Physics

Assessing the viability of using String Theory as a model of Quantum Gravity

Abstract

This report will assess the significance of String Theory regarding the development of humankind’s understanding of Gravity. It will attempt to explain the reason for the need of string theory, based on the shortcomings of Quantum Theory and the General Theory of Relativity. A major advance in String Theory was Juan Maldacena’s discovery of the Anti de Sitter/Conformal Field Theory correspondence which I shall demonstrate can be used to model gravity in a more accurate way within this report. Moreover, the way that String Theory can explain gravity is important in how it can describe Black Holes as well as issues solved or caused by this model of the universe. In this report, I will cover certain issues caused by using a model such as String Theory as well as discussing the problems that can be solved via the use of String Theory. I also intend for this report to be a more easily accessible resource to introduce the layman to the uses of String Theory in Quantum Gravity.

 

Contents

1 Introduction 

2 Literature review  

3 String Theory   

3.1 Fundamentals of String Theory

3.2 Introducing the AdS/CFT Correspondence

3.3 Matter Fields and QFT

4 The Application of String Theory to Gravity                                               

4.1 Background

4.2 The AdS/CFT Correspondence and Gravity

4.3 Black Holes

4.4 Problems with String Theory

4.5 Alternatives to String Theory

5 Conclusions

6 Acknowledgements

7 References

 

1 Introduction

For the past 100 years, two major theories have ruled physics: Quantum Mechanics, which describes the small-scale structure , and General Relativity, which describes the massive structure . Both theories are very well respected scientific theories which have been experimentally tested many times and have proven their worth. However, our description of the universe isn’t quite as perfect as it seems because despite the advantages that the two theories have, a major concern is that these two theories are inconsistent with each other. Neither framework is perfect, Quantum Field Theory (a field framework within QM) fails to incorporate the dynamic nature of spacetime, whereas, General Relativity ignores quantum fluctuations. This means that neither theory is truly perfect and thus, the search for a unified theory of Quantum Gravity is absolutely necessary in order for our understanding of the universe to advance. This is where String Theory is considered a possible way to remove the paradoxes within our idea of the universe and unify the two theories to explain interactions involving the very large and the very small.

 

2 Literature review

One of the most significant resources in preparing this report was the famous ‘A Brief History of Time’ by Stephen Hawking. It explains the significant properties of Quantum Mechanics and General Relativity in relevance to our understanding the universe. It is an effective resource in demonstrating the basic principles which define black holes, especially the work that was done by Hawking himself in this field. This was also a very accessible source of information on String Theory as it explains it in understandable language without the use of simplifications. However, the book does not delve as far as is necessary to fully understand the application of String Theory to Quantum Gravity. It was a very helpful source of information when writing the introduction and section 3.1. Brian Greene drew very similar conclusions about the inadequacy in the lack of correlation between Quantum Mechanics and General Relativity and the necessity for a new theory to bridge the gap in his book ‘The Elegant Universe’. Another source which presents similar information to the others is Michio Kaku’s presentation ‘The Universe in a Nutshell’, it discusses the aforementioned inadequacies of current scientific knowledge alongside discussions of how String Theory can be a remedy for these and other problem areas in our concept of the universe. However, where Hawking offers the Theory as an interesting idea that could be a possible way to resolve the issues. Greene and Kaku seem to imply within their respective works that there is no other answer that is closer to the truth than String Theory. Kaku even went as far as to state “String Theory is the only game in town” in an interview with BigThink.

Section 3.2 is based around one of the most significant developments to come from String Theory, the correspondence between the physics of Anti de Sitter space and Conformal Field Theory, discovered by Juan Maldacena in 1997. It is the logical that one of the sources that I used to write this section would be a lecture by Mr Maldacena himself on the AdS/CFT correspondence. This lecture was very technical and was additionally beneficial in section 4.2 regarding linking the AdS/CFT to how String Theory can be used to model Quantum Gravity. It is, however, a very technical and complex method with which to describe the AdS/CFT correspondence. To gain a more basic understanding of AdS/CFT, I used a simpler source, that being a lecture given by Amanda Peet at the Premier Institute which was a very in depth and easily accessible source of information on AdS/CFT and its application. It is the source which gave me the essential model of the stack of 3-branes which allowed me to properly understand the core logic of the correspondence.

