String Theory: A Short Introduction By Seamus O’Dunn Monday, October 22, 2012

Introduction What are fundamental strings? What are fundamental strings? String theory as a quantum theory of gravity. String theory as a quantum theory of gravity. Extra Dimensions. Extra Dimensions. Problems with verifying string theory. Problems with verifying string theory. Types of string theory. Types of string theory.

What are Fundamental Strings? ∝ cm

What are Fundamental Strings? n=1 n=5 n=4 n=2 n=3

An Interesting Feature String Theory provides an explanation for why we observe the properties we do in the standard model. String Theory provides an explanation for why we observe the properties we do in the standard model.

String Tension Tension is the one number string theory needs to set its scale. Tension is the one number string theory needs to set its scale. In 1974, Joël Scherk and John H. Schwarz proposed one particular pattern of vibration was the graviton. In 1974, Joël Scherk and John H. Schwarz proposed one particular pattern of vibration was the graviton. This indirect method predicts the tension on fundamental strings to be the Planck tension which is about tons. This indirect method predicts the tension on fundamental strings to be the Planck tension which is about tons.

Consequences of High Tension The enormous tension in fundamental strings makes them extremely short: only about cm (Planck Length). The enormous tension in fundamental strings makes them extremely short: only about cm (Planck Length). Indicates that the typical string has a huge amount of energy that is a multiple of the Planck mass, about 2.48 x GeV. Indicates that the typical string has a huge amount of energy that is a multiple of the Planck mass, about 2.48 x GeV.

If the minimal energy denomination of fundamental strings is much bigger than the proton, How can fundamental strings give rise to much lighter elementary particles such as the electron (1 eV)?

Quantum Effects The energy due to quantum mechanical vibrations of the string are negative and can cancel a large portion of the total energy. The energy due to quantum mechanical vibrations of the string are negative and can cancel a large portion of the total energy. Lowest energy vibrational patterns are largely cancelled. Lowest energy vibrational patterns are largely cancelled. The cancellations for the graviton proposed by Scherk and Schwarz work out perfectly. Leaving a zero mass force carrier for gravity. The cancellations for the graviton proposed by Scherk and Schwarz work out perfectly. Leaving a zero mass force carrier for gravity. This is a special case, most fundamental string vibrational patterns yield particles with extremely high masses. This is a special case, most fundamental string vibrational patterns yield particles with extremely high masses.

Many Elementary Particles String theory predicts that every vibrational resonance pattern corresponds to a different elementary particle. String theory predicts that every vibrational resonance pattern corresponds to a different elementary particle. All but a few of these correspond to extremely massive particles. All but a few of these correspond to extremely massive particles. These larger particles could have been around during the big bang, but have since lost energy and decayed into smaller particles. These larger particles could have been around during the big bang, but have since lost energy and decayed into smaller particles.

String Theory as a Quantum Theory of Gravity In quantum field theory, interactions between elementary particles take place at the same point in space. In quantum field theory, interactions between elementary particles take place at the same point in space. The graviton’s scattering amplitude goes to infinity when it interacts with other particles at zero distance. The graviton’s scattering amplitude goes to infinity when it interacts with other particles at zero distance. This is a nonsensical result. The point-like representation of the graviton is not compatible with the mathematics of quantum field theory. This is a nonsensical result. The point-like representation of the graviton is not compatible with the mathematics of quantum field theory.

String Theory as a Theory of Quantum Gravity

String Theory as a Quantum Theory of Gravity Interactions between strings can never be on scales smaller than Planck length. Interactions between strings can never be on scales smaller than Planck length. After a certain limit the energy given to a string will start to overcome the Planck tension, becoming larger. After a certain limit the energy given to a string will start to overcome the Planck tension, becoming larger. Since interactions are not at zero distance, the string formulation of the graviton fits into the equations of quantum field theory. Since interactions are not at zero distance, the string formulation of the graviton fits into the equations of quantum field theory.

Extra Dimensions For current string theory to mathematically consistent, it requires there be 10 space-time dimensions. For current string theory to mathematically consistent, it requires there be 10 space-time dimensions. One explanation is compactification: That there are 6 tiny extra curled up dimensions about each point in space. One explanation is compactification: That there are 6 tiny extra curled up dimensions about each point in space.

Problems With String Theory The energy levels needed to see string theory predictions are of the order of Planck energy, GeV. The LHC at CERN, currently our highest energy accelerator, is only capable of 7 x 10 3 GeV. The energy levels needed to see string theory predictions are of the order of Planck energy, GeV. The LHC at CERN, currently our highest energy accelerator, is only capable of 7 x 10 3 GeV. There was a period where there were 5 different string theories that all seemed to explain quantum gravity. There was a period where there were 5 different string theories that all seemed to explain quantum gravity. From a theoretical standpoint, finding low energy vibrational patterns is extremely hard. There exists no easy way in our current mathematics to derive them. From a theoretical standpoint, finding low energy vibrational patterns is extremely hard. There exists no easy way in our current mathematics to derive them. In the 40 years of string theory’s lifetime, it has failed to produce a testable prediction. In the 40 years of string theory’s lifetime, it has failed to produce a testable prediction. It will be a very long time before aspects of string theory can be directly verified. It will be a very long time before aspects of string theory can be directly verified.

A Brief Table of String Theories

M-Theory

Summary String theory proposes that matter at its most basic level can be described as a vibrating string. String theory proposes that matter at its most basic level can be described as a vibrating string. Its formulation unifies gravity and quantum theory. Its formulation unifies gravity and quantum theory. For string theory to be mathematically consistent, it requires that there be 6 space-time dimensions in addition to the four we know. For string theory to be mathematically consistent, it requires that there be 6 space-time dimensions in addition to the four we know. It is a beautiful and elegant theory, but close to 40 years without a single testable prediction should, perhaps, place it in the realm of philosophy rather than physics… For now. It is a beautiful and elegant theory, but close to 40 years without a single testable prediction should, perhaps, place it in the realm of philosophy rather than physics… For now.

References Greene, Brian. The Elegent Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. 1st Edition. New York: Vintage Books, Print. Greene, Brian. The Elegent Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. 1st Edition. New York: Vintage Books, Print. The Elegent Universe- pbs Documentary The Elegent Universe- pbs Documentary “Basics,” “Basics,”