long, hastily (and probably poorly) written paper about string theory

String Theory: Overview, Main Characteristics, and Problems

While the standard model paints a picture of particle constituents as isolated points in space, string theory views particles as composed of strings that occupy roughly a Planck length in one dimension. String theory posits that the properties of the particles we observe are bestowed by the different vibrational frequencies of these strings. For instance, lighter particles are composed of strings with fewer oscillations. String theory also explains constraints on particle masses: the number of possible heavy particles is limited by upper limits on vibrational frequency due to high string tension. Given this high string tension, unique particles in string theory are predicted to be too heavy to be detected in current particle accelerators, although the reopening of the LHC poses some hope for detection. String theory predicts both open and closed strings, although the nature of the parameter differs between the different subtypes of the theory. The essential sameness of the constituents of all matter allows string theory to unify all of the disparate particles in the standard model, and unlike the standard model, it provides reasons for the properties of those particles. Thus string theory claims to unify all forces at high energy levels, a feat required for a grand unified theory that can explain the universe from its more homogeneous origin.

The history of string theory has been fraught by both great excitements and great disappointments. It commenced in 1968 when the Italian physicist Gabriele Veneziano realized the Euler beta function described strongly interacting particles. In 1970, physicists Yoichiro Nambu of the University of Chicago, Holger Nielson of the Niels Bohr institute, and Leonar Susskin of Stanford refined Veneziano’s idea by announcing that if matter were made up of tiny vibrating strings, it could be described by the Euler beta function. This original version of string theory was specific to bosons, and it predicted a vibrational frequency corresponding to a particle dubbed the tachyon. The tachyon had a negative mass and thus traveled faster than the speed of light. Because this didn’t mesh well with special relativity, it was a great problem with the theory. Physicists Ramond, Neveu, and Schwarz solved this problem by suggesting that the strings were supersymmetric, or containing particle pairs that differed by a spin of ½. This allowed the theory to account for fermions, particles with a spin of ½. John Schwarz and Joel Schenk discovered in 1974 that the modified model also predicted a particle with a spin of 2 whose vibrational properties were consistent with a graviton, the force-carrying particle associated with gravity. This discovery made string theory a candidate for the unification of relativity and quantum theory. It was also discovered that supersymmetry only made mathematical sense (producing non-negative probabilities) in ten dimensions. Physicists Gross, Harvey, and Martinec further improved the theory with the idea of the heterotic superstring, a chiral theory that treated different wave directions differently and yielded more predictions. However, the theory only retained its chirality if the six non-visible dimensions were not curled up as supposed, an existent theory of manifold dimensions that dated back to Kaluza in the early 20th century. So in 1985 Philip Candelas, Gary Horowitz, Andy Strominger, and Edward Witten suggested that the dimensions are actually curled up in Calabi-Yau manifolds, more complicated six-dimensional structures. This first superstring revolution occurred from 1984 to 1986. The revolution was characterized by the exciting emergence of the standard model from string theory. However, the approximation methods used to complete the immensely complicated mathematics of the theory soon became insufficient. 1995 showed the beginning of the second superstring revolution, or rather the era of M-theory/brane-theory, an idea suggested by Edward Witten as a means to unite the differing string theories through dualism. Modern research in string theory consists in elucidating the implications of M-theory.

One of the techniques used to make string theory consistent is super symmetry. Super symmetry is the idea that particles come in different spins, i.e. that for each vibrational frequency there are two particles with spins differing by ½. Since no known particles fit the characteristics of these predicted particles, there must be as-yet unobserved super-symmetric partners to all observed particles. Super symmetry is suggested by cancellations that occur in the quantum mechanical contributions of fermions and bosons. These cancellations can be explained by adjusting parameters in the standard model, but they can be more cleanly explained by super symmetry. Super symmetry can also modify the strength of forces at small distances, allowing for unification between these forces, an ever-present goal of physics. Super symmetry seems to bring physics closer to the tantalizing goal of unification. The more compelling reasons for the implication of super symmetry, however, were already briefly mentioned: super symmetry allows for spin ½ particles (by predicting pairs of particles that differ by spin ½), and it also eliminates the prediction of the tachyon. Thus there are compelling arguments for super symmetry both outside of and within string theory.

Another important characteristic of string theory is the requirement for extra dimensions. Extra dimensions within string theory allow for more directions of vibration necessary for the diversity of predicted particles. It also contributes to symmetry by making a choice of coordinates on the world sheet swept out by the string through time equivalent to any other choice. Additionally, without extra dimensions, string theory math would yield negative probabilities. The idea of extra dimensions began with Kaluza and Klein in 1919. They suggested a tiny, curled dimension, or manifold, in addition to the three spatial dimensions and the time dimension. Additional modifications of this theory use spheres or the donut-shaped torus for the manifolds. The specific geometry of these manifolds predicts the properties of particles in string theory. When the general Kaluza-Klein model didn’t fit with the chirality of the heterotic string or the properties of observed particles, Calabi-yau spaces were suggested. Calabi-yau manifolds are six-dimensional shapes whose physical properties yield the properties of the particles that we observe. Thus extra dimensions were necessary in string theory to explain the properties of our universe and make the string theory mathematics consistent.

Despite all of the predictions and promises of string theory, it also contains a lot of problems. Perhaps the largest problem is that there are many worlds consistent with string theory, and the actual constants that arise in our universe are arbitrary within the theory. String theory gives us a landscape of possibilities rather than predicting our exact universe. This can be countered with the anthropic principle, the idea that there are other worlds but we just happen to be in this one, but that is a weak scientific argument with little explanatory power. Additionally, there are multiple ways of incorporating super symmetry into string theory, partially creating the different subtypes of the theory. There is also the issue that super symmetry itself is not observed in our low-energy universe, but if it is considered broken, then string theory predicts the cosmological constant inaccurately (predicting that it is non-positive when it is experimentally shown to be positive). Along the same lines, there are many possible parameters for the Calabi-yau spaces, and the selection of these parameters also seems arbitrary. The number of dimensions is also chosen in order to make the theory consistent rather than for any physical reason. Another problem is that string theory doesn’t explain the vacuum energy that accounts for the slow acceleration of space. It also doesn’t predict dark energy, discovered in 1998. Finally, it lacks a method of empirical proof, although there is some putative evidence that could arise at LHC.

The modern improvement upon string theory is brane theory, the subject of the second revolution. Brane theory adds an extra dimension, making a total of eleven dimensions, and allows for both the existence of two-dimensional membranes of all shapes and sizes as well as one-dimensional strings which are attached to the membranes. Gauge bosons and fermions are the result of open strings (both ends attached to the membrane), so they are confined to the brane, but gravitons are the result of closed strings, so they can travel between branes within the dimensions (strings stretch between branes). The reason brane theory was so exciting was that it proposed dualities that unified the subtypes of string theory. First, there is a duality of strongly interacting 10-dimensional superstring theory and weakly interacting brane theory, meaning it is the same theory with different descriptions. This duality allows calculations made within one theory to apply to the other theory. The different subtypes of 10-dimensional string theory are also connected by dualism. One type of dualism is S duality, which is a symmetry between the strong and weak coupling regimes. Some of the types of string theories are related by S duality. T duality occurs when swapping momentum modes with strong interactions yields equivalent states. Some of the types of string theory are related by T duality. The discovery of these relations between the subtypes of string theory and between string theory and brane-theory show that all of these theories are only superficially different; they are actually equivalent theories.

Although string theory has a fascinating history and promises to produce a feasible unified theory of gravity, it contains many problems that have caused modern physicists to abandon the effort in lieu of more contemporarily promising alternatives such as loop quantum gravity. Despite its shortcomings, however, string theory, and its consummation M-theory, has allowed for great advancements in the field of theoretical physics and seems likely to offer more in the future.


Works Consulted
Greene, Brian. The Elegant Universe Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: Vintage, 2000. Print.
Greene, Brian. The Fabric of the Cosmos Space, Time, and the Texture of Reality. New York: Vintage, 2005. Print.
Randall, Lisa. Warped Passages Unraveling the Mysteries of the Universe's Hidden Dimensions. New York: Harper Perennial, 2006. Print.
Smolin, Lee. The Trouble With Physics The Rise of String Theory, The Fall of a Science, and What Comes Next. New York: Mariner Books, 2007. Print.
Stephen, Webb,. Out of this world colliding universes, branes, strings, and other wild ideas of modern physics. New York: Copernicus Books in association with Praxis, 2004. Print.