A brief inclusion in this report that I deemed necessary was section 3.3 based on Matter Fields and Quantum Field Theory. This was important as Mr Vemury informed me that whilst I had discussed matter fields in section 3.1, I had not fully explained their relevance in String Theory. The resource that I used for this is was a lecture given by David Tong about matter fields and QFT.

Section 4.1 was a minor inclusion to allow for an explanation into what the necessary features of Quantum Gravity are due to the fact that it is a necessary part of Physics to research as it explains the past and how we can use it to predict the future. For this, Brian Greene’s works which have previously been mentioned were an effective resource in demonstrating how to begin to build up knowledge so that it can be developed upon later.

The lecture by Juan Maldacena also had relevance in section 4.2 as it was a more complex inclusion of gravity to the correspondence and despite incredibly complex mathematics, it was very useful resources for allowing this report to explain the more complex aspects of Maldacena’s work. Another set of resources that I used was the MIT open ware, it’s a set of lectures on String theory which was effective in building up my knowledge on all parts of writing the report. Most notably, the lecture by a lecturer only listed as McGreedy about the geometry of AdS and how it applies to CFT. It explains how the geometry is effective at allowing gravity to only exist on one side and how the decoupling limit explains this due to the existence of gravitons, the boson for gravity, as closed strings, gravity can be separated from matter. Moreover, a lecture at the Nag Conference in 2015 by Shiraz Minwalla entitled ‘String Theory and the Gauge Gravity Correspondence’ was an effective source at demonstrating the AdS/CFT correspondence’s uses to map String Theory onto LQG. It was also useful for sections 1, 3.1 and 3.2 as it starts with a simple introduction as to where String Theory fits into our model of the universe and builds to more complex levels. This is very effective when writing a report attempting to make it easier to learn String Theory.

The lecture given by Amanda Peet, as mentioned earlier, gave some very effective models which allow the average person to decode the complex science that rules these theories. One such model was using branes to explain the way in which a 5-dimensional black hole exists and more importantly, how a black hole can be made up of strings, whilst this source had a very limited amount of information on the fuzzball proposal, it had one of few that an average person would be able to view and understand fuzzballs in black holes. Samir Mathur prepared an excellent PDF explaining the fundamentals of the fuzzball proposal. The difficulty here is that at a beginner level, the only significant information about the fuzzball proposal is that it resolves the problem which is that our current understanding of a black hole is that a singularity exists within the centre and it has a presumed density that tends to infinity. This makes the laws of science break down. The major way that fuzzballs resolve this is to describe a black hole as a large bundle of strings intertwined covering the entire event horizon. Beyond this, it is difficult to find resources which explain much more without expanding to extreme levels. The websites PhysicsWorld.com and PhysicsoftheUniverse.com were some of the only resources that explained these paradoxes relevant to String Theory and they didn’t explain in very much detail how they were fixed by describing a fuzzball. It took all of these resources to build a basic description of fuzzballs and how they are important with the lecture and the PDF being the most crucial parts of the writing.

Brian Greene’s documentary adaptions of his book ‘The Elegant Universe’ titled ‘Welcome to the 11th Dimension’ was effective in explaining the work of scientists at Fermilab and Cern, as well as the hopes that China’s plans to build an atom smasher follow through and that by increasing the size, it will be easier to find proof of String Theory. It also explains that time is running out for scientists trying to prove that String Theory exists, where the only hope is being able to detect gravitons disappearing from our brane, though this will not provide scientific evidence to disprove String Theory and therefore isn’t a definite test of String Theory.

