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An introduction to string theory,
This review is from: The Little Book of String Theory (Science Essentials) (Hardcover)
This book starts with a brief introduction to the basic laws of physics, and the search for an ultimate theory to explain the physical reality. When the author starts describing the string theory, things get complicated. The reader must bear in mind that this is not an easy field to appreciate since it involves multi-dimensions of space and one time dimension; string theory has 26 dimensions, and superstring theory has 10 dimensions. Besides this, the fundamental particles exist as different vibrations of strings in multi spacetime. It is hard to envision how a four dimensional space would look like, and it would be even harder to appreciate the subject given the amount of mathematics that goes into constructing the theory. Although the book doesn't involve any mathematics but the author does his best to make the difficult subject interesting.
A brief summary of the book is as follows: In string theory, the myriad of fundamental particle types is replaced by a single fundamental building block, a string. These strings can be closed, like loops, or open, like a hair. A string is infinitely thin and has an infinitesimal length of 10e(-34) meters. As the string moves through time it traces out a tube or a sheet (the two-dimensional string worldsheet). Furthermore, the string is free to vibrate, and different vibrational modes of the string represent the different particle types. The particles known in nature are classified according to their spin into bosons (integer spin) or fermions (odd half integer spin). The bosons carry forces, for example, the photon carries electromagnetic force; the gluon carries the strong nuclear force, and the graviton carries gravitational force. Fermions make up the matter like the electron or the quark. The string theory described bosons, it does not describe fermions. By introducing supersymmetry to string theory, we can obtain a new theory that describes both bosons and fermions: This is the theory of superstrings. This theory requires that there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). But the problem with this theory is that there are five different superstring theories that display no mathematical inconsistencies and seem to explain bosons and fermions. It turns out that these five are different aspects of one single theory called M theory. This theory is also viewed as an 11 dimensional theory that looks 10 dimensions in spacetime, and propose a membrane as opposed to a string as the fundamental building block. The 11th dimension of the string expands infinitely into a floating membrane. According to this theory, our universe exists on a floating membrane, along with infinite parallel universes on their own membranes. Calculations also suggest that gravity might "leak" into our membrane from another nearby membrane. Thus, accounting for its relatively weak force in comparison to the other three forces (weak nuclear force, strong nuclear force, and electromagnetic force.) One would like to question how could a superstring theory with ten spacetime dimensions turn into a supergravity theory with eleven spacetime dimensions? The duality relations between two superstring quantities relate very different theories; they equate large distance of one theory with small distance of another theory, and exchange strong coupling of one theory with weak coupling of another theory. This seems to suggest that there is another fundamental theory lurking behind this mystery that holds the key for physical reality. Another interesting feature is the compactification of six spaces (out of nine) that account for our three spatial dimensions of our world and it also allows the generation of all known particles of matter.
The author notes three existing problems in physics by M theory; the tension in merging gravity and quantum physics; how strings vibrate and move in spacetime; and the evolution of spacetime from mathematical descriptions of strings. The greatest difficulties in unifying general relativity and quantum physics are due to the concept of renormalizabilty. When an electron is probed very close to it by an electric field, it splits into an electron and positron and a photon. The process multiplies due to its quantum physical uncertainties, and continues to form more photons and a cloud of progeny (virtual particles). The amazing thing is that you can keep track of this multiplicity of particles through renormalization, a mathematical method that tracks them all. The process also reduces (normalizes) the infinite mass and infinite charge of the electron (in the above picture) to its characteristic charge and mass. The trouble with gravitons is that you can't renormalize the cloud of virtual gravitons that surround them. For instance, quantum physical calculation of the force between two gravitons becomes infinite. But unlike particles, strings which also respond to one another like gravitons, but they do not form a cloud of virtual particles. This is because the particle interactions occur at a single point of spacetime (at zero distance between the interacting particles) leading to infinities. In string theory, the strings collide over a small but finite distance, and the string breaks smoothly over a distance. Thus we can combine quantum mechanics and gravity, and string excitation that carries the gravitational force with minimal problems.
Another interesting concept that emerges from superstring-graviton discussion is the concept of spacetime itself. Although the superstring theory predicts gravitons from flat spacetime physics (classical physics) alone, but superstring theory also predicts the Einstein equation will be obeyed by a curved spacetime in which strings propagate. Actually the theory adds an infinite series of corrections to the theory of gravity. At distance scales much larger than a string, these corrections are small. But as the distance scale gets smaller, these corrections become larger until the Einstein equation no longer adequately describes the result. This illustrates that the spacetime is not fundamental according to superstring theory, but it emerges only at large distance scales or weak coupling. This has a far reaching philosophical implication about the nature of physical reality that we understand from our interaction with spacetime and matter.
1. A First Course in String Theory
2. The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory