliminating the massless particles and tachyons altogether. All of his attempts resulted in failure. He played with the theory for four year before he had his revolutionary brainstorm. He wondered if his equations were actually describing gravity. In order for this to be true, Schwarz had to reconsider the size of a superstring. He was forced to conclude that stings must be 100 billion billion times smaller than a single atom (“Fabric” 340). According to Brian Greene, with this arrangement, if you made an atom the size of the entire universe, a superstring would be roughly the size of a tree. This rearrangement depicted the massless particle predicted by the theory as a graviton, the missing piece of the puzzle from the Standard Model (“Fabric” 343). With this new discovery, superstring theory was again submitted for publication. The reception of the paper was equally abysmal.
Around this time, Michael Green joined Schwarz in an attempt to rid the theory of its fatal math anomalies. Math anomalies are contradictory calculations. Greene again provides us with two equations to consider that represent this concept well. Pretend the equations 2x=2 and x/2=1 are equations of a single theory. Because solving the equations yields the results of x=1 and x=2 respectively, the theory has anomalies. Unless the theory can be rearranged in a manner that provides only one value of x, the theory is dead (“Fabric” 343). The future of string theory was determined five years after Greene and Schwarz began their work on a stormy night during the summer of 1984. The duo had one final calculation to complete in order to prove that string theory was free of mathematical anomalies. As the story goes, on one side of the blackboard, they arrived at an answer of 496. If the other side matched, the theory survived. To their delight, they calculated 496 on the other side as well proving that the math of string theory worked (“Fabric” 344). The newly anomaly free string theory seemed to have the mathematical depth to encompass all four fundamental forces. This is more than any previous theory was ever able to accomplish, and is what Einstein was attempting to do when he died. This time, string theory was met with explosive enthusiasm from the scientific community. Because of its ability to encompass all four forces, scientists happily proclaimed that it is a “theory of everything” (“Fabric” 344).
It appears that string theory is able to describe all constituent parts of matter. As we know, all matter is composed of atoms, which are made of protons, neutrons, and electrons. These particles can be further divided into even smaller particles called quarks. String theory predicts that quarks are composed of tiny, oscillating loops of energy called strings. Similarly to how the strings of a cello vibrate to produce the musical notes that we hear, strings vibrate to produce all the constituent components of matter (“Elegant” 263). When a string vibrates one way, it makes one particle, when it vibrates another way, it produces a different particle. With this concept in mind, Brian Greene often describes the universe as a “cosmic symphony.” Perhaps the most exciting characteristic of string theory is that it finally resolves the conflict between general relativity and quantum mechanics. Stings are able to calm the jittery behavior of the quantum world just enough that the two theories unite perfectly under a single framework. In order for it to do so, the theory must add six dimensions in addition to the three spatial dimensions and one of time to which we are accustomed (“Elegant” 263).
Sting theory is not the first to predict extra dimensions. In 1919, a German mathematician named Theodore Kaluza pondered Maxwell’s electromagnetic force. He thought that like gravity, electromagnetism may also be ripples in space-time (“Elegant” 185). The problem was that he needed a place for the ripples to occur. Kaluza solved this problem with the addition of one spatial dimension, sending his new theory to Einstein for approval. Einstein published the theory after two years of wavering, although he initially responded enthusiastically to the new theory. Building on Kaluza’s theory, a Swedish physicist by the name of Oscar Klein provided an explanation for why we are unable to perceive additional dimensions. His idea was that these dimensions are extremely tiny and folded up around each point in space (“Elegant” 188). Brian Greene describes this concept beautifully. Greene urges his readers to consider a telephone wire. From a distance, an observer is unable to tell that the wire has more than one dimension. It appears to be a line possessing only length. Upon closer inspection, one realizes that there is a circular dimension wrapped around the wire. If you were to imagine ants walking along the wire, they would be able to explore not only the dimension of length, but would also be able to walk around the circular dimension. Kaluza and Klein’s combined efforts became known as the Kaluza-Klein theory (“Elegant” 186).
Not only does string theory predict dimensions curled up in a fashion similar to the dimensions in Kaluza-Klein theory, but it also predicts their shape. The theory predicts that the dimensions are folded into tiny, six-dimensional shapes called Calabi-Yau manifolds (“Fabric” 368). This shape is actually very important in determining our everyday experience. Physicists estimate that there are twenty constants that, when changed, have drastic results. These numbers include things like the strength of gravity, strength of the electromagnetic force, or the mass of an electron. All of these properties are set by the manner in which strings vibrate. The way in which strings vibrate is greatly influenced by the shape of the extra dimensions. Strings vibrate within these dimensions and are thus only able to vibrate as the shape allows (“Fabric” 370).
Superstring theory drew so many physicists to the field that it actually became over developed. By 1985, physicists had developed not one string theory, but five of them. All of these “flavors” of the theory seemed equally valid. Some of these theories predicted open ended strings; others predicted that strings were closed loops. One theory even estimated the number of spatial dimensions to be 26! This created an unsettling paradox. How can one universe be described by five different theories? This notion simply does not make sense. As Brian Greene says, this was definitely a situation in which more was less (“Fabric” 370).
The theory was saved at an annual string theory convention held at the University of Southern California in 1995. Edward Witten gave a famous lecture in which he solved string theory’s identity crisis showing that the five different theories were actually five different ways of looking at the same thing. He named his unified string theory M-theory, although it is not clear what the “M” actually stands for (“Fabric” 378). When asked, Witten responded that it stands for magic, mystery, or matrix according to taste. Ed’s new theory renewed hope in the physics community that string theory could indeed be the theory of everything. In addition, M-theory required the yet another dimension, one which would have amazing ramifications (“Fabric” 379).
The newly added dimension allows stings to stretch into a membrane, or “brane” for short. Membranes can be three or more dimensional and with enough energy, these branes can grow to enormous size, even the size of the entire universe! Many physicists believe that our universe actually lives on one of these branes, which in turn lives in a higher dimensional space called the bulk (“Nutshell” 189). This theory speculates that we may be less than a millimeter away from parallel universes on other branes, but unable to perceive or interact with them. The reason for this is because the matter of which we are composed is confined to our membrane. Greene yet again provides us with a visual. He compares this situation to balls on a pool table. The balls are unable to leave the table, but there is one thing that escapes. Every time the balls collide sound wave leave the table, which is why we are able to her them (“Fabric” 384). Proponents of this theory believe that most matter, such as the matter of which we are made, is in turn composed of open ended superstrings. The ends of the strings are bound to the brane on which they exist. Gravitons, the messenger particles of gravity predicted by string theory, are open loops. This being so, gravity is able to leave the membrane, just as sound is able to leave the pool table. If this is correct, it accounts for the relative weakness of gravity to the other forces (“Fabric” 384). Perhaps gravity is just as strong, but diluted because of its ability to leave the membrane.
String theory’s largest criticism currently is that it has not yet proven to be testable. The distance scales are so small that it is unlikely that will ever be able to probe them. This is a huge problem in the real of science. Because there are no experiments that can be done to prove the theory incorrect, it is permanently “safe.” If string theory never proves to be able to be tested the way we test scientific theories, they it’s not science, its philosophy (“Fabric” 457). Many physicists still believe that sting theory will one day prove to be testable. Stephen Weinberg, one of the minds behind the Standard Model, says “I don’t think it has ever happened that a theory that has the kind of mathematical appeal that string theory does has turned out to be entirely wrong.”
A device that may be able to find evidence supporting string theory is currently being constructed on the borders of France and Switzerland by a firm called CERN. The Large Hadron Collider will be seven times more powerful than any atom smasher currently on Earth. Physicists hope to use this device to search for the graviton, extra dimensions, and another prediction of string theory called supersymmetry. Supersymmetry says that for every particle, there is a super heavy counter-particle called a sparticle (“Fabric” 355). These particles may be too heavy to be detected by modern smashers, but the LHC will provide the best bet.
The universe may not be as it seems, as is predicted by string theory. Science fiction may prove to be rather tame when compared to the actual universe. All matter may be composed of tiny, oscillating pieces of string and contain as many as eleven spatial dimensions. The future will most like show that our current understanding of the cosmos is, in fact, quite primitive. I leave it to the reader to decide whether string theory lies in the realm of physics or philosophy. Either way, physicists will always continue to study every facet of the universe, accepting nothing short of a complete understanding.
Work Cited
Born, Max. Einstein’s Theory of Relativity. New York: Dover, 1962.
Born describes Einstein’s theory of relativity in a fairly technical manner. He uses many diagrams and figures to aid in the reader’s comprehension of the subject matter, although it may still be difficult to grasp some of the concepts without formal training in math. This source was unbiased in that Born makes no assumptions and merely explains the principals of Einstein’s theory largely in mathematical terms. It was useful in solidifying my understanding of general and special relativity, but did not attempt to make the material understandable to the layman. This source proved to be mostly out of the scope of the paper.
Feynman, Richard. Six Easy Pieces. New York: Helix, 1994.
Richard Feynman was considered to be one of the most creative physicists of the post- World War II era. In his book he introduces the general reader to basic concepts of physics. These concepts include atoms in motion, basic physics, the relation of physics to other sciences, conservation of energy, the theory of gravitation, and quantum behavior. This source was useful in giving examples of how physics applies to other fields, and thus, the implication of string theory on other fields. It also gives layman’s descriptions of basic physical principals important in understanding string theory. The book is not biased - it merely states facts.
Greene, Brian. The Elegant Universe. New York: Random House, 2000.
Greene is one of the leading theoretical physicists of our time. This book covers a range of topics beginning with a basic explanation of the disagreement between general relativity and quantum mechanics. He continues to discuss further pertinent issues such as N-dimensional space, the need for a unifying theory, Calabi-Yau manifolds, quantum geometry, and future prospects of physics. Greene provides a comprehensive conceptual description of string theory. He explains all of these topics in layman’s terms so his readers are able to comprehend the material without an advanced degree in physics. The source is unbiased as Greene often points out that superstring theory is just a theory and has not yet proved to be testable. This source was very useful in that it follows the history of string theory in a linear fashion.
Greene, Brian. The Fabric of the Cosmos. New York: Random House, 2004.
This book builds on The Elegant Universe, but can be read and understood without having read it. In this source, Greene talks about the physical issues not covered in his previous title. He focuses more on the perception of reality, time as a dimension, cosmological string theory, M-theory, and concludes with more prospective applications of a complete understanding of physics. All of the topics covered in this book are predictions of string theory. Like his previous title, this is written in layman’s terms for an audience that may not be educated on the topic. This source is also unbiased and makes clear what is currently fact and theory.
Gribbin, John. The Search for Superstrings, Symmetry, and the Theory of Everything. New York: Little, Brown, and Company, 2000.
Gribbin begins with a description of alpha and beta radiation, which yielded our current understanding of atomic structure. He gradually uses momentum to lead into a discussion of quantum mechanics and string theory. In his chapter on quantum physics, he explores the Schrodinger’s cat paradox which is essential for understanding quantum superposition. This source was particularly helpful in the area of quantum physics. It gives an accurate description of events leading up to string theory of which an understanding is necessary for comprehension of the theory itself. This makes the source very useful. Gribbin describes the “very small” clearly and in layman’s terms. No biases were noticed in this source.
Hawking, Stephen. A Brief History of Time. New York: Bantam Books, 1988.
Hawking is a leader in his field. He currently holds the position of Lucasian Professor of Mathematics at the University of Cambridge - a position once held by Isaac Newton. This source elaborates on many areas in physics, doing so in a logical order leading up to an explanation of string theory. The text is accompanied by illustrations on almost every page that are extremely helpful as visual aids. Professor Hawking’s book is unbiased and was very helpful in that it provides many good analogies useful in explaining theoretical physics to the layman.
Hawking, Stephen. Black Holes and Baby Universes and Other Essays. New York: Bantam Books, 1994.
This book is a collection of essays on various abstract physics topics. The essays cover a variety of material, from Hawking’s childhood to the quantum mechanics of black holes. A majority of what is covered involves cosmology addressing questions such as “Is the end in sight for theoretical physics?” and “How did the universe form?” Because some of the essays depict Hawking’s personal stance on the subject matter, they are slightly biased. Not all of the essays are opinionated. This source is useful because it addresses some of the questions that string theory is attempting to solve.
Hawking, Stephen. The Universe in a Nutshell. New York: Bantam Books, 2001.
This is an extremely useful source. The layout of this book resembles a tree. The first two chapters comprise the trunk of the tree, while the remaining chapters serve as the branches. Hawking begins with an overview of relativity and time in chapters one and two respectively. In the remaining chapters he addresses issues such as “branes,” time travel, the curvature of space-time, black holes, supergravity, and M-theory. Each page contains several visual aids which are supremely helpful. This is the kind of book that will draw readers in regardless of how fond they are of physics.
Kaku, Michio. Hyperspace. New York: Doubleday, 1995.
Kaku has a similar writing style to Greene and also explains theoretical physics for the layman. He enjoys explaining abstract concepts such as hypercubes - fourth dimensional geometric shapes who’s shadow is a three dimensional cube. He describes the background of many physicists important in the development of string theory such as Einstein and Riemann. Kaku delves into the idea that time travel may be possible, and that wormholes may be used to travel through space-time. Finally, he discusses colliding universes as speculated by M-theory. Like Greene, Kaku clearly states that string theory makes incredibly accurate predictions, but is experimentally untested. This source was useful in describing several abstract concepts within the framework of string theory.
Kaku, Michio. Visions. New York: Random House, 1997.
This book discusses many scientific revolutions and is not limited to physics. The last four chapters, however, and dedicated to the quantum revolution. In these chapters Kaku discusses superstings, the 10 spatial dimensions, the big bang, and the possibility of a multiverse. This book is biased in that Kaku voices his opinion of “what may be to come”. Although informative, issues are not covered in as much depth as in Michio’s other title. Most of the material covered in this book is not within the scope of the paper.
Magueijo, Joao. Faster Than the Speed of Light. Cambridge: Perseus Publishing, 2003.
Magueijo is the mind behind a very controversial theory - that light once traveled faster than it does now. This theory contradicts Einstein’s mantra that the speed of light is a universal constant. Ironically, it solves many paradoxes generated by the big bang theory. This source is very useful in providing a different perspective that has not yet been incorporated in mainstream research. The theory shows just how primitive our understanding of our universe really is. This book is slightly biased in that it is one man’s perspective.
Schwarz, Patricia. The Official String Theory Web Site. 5 Apr. 2006
This website covers many areas of string theory. Additionally, everything can be viewed on two different levels comprehension: basic and advanced. The basic description is a layman’s terms explanation of the selected area while the advanced provides the mathematical equations and theory required for a full understanding of string theory. The site discusses areas such as the math of string theory, its history, important scientists in its development, cosmology, and experiments. This site was helpful in that it provides the equations with which string theory is described which is beyond the scope of many books and websites. It also provides links to videos that reinforce your understanding of various topics. Although this website does a good job explaining many aspects of string theory, other sources do it better.
Thorne, Kip. Black Holes & Time Warps. New York: Norton and Company, 1994.
This book starts with broad topics, such as the relativity of space and time, and eventually moves on to more specific ideas such as black holes. Thorne explains black holes in depth and uses them to describe the nature of wormholes. He also speculates that wormholes are possibly an avenue of time travel. All of these things are aspects of the physical universe that string theory attempts to explain. This book is biased in that much of it is speculation. As the title suggests, it is very useful in describing black holes. The material in this book is generally out of the scope of the paper.
Peter McNeill
Allegra Blake
English 201 TR 3:30
19 Apr. 06
Abstract
Amidst an incredible amount of recent scientific advancement, physicists have been aware of a devastating problem in modern physical theory. The two fundamental theories used to describe the universe both claim that the other in incorrect. This problem is solved by a process of unification, or the combining of the four fundamental forces into one conceptual framework. The theory that has come to provide such a framework is known as superstring theory. String theory makes a number of seemingly outrageous claims about the universe in which we live, sometimes even making the most obscure science fiction seem tame. The theory states that all matter is composed of tiny, oscillating loops of energy called strings. It continues to predict eleven spatial dimensions, enormous multi-dimensional membranes, and parallel universes. Unable to be tested experimentally, many scientists criticize string theory saying that it is not science, but philosophy.
Peter McNeill
Allegra Blake
English 201 TR 3:30
19 Apr. 06
Superstring Theory
For the last half century, physicists have been quietly aware of, as physicist Brian Green puts it, “a dark cloud looming over a distant horizon” (“Elegant” 3). Modern physics rests on two pillars, that is, two profound theories that describe matter and interactions at their most fundamental levels. Both of these theories have been rigorously and experimentally tested over many years and predict observations literally without failure. The problem lies in that both of these theories claim that the other one is incorrect. How can two theories, both seemingly correct and describing the same universe, be mutually exclusive? This problem bothered Albert Einstein immensely, although he understood the problem in a slightly different sense than physicists do today. It bothered him so much that he spent the last two decades of his life at his home in Princeton, New Jersey feverishly attempting to find a single “unified field theory.” This equation, or set of equations, would describe the universe in its entirety within one, breathtakingly elegant framework. Sadly, Einstein passed away before accomplishing his goal (Greene 62). Such a theory, a “theory of everything”, has become the holy grail of modern theoretical physics. Excitingly, many physicists today believe that Einstein’s dream may be realized by a relatively new theory, called superstring theory. Superstring theory, or string theory for short, takes an entirely different perspective than its preceding theories when describing the universe. The theory suggests a world stranger than science fiction, composed of tiny pieces of string, mysterious membranes, and eleven dimensions. Although many physicists believe string theory borders the realm of philosophy, others believe that it possesses the depth to describe the entire universe. This feat is achieved by string theory’s ability to unify both of the fundamental physical theories in a single framework.
Unification has been one of the most common words used to describe the goals of physics over the last century. All the physical theories, the theories to which we attribute all of our astonishing scientific and technological breakthroughs, seem to be converging on one, elusive idea. This idea, termed a unified field theory, is the ultimate goal of modern physics. This unification fad dates back to Isaac Newton in the 1600s (Hawking 17).
Born in 1642, Sir Isaac Newton is regarded today as one of the most influential theorists in the history of science. During his career Newton was interested in light and optics, as well as forces and motion. He is generally accredited with the development of calculus, a form of math which he required to describe his observations. Perhaps his greatest contribution to physics is his famous theory of gravity (“Brief” 5). As the story goes, Isaac was sitting under a tree one day when he noticed an apple fall to the ground. This started within him a brainstorm that would change the world forever. He postulated that the force pulling the apple to the ground was actually the same force that kept the heavenly bodies in orbit. He was able to describe this force, which he called gravity, mathematically and accurately predict observations associated with the force. With the fall of an apple, Newton had unified heavenly orbits and falling objects within a single force (“Brief” 6). His equations are so accurate that they are still used today. In 1969, using no more than Newton’s equations, the United States plotted the course of a rocket that landed people on the moon. Despite the enormous success of his equations, Newton harbored an embarrassing secret. Although his theory of gravitation very accurately describes the strength of gravity, it does not address the mechanism by which gravity actually works. This would remain a mystery for 250 years (“Fabric” 8).
In the early 1900s, Albert Einstein pondered the behavior of light. At age twenty six, Einstein discovered that the speed of light is a cosmological speed limit, that is, nothing can exceed the speed of light. This directly conflicted with Newton’s laws, which said that gravity acts instantaneously over any distance. Brian Green describes this conflict well using a hypothetical situation. Suppose that the sun disappeared one day instantly and without warning. Newton’s laws say that the planets would instantaneously leave their orbits and hurtle off into space (“Elegant” 65). But if nothing can exceed the speed of light, how can gravity? Einstein struggled with this problem for nearly ten years. Eventually, he began thinking of space and time in a revolutionary new way. Instead of looking at the three spatial dimensions and the dimension of time as being separate and unrelated, he combined them into a single entity which he called space-time. Einstein postulated that the fabric of space-time is able to stretch and warp due to mass. The warping of space-time due to mass, said Einstein, is what we know as gravity. This basic idea can be visualized by placing a basket ball on a taut blanket. The weight of the basketball causes it to sink into the blanket, warping the blanket’s once flat surface (“Elegant” 69). Einstein’s new theory of gravity, which he called general relativity, uses this concept to solve the discrepancy between his and Newton’s theories. Albert’s new theory states that the planets remain in orbit because they are following the contours of space-time warped by the mass of the sun. Returning to our hypothetical situation, relativity says that the disappearance of the sun would cause a wave in space-time, much like a wave in the ocean, which would travel at exactly the speed of light. This being so, we would not be affected by the suns sudden absence for about eight minutes, the time that it takes light to reach earth from the sun. This new theory established Einstein as one of the world’s greatest scientists (“Nutshell” 4).
Although pleased with his success, Einstein was not finished. He was still unsatisfied with the fact that the universe required several theories to describe it. Einstein felt that uniting his own general relativity, a theory of gravity, with James Clerk Maxwell’s theory of electromagnetism would be the next step (“Elegant” 88).
Maxwell had united electricity and magnetism only fifty years earlier. He realized that the two forces were related by a simple observation. Whenever a stream of charged particles flows, they produce a magnetic field. This can be seen by holding a compass during a thunderstorm. When lightning strikes nearby, you will notice that your compass needle begins to spin, reacting to the magnetic field produced by the charged electrons. With this in mind, Maxwell wrote down a set of four equations that united electricity and magnetism within a single force, just like Newton before him did with gravity (“Brief” 19).
Einstein felt that uniting general relativity with electromagnetism would yield a theory able to describe the entire universe, a goal shared by superstring theory. However, to his frustration, Albert found that the extreme difference in the strength of the forces outweighed their similarities. Although we tend to think of gravity as a powerful force, in reality, it is actually quite feeble (Gribbin 108). The muscles in your arm are able to overcome the pull of gravity of the entire earth exerted on an apple when you raise it to your mouth. Additionally, if you were to jump off of high ledge, the force of electromagnetism would easily overcome gravity and prevent you from crashing though the ground. The atoms in your body, as well as the atoms composing the ground, all have valence shell electrons with a net negative charge. The electromagnetic repulsion of the like charges is the force that prevents you from sinking into the ground in the previous example. It turns out that electromagnetism is actually some million billion billion billion billion (10^42) times stronger than gravity! This difference in strength prevented Einstein from unifying the two forces (“Elegant” 12).
Although Einstein’s relativity described things on a large scale very precisely, his equations broke down when addressing the microscopic world. Relativity’s equations perfectly described things that were large in size and mass such as planets, galaxies, or the universe as a whole. However, his equations couldn’t be used to describe things that are very small and have tiny masses such as atoms, electrons, and quarks. In the 1920s, a team of physicists headed by Niels Bohr solved this problem with their theory of quantum mechanics. This theory was just as successful in describing the microscopic world as relativity was in describing the macro world. What they found was that the “quantum” world is very different from the macro world. In the world of atoms and quarks, everything is ruled by probability. This is in direct contrast to the world that we experience in which everything is orderly and predictable. The best you can do in the quantum world is predict the probability of one outcome or another (Gribbin 46). All concepts such as left and right, up and down, even before and after break down on quantum scales. Quantum mechanics also predicts strange things such as that if you can not certainly say what will happen, then all possibilities must happen. It also says, in a concept called quantum tunneling, that if you walk directly into a wall, there is a calculable probability that you will simply pass through it unscathed. The probability of this occurring at the macro scale is so small, however, that you would need to do this for nearly an eternity for it to occur (“Elegant” 115). Einstein found quantum mechanics to be quite distasteful. He hated the idea that the universe is not predictable, a feeling he often expressed saying “God, does not roll dice” (“Nutshell” 26). Empirical evidence suggests that Einstein was wrong. Quantum physics has yet to provide one prediction that isn’t realized by observation (“Nutshell” 27).
This exciting new theory quickly became the focus of mainstream physics. With everyone lining up to study the microscopic world using this incredible new tool, Einstein was left to continue his work alone. While probing the structure of an atom, two new forces were discovered (Feynman 43). These forces were named the strong and weak nuclear forces. The strong nuclear force is responsible for “gluing” the protons and neutrons in the nucleus of an atom together. The weak nuclear force allows neutrons to turn into protons giving off radiation in the process (Feynman 44). The strength of these new forces was realized in 1945 at the Trinity test site in the desert of New Mexico. On July 2, the first nuclear bomb was tested at this site. The bomb, a little over five feet across, exploded with the force of 20,000 tons of TNT. This bomb contained a 6kg sphere of plutonium. The reaction was initiated by breaking the bonds of the strong nuclear force, tearing the plutonium nuclei apart and releasing vast amounts of destructive energy. Remnants of the explosion can still be detected today by means of the weak nuclear force. The radiation at the test site is to this day about ten times greater than normal (“Nutshell” 13). Quantum mechanics easily incorporated both of these forces into its framework.
With the inclusion of the nuclear forces into quantum mechanics, all of the fundamental forces were covered by just two theories. One may think that it is not necessary to unite general relativity and quantum mechanics because we can already use one or the other to describe anything we encounter. This is mostly true, but not quite. In everyday life, one or the other is generally enough to describe what we experience. When we look at things that are very large, like stars or galaxies, relativity is all we need. When we look at things that are very small, quantum mechanics takes over. It is only in certain extreme circumstances that neither theory alone is adequate. One such circumstance lies within a black hole (“Essays” 105). With the entire mass of a star crushed into an infinitesimally small space, it is ambiguous as to which theory should be used. Do we use relativity because it is extremely massive, or quantum mechanics because it is tiny on distance scales? The answer is that you can not escape using both. This presents a huge problem, probably the biggest in modern physics. When the two theories are combined, the results simply don’t make sense (“Essays” 107). General relativity and quantum mechanics both claim that the other theory is incorrect. With Einstein’s death in 1955, this problem left physics split into two camps. Physicists either studied the microscopic world using quantum mechanics, or cosmology using general relativity. It seemed that neither camp would be able to offer a complete description of the universe without unification.
The cogs of fate began to turn in 1968 as Gabriele Veneziano searched for an equation that described the strong nuclear force. He stumbled upon a two hundred year old equation written by a Swiss mathematician named Leonard Euler that seemed to do the trick (“Fabric” 339). His discovery was published in a paper which was in turn read by Leonard Susskind, a physicist. Susskind played with Euler’s equations and came to realize that they described a particle that had internal structure. Upon further investigation, he found that the equations represented a string that could not only expand and contract, but also undulate, or “wiggle.” Confident that this discovery would promote him as Einstein’s successor, he quickly submitted a paper for publication. The paper’s reception was very disappointing. The panel reviewing the paper concluded that it wasn’t very good and probably shouldn’t be published (“Fabric” 340).
Meanwhile, the mainstream branches of physics had developed an exciting new tool, the atom smasher. The colossal devises were being used to collide and “smash” atoms into a shower of constituent, sub-atomic particles. New sub-atomic particles were being discovered at an alarming rate - about one a week. Soon, so many particles had been discovered that physicists were running out of letters in several different alphabets with which to name them. This new framework of particle physics made a startling but exciting prediction - that not only matter, but forces can be explained in terms of particles. Particles, called messenger particles, are exchanged to produce what we know as force. For example, the electromagnetic force is associated with a messenger particle called a photon (Feynman 130). Similar messenger particles were found for the strong and weak nuclear forces. Using particles, scientists were again feeling that unification was within their grasp. This new model of particle physics was given the name of the Standard Model by physicist Stephen Weinberg. The Standard Model, however, still failed to include gravity (Feynman 132). The theory did make other exciting advances. Experiments showed that if we were to rewind time back to the extremely hot conditions just after the big bang, the electromagnetic force and the weak nuclear force would “melt” together into a single force known as the electroweak force. Although it is still yet to be proven, physicists also believe that if the clock was rewound further still, that the strong nuclear force would follow suit creating one superforce. Thus, the Standard Model allows us to describe all three forces in one language within quantum mechanics (“Fabric” 264). That is, it provides us with an understanding of how all three forces operate on a sub-atomic level.
As previously stated, string theory was completely overshadowed by the new Standard Model. The proponents of early string theory were tormented by a theory riddled with problems. The theory predicted strange things such as particles that travel faster than the speed of light, now known as tachyons (Magueijo 77). It also predicted ten spatial dimensions which were obviously more than existed. Lastly, it predicted a massless particle not seen in experiments. Despite all of these flaws, John Schwarz worked through the 1970s to solve the predicament of the massless particle and various math anomalies. He attempted things like changing the number of dimensions from ten to four, and eliminating the massless particles and tachyons altogether. All of his attempts resulted in failure. He played with the theory for four year before he had his revolutionary brainstorm. He wondered if his equations were actually describing gravity. In order for this to be true, Schwarz had to reconsider the size of a superstring. He was forced to conclude that stings must be 100 billion billion times smaller than a single atom (“Fabric” 340). According to Brian Greene, with this arrangement, if you made an atom the size of the entire universe, a superstring would be roughly the size of a tree. This rearrangement depicted the massless particle predicted by the theory as a graviton, the missing piece of the puzzle from the Standard Model (“Fabric” 343). With this new discovery, superstring theory was again submitted for publication. The reception of the paper was equally abysmal.
Around this time, Michael Green joined Schwarz in an attempt to rid the theory of its fatal math anomalies. Math anomalies are contradictory calculations. Greene again provides us with two equations to consider that represent this concept well. Pretend the equations 2x=2 and x/2=1 are equations of a single theory. Because solving the equations yields the results of x=1 and x=2 respectively, the theory has anomalies. Unless the theory can be rearranged in a manner that provides only one value of x, the theory is dead (“Fabric” 343). The future of string theory was determined five years after Greene and Schwarz began their work on a stormy night during the summer of 1984. The duo had one final calculation to complete in order to prove that string theory was free of mathematical anomalies. As the story goes, on one side of the blackboard, they arrived at an answer of 496. If the other side matched, the theory survived. To their delight, they calculated 496 on the other side as well proving that the math of string theory worked (“Fabric” 344). The newly anomaly free string theory seemed to have the mathematical depth to encompass all four fundamental forces. This is more than any previous theory was ever able to accomplish, and is what Einstein was attempting to do when he died. This time, string theory was met with explosive enthusiasm from the scientific community. Because of its ability to encompass all four forces, scientists happily proclaimed that it is a “theory of everything” (“Fabric” 344).
It appears that string theory is able to describe all constituent parts of matter. As we know, all matter is composed of atoms, which are made of protons, neutrons, and electrons. These particles can be further divided into even smaller particles called quarks. String theory predicts that quarks are composed of tiny, oscillating loops of energy called strings. Similarly to how the strings of a cello vibrate to produce the musical notes that we hear, strings vibrate to produce all the constituent components of matter (“Elegant” 263). When a string vibrates one way, it makes one particle, when it vibrates another way, it produces a different particle. With this concept in mind, Brian Greene often describes the universe as a “cosmic symphony.” Perhaps the most exciting characteristic of string theory is that it finally resolves the conflict between general relativity and quantum mechanics. Stings are able to calm the jittery behavior of the quantum world just enough that the two theories unite perfectly under a single framework. In order for it to do so, the theory must add six dimensions in addition to the three spatial dimensions and one of time to which we are accustomed (“Elegant” 263).
Sting theory is not the first to predict extra dimensions. In 1919, a German mathematician named Theodore Kaluza pondered Maxwell’s electromagnetic force. He thought that like gravity, electromagnetism may also be ripples in space-time (“Elegant” 185). The problem was that he needed a place for the ripples to occur. Kaluza solved this problem with the addition of one spatial dimension, sending his new theory to Einstein for approval. Einstein published the theory after two years of wavering, although he initially responded enthusiastically to the new theory. Building on Kaluza’s theory, a Swedish physicist by the name of Oscar Klein provided an explanation for why we are unable to perceive additional dimensions. His idea was that these dimensions are extremely tiny and folded up around each point in space (“Elegant” 188). Brian Greene describes this concept beautifully. Greene urges his readers to consider a telephone wire. From a distance, an observer is unable to tell that the wire has more than one dimension. It appears to be a line possessing only length. Upon closer inspection, one realizes that there is a circular dimension wrapped around the wire. If you were to imagine ants walking along the wire, they would be able to explore not only the dimension of length, but would also be able to walk around the circular dimension. Kaluza and Klein’s combined efforts became known as the Kaluza-Klein theory (“Elegant” 186).
Not only does string theory predict dimensions curled up in a fashion similar to the dimensions in Kaluza-Klein theory, but it also predicts their shape. The theory predicts that the dimensions are folded into tiny, six-dimensional shapes called Calabi-Yau manifolds (“Fabric” 368). This shape is actually very important in determining our everyday experience. Physicists estimate that there are twenty constants that, when changed, have drastic results. These numbers include things like the strength of gravity, strength of the electromagnetic force, or the mass of an electron. All of these properties are set by the manner in which strings vibrate. The way in which strings vibrate is greatly influenced by the shape of the extra dimensions. Strings vibrate within these dimensions and are thus only able to vibrate as the shape allows (“Fabric” 370).
Superstring theory drew so many physicists to the field that it actually became over developed. By 1985, physicists had developed not one string theory, but five of them. All of these “flavors” of the theory seemed equally valid. Some of these theories predicted open ended strings; others predicted that strings were closed loops. One theory even estimated the number of spatial dimensions to be 26! This created an unsettling paradox. How can one universe be described by five different theories? This notion simply does not make sense. As Brian Greene says, this was definitely a situation in which more was less (“Fabric” 370).
The theory was saved at an annual string theory convention held at the University of Southern California in 1995. Edward Witten gave a famous lecture in which he solved string theory’s identity crisis showing that the five different theories were actually five different ways of looking at the same thing. He named his unified string theory M-theory, although it is not clear what the “M” actually stands for (“Fabric” 378). When asked, Witten responded that it stands for magic, mystery, or matrix according to taste. Ed’s new theory renewed hope in the physics community that string theory could indeed be the theory of everything. In addition, M-theory required the yet another dimension, one which would have amazing ramifications (“Fabric” 379).
The newly added dimension allows stings to stretch into a membrane, or “brane” for short. Membranes can be three or more dimensional and with enough energy, these branes can grow to enormous size, even the size of the entire universe! Many physicists believe that our universe actually lives on one of these branes, which in turn lives in a higher dimensional space called the bulk (“Nutshell” 189). This theory speculates that we may be less than a millimeter away from parallel universes on other branes, but unable to perceive or interact with them. The reason for this is because the matter of which we are composed is confined to our membrane. Greene yet again provides us with a visual. He compares this situation to balls on a pool table. The balls are unable to leave the table, but there is one thing that escapes. Every time the balls collide sound wave leave the table, which is why we are able to her them (“Fabric” 384). Proponents of this theory believe that most matter, such as the matter of which we are made, is in turn composed of open ended superstrings. The ends of the strings are bound to the brane on which they exist. Gravitons, the messenger particles of gravity predicted by string theory, are open loops. This being so, gravity is able to leave the membrane, just as sound is able to leave the pool table. If this is correct, it accounts for the relative weakness of gravity to the other forces (“Fabric” 384). Perhaps gravity is just as strong, but diluted because of its ability to leave the membrane.
String theory’s largest criticism currently is that it has not yet proven to be testable. The distance scales are so small that it is unlikely that will ever be able to probe them. This is a huge problem in the real of science. Because there are no experiments that can be done to prove the theory incorrect, it is permanently “safe.” If string theory never proves to be able to be tested the way we test scientific theories, they it’s not science, its philosophy (“Fabric” 457). Many physicists still believe that sting theory will one day prove to be testable. Stephen Weinberg, one of the minds behind the Standard Model, says “I don’t think it has ever happened that a theory that has the kind of mathematical appeal that string theory does has turned out to be entirely wrong.”
A device that may be able to find evidence supporting string theory is currently being constructed on the borders of France and Switzerland by a firm called CERN. The Large Hadron Collider will be seven times more powerful than any atom smasher currently on Earth. Physicists hope to use this device to search for the graviton, extra dimensions, and another prediction of string theory called supersymmetry. Supersymmetry says that for every particle, there is a super heavy counter-particle called a sparticle (“Fabric” 355). These particles may be too heavy to be detected by modern smashers, but the LHC will provide the best bet.
The universe may not be as it seems, as is predicted by string theory. Science fiction may prove to be rather tame when compared to the actual universe. All matter may be composed of tiny, oscillating pieces of string and contain as many as eleven spatial dimensions. The future will most like show that our current understanding of the cosmos is, in fact, quite primitive. I leave it to the reader to decide whether string theory lies in the realm of physics or philosophy. Either way, physicists will always continue to study every facet of the universe, accepting nothing short of a complete understanding.
Work Cited
Born, Max. Einstein’s Theory of Relativity. New York: Dover, 1962.
Born describes Einstein’s theory of relativity in a fairly technical manner. He uses many diagrams and figures to aid in the reader’s comprehension of the subject matter, although it may still be difficult to grasp some of the concepts without formal training in math. This source was unbiased in that Born makes no assumptions and merely explains the principals of Einstein’s theory largely in mathematical terms. It was useful in solidifying my understanding of general and special relativity, but did not attempt to make the material understandable to the layman. This source proved to be mostly out of the scope of the paper.
Feynman, Richard. Six Easy Pieces. New York: Helix, 1994.
Richard Feynman was considered to be one of the most creative physicists of the post- World War II era. In his book he introduces the general reader to basic concepts of physics. These concepts include atoms in motion, basic physics, the relation of physics to other sciences, conservation of energy, the theory of gravitation, and quantum behavior. This source was useful in giving examples of how physics applies to other fields, and thus, the implication of string theory on other fields. It also gives layman’s descriptions of basic physical principals important in understanding string theory. The book is not biased - it merely states facts.
Greene, Brian. The Elegant Universe. New York: Random House, 2000.
Greene is one of the leading theoretical physicists of our time. This book covers a range of topics beginning with a basic explanation of the disagreement between general relativity and quantum mechanics. He continues to discuss further pertinent issues such as N-dimensional space, the need for a unifying theory, Calabi-Yau manifolds, quantum geometry, and future prospects of physics. Greene provides a comprehensive conceptual description of string theory. He explains all of these topics in layman’s terms so his readers are able to comprehend the material without an advanced degree in physics. The source is unbiased as Greene often points out that superstring theory is just a theory and has not yet proved to be testable. This source was very useful in that it follows the history of string theory in a linear fashion.