The arguments behind String Theory rely on a sort of trust that there will eventually be proof that it describes our universe or that some of the other theories are untrue or have aspects that are true but aren’t completely accurate. I accessed a PDF by Carlos Rovelli named ‘Loop Quantum Gravity’, it is very effective in explaining the intricacies of Loop Quantum Gravity as it starts with the basic concepts and builds upon them to ensure understanding. It is a very effective resource in explaining Loop Quantum Gravity to the full extent necessary for this report. A PDF prepared by Erik Verlinde titled ‘Emergent Gravity and the Dark Universe’ was a source of information that I used to research Emergent Gravity as an alternative to String Theory as a description of Quantum Gravity. The source discussed the progression of thought from Einstein’s ideas on spacetime geometry to modern ideas and how his work can be furthered into building a potential framework for spacetime which describes gravity with respect to entanglement.

 

3 String Theory

3.1 Fundamentals of String Theory
Throughout most of the 20th century, scientists explained the universe using two important fields of physics, General Relativity and Quantum Mechanics. Both theories were incredibly important in our understanding of the universe as they explained an incredible amount on their respective size scales. However, when they’re both used in combination, the results can become inaccurate or just simply incorrect. String Theory was a development which could be used to unify the two theories by approximating the point particles (which the theories describe as being the fundamental particles in the universe) as one-dimensional strings of energy (Greene 2003). String theory predicts that universe has at least 6 more dimensions other than the four dimensions as most calculations expect that the universe is at least 10 dimensional. String Theory is especially relevant where the large and the very small meet and thus it has allowed us to reconsider our ideas on concepts such as the big bang and black holes alongside the structure of the universe. Moreover, the inclusion of solutions to many paradoxes and errors that aren’t explained by other theories could be brought about when the appropriate evidence comes to light to prove String Theory. It was theorised that there were two forms of string, closed and open strings. Over the years, it was discovered that the theory required objects called branes (A brane is an extended object, an n-brane is extended into ‘n’ dimensions and, a string is a 1-brane object). Strings can attach to a brane, which can be up to 9 dimensional, at one or both ends. A string can be viewed as a 1-brane (a one-dimensional brane) and point particles as a 0-brane. The relevance of strings being one dimensional is that rather than having a world line, they have a world sheet on a Minkowski space time graph. A Minkowski space-time graph is a tool used to map a sequence of space-time events that happen to an object over its history. A worldline is a curve within this diagram to which each point of the line relates to a time coordinate and three spatial coordinates. A worldline represents the events of a point particle over its history. It differs from a world sheet as the extra dimension of the string allows it to create an area within the diagram as opposed to a line. This area is what is known as a world sheet (Hawking 1988).

Spin is a property of particles, it is a form of angular momentum which involves charge in the form of charged particles. A particle’s spin can be an integer (1, 2, 3…) or a half-integer (0.5, 1.5, 2.5 …). Particles with a spin that is an integer are called Bosons and those with a half integer spin are called Fermions. Bosons are particles which carry forces, whereas Fermions are particles of matter. Fermions are represented as open strings which are attached to a brane, Bosons are represented by closed strings which cannot attach to a brane. Current theory on Fermions is that they consist of quarks (This is known as the standard model) which determine their properties. String Theory suggests that particles exist as vibrating strings, the properties of which are determined by the mode of vibration of the strings. A property known as string tension is theorised to determine the rest energy of the string.

In addition to this, general relativity is naturally incorporated into the theory, this was shown when scientists used equations of quantum mechanics in String Theory and they discovered that the equations of the general theory of relativity could be derived (Kaku 2003). String theory is theorised to be the means to which scientists can unify quantum theory and general relativity by describing gravity (explained by general relativity) and the strong nuclear force, weak nuclear force and electromagnetism (described by quantum physics) as the four fundamental forces.  It is even more suited to this unification because if it can be proven, it provides an explanation for quantum physics which isn’t as wild and unpredictable. This is significant because general relativity is an essential part of the framework of a consistent quantum theory. A crucial part of String Theory is Supersymmetry, a type of symmetry in physics which explains the relationship between corresponding Bosons and Fermions. Non-supersymmetric bosonic string theories exist but the lack of Fermions which are thought to exist render these theories unrealistic. Moreover, it is common within String Theory for theories to have the ability to predict the dimensions in which they live. It is most common that these theories will work in 10 dimensions but sometimes, calculations allow for 11, 26 or even 28. When calculating a pair of strings’ total perturbative expansion, the world sheets of the strings are summed. There is currently an ongoing search for a non-perturbative string theory that properly describes quantum gravity which requires proof. Perturbation theory is a way of finding an approximation of a solution by using the exact answer from a simpler problem. The computation of two strings’ scattering amplitude is defined by the coupling constant of the two strings called the string coupling which describes the probability of a string splitting and re-joining. A coupling constant is a constant representing the magnitude of interaction between a particle and a field (Schwartz 2007).

To summarise, the nature of String Theory is perfectly adapted to bridge the gap between two dominant theories in modern theoretical physics. If it is correct, it will reinvent current theory on the nature of particles.

3.2 Introducing the AdS/CFT Correspondence
A significant development which helped string theory to become a theory applicable to the real world was the development of the Anti de Sitter/Conformal Field Theory correspondence. However, before this, Leonard Susskind (after being one of the first scientists to theorise string theory) devised the holographic principle. The principle states that the things that we experience in three dimensions can be explained in two. He showed this further by calculating physics which exists in 3-dimensional space within 2-dimensional space, this suggests that it is possible to accurately approximate calculations which are based on (N+1) dimensions by setting calculations to be in N dimensions. The Anti de Sitter/Conformal Field Theory correspondence can be explained when it is imagined visually. Consider a stack of 3 dimensional branes (3-branes) which have open and closed strings interacting near around them, if the energy of the system is below the decoupling limit, then the open and closed strings will no longer interact. This would mean that you could model the situation in terms of the open and closed strings respectively. Modelling these in terms of open and closed strings allows you to describe the open strings in a 4-dimensional gauge theory which is described as a conformal field theory due to many symmetries within this model, where there are 3 spatial dimensions and one time dimension. If you look at this example respective to the closed strings, then the decoupling limit allows you to focus on the near-core region of the geometry of 3-brane spacetime, this show that the geometry describes a 5-dimensional AdS which has closed strings and therefore, gravity. The importance of this comes from a realisation that Juan Maldacena had about this example which was that because both of these models had the same origin, the stack of 3-branes, the physics of the two situations should be the same. This was significant as it meant that it was possible to describe the Quantum Gravity of 5-dimensional AdS using the 4-dimensional CFT. By increasing the temperature of this system, you can then model black holes in 5-dimensional AdS, this is significant as it allows application of string theory to real world science (Peet 2015).

The major information to take away from reading this section is that the uses of String Theory when defining quantum gravity extend beyond the unification of the two major theories and now has been shown to be a method of approximating between multi-dimensional situations with and without gravity.

3.3 Matter Fields and QFT
The best theories of the structure of our universe don’t involve particles at the smallest scale. The most accurate description that we can give is to describe them as fields. A field is a region in which any force can be experienced. It takes a particular value at every point in space that can change in time. Faraday described the effect with the EM field which he correctly predicted could describe light. Combining this idea with quantum mechanics, you arrive at Quantum Field Theory, the major concept of which is that, much in the way that an electromagnetic field can be thought of as quanta, all particles exist within a similar field. The idea of a fluid field is considered to be how photons of light exist. . There are similar waves that exist for each fundamental particle, such as up quarks and down quarks. There are 12 of these in total which describe matter and they are named matter fields. Their interactions with other waves determine properties such as electric charge (EM field). It is a relevance to the way that String Theory applies to Quantum Gravity as it can show how strings can exist and be understood in the real world regarding how they can represent gravitons as closed strings (Tong 2009).

This section is included for the sake of explaining more about the calculations mentioned in the previous section that determine features of a string existing within a matter field.

 

4 The Application of String Theory to Gravity

4.1 Background
One of the most important discoveries in Quantum Physics was Max Planck’s realisation that light could be quantized. It is expressed in the famous equation E=hF, where ‘E’ is the total energy, ‘h’ is Planck’s constant and ‘F’ is the frequency of the emission of photons. This showed that photons (light particles) had a finite amount of energy. The individual packets of energy were known as quanta, hence the name for the process of explaining the waves as particles became known as quantization. This meant that he had also quantized the electromagnetic force. Modern day physicists are searching for a way to quantise the force of gravity and describe its boson (the graviton). String Theory is applicable to Quantum Gravity because it uses General Relativity and its explanations of Gravity as a basis for how gravity works as well as its inclusion of aspects of Quantum Mechanics so that both theories can be incorporated into one unified theory. The concept of a gravity which is quantized is also included within String Theory as it allows for a gravitational boson (a graviton). Brane cosmology also explains why gravity is so weak as it is a closed string so it doesn’t connect to our 3-brane and therefore can escape into other branes. This is development into theories of gravitation which no other theories can explain and therefore, with significant evidence, String Theory could be potentially shown as the newest innovation of Quantum Gravity. It can also be mapped onto other theories which haven’t yet been shown to be true, namely its main rival, Loop Quantum Gravity.

4.2 The AdS/CFT Correspondence and Gravity
AdS/CFT allows String Theory to meet Loop Quantum Gravity. String scattering is measured in order to add the world sheets, using the string coupling to determine if the strings would split. The two parameters are the string coupling and length. Above the string length, point particles can be used as an approximation. There is a search for a non-perturbative string theory but beyond minor theories, very little is known about this section of string theory. Loop Quantum Gravity is the quantization of GR and matter fields, where it is assumed that there is no background space time. Quantum geometry is required, a typical computation would be the properties of one such geometry with another such geometry. The dimension and matter content of LQG is your own choice. LQG and ST compute different quantities, you either require particle scattering in LQG or quantum gravity in ST in order to progress. There has not been much progress in the former requirement, however the latter has seen great advances and is now possible using the AdS /CFT correspondence. A common way to understand AdS/CFT is to consider a cylinder, in this example, the AdS is represented by the bulk inside of the cylinder and the CFT is the boundaries of the aforementioned cylinder. The correspondence relates observable on the bulk and boundary. A problem with using String Theory to determine values is that a discrete value is gained from fixed graphs of AdS/CFT. Moreover, many computations require classical gravity rather than quantum gravity which is an issue as quantum gravity is a better description of gravity. We must go beyond the classical gravity limit of AdS/CFT as LQG has the necessary structure for AdS/CFT to be a bridge between ST and LQG. It is largely unknown how to successfully proceed in a way that would yield scientific proof (Maldacena 2003).

The decoupling limit allowed for the stoppage of interactions between open and closed strings, if this low energy limit is reached, then the four-dimensional gauge theory, which describes open strings, is left without the complicated string/loop corrections between the transfers from ST to LQG. This is a Conformal Field Theory as there is very many symmetries. The closed string physics is described by an Anti de Sitter space (AdS₅ X S⁵) which Juan Maldacena showed both came from a stack of 3-branes and so the AdS should follow the same rules as the CFT. This shows that the appearance of Quantum Gravity is holographic (Minwalla 2015). Moreover, it opens up a possibility that we may be able to model the universe in one fewer dimensions and without gravity. This allows for many possible solutions as to how we could use the AdS/CFT to develop our understanding of gravity beyond any concepts devised due to distinctions between the two models and the fact that each has the same laws but different geometries and physical differences. By examining the two scenarios, we might be able to gain a further insight into the actual effects that the different properties fully have (McGreedy 2008).

This section states that the purpose of the Anti de Sitter/Conformal Field Theory Correspondence in relevance to String Theory is to be able to use situations of lower dimension to eradicate gravity as well as other forces from problems. This is a way to use comparisons to define properties of the graviton and further modern understanding on quantisation of gravity.

