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AMSTERDAM UNIVERSITY COLLEGE Understanding the Theory of Everything: Evaluating Criticism Aimed at String Theory Paul Verhagen 5/27/2015 Major: Science Name supervisor: dr. S de Haro, Amsterdam University College Name reader: dr. H.W. de Regt, Vrije Universiteit Name tutor: dr. A. de Graaf, Amsterdam University College Student number: 6289223 Capstone Thesis submitted in partial fulfilment of the requirements for a degree of Bachelor of Science Word count: 12840 vi Abstract The scientific status of string theory is a highly contentious topic within theoretical physics. Some claim that it represents the pinnacle of modern physics, while others reject is as an untestable philosophy. The question examined in this thesis is the following: How should we evaluate string theory; can a theory that has considerable difficulty with experimental verification be classified as science, or have we unknowingly wandered into the realm of philosophy? This thesis breaks down the problem by: (I) analyzing the origins of the various concepts used in string theory, each of which exist in older theories of physics; (II) reiterating the need for a grand unified theory as a solution to several fundamental problems in physics; and (III) focusing the different evaluations of string theory’s scientific status. Some claim that string theory has failed, and will continue to fail, in providing experimental results and thus argue that string theory has been a complete failure. Others point towards the theoretical advances made by string theorists and argue for the reexamination of how science is evaluated. There appears to be a ‘meta-paradigmatic rift’ between experimentalists and theoreticians, in terms of what makes a theory qualify as science. The conclusion of this thesis is that labeling string theory as either a science or a philosophy, is deeply problematic. Doing the latter would ignore the theoretical and historical foundation of string theory; the former ,even more worrying to some, requires a reexamination of what it means to do science itself. i Table of Contents 1. Introduction 1.1 Conceptual Physics 1 1.2 Purpose and Structure 2 Part I: Understanding String Theory 2. What is String Theory? 3 3. Unification of Forces and Particles 3.1 Early Unification in Electromagnetism 5 3.2 Unification of Physics 6 3.3 Potential Problems 8 4. The Geometrical Nature of the Universe 4.1 Gravity as Geometry 10 4.2 Beyond 4D Space 11 4.3 Dimensional Compactification 12 4.4 The Calabi-Yau Manifold 13 5. The Problem of Quantum Gravity 5.1 The Problem 14 5.2 The Current Status 15 5.3 The Solution? 16 6. Black Hole Thermodynamics 6.1 Modern Black Holes 18 ii 6.2 Stringy Black Holes 19 7. The Dual Nature of Reality 7.1 Dualities 21 7.2 Anti-de Sitter/Conformal Field Theory Correspondence 22 8. A Brief Introduction to String Theory 8.1 A Glimpse of Formalism 24 8.2 Fundamental Entities 25 8.3 D+1 Dimensions 26 8.4 The Weakness of Gravity 26 Part II: Evaluating String Theory 9. Philosophy of Science 9.1 Another Introduction 28 9.2 Structure and Purpose 28 10. The Role of Experimentation 10.1 Definitions 30 10.2 Unfalsified versus Unfalsifiable 31 10.3 Consequences for String Theory 32 11. The Role of Theory 11.1 A bold/unscientific Proposal 34 11.2 The ‘meta-paradigmatic shift’ 35 11.3 Theory-driven Confirmation of Physics 36 12. Considerations in the Pursuit of String Theory iii 12.1 Potential versus Productivity 38 12.2 The Other Contenders 39 12.3 The Pragmatic Answer 39 13. Conclusion 41 14. List of References 44 15. Appendices 48 iv Acknowledgements First and foremost, I want to thank my supervisor Sebastian de Haro for his patient and insightful comments throughout this project. His support and enthusiasm have made this capstone ,which wanders off the beaten path, possible. Henk de Regt has my thanks for being my second reader and teaching an inspiring course on philosophy of science during my AUC career. My gratitude to Patrick Decowski and David Berge for their willingness to listen to my ramblings on string theory and their helpful comments. Matthew Lippert and Fabio Zandanel for recommending sources to me that have made my research more substantial. I want to thank Cas Smulders for his philosophical reflections on the nature of doing a capstone and our imminent graduation. Ivana Neamtu has brought an element of competition to this entire endeavor that has undoubtedly made this a better paper and a more enjoyable experience overall. Finally I want to thank Coco Kleijn for her scatological humor aimed at alleviating my stress levels and Jo Kleijn for providing some much needed intellectual companionship. v To my mom and dad. Without you none of this would have been possible. vi Chapter 1 Introduction ‘Do not merely practice your art, but force your way into its secrets. For it and knowledge, can raise men to the Divine.’ -Ludwig van Beethoven String theory has been subject to some harsh critique concerning its status as a scientific theory. In popular science it is sometimes conflated with a philosophy rather than a theory of physics, on the basis that it provides no experimental evidence. While this accusation is not entirely without merit, there is an amount of misunderstanding surrounding the nature of string theory, which I will assess [1]. As such, the purpose of this paper is to elucidate some of the confusion surrounding the empirical status of string theory, and conceptually engage in what this might mean for the scientific methodology as a whole. By careful analysis of the established modes of thinking on string theory, and critically applying theories from philosophy of science, the ultimate goal of this paper is to reflect on the new approach toward scientific inquiry that has been brought about with string theory and understand its philosophical foundation. 1.1 Conceptual Physics As is often the case with bold claims, the truth behind string theory resists simplicity. It is unfortunate that in the absence of a deep mathematical understanding of the theory such claims are made. A proper mathematical treatment of the theory however, is beyond the understanding of all but the most seasoned physicists. Yet this should not bar anyone from trying to understand what string theory entails on a conceptual level. The approach that I will strive to take throughout this paper, is to explain the thinking behind string theory. I want to state, unequivocally, that I do not have the mathematical background to work with string theory. This ability is unfortunately reserved for experts, 1 a fact that might have contributed to the contemporary controversy. What I will strive to do instead, is provide a conceptual overview of the ways that physicists think about the world and how this has led to the development of string theory. 1.2 Purpose and structure As such, this paper will be divided into two distinct parts. The first will both motivate and explain string theory by examining concepts from physics that has been significant to its development, as well as illustrate how it applies to its modern formulation. Through the conceptual analysis of these concepts I hope to provide an overview of why string theory is so desirable from the current paradigm of physics, and will conclude with a somewhat more technical chapter to provide a basic overview of the mechanics involved in string theory. The second purpose of this paper is to evaluate various different criticisms that have been raised against string theory. The claim that string theory has not, and will not, present experimental data is unfortunate and does not reflect the complexity of string theory. Yet it is not an argument without merit, and there are indeed significant problems with the experimental appraisal of string theory. That being said, the role of experimentation in theoretical physics has varied over the centuries since Galileo. Some authors have even suggested that string theory represent a novel kind of theory that requires a different method of verification, beyond the traditional experimental falsification criterion. How should we evaluate these kinds of statements about string theory? I will try to elucidate the question at hand by analyzing historical examples of theories in physics of which their experimental verification was not straightforward or even possible at the time. Furthermore, philosophy of science has its role to play in string theory, as it does present a kind of ‘meta-theory’ that provides a deeper insight into how physics as whole can be put together from its component parts. Does string theory necessarily entail reductionism? And what are the alternatives to string theory; Are these in a better position than string theory to uncover the elusive theory of everything? 2 I hope to answer these questions over the course of this paper and provide some insight into a world that is, by any standard, near impenetrable without a level of mathematical mastery that only few have obtained. Thus I will use mathematics, where it is helpful, but the focus of this paper is on a conceptual understanding, and ,perhaps equally important, on paving the way for a discussion on the idiosyncrasies of string theory that is accessible to more than just the experts. 3 Part I: Understanding String Theory Chapter 2 What is String Theory? ‘I don’t think that any physicists would have been clever enough to have invented string theory on purpose… Luckily, we invented it by accident.’ -Edward Witten To fully understand string theory is not a trivial endeavor. It is a synthesis of over a century of scientific advancement and draws from a wide variety of concepts familiar to physicists. String theory is often presented as a so-called grand unified theory (GUT); an attempt to describe the behavior of reality within the scope of a single theory. GUT is the perennial holy grail of modern physics and has been pursued by some of the greatest scientists of modern history. The most concise way of describing string theory, is as follows: It is a GUT that proposes everything is made up out tiny one dimensional string of energy that can move in 10 dimensions [2]. The geometry of the strings being either open string or closed loops and the various ways in which these may vibrate gives rise to all the complexity we experience in the natural world. Yet this description does not do the theory justice. String theory aims to solve several foundational problems in modern physics and has arguably been quite successful in doing so. As such, understanding string theory is about more than just describing the theory itself, but includes the scientific thinking that has lead up to its establishment. To this end, in my attempt to explain what string theory is, I will focus on five distinct topics in physics that each relate to the development and formulation of string theory. By observing the historical background in which string theory is developed we may both gain an appreciation for the theory from an developmental perspective, as vi Part I: Understanding String Theory well as adequately frame the question it attempts to answer: What is the fundamental nature of the universe, and how can we describe it? The first concept to analyze is that of unification in Chapter 3, since string theory is a theory of everything, it must somehow combine all the existing frameworks of physics within its scope. This type of event has happened before, the most famous example being the unification of electromagnetism. Perhaps one of the most well-known features of string theory is that it lives in 11 dimensions, and as Chapter 4 will hone in on the role geometry plays in string theory. Geometric properties of the universe is relevant to a myriad of fields, Einstein’s general relativity and arguably forms a cornerstone of modern thinking about gravity. Chapter 5 will discuss the curiosities of applying gravity to the quantum scale. This remarkably tenacious corner in physics is an open problem and requires solving if string theory is correct. One of string theory’s challenges lies in the breadth of theory that is seeks to describe; Black hole thermodynamics is an area of physics that sheds light correspondence between string theory and conventional physics discussed in Chapter 6. String theory also comes in many different forms, and a major breakthrough in its development came through the conceptual application of duality. Chapter 7 will elaborate on these intriguing mathematical relations, most notably in the form of the (in)famous AdS/CFT correspondence. Finally Chapter 8 will seek to provide an introduction into the idiosyncrasies of string theory itself, how it is formulated and how it can be understood. 5 Part I: Understanding String Theory Chapter 3 Unification ‘The universe is made of twelve particles of matter, and four forces of nature. That’s a wonderful and significant story.’ – Brian Cox 3.1 Early Unification in Electromagnetism James Clerk Maxwell is a figure of titanic proportions in the history of science. A Scottish scientist who lived in the middle of the 19th century, Maxwell’s equations are an essential piece of mathematical equipment for any physicists who wants to describe the electromagnetic force. In fact, before Maxwell, there was no such thing as the electromagnetic force. What Maxwell achieved in the year 1865 with the publication of A Dynamical Theory of the Electromagnetic Field is known in physics as unification. This concept entails that two different phenomena that had previously been thought of as unrelated, in the case of Maxwell electricity and light, can be described by a single theory that spans both previous fields. The realization that electricity and light are both different aspects of the broader phenomena that is now known as electromagnetism has been of great significance for the development of modern physics. This unification is often associated with a paradigm shift, and it is the type of event that forces scientists to reexamine previously accumulated knowledge from a different perspective [3]. 1) ∇ ∙ 𝐸 = 𝜌 4) ∇ × E = 𝜀0 𝛿𝑡 𝐽 2) ∇ ∙ 𝐵 = 0 3) 𝑐 = −𝛿𝐵 1 𝛿𝐸 5) ∇ × B = 𝜀0 𝑐 2 + 𝑐 2 𝛿𝑡 1 √𝜀 0 𝜇0 6 Part I: Understanding String Theory The above Maxwell equations are written in their differential form in the absence of any magnetic or polarizable medium. As can be seen explicitly in equations 4, there is a relation between a change of a magnetic field B over time and the curl of an electric field E, implying that both fields are part of the same phenomena. Equation 4 describes the curl of a magnetic field in terms of the current density J and a the change over time of electrical field, divided by the speed of light c squared. The constant ε0 represent the electric permittivity of the vacuum, and can, together with constant μ0, the magnetic permittivity of the vacuum, be seen more explicitly in equation 3 to be related to the speed of light in vacuum. All these equations together show the relation between magnetism and electrical fields in addition to describing light as an explicitly electromagnetic phenomena. 3.2 Unification of physics Unification has obvious appeal for a variety of different reasons. First of all, it means that a more fundamental theory has been found, one that more closely describes a broader section of reality within the scope of a single theory, in this sense it is more ‘true’. Second, unification allows physicists to describe phenomena which had previously not been understood, by providing a new theory that sheds light on longstanding problems. I will return to this point in great detail with the contemporary discussion of QM vs GR in the chapter 5. Because of the advantages offered by unification, and its historical success when it has occurred in terms of advancing science, it is considered to be a desirable aspect of any new theory of science. A framework that offers complete unification is colloquially known as a Grand Unified Theory or the theory of everything. As their namesakes indicate, these theories attempt to describe various different phenomena as the manifestation of a single concept that explains, well, everything. Unification is a topic that has certain associations, and although it can be confused with reductionism, it is not the same concept. This relation will be examined further in section 11.1. 7 Part I: Understanding String Theory String theory is a grand unified theory, or at least it is often presented as such. One of the most intriguing characteristics that string theory displays is that it unifies what is known as the four fundamental forces of nature. These forces, gravity, the electromagnetic force, the weak nuclear force, and the strong nuclear force together represent the ‘known’, that is the collection of theories that are generally accepted, about physics. In 1979 Sheldon Glasgow, Abdus Salam and Steven Weinberg were awarded the Nobel Prize in physics for their work on unifying the electromagnetic and weak nuclear force into the electroweak force. Subsequent theories have indicated that it is possible to unify the electroweak force and the strong nuclear force together in what is known as grand unification [4]. One of the experimental predictions that this grand unification makes is that the proton is unstable over large time scales, although this effect has yet to be observed [5]. Various research groups around the globe are currently attempting to observe this decay, as well as magnetic monopoles, another prediction of the theory [6]. As of the moment however, grand unification is still placed firmly within the realm of theoretical physics. Nonetheless, the idea of unification has proven extremely powerful as a concept among physicists; Einstein famously spent his final decades pursuing a unified field theory with the purpose of unifying all four fundamental forces. The way that string theory formulates reality does not only allow for the unification of the four fundamental forces, it also provides an explanation for the twelve fundamental particles of matter that we know of. These particles are codified in the Standard Model (SM), the current pinnacle of our understanding of reality. The SM divides matter up into twelve particles that are fundamental and irreducible, and from these particles we may understand the strong, weak and electromagnetic force and their interactions [7]. It explains what protons and neutrons are built of and provides explanations for many of the phenomena we see in the physical world. Although we know it must be incomplete since it does not provide an explanation for gravity, it has been experimentally verified many times over and has made genuine predictions that have been confirmed with a high degree of accuracy. Examples include the observation of the W and Z bosons [8], 8 Part I: Understanding String Theory the decay of Z bosons and most recently the discovery of the Higgs boson [9]. In recent years there have been multiple challenges to the SM that seem to indicate that it is at the very least incomplete, and although the scope of SM is impressive, it does not extend to the likes of neutrino oscillations [10] or dark matter and energy [11]. 3.3 Potential Problems String theory offers an alluring path forward; accepting that the universe is made up of only twelve particles of matter is an appealing notion, but it begs the questions: Is there not a more fundamental currency of reality? In string theory, sometimes used interchangeably with M-theory, the universe is built up of tiny string that can move in 10 dimensions in the former and 11 in the latter. The combination of the frequency, dimensionality and continuity of the strings correspond to different higher level manifestations of particles. Thus in string theory, the twelve particles of matter are reducible to the various permutations of the strings. This presents yet another unification of theory, as the SM, while extremely successful in describing the properties of the various particles, fails to explain why there are only twelve particles, no more, no less. One might argue that there is an underlying presupposition with unification namely, why would there be only one currency of reality? There is no inherent reason that there should be only a single unit that governs all physical interactions. To this I can only answer that unification is an incredibly appealing concept to physicists both on an aesthetic and epistemic level. The epistemic merits of unifying theories into new frameworks that require less free parameters is extensively discussed in the philosophy of science [12][13]. The idea of finding a truth that is more fundamental, that reduces a larger portion of reality and encompasses it within a single notion is undeniably epistemologically pleasing. The topic of the free parameters and their exact numerical values is dealt with in more depth in chapter 6 as it is another significant contributor to string theory’s appeal. I will further delve into the issue of the desirability of string theory on a conceptual level in the subsequent section of this paper. For now suffice it 9 Part I: Understanding String Theory to say that the unification of the four fundamental forces and the fundamental particles is an incredible achievement within the current paradigm of physics; it justifies the claims that physicists as esteemed as Hawking make, stating that M-theory is the only ‘viable’ candidate for a grand unified theory [13]. 10 Part I: Understanding String Theory Chapter 4 The Geometrical nature of the Universe ‘Mass tells space-time how to curve, and space-time tells mass how to move’ - John Wheeler 4.1 Gravity as Geometry Originally formulated by Einstein in 1915, general relativity (GR) describes gravity in terms of the curvature of a four-dimensional construct called space-time. Einstein’s theory puts forward a mathematical framework that combines the three familiar dimension of space with a dimension of time. This space-time behaves very much like a stretched piece of fabric; imagine placing a heavy orb in the middle of a taut sheet. The weight of the orb will bend the fabric around it into a concave depression with the orb at the center. If one now takes a much smaller orb and sets it in a motion perpendicular to the normal of the orb, it will follow the curve of the fabric and remain in an elliptical orbit around the orb. This analogy represents only a conceptual sketch of the mechanism that according to Einstein is responsible for gravity. Massive objects warp space-time around them and thus cause objects to fall into the gravity well around them. These objects in turn will then follow the curvature of space time and remain in orbit around the massive object. GR has proven to be extremely accurate in describing the behavior of the most massive objects we know of in the universe ranging from stars to entire galaxies. Einstein’s formulation of gravity is elegant and conceptually simply, the sweeping, smooth geometry of warped space time is rightfully considered to be a milestone in the establishment of modern physics [14]. Of particular interest to string theory is the importance of geometry in GR, note for instance that the emergence of gravity follows quite naturally from the geometric properties of space-time. Geometry, 11 Part I: Understanding String Theory and in particular those of extra dimensions other than our conventional four, plays an important role in the development of string theory. 4.2 Beyond 4D Space In particular the formulation of Kaluza-Klein theory can be considered to be the conceptual predecessor of string theory. Originally formulated by Theodor Kaluza in 1919 and elaborated on by Oskar Klein in 1920, it was an attempt to unify the forces of gravity and electromagnetism by adding a 5th dimension to Einstein four-dimensional space-time. More specifically, Kaluza found that if one added this dimension to GR, electromagnetism emerged from Einstein’s formulation of gravity. This of course is a powerful indication that GR is in fact the correct description of not only gravity but of electromagnetism as well. Yet despite the beautiful mathematical description of space as 5-D, one has to ask: where is this 5th dimension? To answer this question, one may consider how the gravitational constant would change in a higher dimensional space. This constant may be defined by its relation through the Planck length as shown in equation 6. 𝑙𝑃 = (𝐺)𝛼 (𝑐)𝛽 (ℏ)𝛾 6) Here the Planck length lP, is related to the gravitational constant G, speed of light c and reduced Planck constant ℏ. In the case of familiar four dimensional space time the gravitational constant is given by filling in the various exponent variables to the values of γ=α=1/2 and β=-3/2, plugging these values into equation 6 yields the gravitational in the familiar units. 7) 𝐺 (4) = 2 3 𝑙𝑃 𝑐 ℏ The notation G(4) shows the dimension D in the exponent. The exact units of this constant vary with different number of dimensions as generally described in equation 8. Since G(4) does not have the same units as G(5) however, a direct comparison of the two 12 Part I: Understanding String Theory values is impossible. Since Planck length is constructed directly from G, c and ℏ, the Planck length can be compared through the following result. 8) (𝐷)𝐷−2 (𝑙𝑝 )= ℏ𝐺 (𝐷) 𝑐3 = (𝑙𝑝 )2 𝐺 (𝐷) 𝐺 Through this result it quickly becomes apparent that spaces with a higher number of dimensions than our familiar four has far reaching consequences for the properties of the gravitational force and all other physical processes which involve gravitation. Indeed the interpretation of this result is that the Planck length in 4 dimensions is related to a higher dimensional space where these dimension are both curled up and compactified [16]. 4.3 Dimensional Compactification To conceptually understand this notion, imagine traveling towards another far away planet in a spaceship. For a significant portion of the journey the planet would appear as a 2-D circle instead of a sphere. It is only when we are relatively close to the planet that it becomes apparent it is in fact a 3-D object. Its curvature is not obviously visible from far away, yet is completely obvious from a different perspective. This analogy may illustrate the way in which the 5th dimension is hidden to our eyes in Kaluza-Klein theory; the extra dimension is curled away so that to us, it appears as a point. Only on a much smaller scale, does it become clear that these points are in fact spheres [15]. Thus in Kaluza-Klein theory, each point is covered by a sphere that is too small to perceive directly but means that we in fact live in a 5-D world, although it appears to us as only 4D. Once again this is a rather elegant solution to this problem and it was hailed as a revolution by Einstein himself. Unfortunately, the theory proved to be incorrect. In order for it to work the radius of the spheres, analogous in this case to the 5 th dimension, had to remain frozen in space and time. That is, to get the correct version of electromagnetism out of Kaluza-Klein theory, the geometry of space had to be static in the 5th dimension, while the essence of GR is that the geometry of space is dynamic. Ultimately this type of preferential treatment of the 5th dimension proved to be the 13 Part I: Understanding String Theory theory’s undoing. Allowing for a dynamical radius of the spheres to vary, in accordance to GR, lead to all sorts of strange results including gravity spontaneously changing into electromagnetism and the variations of the electrical charge over time. Furthermore the theory proved to be highly unstable, as even the smallest permutations could either cause the 5th dimensions to expand to enormous proportions or make the spheres vanish completely. 4.4 The Calabi-Yau manifold Although Kaluza-Klein theory ultimately failed to provide an acceptable unification of electromagnetism and gravity, the idea that extra dimensions may be hidden away from plain sight is one of the central premises of string theory. Since string theory and Mtheory, are theories with a higher dimensional geometry, they too require some sort of explanation for where these hidden dimensions live. Perhaps unsurprisingly, string theory borrows heavily from Kaluza-Klein theory and posits a 6 dimensional, space that is referred to as a Calabi-Yau manifold [17]. To fully explain this concept is both beyond the scope of this paper and the capacity of all but the most accomplished mathematicians. For the purpose of this endeavor, namely, to understand what string theory is, it is important to appreciate that the dimensionality of space is a direct result of how we look at it. At different distance scales the universe might appear as either 4 or 11 dimensional. It is the geometry of these Calabi-Yau spaces that play a crucial role in the precise formulation of string theory, and consequently in providing possible experiments that might test these spaces. I will return to the issue of these Calabi-Yau spaces but for now we may conclude that geometry of space-time be it in 4 or 11 dimensions plays an important role in both GR and contemporary string theory. 14 Part I: Understanding String Theory Chapter 5 The problem of Quantum Gravity ‘Thoroughly conscious ignorance is the prelude to every real advance in science.’ - James Clerk Maxwell 5.1 The problem To understand the next fundamental problem that string theory might solve, one must consider the long lasting contradiction between quantum mechanics and general relativity. These two theories arguably lie at the heart of modern physics; Each has been incredibly successful in its respective field and is parochially considered to be, for lack of a better word, true [18]. Many attempts have been made to disprove either one over the past 90 years, yet none have succeeded. Experiments that seem to contradict either theory generally make it to the front page of various science blogs accompanied by the grandiose claim that ‘It might be time to rewrite the textbooks!’ [19] While GR rules over the very massive, quantum mechanics (QM) dictates the behavior of the smallest objects; photons and subatomic particles are all governed by the laws of QM. The theory proposed by Schrödinger, Bohr and many others in the early 1920’s, comes with considerably more conceptual difficulties than GR. The behavior that QM describes is a far cry from the smooth geometry of space-time that Einstein favored. Instead it describes all particles are being either a particle or a wave, and until an observation is made it is best described as both. The role of the observer is of monumental importance in QM and can mean the difference between locating an object as a point particle or a cloud of probabilistic uncertainty. The ever shifting quantized behavior of particles in QM has been the subject of many different philosophical questions, and although most of these questions concerning the correct interpretation of the quantum theory remain open, it has proven to be an exceptionally fruitful theory 15 Part I: Understanding String Theory [20]. Despite a lack of clarity on how we should interpret the implications of the theory, QM has been a cornerstone of modern physics since its inception nearly a century ago. 5.2 The Current Status To say either QM or GR is incorrect would constitute a paradigm shift of monumental proportions. Yet we know, and have known for a while, that at the very least they are incomplete. Problems start occurring when one attempts to combine QM and GR and intersects their domains [21]. GR describes the behavior of the most massive objects known, and QM provides insight into the very small. When physicists try to combine two, the theories completely break down. Not only do the mathematical equations start spewing out uninterpretable nonsense, it is unclear how we can conceptually harmonize with two descriptions of reality that vary so fundamentally. A worldview that alternately describes the fabric of reality as smooth and sweeping at a distance and simultaneously jittery and chaotic when we zoom in is completely incommensurable. Ultimately the problem that lies at the heart of this conflict is our lack of a theory that describes gravity at the quantum scale. This issue often referred to as the problem of quantum gravity, and it just so happens that string theory offers a potential solution. It should be stressed however, that this problem only arises in the context of unification, as no anomalies have yet been found in QM. Furthermore anomalies of GR have traditionally been attributed to dark matter, and although this is another area in need of further research, it does not specifically relate to string theory. While this problem of quantum gravity is still unsolved, the more specific issue of the Black Hole Information Paradox, which is related to it, is an area where results may be directly attributed to string theory. This paradox specifically refers to Hawking radiation, a theory that predicts black holes have a temperature and radiate energy [22]. There appears to be a violation of unitarity, the quantum requirement that the sum of all possible outcomes equals 1 , as the microscopic information associated with the star that collapsed to form the black hole cannot be retrieved from this thermal radiation. Black hole thermodynamics is one of the problem areas where string theory has 16 Part I: Understanding String Theory provided theoretical breakthroughs by equating gauge theory and gravity in the celebrated AdS/CFT (anti-de sitter/conformal field theory) correspondence which relates quantum field theory (QFT) with a theory of quantum gravity. Once again the mathematical details are beyond the scope of this paper but string theory has directly led to the first microscopic derivation of Hawking’s black hole entropy formula [23]. This is an important result, as “this gauge theory/geometry correspondence exhibited by string theory clearly hints at a fascinating deeper structure underlying, and novel ways of thinking about, string theory and quantum gravity” [23]. Quantum gravity may ultimately be related to space-time geometry as general relativity space-time appears to collapse into black holes at sufficiently high energy-density scales. As such the classical geometry of space-time is unable to provide insight into these outstanding issues and is in need of replacement by a ‘quantum geometry’. 5.3 The solution? It is important to note however, that our understanding of gravitational singularities is among the most glaring gaps in modern physics, and is thus the subject of intense scientific scrutiny. It should come as no surprise then that string theory is not the only theory that aims to solve the problem of quantum gravity. Various different approaches have been proposed, ranging from quantum loop gravity to doubly special relativity and entropic gravity [15]. It is also of importance to note that none of these alternatives claim to be a grand unifying theory. As a consequence the challenges associated with string theory are substantially greater, as it attempts to solve quantum gravity within the scope of a unified theory. Although a full treatment of these alternative methods of describing quantum gravity fall beyond the scope of this paper, I will return to some of the experimental issues that both string theory and alternative approaches share. Black hole thermodynamics is only one of the areas where string theory has provided evidence of its physical significance in terms of providing an accurate picture of quantum scale gravity. This is an important result as quantum gravity has been an area of physics where theoretical progress has been relatively slow. 17 Part I: Understanding String Theory It should also be noted that before 1984, or the ‘first string theory revolution’, string theory was not normally discussed in the context of unification. Rather, early string theory was an attempt to describe quark containment and the strong nuclear force. Work done by John Schwarz and Michael Green that proved a ten-dimensional supersymmetric string theory eliminated an anomaly which had plagued string theory, promptly changed the discussion of string theory as merely a description of the strong force to a potential theory of everything. The results of Schwarz and Green were followed by a torrent of theoretical advances, as their proof that certain versions of string theory were consistent with the principles of quantum mechanics led to increased interest in its pursuit. It is in this time period that the aforementioned Calabi-Yau manifold was introduced into string theory and that geometry became an integral part of the theory. This was not met with universal acclaim however, as the various permutations of this manifold created different versions of particle physics. According to Yau himself, up to a hundred-thousand different manifolds might be possible each corresponding to a different particle physics, leading to Feynman’s and Glashow’s accusations that string theory was subject to post-hoc additions to keep the theory consistent [15]. Indeed the fact that so many different versions of string theory existed was a problem in need of solving, and solved it was, during the second string theory revolution. 18 Part I: Understanding String Theory Chapter 6 Black Hole Thermodynamics ‘Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can’t be seen’ - Stephen Hawking 6.1 Modern Black Holes Through the application of thermodynamics on black holes, one may relate the entropy of black holes to a specific temperature, referred to as the Hawking temperature. 10) ℏ𝑐 3 𝑇𝐻 = 8ᴨ𝐺𝑀𝑘 𝐵 This equation is intriguing for a number of different reasons, firstly the process it describes is quite explicitly a combination of both gravitational and quantum effects. As discussed before, the experimental verification of Hawking radiation resulted in a full blown crisis in physics [26]. The second reason this formula is of particular interest is that it contains some of the most important constants of nature. In particular, ħ is the aforementioned reduced Planck constant, G is the gravitational constant, c the speed of light, and kB is the Boltzmann constant which relates energy with temperature. In addition we have ᴨ and variable M which indicates the mass of the black hole. These four constants mentioned are among the most ubiquitous in physics, and each could be said to represent a different corner of physics, being respectively, quantum mechanics, general relativity, special relativity and thermodynamics. This is of course not to say that these constants only appear within these fields, but it is illustrative of their importance in their respective fields. Of course each of these constants corresponds to a certain numerical value, which has been exhaustively tested to an incredible amount of precision. Yet despite our detailed 19 Part I: Understanding String Theory knowledge of the value of each constant, we are at a loss to explain why it is precisely this value and not some other. In fact, it turns out that the universe is balanced around 20 or so numbers, and that it must be precisely the value we find for the universe to be stable. This is sometimes referred to as the problem of fine tuning. Our universe is balanced precariously, like a pencil on its tip, and even the tiniest deviation creates a universe that is radically different than ours. Thus the question to be asked is: Why do the constants of nature have the value we measure and not some other arbitrary number? 6.2 Stringy Black Holes The solution string theory offers is that all these different constants are relatable through the breaking and bonding of strings, and that this interaction is governed by only a single constant g, the string coupling constant [15]. Whereas we normally use a plethora of different theories with a variety of constants to describe the range of phenomena we experience, string theory reduces all of these different phenomena to the breaking and bonding of strings. As such all physical interactions are governed by only a single constant from which the rest may be derived, and although it is true that the string coupling constant might be yet another arbitrary number, having only a single constant is a pronounced step forward from having twenty. Indeed string theory has proven to be exceptionally well suited to describe a particular type of black hole known as extremal black holes. These objects are a particular instance of charged black holes where its mass is equal to its charge, in suitably chosen units. This limit is known as the extremal limit. Extremal black holes are characterized by having highly unstable event horizons, and although they have, as of yet, not been observed, they are a relatively well studied object within the realm of theoretical physics [26]. They are also of particular interest to string theorists, as extremal black holes can be described in string theory in the form of branes is precisely compatible with the more traditional theoretical physics. Indeed the compatibility is not just limited to extremal black holes, but also to near extremal black holes, meaning this correspondence appears to be more than just a boundary case relation, but a deeper connection. The topics of branes is of particular 20 Part I: Understanding String Theory interest in string theory, as it in many ways epitomizes our modern understanding of string theory, and is related to the aforementioned AdS/CFT correspondence, which will be topic of the next chapter. For now I will conclude that string theory has been quite successful in reducing the number of free constants of nature, and produces results that conform to more widely accepted descriptions of black holes. As mentioned before, black hole thermodynamics is among the most interesting fields in theoretical physics, and string theories success in describing even a small section of black holes is a remarkable achievement. 21 Part I: Understanding String Theory Chapter 7 The Dual nature of Reality ‘If you ask the smartest physicists around: ‘Who is the smartest physicist around?’, in my experience most will say Ed Witten. The other half will tell you they don’t like the question.’ - Sam Harris 7.1 Dualities As discussed, the first string revolution did not immediately solve all the problems that had been associated with string theory. Because string theory was now discussed within the context of unification, a whole new array of problems appeared in need of solving. The first, and arguably most pressing, was the fact that the 1984 revolution left us with five different versions of string theory. Naturally, having several different versions of a Grand Unifying Theory is somewhat of a contradiction. It was not until the work of Edward Witten in 1995, and Juan Maldacena in 1997 that string theory reached the form it is known as today. To understand both contributions, one must delve into the notion of duality. The solution that Witten proposed was that these five different versions of were all part of a single framework, now known as M-theory. Black holes and AdS/CFT brings us neatly back to the five different versions of string theory we were left with at the end of the 1984 revolution. Each of these versions provided a different description of string theory, a rather unsatisfactory property for a theory that was supposedly the one theory to rule them all. The breakthrough that came at the hands of Edward Witten was that these different version were in fact pairs, through something called duality. What it implies is that two different string theories might describe the same phenomena but focus on different quantities. In particular, the behavior of strings in a dimension with a large radius R where the quantity might be 22 Part I: Understanding String Theory momentum, may be related to the behavior of string is a dimension with small radius 1/R where the string is wrapped around this circular dimension where the quantity in question is the number of times the string winds around the circle. These two descriptions, in string theories that exhibit duality, are complementary, that is, the behavior of the one is described by the other from a different perspective. This particular type is referred to as T-duality, as it relates to the topological nature of string objects. There are other types of duality in string theory that I will not delve into at this moment, but it is of interest to note that Maxwell’s equations in section 3.1 are also invariant under duality transformation. That is, under operation 11) 𝑦𝑖𝑒𝑙𝑑𝑠 ⃑⃑⃑ 𝐵 ⃑)→ (𝐸, ⃑ , 𝐸⃑ ) , (−𝐵 the Maxwell equations do not change, this is known as the duality symmetry of electromagnetism. 7.2 Anti-de Sitter/ Conformal Field Theory Correspondence Finally we may discuss the importance of AdS/CFT correspondence; it is similar to a duality, in that it allows for the description of a three dimensional field theory, say, quantum gravity within the event horizon, by mapping it to a two dimensional theory on the surface of the black hole. What is effectively proposed in AdS/CFT , is that we may describe the interior workings of the black hole, by describing only a theory that lives on the boundary of this object, allowing for a theorists to switch between a 2-D and 3-D description of the object that is completely equivalent. Although an outright mathematical proof of AdS/CFT is lacking, there have been many different indications of its correctness and as a result its first formulation by Maldacena is the single most cited paper in the history of physics. AdS/CFT is of particular relevance to string theory, as it, together with Witten’s proposal of duality, led to the modern formulation of M -theory, which stands for “magic-, mystery- or matrix-theory, according to taste” [28]. The brilliance of Witten was to see that these five different versions of string theory, were different aspects of this broader M -theory. Thus the deeper lying theoretical framework that underpinned all these different versions, encompassed all of these preceding 23 Part I: Understanding String Theory versions. This unification of string theories, if you will, came at a price however, as it required the addition of yet another dimension, increasing the total amount to 11. Furthermore it allowed for the introduction of D-branes, membranes of varying dimensions that float in a higher dimensional space. Branes are among the most abstract objects in string theory, and come with an accordingly high level of mathematical complexity. As such, for our purpose of describing string theory, what is most significant is that these branes can be of a higher dimension than the strings. The most widely studies of these objects are D3-branes which correspond to three dimensional space. In addition, open strings must end on a brane with at least one end, meaning that free floating strings are not possible and branes may be juxtaposed to form stacks of branes. These branes may also be manipulated in much the same way as strings are, by wrapping them around the geometry of different dimensions. Finally branes carry both magnetic and electrical charges, and are also subject some upper limit of charge per brane. A brane that is maximally charged is referred to as an extremal brane and it is these objects , wrapped around the geometry of dimensions that produce the aforementioned successful application of m-theory in the description of extremal black holes[26]. 24 Part I: Understanding String Theory Chapter 8 A Brief Introduction to String Theory ‘Nature is full of infinite causes which were never set forth in experience’ - Leonardo da Vinci 8.1 A glimpse of formalism At long last we have now arrived at a point where we may discuss what M-theory exactly describes and how it is formulated. For this second point, string theory has the unfortunate quality that it lacks a single formula with the same general applicability of the Schrödinger equation or Einstein’s field equations. This, combined with the overall complexity of the mathematics involved in string theory, makes it difficult to provide direct insight into the mathematical behavior of strings. Perhaps the most pertinent equation relates the mass of a string to its internal oscillations. It is this behavior that allows string to form different kinds of particles and allows for the description of the standard model of particle physics through string theory. The formulation of the mass of a string in terms of these oscillations is given below in equation 12 [16]. 12) 1 𝐼 ∗ 𝐼 𝑀 2 = 𝛼 ′ ∑∞ 𝑛=1 𝑛 𝑎𝑛 𝑎𝑛 Where M is the mass of the string, α’ represents the square of the string’s length scale , I =1,2,…, 8 running over the dimensions of space and coefficient an is described by the following relation.1 13) 1 𝐼 𝛼𝑝𝐼 √2𝛼 ′ 𝛼𝑛− = 𝑝+ ∑𝑝∈ℤ 𝛼𝑁−𝑝 1 Note that some authors describe this relation in terms of string tension. This is equivalent to mass since tension is simply mass per unit length. As the length scale of the string is included in this description, it is equivalent to the formulation in terms of string tension. 25 Part I: Understanding String Theory Where p represents the momentum varied over all positive and negative integer values, and p+ is the momentum, evaluated in light-cone coordinates, which are well suited to the description of light-like propagation. Result 12, which is explicitly classical, does not survive quantization. This is a desirable aspect, since we do not observe particles having continuous values for their masses. Furthermore the string states cannot take a continuous spectrum of values. Equation 12 is further complicated by the addition of quantum mechanics, which requires added constants to allow for correspondence to certain physical theories[16]. Finally this equation only extends to the description of open strings, again indicative of the mathematical complexities that are associated with string theory. For the our purposes however, it provides clear justification for the statement that the motion of strings correspond to the emergence of various particles with corresponding masses and properties. 8.2 Fundamental entities But what is this relation between particles and the mass of string exactly in conceptual terms? As mentioned before, branes characterize themselves as the location where open strings must end. Strings can be differentiated not only on their geometric properties, but can also be labeled as so called F-strings, fundamental strings, and their counterparts D-strings. The latter are built up out of F-strings, and are sometimes referred to as D1-branes. This term refers to the fact that it is a one-dimensional brane subject to Dirichlet boundary conditions. D-strings, due to being built up out of F-string, are much heavier and thicker than their fundamental counterparts. These open strings then terminate on a brane, for the sake of conceptual simplicity let’s say a D2-brane, which is analogous to a conventional membrane. Now, imagine a F-string, extended in the z direction, very thing and light terminating on the D2-brane, extended in an xy plane. The intersection of these two objects on the brane would constitute a single point x,y,z. Remember that the D2-brane has no discernable thickness in the z axis. Thus the F-string termination point would, to inhabitants of this D2 brane look like a zero dimensional point particle, say an electron. 26 Part I: Understanding String Theory In the same way, a D1-string terminating on the brane would result in a three dimensional particle, since the D1 brane, in addition to being extended in the z direction has a thickness associated to it in the xy plane. The F-string termination would result in an electron, the D-string termination in, for example, a Higgs boson. Thus the way the strings intersect with the branes translates to what sort of particle it is observed as, in that particular brane. This is how the mass of a string, equivalent to its thickness relates to the mass of the particle observed. 8.3 D+1 Dimensions D-branes come in many different forms and sizes, and these are made up out of F-strings. The simplest of such objects is known as a D0 brane, which represents a point particle. Strings that are open must end on a brane, in the case of the D0 brane, one can think of it as a pointlike magnet, where all field lines need to originate and terminate on the source. Probing such an object by scattering something off it would reveal more and more F-strings. As discussed before, branes can also be stacked. Imagine two D2-branes floating parallel to one another at a fixed distance. Let’s call the bottom brane the floor and the top brane the ceiling. If the distance between the floor and ceiling is very small, the physicists living on the D2-brane will, for all intents and purposes, not be able to distinguish this distance and conclude that they live in a D2-space. This example illustrates a compactified dimension, and should serve as a crude example for the CalabiYau manifold. Now let us suppose that the distance between the floor and the ceiling corresponds to a parameter g, the string coupling constant. When g<<1, the extra dimension is very hard to observe. As g grows however, the floor-ceiling distance begins to grow, and becomes more and more noticeable. When g>>1, a fully extended dimension is observed, and the physicists must conclude that instead of living in a 2D space, they live in a 3D space. 8.4 The Weakness of Stringy Gravity To complete this picture we must consider another type of duality, namely S-duality, which stands for strength duality. Imagine two strings, a F-string and a D1-brane, and say 27 Part I: Understanding String Theory g<<1. In this scenario the D-string will be much heavier than the F-string and as discussed, when they terminate on a brane will respectively translate to an extended particle and a point particle. Now as g is varied and eventually g>>1, the D-string will start dissolving, shedding off strings and turn into an F-string. Simultaneously the Fstring will start drawing in more strings and become thicker and heavier, eventually turning into a D-string. Accordingly, the particles these strings correspond to are now swapped as well, what used to be the D-string now becomes a point particle, and vice versa. This is perhaps one of the most intriguing aspects of string theory, because it implies that at a fundamental level, one can no longer distinguish between the fundamental and other particles/strings [27]. Finally let’s consider how gravity comes into all of this. As g changes, we have seen that both the dimensionality of a space and the nature of the particles can change. Something quite bizarre happens to the D0 branes when this S-duality occurs. As g grows these heavy point-like string constructs start shedding weight and strings, just like the D-string. When g reaches the sufficient condition these D0 branes turn into gravitons inside the compactified dimension. In effect, string theory allows for gravity to ‘cross over’ between branes, while the other particles are still confined to the dimensionality of the branes themselves. This explanation, although phrased in mathematically dense terms, is one of the reasons for the relative weakness of gravity compared to the other fundamental forces. Gravity can cross all 10 dimensions of space in M-theory, whereas the other forces are confined to live in only 3. I have said before that it is very difficult to fully understand string theory without the mathematical toolkit required, and the picture I have sketched here is overly simplistic. There is much more depth to the mathematical conjectures and descriptions of string theory that will undoubtedly be of importance to a much higher level of discussion on the exact nature of string theory. That being said, an understanding of the theory in terms of branes and strings should be sufficient for the purpose of this paper, namely the evaluation of string theory as a scientific theory. 28 Part II: Evaluating String Theory Chapter 9 Philosophy of Science And now for something completely different! - John Cleese 9.1 Another Introduction This chapter in many ways is the opening of a different type of paper. The overarching purpose of this project has been twofold; first to understand what string theory exactly is and how it has been developed. This has been done through a conceptual analysis, by delving into the foundational problems of physics and the various historical methods and solutions that have been proposed throughout the 20 th century. Second, to evaluate some of the claims surrounding the scientific status of string theory. Thus we move away from the realm of theoretical physics and step into the domain of philosophy of science, with all the novel idiosyncrasies that this shift entails. Statements in the philosophy of science are more subject to formulation and interpretation, and care must be taken to reflect on what this means for both myself as writer and for yourself as the reader. Having said this, let us without further ado delve into examining the claims surrounding string theory and its status as a scientific theory. 9.2 Structure and Purpose As before, my analysis will be broken up into different perspectives that can be taken to criticize or defend string theory. First, it is true that the role of experimentation in string theory, and arguably physics in general, is a source of much contention in the field of theoretical physics. Thus chapter 10 is dedicated to analyzing how we think of experimentation and its relation to the falsifiability of theories. As mentioned before, several claims have been made, both in and outside of academia, that string theory is a philosophy because there are ‘no falsifiable predictions’ that are made by string theory. To evaluate such claims we must both understand what sort of predictions string theory 29 Part II: Evaluating String Theory makes, and how we might test such predictions. Furthermore, one must consider the role that experimentation has had in historically significant theories, as there are various theories where experimental confirmation was achieved long after mainstream acceptance of the theory. A second problem is elaborated in chapter 11; string theory postulates certain mathematical conjectures of which it is unclear on how they should be proven [25]. Can a theory that is so explicitly rooted in the mathematical formalism still be proven through experimentation and is this the most prudent way to go about it? Various philosophers and scientists alike have pointed out that the increasing dependence on theory in modern physics might mean that it is time to reevaluate our standards of scientific results. What exactly is the role that theory plays in the evaluation of string theory, and how does this compare to other, more widely accepted, theories such as cosmic inflation? Finally, a word must be said about the alternatives to string theory. Many of the challenges associated with string theory are not unique to it. The scope of string theory as a grand unified theory bring certain challenges with it, so it would serve to evaluate some of the alternative frameworks that have been proposed . Some physicists, most notably Lee Smolin, have claimed that string theory has taken up a dominant position in theoretical physics and has been ‘pushing out’ alternative theories. Although I will not explicitly delve into this argument, it is anecdotally interesting in illustrating the perception that string theory is the only candidate for grand unified theory, a claim made by Hawking as well. Chapter 12 will be dedicated to understanding what sort of alternatives exist to string theory and how we should evaluate these alternatives. 