Why String Theory?

by Joseph Conlon

  All research involving quantum gravity lacks this gold standard. The silver standard is to make predictions for theoretical problems, for which the answer is not known in advance but can be checked using very different techniques. This silver standard has been abundantly satisfied in string theory. This is through the applications, which we encountered in chapters 8 and 9, to both mathematics and the formal, exactly soluble parts of quantum field theory. The equation towards the end of section 8.2, on tests of the AdS/CFT correspondence, illustrates what is meant by this – no idle argument could ever reproduce that formula.

  The silver standard has however never been attained for loop quantum gravity. The reason why loop quantum gravity – or indeed any other alternative theory of quantum gravity – has not had the success of string theory is that it has never solved someone else’s problem. Loop quantum gravity has never solved an unknown problem, a problem that belongs to a different field and that can be formulated in an entirely different language. The only problems it claims to solve are those where the answer is either uncheckable or is, in a certain sense, known in advance. These claims are all controversial in themselves – for example, there is certainly no widespread agreement that loop quantum gravity leads to a calculation of black hole entropy – but they all involve known problems.

  The reason for string theory’s sociological success is the same as the reason for its scientific success: it has both formulated and solved unknown problems that were not even phrased when the subject was born. No one working on string theory in the 1970s could have foreseen the mathematical and other applications of the subject that would arise from the 1980s to the present day. In doing so, the string theory ‘user community’ has expanded to include many, many physicists who have absolutely no concern about quantum gravity. It is a theory that is of interest to those of wildly disparate interests.

  None of this says that currently proposed alternative theories of quantum gravity should not have physicists working on them, or that any attempt should be made to prevent new proposals for quantum gravity. Much scientific success has come from funding smart people to work on what they want, how they want. For example, the United Kingdom’s national science academy, the Royal Society, runs a highly successful scheme that funds promising young scientists to work on projects of their choice for up to eight years, giving them maximal freedom and minimal bureaucracy.2

  This funding model is the venture capital approach to scientific research. Many paths are dead ends, but those that are not open up a thousand new routes. However – few scientists are interested in quantum gravity and fewer still will be convinced by your personal prior beliefs as to what quantum gravity must be like. Theories of quantum gravity have some similarities with religions – easier to found than to attract followers. It requires very good reasons to convince people to work on someone else’s theory of quantum gravity.

  A major theme of this book has been that string theory has succeeded because it has provided these reasons. It is many things to many people, and it has proved so much more than just an approach to quantum gravity. It is not simply for the true believers; it is a tool as well as an ideology.

  14.3 PREDICTING THE FUTURE

  What does the future hold for string theory? As the book has described, in 2015 ‘string theory’ exists as a large number of separate, quasi-autonomous communities. These communities work on a variety of topics range from pure mathematics to phenomenological chasing of data, and they have different styles and use different approaches. They are in all parts of the world. The subject is done in Philadelphia and in Pyongyang, in Israel and in Iran, by those with every variety of opinion, appearance and background.3 What they have in common is that they draw inspiration, ideas or techniques from parts of string theory.

  It is clear that in the short term this situation will continue. Some of these communities will flourish and grow as they are re-invigorated by new results, either experimental or theoretical. Others will shrink as they exhaust the seam they set out to mine. It is beyond my intelligence to say which ideas will suffer which fate – an unexpected experimental result can drain old subjects and create a new community within weeks.

  I can say with confidence that as mathematical results are eternal, the role of string theory in mathematics will never go away. It may wane or wax in fashion, but it will always be there. String theory is a consistent structure of something, and that consistent structure leads to interesting mathematics. These parts of mathematics are true in the same unqualified sense that the rest of mathematics is true, and they will always be true independent of what any experiment may ever say about the laws of physics.

  The same is true about formal aspects of quantum field theory or gravity. Although they may be phrased in the language of physics, in style these problems are far closer to problems in mathematics. The questions are not empirical in nature and do not require experiment to answer. The validity of the AdS/CFT correspondence has been checked a thousand times – but these checks are calculational in nature and are not contingent on experiment.

  What about this world? It is because of the surprising correctness and coherence of string theoretic ideas such as AdS/CFT that many people think string theory is also likely to be a true theory of nature. This comes from a prior belief that deep, interesting structures incorporating both gravity and quantum field theory are rare, and a rich example of such a structure is unlikely to be simply surplus to nature’s requirements.

  Will we ever actually know whether string theory is physically correct? Do the equations of string theory really hold for this universe at the smallest possible scales?

  Everyone who has ever interacted with the subject hopes that string theory may one day move forward into the broad sunlit uplands of science, where conjecture and refutation are batted between theorist and experimentalist as if they were ping-pong balls. This may require advances in theory; it probably requires advances in technology; it certainly requires hard work and imagination.

  However, the laws of nature are what they are, and it is not given to us to know whether the next major discovery lies either around the corner or a century hence. As I write this, the Large Hadron Collider has just recommenced operations with its second run, colliding protons at a new record energy of thirteen tera-electronvolts. As more data is collected, this run could lead to great discoveries – or simply more evidence for the Standard Model. We do not know. We can only look and see what is there.

  There is no royal road to direct experimental evidence for string theory. The only way to proceed is by working hard, avoiding silly statements, and carefully exploring all possibilities – and through more data, always more data.

  1For similar reasons, I believe that to a non-expert the most compelling tests of formulae for black hole entropy in string theory are not the original calculations by Strominger and Vafa, but rather the later ones that successfully match expressions for subleading corrections to the entropy. These subleading expressions have far more structure than the leading factor of simply one quarter, and so they are much harder to get right by accident.

  2I declare an interest in this scheme; I am a fortunate holder of one of these fellowships, and they are fantastic.

  3While personal enjoyment is not in the strict sense a good scientific reason, this adds to the fun of working in the subject.

  Notes and Bibliography

  A reference of the form arXiv:yymm.nnnn or arXiv:hep-th/yymmnn refers to an article identification number on the online arXiv preprint server, currently located at http://arXiv.org.

  Chapter 1

  1. Gross and Wilczek’s paper is Ultraviolet Behavior of Nonabelian Gauge Theories, in Physical Review Letters 30 (1973) pp1343–1346.

  2. Politzer’s paper is Reliable Perturbative Results for Strong Interactions?, in Physical Review Letters 30 (1973) pp1346–1349.

  Chapter 2

  1. An expenditure figure of £160 per person has been used. The number was taken from Scienceogram UK, h
ttp://scienceogram.org/in-depth/government-spending/, in September 2015.

  Chapter 3

  1. The text of the Principia is easily available online. The quotation is from the Scholium to the definitions, the wording from Motte’s translation (1729).

  2. Wordsworth’s poem (1805) is The French Revolution as It Appeared to Enthusiasts at Its Commencement and is available online or in any edition of his works.

  3. The quote from Schwinger can be found on p336 of The Birth of Particle Physics, ed. L. Brown and L. Hoddeson, Cambridge University Press (1983).

  4. The history of quantum field theory (including the saying about infinity) is summarised in the first volume of The Quantum Theory of Fields (3 vols), Steven Weinberg, Cambridge University Press (2005).

  5. Weinberg’s paper is A Model of Leptons, in Physical Review Letters 19 (1967) pp1264–1266, and citation records can be found via the INSPIRE database, http://inspirehep.net.

  6. The quote from Coleman can be found in the preface of Aspects of Symmetry: Selected Erice Lectures, Sidney Coleman, Cambridge University Press (1988).

  7. The Matthean principle [Matthew 16:18–19] is taken from the King James Version of the Bible.

  8. ‘Ten Green Bottles’ and ‘The Grand Old Duke of York’ are traditional British nursery rhymes.

  9. Fermi is quoted in More Random Walks in Science, R. L. Weber, CRC Press (1982), although this may not be the original source.

  10. Dyson’s remark is reported in an interview with Frank Wilczek, ‘Discovering the Mathematical Laws of Nature’, in the New York Times of December 28th, 2009, currently available at http://www.nytimes.com/2009/12/29/science/29conv.html?˙r=0.

  Chapter 4

  1. Goroff and Sagnotti’s paper is The Ultraviolet Behavior of Einstein Gravity, in Nuclear Physics B266 (1986) pp709–736.

  2. The Feynman quote is taken from What Do You Care What Other People Think? Further Adventures of a Curious Character, Richard Feynman, Penguin (2007).

  Chapter 5

  1. The quote from Joel Shapiro appears in his 2007 article Reminiscence on the Birth of String Theory, arXiv:0711.3448.

  2. The quote from Lovelace appears in Dual Amplitudes in Higher Dimensions: A Personal View, at p199 of The Birth of String Theory, ed. Cappelli, Andrea et al, Cambridge University Press (2012).

  3. Rutherford’s quote can be found on p111 of Rutherford and the Nature of the Atom by E. