Why String Theory? Read online

  String theory is most famous as a theory of quantum gravity and a candidate theory of fundamental interactions at the smallest possible scales, scales that are as small compared to an atomic nucleus as an atomic nucleus is to a person. These scales are also far smaller than can be directly probed by any experiment, even the Large Hadron Collider at CERN. This raises a natural question – if you cannot test string theory directly, how do you know it is right? And if you do not know it is right, and you will not know anytime soon, why do so many people work on it? Surely science advances by experiment, and without experiment there can be nothing but stagnation.

  This is a question posed by many decent, smart and inquisitive people. They may be undergraduate students of physics; they may be evolutionary biologists; they may be observational astronomers; they may be intellectually curious members of the general public who are excited about the fundamental laws of physics. Those who ask this question are people of good will and good faith, who in all charity cannot understand how any one scientific idea without direct experimental support could ever command the time and allegiance of such a large fraction of the relevant experts.

  For it is true that, the closer you approach the subject professionally, the fewer and fewer people you find who continue to ask these questions. Scepticism about string theory tends to diminish as technical knowledge about the subject increases. In practice, the hard acid that dissolves scepticism is the ability to calculate. The greater the ability to calculate in theoretical physics, the clearer the appeal of string theory becomes, both for its own intrinsic perfectly fitting calculational structure and also for its ability to shed light on results in other areas. However it is also true that in return for this ability to calculate, one must pay dearly in terms of time, effort and earning ability. Most people, however strong their interest or aptitude, are for perfectly good reasons not able to follow this route.

  This book is written for these people and aims to answer the questions above. I want to explain, to my wonderful fellow citizens who support scientific research through their taxes, why string theory is so popular and why, despite the lack of direct empirical support, it has attained the level of prominence it has. I want to explain how string theory fits into the broader picture of science, and just why experts find it so compelling. If all the varied rationales of this book were condensed into one single aim, it is to answer the question: why do so many experts choose to work on a theory that has no direct experimental support? My dear colleagues know the answer already, but this book is not written for them.

  This is also, for obvious reasons, a book (almost) without equations. There exists an opinion that if you have true understanding, equations are unnecessary and you can convey concepts with no losses in transmission. I do not share this view. Mathematics is the light that illuminates physics, and mathematics-free physics has marked similarities to alcohol-free wine. Mathematics is the most powerful tool available for explaining and understanding physics, being to a physicist what fingers are to a pianist. Nature really is written in the language of mathematics, and many results that flow easily using it are hard to justify in any other way. In this subject mathematical training is a pure and unqualified good: there is no additional raw creative freshness available through its absence.

  So I apologise now for the fact that the argument made in this book is only a shadow of the argument I would like to make. I am also sorry, despite my best efforts, for the parts of this book that appear less than clear, or where the logical jumps seem broad and unjustified. That said, that which is worth doing is also worth doing poorly. One does not need the palate of Carême to enjoy food, or the ear of Barenboim to listen to music. The rose windows of Chartres are both for those who can follow the biblical stories there and for those who cannot – and the great structure of physics, at least in its outline, is part of the inheritance of all interested minds.

  I now want to describe the structure of the book and the overall organisation of its argument. The first part of the book aims to place string theory the theory of quantum mechanical, relativistic strings – within the broader context of both science as a whole and more specifically theoretical particle physics. There is a lot of science – most of science, indeed almost all of science that has nothing to do with either the fundamental laws of nature or the discovery of new physical principles. My first aim is to isolate the small part of science for which string theory is potentially relevant, and then to describe the important truths that are already known in this area. These topics are covered in chapters 2 and 3. Chapter 2 deals with science as a whole, classifying it by the different length scales that are appropriate. Chapter 3 focuses specifically on physics and on the confirmed results that have been used to build up the modern picture of both particle physics and cosmology.

  Whatever string theory may be, it is certainly outside the canon of established and experimentally confirmed theories. Why do we even need anything new at all? Chapter 4 makes the case for this. It argues that what we have is not enough: despite all previous successes, there is still a need for ideas and structures that go beyond what we already have. When we look at what we have learnt, we see that indeed it is very good – but it does not suffice. Chapter 4 makes no argument for string theory as such. It instead argues for something new. It argues that there must exist something that is not included in our existing theories but instead sits above and beyond them. It explains why theory, observation and experiment all demand that what we currently know is not ultimately at the top of the intellectual food chain – we are still missing a Godzilla theory that is the top predator.

  String theory is, in the first instance, a candidate for that something. It is introduced in the second part of the book and is the subjects of chapter 5 and 6. These are devoted to explaining first what string theory was, and then what string theory is. What do the words ‘string theory’ actually refer to? What does the expression ‘string theory’ even mean? This is a simple question with a complicated answer that has changed dramatically over the last fifty years. What ‘string theory’ meant in 1970 was not what it meant in 1985, which in turn was not what it meant in 2000. Likewise, the motivations for working on the subject have also changed over these periods. The reason for first studying string theory in 1970 was a very bad reason for studying string theory in 1985 but had returned to be one of the most common reasons in 2010. While the underlying equations and calculations have undergone a mostly smooth development, the conceptual picture of what string theory is and how it fits into physics has changed dramatically.

  These chapters are therefore both explanatory and historical. To appreciate what ‘string theory’ means in 2015, it is helpful to know what ‘string theory’ had previously meant in both 1970 and 1985. Over this period, the history of string theory interleaves with the history of particle physics. Chapter 5 is concerned with past understandings of string theory, while chapter 6 presents a more current view.

  Having reviewed the history and nature of string theory, the third part of the book describes motivations for doing research on it. Chapter 7 is devoted to the external correctness of string theory. It reviews the direct experimental evidence proving that string theory is the correct theory of nature at the smallest possible scales.

  The following four chapters explore several particular topics in further depth. The essence of these chapters is that scientists work on string theory because string theory is useful to them. The human foibles of scientists are often appreciated more in the abstract than in the reality. Scientists have their own pet topics, and they care most about what will assist them in their own passions. One of the dirty great secrets about ‘string theory, the candidate fundamental theory of everything’ is that the majority of people who work on this subject actually care little for strings per se and absolutely nothing for fundamental theories of everything. Instead, they have their own interests, which are generally not formulated in terms of string theory, and they care about string theory because it can hel
p them understand what they are actually interested in. The third part of the book describes this in detail and explains why people really choose to work on string theory.

  Chapter 8 is on quantum field theory. We do not know whether string theory is the correct theory of nature. We do however know that the Standard Model is a correct theory of nature, and the Standard Model is built up by describing the strong, weak and electromagnetic forces through what is called a quantum field theory. Quantum field theories are a known part of nature, and they are used not just in particle physics but also in the physics of matter, to describe the way quantum behaviour manifests itself in macroscopic bodies such as insulators or conductors both semi- and super-. This ubiquity of quantum field theory causes many physicists to be interested in understanding it better. They care both about special examples where a quantum field theory can be solved exactly, and also about general insights into how to understand and work with quantum field theories in regimes where all normal techniques break down. Indeed, probably the most popular reason to work on string theory in the years since the millennium has been for the help it provides in understanding quantum field theory.

  Another reason for working on string theory, covered in chapter 9, stems from an interest in mathematics. The developmental logic of string theory was that of physics: it has been constructed by physicists using the techniques and standards that apply in theoretical physics. Nonetheless, it involves geometric ideas and the subject has many overlaps with topics of interest to mathematicians. This creates a fortunate situation – it offers a perspective that is removed enough to be novel but close enough to be useful. The logic of physics is different to that of mathematics, and what is obvious in physics is not obvious in mathematics, enabling the discovery of results that are both new and striking. Since the middle of the 1980s, string theory has acted as tinder for the historic romance of physics with mathematics, provoking both new mathematical techniques and new approaches to existing problems.

  Of course, many people who work on string theory (including me!) do so because they are fascinated by particle physics and cosmology and want to know what lies beyond our existing boundaries of knowledge. This is the topic of chapter 10. String theory provides a rich structure that links onto what we already know about physics while also offering many suggestions for what may lie beyond. While it is implausible to claim that string theory offers any unique extension of the Standard Models of particle physics and cosmology, it provides plentiful examples of types of new physics that one would not otherwise think about. In this respect, string theory is a fine muse and a fertile source of ideas for new ways of thinking about new physics. String theory may not easily be definitively tested, but it is a good source of ideas that can be. These ideas then enter the conventional process by which experiments can be proposed and built to check their veracity.

  Chapter 11 deals with string theory as a theory of quantum gravity. This is the headline application of the subject and has indeed seen a significant amount of work over the years. The chapter describes both the reasons for believing that string theory offers a quantum description of the gravitational force, as well as specific applications to some of the classic problems of classical and quantum gravity.

  The fourth and final part of the book discusses the social aspects of science. The public view of string theory and string theorists has fluctuated over time. One perspective has seen string theorists as the intellectual equivalents of John Wayne, using the power of pure thought to conquer the untamed territories of physics. A more recent outlook sees them as surrender monkeys who inherited the great tradition of theoretical physics and fled from experiment for a combination of mathematical arcana and personal wonga. I hope to show that the truth is more human than the first and richer and more powerful than the second.

  One of the overarching themes of the book is that of diversity. Different scientists care about very different topics, and there are as many approaches to physics as there are physicists. Geoffrey Boycott and Kevin Pietersen were both excellent cricketers who garnered a sackful of runs, despite having personalities and playing styles that could not have been more different. The same holds true in physics. Some prefer deep and intricate calculations with a clear right answer that emerges only after many pages of precise and exact work. Others prefer drawing big picture connections between disparate areas with no apparent relation. Some are only happy when working in close tandem with experiment, while others find satisfaction in the pristine purity of mathematics and are repulsed by the dirtiness of data. There are many ways to be a first-rate physicist and no one choice is best. Chapter 12 is devoted to pen portraits of some of these different styles of doing physics.

  Chapter 13 considers criticisms of string theory. String theory is discussed in fora that reach far beyond the circles of theoretical physics, and it is a tribute to the culture and education of our society that many people care about aspects of fundamental physics so removed from their daily lives. In the same way that honest and engaged citizens can have markedly opposed political views, attitudes to string theory vary sharply, and some scientists are passionately concerned that string theory is damaging physics. This chapter aims to take these attacks, frame them in their most convincing form, and reply to them.

  The final chapter summarises the overall message of this book: why is string theory so appealing? There are other speculative theories of physics at the smallest possible scales. This chapter explains why string theory has been so much more successful than them. What makes string theory special? The short answer is that, in contrast to other approaches, string theory is so much more than just a candidate theory of quantum gravity.

  Other theories of quantum gravity are precisely that – other theories of quantum gravity. In contrast, string theory is a theory for the pragmatic as well as for the ideological. It has outgrown its origins and has something to offer those who are completely uninterested in quantum gravity. Its success in solving problems and contributing deep insights to so many topics has made it popular with many; the same deep insights, far away from its native subject, also convince many that it is the most plausible idea on its home ground. String theory has given much to many, and its enduring popularity comes from the fact that, over several decades, it has remained a theory that just keeps on giving.

  CHAPTER 2

  Scales of Science: Little and Large

  ‘As-salaam alaikum, from where are you coming and to where do you go?’ The ancient call of the desert, from caravan to caravan as they passed on the spice road, also applies to science. A subject with no past can lack the techniques necessary to do science. A subject with no idea as to the problems it is trying to solve has no future.

  This is a book about string theory. Where does string theory fit into the larger canvas of science and physics? ‘Science’ is a big tent with many tent dwellers. Its discoveries have been the primary facilitator of the enormous economic growth of the last few centuries, and few politicians fail to pay at least lip service to it. In the United Kingdom, the annual government budget for science is around ten billion pounds,1 although the overall sum spent is slightly larger because of charitable funding of medical research and the industrial research done in large pharmaceutical and engineering companies. In this big friendly tent, where does string theory fit in? The short answer is: not where the money is. In the most recent academic year, string theory research received somewhere south of one tenth of one per cent of total science funding in the United Kingdom. In the affairs of pounds, shillings and pence, string theory is a tiny tiddler even within a relatively small pond.

  Cost represents one way of classifying different branches of science. Another more subjective measure is by practical utility. String theory belongs clearly to those branches of science that are the canaries in the coal mine for curiosity-driven research. These branches are pursued for the value of intrinsic understanding rather than for any vision of commercial application. As with astronomy or particle physics, string
theory is clearly pure, rather than applied, science.

  It is true that the pure science of one generation has tended to become the applied science of the next. The quantum theory of the electron underpins the semiconductors and transistors that sit behind all modern electronics. The accuracy of a GPS device relies on Einstein’s laws of general relativity. ‘Proton therapy’, the poster child of advanced cancer treatments, is applied particle physics. However, whatever the unknown future may be, it is important to be clear upfront that there are no currently foreseeable economic applications for string theory.

  We will arrange our scientific taxonomy differently, classifying sciences according to their characteristic distance scales – the size of the phenomena they study. ‘Characteristic’ is a wooly word that is nonetheless more useful than an overly exact definition. Its usage is best illustrated by example. The characteristic size of a blade of grass is a couple of centimetres. The characteristic size of a mountain is a couple of kilometres. The characteristic size of a galaxy is a hundred thousand light years.

  We are all human. Excepting hobbits and point guards, an adult member of homo sapiens is typically between 150 and 190 centimetres tall. He or she is made predominantly of water and weighs between forty-five and ninety kilograms. These basic facts determine our first scientific, or rather proto-scientific, intuitions. Our growing lives are conditioned by and organised around the effects of gravity. Children learn at an early age that they cannot walk up walls and that if they fall over they hurt themselves. These ‘natural’ effects are natural only due to our characteristic size. Intelligent ants would experience the world very differently. Gravity is far harder to discover if you can walk up a wall without difficulty and fall down a mineshaft without danger. There is not that much ant for gravity to act on, and it is surface tension, rather than gravity, that plays the crucial role in daily myrmecological life.