30 Part II: Evaluating String Theory Chapter 10 The Role of Experimentation Measure what is measurable, and make measurable what is not. - Galileo Galilei 10.1 Definitions Experimentation and physics have a long and very complicated relationship, entire books have been dedicated towards elaborating the dynamic between them. 2 Perhaps one of the pivotal problems one comes across when discussing the role of experimentation is that it has varied over time how philosophers of science and physicists have envisioned the relation between experimentation and scientific knowledge. One characterization of experimentation from the famously pragmatic Feynman is: “The test of all scientific knowledge is experiment. Experiment is the sole judge of scientific truth”[29]. For the purpose of this paper, I will hold to the ‘naïve’ definitions of experimentation in the sense that I will define experiment as using a measurement apparatus that allows physicists to measure some set quantity of the universe and return the magnitude of this quantity. Furthermore, for the sake of brevity I will not delve into interpretational questions on the role of experimentation, and simply follow Poppers criterion of falsification to complete my analysis of whether experimentation prove that string theory is ‘correct’. These definitions, although open to criticism and contention, I believe are sufficiently intuitive that I need not further elaborate on them. 2 For a nice introduction on the topic, the Stanford Encyclopedia of Philosophy offers a wonderful summary of the interaction that experimentation and physics specifically, but the hard sciences in general, has historically had and how this relation has shifted. http://plato.stanford.edu/entries/physicsexperiment/ 31 Part II: Evaluating String Theory 10.2 Unfalsified versus Unfalsifiable Within the context of the definitions provided, we may formulate the question on whether or not string theory may be testable, and answer some of the claims that critics make that string theory offers no predictions that may be falsifiable. It is indeed true that some of the predictions that string theory makes are difficult, if not impossible to falsify. Examples include the existence of parallel universes, as it is currently unclear how, if at all, one might probe universes that could potentially have different physics than ours [30]. On top of this, some of these pocket universes may be accelerating away from us at velocities higher than the speed of light, casting further doubts on the testability of such predictions. Although later sections will elaborate on this point, string theory is not the only framework that makes these type of predictions. Such predictions I will label inherently unfalsifiable, meaning that within the scope of current physical theories they are effectively removed from us in such a way that they are un-probable. A second type of prediction is related to observations that might be testable at extremely high energies, typically approaching the Planck scale. These predictions are as of yet also untestable, because they are subject to financial and technological constraints that render these kinds of experiments unfeasible. It is crucial to note however that these predictions are not impossible to falsify in principle. To put the technological constraints into perspective, the maximum energy currently achievable at LHC in Geneva is around 14 TeV, the Planck scale is closer to 1015 TeV. It is not uncommon for theories in physics to outpace technological development, as there are many historical examples of theories that were non testable at their conception. Examples include the Higgs Boson postulated in 1964 and discovered in 2012, neutrinos postulated in 1930, discovered in 1956 and was rewarded with the Nobel Prize in 1995 as well as the ongoing search for gravitational waves [31]. This is not to say however that all is well in the experimental string theory department, some of the predictions made by string theorists, such as microscopic black holes and low energy super symmetric particles have been falsified through observation [24]. These results are indeed problematic, but are not completely fatal to string theories 32 Part II: Evaluating String Theory because they are observations compatible with string theory rather than direct results of string theory. This problem is related to the so-called landscape problem, which is a point of major contention within string theory. The landscape problem refers to the fact that many of the fundamental constant of nature including the proton mass and the charge of the electron are a result of ways in which the Calabi-Yau manifold can be folded. The topology of these manifolds and how they may be compressed is a crucial problem in string theory, as there are over 10500 different permutations, each of which correspond to a different standard model with different values [25]. This is rather unsettling, as experiments that appear to refute the predictions of string theory may simply be dismissed as the wrong permutation, leaving the theory as a whole intact. Of course the sheer number of permutations makes testing of each version an extremely impractical endeavor. As a result, the landscape problem is a rather polarizing feature in string theory, with some hailing it as a beautiful conceptual flexibility in need of exploitation and others claiming it allows for post-hoc adjustments [32]. 10.3 Consequences for the experimental validation of string theory How should we evaluate the claims surrounding the experimental status of string theory then? It seems that there are indeed issues, the first being predictions that are inherently beyond the our capacity to measure by virtue of their causal disconnect [30]. String theory is by no means the only theory that predicts these kinds of results however, and as such it is not a strong argument against string theory in particular. That being said, the fact that all predictions of string theory have thus far been falsified is worrisome and a valid cause for concern. Worse still the landscape problem is a problematic feature of string theory and is in need of being addressed. Solutions that have been proposed include the anthropic principle, implying that we may select from the different permutations those universes that create conditions suitable to the emergence of sentient life. Various scientists and philosophers alike have taken issue with this principle however, although their objections are too verbose to be done full justice here[33]. Another problem string theory faces is that dark energy falls beyond its scope; 33 Part II: Evaluating String Theory many of the permutations offer universes with a negative cosmological constant whereas the recent discovery of dark energy implies a positive one for at least our universe. Indeed dark matter/energy, although it is poorly understood, was not predicted by string theory, a rather awkward caveat for a theory of everything. Despite this, claims that string theory is inherently falsifiable, although not entirely without merit, are a gross oversimplification of the theory. Many of the predictions string theory makes are simply not yet accessible and it is thus not prudent to dismiss their content immediately. Recent results from fields far removed from string theory, for example condensed matter physics3, have been catalyzed by using theoretical results from string theory [35]. In particular the study of entanglement in superconductors draws heavily on the ideas of duality and extra spatial dimensions that had been more fully developed in string theory. Using the duality between four-dimensional gauge theories and five-dimensional gravity, string theorists have been able to predict the experimental value of the entropy density-to-viscosity in a quark gluon plasma: a result that is not achievable with any other theoretical model on account of the fact that gauge theory is strongly coupled. Although this is not an outright experimental validation of string theory, it does offer tantalizing hopes of finding a falsifiable experimental prediction from an unexpected corner of science. Nonetheless there are few indications that direct experimental justification will be reachable within the foreseeable future. To make matters worse, since string theory is not theoretically complete, our understanding of the framework is not sufficiently well understood to indicate the most efficient way towards developing string theory to the point where it might be experimentally tested [34]. 3 There are several other attempts at experimental applications of string theory, including the testing of AdS/CFT at RHIC and LHC [40], the another experimental test of holography at Fermilab [41]. 34 Part II: Evaluating String Theory Chapter 11 The Role of Theory Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. - Steven Weinberg 11.1 A bold/unscientific proposal Some authors, notably Richard Dawid, have argued that string theory is a new form of scientific theory, which falls beyond the scope of the older experiment driven paradigm of science. He suggests that physics is currently in the midst of a meta-paradigmatic shift in that modern theories such as string theory are so far ahead of our experimental capacity that a new method of scientific justification is required. In his book String Theory and the Scientific Method, he proposes a reexamination of what is considered an acceptable method of deciding whether theories are ‘true’. As we have seen from the previous chapter, experimental verification of string theory seems beyond our grasp, at least for the near future. This chapter will thus be dedicated towards evaluating the merits of a ‘meta-paradigmatic rift’. To illustrate Dawid’s proposal a brief conceptual sidetrack will be taken examine whether or not string theory automatically entails strict reductionism. First and foremost, unification itself does not necessarily entail reductionism, a further elaboration will not be given here since our purpose is to evaluate string theory specifically.4 When considering the possible reductionist tendencies present in string theory, we must return to the notion of dualities. 4 Various authors have defended and criticized the seminal paper by Philip Kitcher Explanatory Unification from 1981, Todd Jones offers interesting thoughts in Reductionism and Unification Theory of Explanation but there are not fully relevant to our purposes of evaluating string theory. 35 Part II: Evaluating String Theory We have already seen that S-duality problematizes the question of which particles are fundamental. Dualities are mathematically equivalent and there is no clear reason to favor one frame of reference over the other since it is ultimately a question of energy scale that determines which frame is fundamental. In a similar way AdS/CFT ‘translates’ a 2D theory on the surface of a sphere into a 3D theory describing the interior of the sphere. Neither description is more fundamental, rather the two are complimentary. The question on whether or not string theory is reductionist does not quite make sense. Indeed Leonard Susskind even makes the bold assertion that modern physics has spelled the end for reductionism [29]. How may we relate this to the question of experimentation in string theory? 11.2 The ‘meta-paradigmatic rift As discussed, there are indeed problems with the experimental verifiability of string theory. In fact so much critique has come from this corner that some have argued that experimental verification is not the correct way of pursuing string theory. Dawid opens with the following observation: ‘I note that the general scientific acceptance of specific unobservable scientific objects in the early twentieth century or the confident prediction of new particles based on the particle physics standard model may be taken as significant stages in a process that leads towards increasing trust in theoretical conceptions based on the assessment that, under some circumstances, an equally convincing theoretical structuring of available data with substantially different prognostics is unlikely to exist ‘. [1] An example that has been proposed based on mostly theoretical grounds is that of cosmic inflation. First proposed by Alan Guth in 1979, cosmic inflation explains why the cosmic microwave background (CMB) has only tiny variations in temperature between various different regions that were not in direct contact. The solution was that the universe expanded extremely rapidly in the first moments after the big bang and that areas which today seem far removed from one another were once close together. Yet the most recent attempt to experimentally confirm cosmic inflation, together with the 36 Part II: Evaluating String Theory detection of primordial gravitational waves in the BICEP2 experiment was unsuccessful in 2015 after a false positive [36]. Despite this, cosmic inflation is widely accepted in various different fields of physics even if experimental proof has been limited. Noting this dependence on theory, Dawid states: ‘the current situation in fundamental physics shows that the focus on purely theoretical argumentation is considerably stronger in some other fields than in string physics proper.’ [1] The question this raises is whether or not experimental validation of highly abstract theories such as string theory are the right way of going about falsifying. As mentioned, the landscape problem poses a major problem to experimental verification of string theory, to say nothing about the inaccessibility of the Planck scale to experimentalists using current technology. Dawid argues that we are in the midst of a ‘meta-paradigmatic rift’, where our ability to make theoretical advances has outpaced our experimental capacities. As a results he raises the point that it might be necessary to reevaluate the nature of scientific validity to allow for more theoretical arguments besides experimental data [34]. 11.3 Theory-driven confirmation of physics Understandably his proposal that we must redefine how scientific inquiry is formulated is controversial. Opponents of such a move claim that it conveniently moves the goal posts for a theory that has failed to make adequate predictions. String theorist are (generally) more accepting of the idea and argue that experimental falsification is not inherently the best method of doing science. Arguments from either side are by definition unacceptable to the other, leading to a discussion that is characterized by a profound mismatch in positions. Accordingly both sides accuse one another various personal insufficiencies, hubris on the side of the string theorists and of insufficient intellectual acuteness on the end of the critics [1]. This being said, changing the standard of validity for scientific theories is indeed a bold move. It is true that the success of Galileo, where his experiments directly led him to theoretical insights into the behavior 37 Part II: Evaluating String Theory of material objects, most famously in the cathedral of Pisa that the frequency of a pendulum is independent of arc length, is no longer the modus operandi of modern scientists. Einstein devised general and special relativity through his daytime dreaming at a Swiss patent office on what it would be like to travel next to a beam of light. Does it constitute such a leap of faith to think that the role of experimentation might be in need of reconsidering? Debate is currently ongoing in this area, but it is perhaps a statement to the trust string physicists have in their work that they are willing to develop a new type of science around it. 38 Part II: Evaluating String Theory Chapter 12 Considerations in the pursuit of string theory ‘God does not play with dice’ - Albert Einstein 12.1 Potential versus Productivity Another argument can be raised against string theory of a different nature altogether. Namely, that it has been a significant intellectual investment that has achieved relatively little in return. Smolin in particular has been vocal in claiming that string theory is consuming all the resources in the field of theoretical physics and that science would be best served by ‘hedging its bets’. The statistics Smolin presented as evidence of the dominance of string theory have been drawn into question by various authors and although it is not the purpose of this paper to evaluate the sociology of theoretical physics, it does raise an interesting point[37]. Is it perhaps time to give up on string theory? Larry Laudan argued that the most rational decision a scientist might make is to pursue the research tradition that has the highest problem solving rate[38]. This naturally brings about the problem of evaluating string theory’s productivity, which once again depends on the perspective of the evaluator. Critics say that string theory has had its time in the sun and has not offered us the types of advances needed to merit such a large investment of intellectual capital. Worse still, it has not come closer to presenting itself in a format that is in accordance with the predominant standard of scientific verification, that of experimental falsification. String theorists will interject that large theoretical advances have been made, and that there has been a ‘surprising explanatory coherence of string theory… and a considerable number of interconnections between different theoretical problems have emerged in the context of string theory although the theory was not devised to deliver them’ [1]. Indeed it is an intriguing fact that string theory, 39 Part II: Evaluating String Theory despite originating from an attempt to describe gluon interaction, does translate into a theory that encompasses the full scope of a grand unified theory. 12.2 The other contenders Since evaluating string theory’s problem solving rate is problematic, might it make sense to evaluate alternative theories and compare them to the success or failure of string theory? As discussed, one of the main differences between string theory and alternate theories, is that string theory attempts to solve the problem of quantum gravity within the context of unification. Various other theories have been proposed to solve the much more specific problem of quantum gravity, most notably loop quantum gravity(LQG). Unfortunately many of the same problems that plague string theory’s experimental verification are applicable to LQG5. As it stands, LQG has not yet been developed to a point that it is able to make falsifiable claims, rendering it vulnerable to exactly the same criticism that has been spelled out above. Smolin claims that fields like LQG have been consistently underrepresented and that science as whole would benefit from as many different possible approaches to solving the problem as possible [15]. Some authors, including Duff, have accused Smolin of a double standard, in that he is willing to accept LGQ , a field that he developed along with Ted Jacobson, while it still subject to more or less the same objections as string theory[23]. Smolin’s idea about the diversity of science is nonetheless interesting, although it appears this diversity does not extend to the likes of Dawid’s proposal for a new method of scientific verification. 12.3 The Pragmatic Answer How then to make sense of these different positions? Perhaps the following hypothetical will be helpful: Suppose that all string theorists decide to abandon their work and pursue other endeavors. What would happen? Is there a different theory that they all might work on to still achieve the perennial holy grail of physics, the grand unifying theory? Thus far it appears that there are no other realistic candidates for such 5 Various other approaches have been proposed including causal sets and cause dynamical triangulations which have similar problems as string theory. A full treatment of their respective issues has not been given but interesting sources are The deep metaphysics of quantum gravity[42] for a philosophical perspective and How far are we from the quantum theory of gravity? [43] for a more quantitative view. 40 Part II: Evaluating String Theory a theory[36]. In the pursuit of the ‘theory of everything’ there seems to be no other way forward than continue working on string theory. Quantum gravity itself does have alternative ways that might lead to results, including quantum loop gravity but with a substantially more modest goal. This argument, that string theory is the only suitable candidate for the task at hand is sometimes referred to as the ‘No alternatives argument[39]. Whether this a good argument or a simple truism I leave up to you. 41 Part II: Evaluating String Theory Chapter 13 Conclusion ‘It is not enough that you should understand about applied science in order that your work may increase man’s blessings. Concern for the man himself and his fate must always form the chief interest of all technical endeavors; concern for the great unsolved problems of the organization of labor and distribution of goods in order that creations of our mind shall be a blessing and not a curse to mankind.Never forget this in the midst of your diagrams and equations.’ -Albert Einstein Over the course of this paper I have tried to complete two distinctly different tasks, each related to the other, yet framed from different disciplines. The first, from the domain of theoretical physics, was to understand what string theory is, and where it came from. In order to do so I have tried to focus on the motivation behind string theory. As said before, the world of theoretical physics can be somewhat impenetrable without the mathematical acumen that typically only comes from extensive training. It is perhaps for this reason that the debate surrounding string theory has been so murky and prone to misinterpretation. Yet this should not keep anyone from trying to understand what this potential theory of everything is truly about, and why it is such a desirable thing for physicists and scientists in general. Through understanding what it is that physicists try to achieve, namely unification of all forces and particles, we have examined the different domains of quantum mechanics and general relativity. The problem of quantum gravity has been made explicit and the various solutions that have been proposed over the years, ranging from Kaluza-Klein all the way to the modern 11-dimensional M-theory, have been elaborated. M-theory is a grand attempt to describe the totality of the universe within the scope of a single theory, with a single free parameter. I concluded 42 Part II: Evaluating String Theory this section with a brief summary of the worldview that M-theory sketches, thus closing what for some might be the harder, for others the easier part of this research project. The second task set was to evaluate the various critiques that have been leveled at string theory and asses the merits of their arguments. As discussed, experimental verification of string theory is indeed a problem, but the claims that string theory is inherently unfalsifiable, while not without merit are not entirely correct. There are indeed predictions made by string theory which might at some point be falsifiable, but with our current technological constraints there is little hope of running an experiment that will outright confirm or debunk string theory in the near future. Worse still, the problem of the landscape poses a major challenge to any future attempts to falsify some of the lower energy predictions that string theory might offer. Indeed various authors have suggested that experimental verification might not be the best way of going about testing string theory and have proposed different methods of scientific verification altogether. Finally we have examined some of the alternatives to string theory that have been proposed, and uncovered that although there are options in terms of solving quantum gravity, none can challenge string theory in the endeavor of uncovering the grand unified theory. To conclude, perhaps a fair evaluation of string