4.3 Black Holes
The force of gravity is represented by a closed string of spin 2, this is important as the fact that the graviton is a boson means that it must have an integer spin. Black holes can be represented in String Theory as fuzzballs. A fuzzball is a big ball of intertwined strings which Samir Mathur defined as spheres of strings which have a finite volume. Within fuzzballs, there is no singularity, which is defined as a point in space which has zero volume but within which the mass is concentrated. It provides a solution to two important paradoxes: The first of which is the singularity paradox, the idea that the centre of a black hole contains a singularity. This becomes an issue as the laws of physics start to break down due to the infinite curvature of spacetime that a singularity within a black hole would describe, proven by Stephen Hawking.

The image included is a visualisation of the infinite curvature of spacetime in the presence of a gravitational singularity. This is based on the explanation of gravity as a distortion of spacetime as explained by Albert Einstein. Hawking also described the information paradox, the idea that beyond a black hole, there is a very little amount of information that can be known about it. More specifically, we can only know the mass, the charge and the spin, more commonly known as the information paradox. This is the idea that once matter crosses an event horizon, it loses its information permanently, only retaining its mass, charge and spin. This is an issue because in Quantum Mechanics, it isn’t possible for information to be lost. Hawking recently accepted after many years that there were possibilities within his calculations for this information to be transferred from the matter as it enters the event horizon and emitted via fluctuations in the black hole’s radiation field. Further applications of the Holographic principle and the AdS/CFT correspondence to this problem show possibilities for this information to be encoded in some form in the surface area of the black hole. Black holes were later shown to emit Hawking Radiation based upon the Hawking Temperature. Because of the emission of particles, black holes lose information over time due to the mass being the only significant factor in the quantity of Hawking Radiation that a black hole emits. The reason why the application of a theory of quantum gravity is necessary is that Quantum Mechanics and General Relativity do not work together and there are instances, such as black holes, in which the very small and the very large must both be described the same way. String theory merges general relativity and quantum mechanics because when you attempt to use the equations of quantum mechanics on strings, you find the equations of general relativity. String Theory can be used to calculate the warping of spacetime, via the distortion of the branes (more specifically it is proportional to the string coupling multiplied by number of branes that it exists on). Branes of the same number of dimensions have no forces between them, another way that no forces can exist between Branes is to have a 5-dimensional brane with a 1-dimensional brane lying along one of the 5-dimensional brane’s dimensions to prevent there being interactional forces between them. This is significant as the branes can have different charges. Because black holes are compact objects, you must wrap up the 5 dimensions of the 5-branes on 5 circles and the 1 dimension of the 1-branes on 1 shared circle. As superstring theory requires 10 dimensions, this allows for five dimensions that the black hole can exist on. Black holes being modelled in this way allowed for the calculation of the entropy of this system of a black hole. This is important as it gave the exact answer that the Bekenstein-Hawking calculations predicted almost 40 years earlier. Black holes typically have zero charges, whereas the equation [2π{(charge of 1-brane)(charge of 5-brane)(charge of closed strings)}^-1/2] requires high values of charge which allow for the same result to be calculated. This shows the limits to this model and how it can be used as an approximation beyond modern knowledge (Mathur 2005).

Modern scientists have discovered a method with which to create a black hole within the framework of String Theory. The black hole created resolves the two major paradoxes within modern theory on black hole physics. There has even been scientific proof in the form of reaching a derived equation proven by Hawking earlier. However, this proof is not sufficient as it is not as accurate as experimental evidence.

4.4 Problems with String Theory
There is a criticism of String Theory that is still unresolved. The fact that there is no physical proof that it is a realistic theory. There are some proposed solutions as to how we can prove that the theory is logical. At Fermilab, in Chicago, the method that has been employed to find evidence of string theory is to put electricity through hydrogen particles to give them high energy so that the electrons can reach a level of excitation in which they escape the atom. The protons are then launched in a circle, colliding with each other so that gravitons can be emitted and measure so that if they escape the brane, it will be detected. CERN plans to construct an atom smasher that is seven times as long. A method of finding proof of strings is to consider that at the start of the big bang, strings may have made an indication of their existence on things around them that were at that time small, but have now grown since the universe expanded and got bigger. One added complication to proving String Theory is that some string theories require tachyons to exist, a tachyon is described as a massless particle which moves faster than light. The immediate issue is that one of the key concepts to come from the special theory of relativity was that the speed of light is the fastest speed within the universe as equations demonstrate that for it to be possible to go beyond the speed of light, time would begin to go backwards for the particular object travelling faster than light. There is an equation in special relativity which is, , in this equation, Δt’ is the dilated time, Δt is the proper time, v is the velocity of object and c is speed of light. According to this equation, if the velocity of an object will increase, time will slow down for the object, if it will reach the velocity of light, time will stop for the object, this means that if speed of light will be exceeded, time will start to run backwards for the object.

