Download Part I: Understanding String Theory

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
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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.
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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
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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
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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.
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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
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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.
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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
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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.
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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],
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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].
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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,
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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
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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
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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.
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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
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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
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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/
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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
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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;
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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
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[2] Claus Grupen, Astroparticle Physics
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[11] Ellis, John. "Physics Beyond the Standard Model." Nuclear Physics A 827.1-4 (2009): 187c-98c. Web.
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next. Boston: Houghton Mifflin, 2006. Print.
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[20] Griffiths, David J. Introduction to Quantum Mechanics. Upper Saddle River, NJ: Pearson Prentice Hall,
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[36] Lizarraga, Joanes, Jon Urrestilla, David Daverio, Mark Hindmarsh, Martin Kunz, and Andrew R. Liddle.
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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