theory is that it is a work in progress. The quality and quantity of results depends largely on individual attitude toward string theory and there is much disagreement within the physics community concerning string theory. Like quantum mechanics, there is a distinct gap between our capacity to work with the mathematical complexity of string theory and our conceptual and philosophical understanding of it. Unlike quantum mechanics, we do not have hard experimental evidence to sooth our fears that we might have taken a wrong turn somewhere. My personal evaluation of string theories success as a theory of science is somewhat mixed. On the one hand I am sympathetic to the complaints of Smolin and others that string theory has not offered the results that were promised during the second string theory revolution. On the other, I also realize that string theory’s potential lack of success is a question of perspective, and that theoretical advances have been made even if they do 43 Part II: Evaluating String Theory not fully translate to falsifiable predictions. Dawid’s proposal is intriguing and although I am unsure about whether it is his precise formulation that will ultimately prevail, it seems to me that there is a need to perhaps reconsider, or at the very least reexamine in light of recent developments, what it is that science precisely entails. It is true that there is nothing inherent about experimentation as the golden and sole standard of truth measuring, but it is equally troubling that we might accept a theory that is no longer clearly relatable to our empirical reality. Experimentation has ,without a doubt, a major role to play in physics, but a more varied set of validation methods, including indirect observational evidence and confirmation, might be prudent and even necessary. In light of the increasingly prominent misunderstandings of what it is that science exactly means, be it from a religious or ideological perspective, perhaps it is time for an academic discussion on what it is that science does and how it might go about doing this. If science is truly the self-correcting mechanism that it sometimes claims to be, free from God-like standards of absolute normativity, we should welcome a discussion on the foundational questions surrounding its nature. In the meantime, I think that all physicists agree that we do eventually want to achieve this elusive theory of everything and that, as it stands, string theory is still our best option. 44 References: [1] Dawid, Richard. "On the Conflicting Assessments of the Current Status of String Theory." Philosophy of Science 76.5 (2009): 984-96. Web. [2] Claus Grupen, Astroparticle Physics [3] Nicholas Maxwell, Unification and Revolution: a Paradigm for Paradigms, Journal for General Philosophy of Science, 2014, Vol.45(1), pp.133-149 [4] Langacker, Paul. "Grand Unification." - Scholarpedia. N.p., n.d. Web. 25 Mar. 2015. [5] S.Raby. “Proton Decay” talk presented at SUSY’02, DESY, Hamburg, Germany [6] G. Aad, S. Bentvelsen et al. “Search for magnetic monopoles in √s 7 = TeV pp collisions with the ATLAS detector”, Physics review letters. [7] Claus Grupen, Astroparticle Physics [8] Florent, Alice. "Production of W and Z Bosons in Heavy-ion Collisions with CMS." N.p., n.d. Web. 25 Mar. 2015. [9] Naik, Guatam. "New Data Boosts Case for Higgs Boson Find." WSJ. N.p., n.d. Web. 25 Mar. 2015. [10] Szafron, R., and M. Zralek. "Neutrino Oscillation beyond the Standard Model." CAS – Central Authentication Service. N.p., n.d. Web. 25 Mar. 2015. [11] Ellis, John. "Physics Beyond the Standard Model." Nuclear Physics A 827.1-4 (2009): 187c-98c. Web. [11] Kitcher, Philip. “Explanatory Unification” Philosophy of Science, Vol. 4, (Dec., 1981): 507-531 [12] Schurz, Gerhard. "Explanation as Unification." Synthese (1999): 95-114. Web. [13] Hawking, Stephen, and Leonard Mlodinow. The Grand Design. New York: Bantam, 2010. Print. [14] Greene, B. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: W.W. Norton, 1999. Print. [15] Smolin, Lee. The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes next. Boston: Houghton Mifflin, 2006. Print. [16] Zwiebach, Barton. A First Course in String Theory. New York: Cambridge UP, 2004. Print. [17] Yau, Shing-Tung. "Calabi-Yau Manifold." - Scholarpedia. N.p., n.d. Web. 23 Apr. 2015. [18] Will, Clifford M. "Gravitational Radiation and the Validity of General Relativity." Physics Today 52.10 (1999): 38. Web. [19] "The Speed Of Light Can Vary In A Vacuum." IFLScience. N.p., 20 Jan. 2015. Web. 25 Mar. 2015. 29 Part II: Evaluating String Theory [20] Griffiths, David J. Introduction to Quantum Mechanics. Upper Saddle River, NJ: Pearson Prentice Hall, 2005. Print. [21] Macías, Alfredo, and Abel Camacho. "On the Incompatibility between Quantum Theory and General Relativity." Physics Letters B 663.1-2 (2008): 99-102. Web. [22] Bekenstein, Jacob D. "Bekenstein-Hawking Entropy." - Scholarpedia. N.p., n.d. Web. 23 Apr. 2015. [23] Rovelli, Carlo. "A Critical Look at Strings." Foundations of Physics 43.1 (2013): 8-20. Web [24] Blau, Matthias, and Stefan Theisen. "String Theory as a Theory of Quantum Gravity: A Status Report." General Relativity and Gravitation 41.4 (2009): 743-55. Web. [25] Susskind, Leonard. "Topics in String Theory." Stanford's Continuing Studies Program. Stanford University, Stanford. 10 Jan. 2011. Lecture. [26] Susskind, Leonard, and James Lindesay. An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe. Hackensack, NJ: World Scientific, 2005. Print. [27] Alvarez-Gaume, Luis, and S.F. Hassan. "Introduction to S -Duality in N = 2 Supersymmetric Gauge Theories." (1997): n. pag. Web. [28] "Mathematical Physicist Edward Witten Interview - 1 of 2." YouTube. YouTube, n.d. Web. 27 Apr. 2015. [29] Feynman, Richard P., Robert B. Leighton, and Matthew L. Sands. The Feynman Lectures on Physics. Reading, MA: Addison-Wesley Pub., 1963. Print. [30] Freivogel, Ben. "A Multiverse of Probabilities." A Multiverse of Probabilities. N.p., Mar. 2010. Web. 06 May 2015. [31] Mckernan, B., K. E. S. Ford, B. Kocsis, and Z. Haiman. "Stars as Resonant Absorbers of Gravitational Waves." Monthly Notices of the Royal Astronomical Society: Letters 445.1 (2014): n. pag. Web. [32] Smolin, Lee. "A Perspective on the Landscape Problem." Found Phys Foundations of Physics 43.1 (2012): 21-45. Web. [33] Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic, 2001. Print. [34] Dawid, Richard. String Theory and the Scientific Method. N.p.: n.p., n.d. Print. [35] Sachdev, Subir. "Strange and Stringy." Sci Am Scientific American 308.1 (2012): 44-51. Web. 48 Part II: Evaluating String Theory [36] Lizarraga, Joanes, Jon Urrestilla, David Daverio, Mark Hindmarsh, Martin Kunz, and Andrew R. Liddle. "Fitting BICEP2 with Defects, Primordial Gravitational Waves and Dust." J. Phys.: Conf. Ser. Journal of Physics: Conference Series 600 (2015): 012025. Web [37] Duff, M. J. "String and M-Theory: Answering the Critics." Found Phys Foundations of Physics 43.1 (2011): 182-200. Web. [38] Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: U of Chicago, 2003. Print. [39] Dawid, R., S. Hartmann, and J. Sprenger. "The No Alternatives Argument."The British Journal for the Philosophy of Science 66.1 (2014): 213-34. Web. [40] Horowitz, W. A. "Testing PQCD and AdS/CFT Energy Loss at RHIC and LHC." (2012): n. pag. Web. [41] Akbari, Homaira, and Hans I. Bjelkhagen. "Holography In 15-Foot Bubble Chamber at Fermilab." Practical Holography (1986): n. pag. Web. [42] Slowik, Edward. "The Deep Metaphysics of Quantum Gravity: The Seventeenth Century Legacy and an Alternative Ontology beyond Sub stantivalism and Relationism." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44.4 (2013): 490-99. Web. [43] Woodard, R. P. "How Far Are We from the Quantum Theory of Gravity?"Rep. Prog. Phys. Reports on Progress in Physics 72.12 (2009): 126002. Web 49 Curriculum Vitae Contact details Name: Paul Julius Verhagen Address: Carolina Macgillavrylaan 1144, 1098XC, Amsterdam Telephone: 06-41164290 E-mail address: [email protected] Place of birth: Amsterdam Date of birth: 29-11-1991 Nationality: Dutch/American Burgerservice number: 207634920 Education June 2013- August 2013 Fudan University Summer Program: Fudan International Summer Session Courses taken: Confucian Studies & Mandarin (3.75 GPA) Details: Scholarship granted by University of Amsterdam Sept 2012 – Present Amsterdam University College Bachelor: Liberal Arts & Science (3.48 GPA) Details: Major in Sciences with a minor in Humanities 6 Studies centered on physics, computational sciences, mathematics and philosophy Graduation expected in June 2015 June 2012- August 2012 University of Hong Kong Summer Program: HKU International Summer Session Courses taken: Mandarin Studies (4.0 GPA) 6 Relevant courses: Physics of Heat, Quantum Mechanics, Physical Biology of the Cell, Advanced Logic, Astro-particle Physics, Partial Differential Equations, Philosophy of Science, Philosophy, Academic English II, LEU 48 Part II: Evaluating String Theory Sept 2010 – June 2012 University of Amsterdam Bachelor: Physics & Astronomy Details: Unfinished at 60 ECP Extra-curricular Activities May 2015 Research Presentation Institution: Harvard Graduate School of Education Description: Invited to co-present a lecture entitled: Innovation in Higher Education: Reflections from International Practice, centered around my involvement with the AUC Big Data project. As such my task included providing an overview of how AUC makes use of student-driven initiatives to innovate the Liberal Arts & Science curriculum and relating this to the ongoing discussion on what educational innovation entails in a practical sense. February 2015 Conference: Big Data, are we in the midst of a paradigm shift? Institution: Amsterdam University College Description: Conference organized to launch a new addition to the Amsterdam University College curriculum centered on Big Data. This course was designed by a student think tank which included myself, and is aimed at providing a general overview of the idiosyncrasies of the digital age, both in terms of societal issues and conceptual paradigms. My contribution involved presenting the official course design to Amsterdam University College faculty and students. June 2014- February 2015 Internship Organization: AUC Big Data Student Think Tank Description: Internship centered on setting up a course: Big Data to be taught at Amsterdam University College in 2016. The course will focus on an interdisciplinary approach to the digital revolution ranging from social issues such as regulation of information services to technical infrastructure and paradigmatic change in the broader sense. My responsibilities included coordination between different focus groups 49 Part II: Evaluating String Theory in addition to being the spokesperson of the Big Data Think Tank towards outside institutions (UvA, Oxford etc.) January 2014 Conference: How did it all start? Institution: Netherhall, London Description: 16th Interdisciplinary conference at Netherhall aimed at reconciling Biology, Physics, Astronomy and Religious Studies. The overarching question framed throughout the conference was to what degree religion is still compatible with a modern scientific mindset. My contribution includes participation in moderated debates and giving a lecture entitled: A conceptual introduction to Cosmology with the purpose of illustrating the idiosyncrasies of quantum physics and general relativity theory to an audience unfamiliar with physics. Publications Title: Course Report: AUC Big Data Course Published by: Amsterdam University College Title: Comparing the Role of the Teacher: Platonism and Confucianism Published by: AUC Undergraduate Journal of Liberal Arts & Science, Open Issue Vol. 4, 2014 Course: Confucian Studies (Fudan University) Term papers Title: Wave Function Collapse and Decoherence: Philosophical implications of decoherence in quantum mechanics Course: Quantum Mechanics 50