Anything having some rest mass can’t travel faster than light because to accelerate it to the speed of light, it would require an infinite amount of energy, because according to special relativity, E = mc2, where ‘E’ is energy, ‘m’ is mass and ‘c’ is speed of light and when any object moves with some velocity its mass increases. This effect is described by another equation in special relativity which is . In this equation, ‘m0’ is the rest mass, ‘m’ is the increased mass, ‘v’ is velocity of the object and ‘c’ is the speed of light. If any object would travel at speed of light, its velocity, ‘v’ will be equal to ‘c’, after solving this, we will get the value of ‘m’ as infinite and because E = mc2, an infinite amount of energy will be required to accelerate any object having some rest mass to speed of light. Another way for proof of string theory to be gathered would be finding heavier particles called sparticles (superpartners) of particles which supersymmetry requires.

4.5 Alternatives to String Theory
The major rival theory of String Theory (as a model of QG) is Loop Quantum Gravity. In Loop Quantum Gravity, there are discrete, quantized units of spacetime because General Relativity describes gravity as a manifestation of the geometry of spacetime. It differs from String Theory because LQG adds features of Quantum Mechanics to Relativity, whilst String Theory attempts to apply gravity to Quantum Mechanics. The theory suggests that space is granular, because of the quantization, the granularity is like that of photons in electromagnetic waves as described by Quantum Mechanics. This theory suggests that space is a set of finite loops intertwined in a network of loops known as a spin network. An estimated size of these structures is the Planck’s length (10^-35m). An implication of this is that distances below the Planck’s length are insignificant (Rovelli 1997). Moreover, LQG predicts that space itself has an atomic structure. It has applications in calculating the entropy of a black hole via loop quantization, it gives the same results calculated prior to its application by Stephen Hawking and Jacob Bekenstein.

S=Akc3/4Gℏ (1.1)

and,

T=ℏc3/8πGMk (1.2)

General Relativity suggests that the only essential property of spacetime is its curved geometry. The suggestion is that spacetime is merely a stage on which forces can interact with matter and move it. The theory of Emergent Gravity suggests that spacetime has more significance in the universe than that. The equation (1.1) is that which can be used to calculate the Bekenstein-Hawking entropy, it has also been shown to determine the amount of quantum entanglement in a vacuum. The fact that the entanglement entropy of a vacuum can be determined using the equations (known as the Bekenstein-Hawking Area Law) has inspired scientists to build a framework in which spacetime geometry is described as the structure of the entanglement in a microscopic quantum state, a state of matter with microscopic properties. Gravity emerges from this theoretical framework by describing the change in entanglement caused by matter across spacetime (Verlinde 2016).

 

5 Conclusions

The inadequacies between the lack of correlation between Relativity and Quantum Mechanics have almost miraculously been shown to be resolved by replacing the concept of a zero-dimensional point particle with a one-dimensional string of energy. This allows for a working model of the universe where the two theories are unified. The application of String Theory also allowed for a working model of the Holographic principle known as the AdS/CFT correspondence which showed that in an N-dimensional space with gravity can be approximated to an (N-1)-dimensional space without gravity and the work of Leonard Susskind on the Holographic Principle as well as the work of Juan Maldacena on the AdS/CFT correspondence showed that the two spaces shared the same laws of physics. This showed that one could explain the universe with and without gravity which allows for the possibility of using a model of the universe without gravity to be able to show us how our universe truly exists. Moreover, modelling a black hole using branes shows incredibly similar results to those determined using the Black Hole Area law based upon the calculations of their respective entropies being the same result. This shows that one day String Theory may be able to claim its title as ‘the Theory of Everything’.

