Physics: Superstring Theory Essay

Outline

This paper focuses on superstring theory and its evolution from the relevant string theories. It also describes the need for unification theory and influential theories like general relativity and quantum mechanics as well as KK theory in connection with string theory.

Introduction

Superstring theory is one of the theories that offered or opened the door to clear many of the misgivings the scientists have regarding the universe. Saying about the universe is one of the vast topics for scientists to achieve, even now regarding the universe, there are plenty of things floating here and there giving unresolved answers to the questions that arise about the universe. String theory offers a great kind of formulation for all kinds of forces that are present in the universe.

The significant thing about string theory is it provides plenty of information about different types of forces, where formulations got from the other theories cannot reach anywhere near the string theory. The proof obtained from this theory is great and indisputable. The solution got from this theory is flawless as mathematical formulas are depicted in this theory. The string theory otherwise can be called a complete theory of physics.

But, there are certain doubts among the scientists whether the string theory can describe or explain the universe with the collection of available forces and matters. The flaw with this theory is the predictions got from this theory may not be accurate but at the same time, it can give only the approximate value.

Being a theory of everything, the string theory can provide a solution for quantum gravity. In addition to this, it can describe various interactions occurring which are similar to electromagnetism and different forces present in nature. Also, superstring theory includes matters which are present as building blocks. This theory leads to various advancements in mathematics of knots, calabi-you-space, and numerous other fields. All these things improve or validate the string theory.

Historical background

Albert Einstein and his general and special relativity theory

Albert Einstein’s general relativity theory has got an important role in superstring theory. “In this theory, one finds a striking conceptual unification of the separate notions of space and time.” (Zwiebach, 2009, p.4). The things or rules got from this theory can be used to extract physical predictions. Einstein described different fundamental forces present in nature and one of the forces is a force of gravity. Einstein has reformulated this while explaining his theory of general relativity. “In this theory, the space-time arena of special relativity acquires a life of its own, and gravitational forces arise from the curvature of this dynamical space-time.” (Zwiebach, 2009, p.4).

Most of the scientists believe that from this standard model evolution of complete theory emerged. The String Theory is an extension of this Theory of Relativity and thus it can be validated and one can make sure there is no flaw in the theory.

Quantum Theory

The use of quantum theory emerged at the time of analyzing extra dimensions which is very small. For analyzing this, one needs to use the equation which was implemented by Schrödinger. The modification of general relativity theory has been done to “make it consistent with quantum mechanics.” (Zwiebach, 2009, p.58). But one thing that needs to be highlighted in this scenario is the “conceptual framework which underlies these modifications is not clear yet.” (Zwiebach, 2009, p.58). But there is no doubt that knowledge regarding the string theory can make this theory stupendous in coming years. The use of quantum mechanics also proves the effectiveness of the string theory.

Maxwell’s accomplishments and work on the multidimensional universe

Maxwell’s equations “unify electricity and magnetism into a consistent whole.” (Zwiebach, 2009, p.3). The electromagnetic force present in the universe is described with the help of Maxwell’s equations. “Electromagnetism, or Maxwell theory, is formulated as a classical theory of electromagnetic fields.” (Zwiebach, 2009, p.4) “Maxwell theory is fully consistent with special relativity.” (Zwiebach, 2009, p.4) With the help of this physicists have formed a quantization method that is used in the conversion of classical theory into quantum theory. This theory is used to calculate the principles that are involved in quantum mechanics. This can be otherwise termed quantum electrodynamics. This has been used with weak interaction and since it has come with a strong force, this can be called quantum chromodynamics. All these things together are called the standard model.

“Most physicists believe that the Standard Model is only a step towards the formulation of a complete theory of physics.” (Zwiebach, 2009, p.6). Apart from these, a more complete version of this model includes supersymmetry. This has been used in the study of the big bang and black holes. Thus, it has been used in the work of the multidimensional universe.

A briefing on Kaluza and Klein and KK-theory

Kaluza and Klein’s theory provides the relationship between the general theory of relativity and Maxwell’s equations which led to a discussion on the development of a newer field of particle physics. This also involves the usage of higher dimensions for describing various forces in nature. The general relativity theory has been derived to cover five dimensions. Thus, the ideas of String Theory began to develop as a part of the increasingly paced improvement in theoretical physics.

KK theory is also known as Kaluza-Klein theory in physics. This can be described as a model which plays an important role in unifying the two fundamental forces – gravitation and electromagnetism. The equations generated from this theory are two sets. One set is equivalent to the Einstein field equations and the other set is equivalent to Maxwell’s equation. Both these equations are meant for the electromagnetic field and both are used in the superstring theory.