Greene, Brian. The Fabric of the Cosmos. New York: Random House, 2004.
This book builds on The Elegant Universe, but can be read and understood without having read it. In this source, Greene talks about the physical issues not covered in his previous title. He focuses more on the perception of reality, time as a dimension, cosmological string theory, M-theory, and concludes with more prospective applications of a complete understanding of physics. All of the topics covered in this book are predictions of string theory. Like his previous title, this is written in layman’s terms for an audience that may not be educated on the topic. This source is also unbiased and makes clear what is currently fact and theory.
Gribbin, John. The Search for Superstrings, Symmetry, and the Theory of Everything. New York: Little, Brown, and Company, 2000.
Gribbin begins with a description of alpha and beta radiation, which yielded our current understanding of atomic structure. He gradually uses momentum to lead into a discussion of quantum mechanics and string theory. In his chapter on quantum physics, he explores the Schrodinger’s cat paradox which is essential for understanding quantum superposition. This source was particularly helpful in the area of quantum physics. It gives an accurate description of events leading up to string theory of which an understanding is necessary for comprehension of the theory itself. This makes the source very useful. Gribbin describes the “very small” clearly and in layman’s terms. No biases were noticed in this source.
Hawking, Stephen. A Brief History of Time. New York: Bantam Books, 1988.
Hawking is a leader in his field. He currently holds the position of Lucasian Professor of Mathematics at the University of Cambridge - a position once held by Isaac Newton. This source elaborates on many areas in physics, doing so in a logical order leading up to an explanation of string theory. The text is accompanied by illustrations on almost every page that are extremely helpful as visual aids. Professor Hawking’s book is unbiased and was very helpful in that it provides many good analogies useful in explaining theoretical physics to the layman.
Hawking, Stephen. Black Holes and Baby Universes and Other Essays. New York: Bantam Books, 1994.
This book is a collection of essays on various abstract physics topics. The essays cover a variety of material, from Hawking’s childhood to the quantum mechanics of black holes. A majority of what is covered involves cosmology addressing questions such as “Is the end in sight for theoretical physics?” and “How did the universe form?” Because some of the essays depict Hawking’s personal stance on the subject matter, they are slightly biased. Not all of the essays are opinionated. This source is useful because it addresses some of the questions that string theory is attempting to solve.
Hawking, Stephen. The Universe in a Nutshell. New York: Bantam Books, 2001.
This is an extremely useful source. The layout of this book resembles a tree. The first two chapters comprise the trunk of the tree, while the remaining chapters serve as the branches. Hawking begins with an overview of relativity and time in chapters one and two respectively. In the remaining chapters he addresses issues such as “branes,” time travel, the curvature of space-time, black holes, supergravity, and M-theory. Each page contains several visual aids which are supremely helpful. This is the kind of book that will draw readers in regardless of how fond they are of physics.
Kaku, Michio. Hyperspace. New York: Doubleday, 1995.
Kaku has a similar writing style to Greene and also explains theoretical physics for the layman. He enjoys explaining abstract concepts such as hypercubes - fourth dimensional geometric shapes who’s shadow is a three dimensional cube. He describes the background of many physicists important in the development of string theory such as Einstein and Riemann. Kaku delves into the idea that time travel may be possible, and that wormholes may be used to travel through space-time. Finally, he discusses colliding universes as speculated by M-theory. Like Greene, Kaku clearly states that string theory makes incredibly accurate predictions, but is experimentally untested. This source was useful in describing several abstract concepts within the framework of string theory.
Kaku, Michio. Visions. New York: Random House, 1997.
This book discusses many scientific revolutions and is not limited to physics. The last four chapters, however, and dedicated to the quantum revolution. In these chapters Kaku discusses superstings, the 10 spatial dimensions, the big bang, and the possibility of a multiverse. This book is biased in that Kaku voices his opinion of “what may be to come”. Although informative, issues are not covered in as much depth as in Michio’s other title. Most of the material covered in this book is not within the scope of the paper.
Magueijo, Joao. Faster Than the Speed of Light. Cambridge: Perseus Publishing, 2003.
Magueijo is the mind behind a very controversial theory - that light once traveled faster than it does now. This theory contradicts Einstein’s mantra that the speed of light is a universal constant. Ironically, it solves many paradoxes generated by the big bang theory. This source is very useful in providing a different perspective that has not yet been incorporated in mainstream research. The theory shows just how primitive our understanding of our universe really is. This book is slightly biased in that it is one man’s perspective.
Schwarz, Patricia. The Official String Theory Web Site. 5 Apr. 2006
This website covers many areas of string theory. Additionally, everything can be viewed on two different levels comprehension: basic and advanced. The basic description is a layman’s terms explanation of the selected area while the advanced provides the mathematical equations and theory required for a full understanding of string theory. The site discusses areas such as the math of string theory, its history, important scientists in its development, cosmology, and experiments. This site was helpful in that it provides the equations with which string theory is described which is beyond the scope of many books and websites. It also provides links to videos that reinforce your understanding of various topics. Although this website does a good job explaining many aspects of string theory, other sources do it better.
Thorne, Kip. Black Holes & Time Warps. New York: Norton and Company, 1994.
This book starts with broad topics, such as the relativity of space and time, and eventually moves on to more specific ideas such as black holes. Thorne explains black holes in depth and uses them to describe the nature of wormholes. He also speculates that wormholes are possibly an avenue of time travel. All of these things are aspects of the physical universe that string theory attempts to explain. This book is biased in that much of it is speculation. As the title suggests, it is very useful in describing black holes. The material in this book is generally out of the scope of the paper.