However, String Theory has some severe limitations regarding how difficult it is to prove alongside concerns regarding the fact that despite a desperate search for evidence, no scientific results have been found. One of the major issues of this is the amount of funding that is required to search for proof is very demanding and when the search for evidence yields nothing, the loss of credibility of the theory limits the amount of money that will be given to proving String Theory. This means that there is a race against time for string theorists to find some method of proving the theory as its credibility diminishes with each failed experiment.

 

6 Acknowledgements

I am very grateful to Mr Chandra Vemury at Teesside University for providing the means for my involvement with the project, especially during the first two weeks in which I was unable to be at the campus, Mr Vemury ensured that I was emailed with tasks for the day to build up my understanding of necessary aspects of theoretical physics to a high enough standard to be able to write this report and that I was allowed regular skype calls to ensure progression. Furthermore, I am thankful to Claire Willis at Nuffield for working hard to find an enjoyable placement perfectly suited to my needs as well as Nuffield for making the placement a possibility.

 

7 References

  1. Peet, A. (2015) String Theory Legos for Black Holes.
  2. Minwalla, S. (2015) String Theory and the Gauge Gravity Correspondence.
  3. Kaku, M. (2011) The Universe in a Nutshell.
  4. Rovelli, C. (1997) Loop Quantum Gravity [PDF] Available at: https://arxiv.org/abs/gr-qc/9710008 [Accessed 15/08/17]
  5. Verlinde, E. (2016) Emergent Gravity and the Dark Universe [PDF] Available at: https://arxiv.org/pdf/1611.02269.pdf [Accessed 14/08/17]
  6. Becker, K., Becker, M. and Schwartz, J. (2007). String Theory and M Theory: A Modern Introduction. Cambridge: Cambridge University Press, pp.3-5
  7. Hawking, S. (1988) A Brief History of Time. Updated Edition. Cambridge: Bantam Dell Publishing Group
  8. Green B. (2003) The Elegance of the Universe. Available at: https://www.youtube.com/watch?v=-kQXy9GZMuc [Accessed:08/08/17]
  9. Green B. (2003) Welcome to the 11th Dimension. Available at: https://www.youtube.com/watch?v=gvDeXfIomcc [Accessed:08/08/17]
  10. Tong, D. (2009) String Theory. [PDF] Cambridge: Centre for Mathematical Sciences. Available at: http://www.damtp.cam.ac.uk/user/tong/string/string.pdf [Accessed:07/08/17]
  11. Super String Theory. (2015) String People: Ed Witten. [Online] Superstringtheory.com Available at: http://www.superstringtheory.com/people/witten.html [Accessed: 09/08/17]
  12. home. cern (2015) The Large Hadron Collider [Online] Available at: https://home.cern/topics/large-hadron-collider [Accessed 09/08/17]
  13. Physics World. (2011) Information Paradox Simplified [Online] Available at: http://physicsworld.com/cws/article/news/2011/aug/15/information-paradox-simplified [Accessed 09/08/17]
  14. Physics of the Universe. (2014) Singularities. [Online] Available at: http://www.physicsoftheuniverse.com/topics_blackholes_singularities.html [Accessed 09/08/17]
  15. Mathur, S. (2005) the fuzz ball proposal for black holes: An elementary review [PDF] Crete: RTN. Available at: https://arxiv.org/abs/hep-th/0502050
  16. Super String Theory. (2015) String People: John Schwarz. [Online] Superstringtheory.com Available at: http://www.superstringtheory.com/people/johns.html [Accessed: 09/08/17]
  17. Space-time infinitely curving due to a singularity [image] [Accessed:10/08/17]
  18. Maldacena, J. (2003) AdS/CFT Correspondence.
  19. McGreedy. (2008) CFT continued; geometry of AdS

Leave a Reply

Your email address will not be published. Required fields are marked *