Issues with working with quantum theory and general relativity together

There are some issues related to the working of quantum theory and general relativity together. General relativity does not hold for intense gravitational fields. This is the area where quantum theory is essential. General relativity is modified by string theory to make it reliable with quantum theory. General relativity describes the elements of the universe on a huge level.

The big bang theory, singularities

Big bang theory was proposed to explain the origin of the universe. The theory tells that the universe emerged as a singularity billions of years ago. Singularities are zones that are considered to exist at the center of the black holes. These zones have high densities. “Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something – a singularity.” (Bing bang theory- the premises, 2009, para.2)

Big bang theory states that the universe had been formed as a result of inflation. Initially, it was very small and very hot. Gradually, it started to expand and cool and reached the size and temperature of the present universe.

Dark matter and dark energy

The majority of the objects in the galaxies of the universe are invisible. Galaxies are the biggest structures in the universe and thus it is considered that the majority of the matters in the universe are invisible. This invisible matter is referred to as dark matter. Dark energy is the energy that helps in the expansion of the universe. Dark energy provides acceleration for the expansion of the universe.

Black holes and polar stars

A black hole is produced when the mass of an object increases but the size of the object stays the same or vice versa. It is an object that is collapsed gravitationally. It has been discovered that black holes exist in our universe. Scientists have recognized the existence of a supermassive black hole in the middle of our galaxy. Our galaxy contains millions and millions of black holes which are the leftovers of some stars which maybe even bigger than the sun. Quantum mechanics says that there is radiation of energy from black holes. Black holes also have thermodynamical temperature and entropy. The entropy is directly proportional to the square of its mass. String theory has helped in knowing about the entropy of black holes.

Theory of everything

The theory of everything is a theory that explains and connects all the physical phenomena in the world. It was a theory that was found out to expand the theory of general relativity and as a substitute to the theory of quantum mechanics.

Some work by leading string theorist Brian Greene and his work on the calabi-Yau manifold

Brian Greene is an American theoretical physicist who had studied mirror symmetry. The role of the Calabi-Yau manifold in string theory is important, which states that in addition to four space-time dimensions, there are six more dimensions present, which are not seen in other methods. String theory and mirror symmetry are important developments in the field of theoretical physics. Mirror symmetry can be called the relation that is present between two calabi-Yau manifolds. Sometimes, mirror symmetry is used to find out the difficulties of counting the curves on Calabi-Yau three folds and then by reducing the difficulty of calculation. The flop transition present in the calabi-yau model can become a mild form of topology. The changes happening in this can make a change in the conifold point.

Superstring theory has some predictions, formed from real actions. Superstring theory postulates that the small strings of energy in vibration help in the subsistence of matter at all levels. The matter results from the frequency and amplitude of these vibrations. Brian Greene showed that the topology can change at conifold. “Unlike manifolds, conifolds can contain conical singularities i.e. points whose neighborhoods look like cones over a certain base.” (Conifold, 2009, Para.1).

When a singularity develops within a manifold it becomes a conifold. They are important components in string and superstring theories. The geometrically singular conifolds can help in smooth strings. The exact low energy field theory uses the property of the singularity in the conifolds. These singularities are due to the masslessness of one or more particles. The transition of the conifolds is a type of topology change. This is caused due to the massless black holes at the conifold points. These black holes can come back as elementary particles. Thus, through the conifold transitions, the black holes and elementary particles can change into one another.

The change of topology happens in a non-singular way. The singularity of the conifolds can cause transitions in the topology of their neighbors. These transitions can help in the connection of Calabi-Yau manifolds. A Calabi-Yau manifold can be obtained either by resolving the conifold or deforming the conifold. The passing of the Calabi-Yau manifold through a conifold in the moduli space can change the topology of the Calabi-Yau manifold.

The string theory explains that there are more than three dimensions of space. It also explains why these extra dimensions are not recognized. One explanation is that they are not noticed because these dimensions are very small. When the dimensions that are extra take the form of a Calabi-Yau manifold, supersymmetry is exhibited. Mirror symmetry relates the conifold to orbifolds. A flop transition is a mild form of topology change that has shown that the topology can change at the conifold point.

The knowing of the string theory at the conifold points has been a huge development in string theory. It has shown that the topology can change without any harm. At this point, the string theory is smooth.

How does superstring theory explain the big bang?

The superstring theory explaifor the big bang. It explains that the universe began as a 10-dimensional universe without anything in it which was not stable. This 10-dimensional universe is broken into four and six-dimensional universes. The four-dimensional universe expanded and created the big bang while the six-dimensional universe has shrunken down into small sizes.

Relevance of string theory to superstring theory (m-theory)

Barton Zwieback gave an idea about string in his book “The first course in string theory” that String theory is one of the most exciting fields in theoretical physics.

(Zwiebach, 2009). This theory offers the potential of unifying gravity and all the other forces of nature and all forms of matter into one unified conceptual structure called strings. String theory is considered a quantum theory of gravity because it utilizes both Maxwell’s theory and the concept of gravity. The dimensionality of space-time is fixed in this case, which is an exceptionality of string theory. The dimensional parameters are not adjustable in this case, which is a unique feature of string theory. That means we can’t make any changes in this theory by changing the parameters.

Strings are of two types, open and closed. The difference between an open string and a closed string is that a closed string has no endpoints but an open string has two endpoints. Generally, we consider the theories of closed strings. The other division is the bosonic string theories and the superstring theories. Bosonic string theory is not realistic because of the lack of fermions. In the book a first course in string theory –the second edition the author Barton Zwieback narrates that “the superstrings live in ten-dimensional space-time, and their spectrum of states includes bosons and fermions.” (Zwiebach, 2009, p.8).

The bosons and fermions are associated with super-symmetry. The vibrating mode of gravity is present in all the string theories. Later, the 11 dimensional M Theory was developed by considering the strong coupling limit of the superstrings. Type I superstring theory comprises open and closed strings, with Supersymmetry N =1. It describes the disoriented string. SO (32) gauge symmetry is present in this theory. Type II A theory includes a closed string with N=2 symmetry which has got gauge symmetry. However, it is not capable of describing all states of particles in nature but can describe gravity and electromagnetism.

This theory considers two supercharges of opposite chirality. That is, each fermion has got a partner with opposite chirality (a particle with spin 1/2). Type II B theory gives an idea about closed, oriented strings with no gauge symmetry. It has got asymmetry of N=2 with fermions of the same chirality. Two heterotic theories are describing closed and oriented strings. It is a combination of bosonic and superstring theories.

In this mode, moving in one direction can be described using bosonic theory, and moving in the opposite direction can be illustrated with the help of super-symmetry N=1. Heterotic SO (32) means group symmetry is SO (32). But E8 x E8 means group symmetry is E8xE8. These five superstring theories are related to one another using some transformations called duality. In this, we consider two types of duality. They are T-duality (T stands for toroidal) and S-duality.

What are T-duality and its relevance to superstring theory

T-duality “relates a theory which is compactified on a circle with radius R, to another theory compactified on a circle with radius 1/R. Therefore when one theory has a dimension curled up into a small circle, the other theory has a dimension which is on a very large circle (it is barely compactified at all) but they both describe the same physics! The Type IIA and Type IIB superstring theories are related by T-duality and the SO (32) Heterotic and E8 x E8 Heterotic theories are also related by T-duality.” (Superstrings! String duality, n.d., para.2).

“S-duality relates the strong coupling limit of one theory to the weak coupling limit of another theory” (Superstrings! String duality, n.d., para.3)

That is, S-duality relates type I string theories and heterotic theories. This S- duality also relates the strong and weak coupling of the IIB string theory.

(Superstrings! String duality, n.d.). From this figure, it transpires that Type IIA and E8XE8 relate using the theory known as M-theory, which gives an idea about the existence of 11 space-time. It has no strings but it has a membrane and 5-branes.M-theory solves many difficult problems and it can describe the quantum effects in black holes. The major working area of duality is Maxwell’s theory. That is, in Maxwell’s theory dual transformation occurs between electric field and magnetic field.

Super-symmetry Validation in superstring theory

Super-symmetry is an important concept while considering the superstring theory. According to this concept, every particle has a super-symmetric colleague. They are known as particles. The super-symmetric partners are of the opposite type. But, no supersymmetric particles are observed now. Super-symmetry is an important concept while considering the superstring theory.

Superstring theory is an extended form of bosonic string theory. Supersymmetry gives an idea about the relationship between the fermions and the bosonic partner. In other words, every fermion has a bosonic partner and vice versa. Some examples include photon (spin1) has a superpartner called photino (spin1/2) and electron (spin1/2) has a superpartner called selectron (spin0). This theory removes tachyon from the spectrum and involves gravitation. So superstring theory can be generally perceived as an exposition of gravity and can be described by the number of supercharges, whether the strings are oriented or otherwise, and irrespective of whether they are open or closed strings.

How does vibrating string make up particles and matter in our universe?

String theory proposes that particles and matter are composed of vibrating strings. The elementary particles include electrons, photons, neutrinos, quarks. They are the different expressions of basic strings. The frequency of the spring is determined by the type of particle.

What is brane who formulated this theory, why?

Open strings are having free ends in the Neumann boundary condition while strings are attached between membranes called brane or D-brane or Dp-brane in the Dirichlet boundary condition. The p in the Dp-brane stands for the number of dimensions of the brane. Branes or D-branes are multidimensional membranes that are true physical objects in the string theory. The objects with dimensions higher than the lρ can be detected with the accelerators of particles and this validates the string theory. This proves the existence of string theory in theoretical physics.

Since the branes are multi-dimensional, they should exist in a higher-dimensional space itself. The space of higher dimensions is called bulk in which the branes are moving. Joseph Polchinski proved that D-branes are not static or stationary but are multi-dimensional objects which can have multi-dimensional movements. The most effective feature of brane cosmology is that it can explain the weakness of gravity which is related to fundamental forces present in nature. This is the basis of evidence for the validation of string theory.

Three brane and two brane and other brane formulations, a brief explanation

In the three-brane formulation, the open strings in the Dirichlet boundary condition are attached to D3-branes in which there are two space dimensions and a one-time dimension in the space-time domain. In the two-brane formulation, the strings are attached to D2-branes which have only one space as well as a one-time dimension in the space-time domain. The superstring theory formulates a 10-dimensional brane system i.e. D10-brane system. According to that, the open strings with Dirichlet boundary configurations have 9 space and one time dimensions.

The particle collider in Switzerland and its relevant connection to superstring theory validity

The large hadron collider (LHC) is located on the Franco-Swiss border near Geneva in Switzerland. It is placed in a tunnel that is 27km in circumference. This LHC is one of the largest and highest particle accelerators which are intended to collide with the particle beams which are opposing in nature. These particle beams can be either proton or lead nuclei. The main aim of building this collider is to test various predictions involved in high-energy physics. One kind of anticipation that spread over with this collider is that it tends to rule out the existence of the Higgs boson.

The existence of super-symmetry can be proved by the particle collider as it evaluates the various characteristics of the particles and branes which in turn validate the string theory.

Demonstration of unified forces? Possible experiments for proof of m-theory

The various theories on particle physics and forces between the particles are to be united to prove the validity of different theories on particles evolved. The combined theory known as the unification theory was formulated from the principles of quantum theory and general relativity. General relativity, as well as the quantum theory, validates the string theory while the combination of both gives a much stronger basis for the string theory.

The grand unified theory settles between the weaker forces of electric and magnetic fields as well as the strong force of attraction within the atoms. Thus, to be clear, it deals with the gravitational forces in the universe and hence it is also known as the theory of everything.

M-theory is an extension of string theory with D11-branes. According to this theory, there are ten spatial dimensions and a one-time dimension in the space-time domain. Since it has one dimension more than that available in the string theory, it is said to be an expansion of the string theory. M-theory is seen to be a unified form of all the five types of string theories available. Thus, the evolution of M-theory leads to the idea that more works are executed and extended in the field of string theory whose validation leads to a real-time development of particle physics.

Conclusion

“String theory has provided new and powerful tools for the understanding of conventional particle physics theories, gauge theories in particular.” (Zwiebach, 2009, p.11). There are lots and lots of studies yet to be conducted in this field. Still, many physicists admit the validation of the string theory and its major role in describing a variety of things. One thing is sure that this string theory has got a concrete base because this theory has emerged from the work of different eminent physicists. So, there is no doubt that it has got great power in finding many new things. This theory has shown the path or way for physicists and scientists to explore new things.

Reference List

Bing bang theory- the premises. (2009). All about Science. Web.

Conifold. (2009). Absolute Astronomy. Web.

Superstrings! String duality. (n.d.). Web.

Zwiebach, B. (2009). A first course in string theory: The road to unification. 2^nd ed. Cambridge University Press. 4.

Zwiebach, B. (2009). A first course in string theory: Gravitation and Planck’s length. 2^nd ed. Cambridge University Press. 58.

Zwiebach, B. (2009). A first course in string theory: The road to unification. 2^nd ed. Cambridge University Press. 3.

Zwiebach, B. (2009). A first course in string theory. 2^nd ed. Cambridge University Press.

Zwiebach, B. (2009). The first course in string theory: String theory as a unified theory of physics. 2^nd ed. Cambridge University Press. 8.

Zwiebach, B. (2009). A first course in string theory: Developments and outlook. 2^nd ed. Cambridge University Press. 11.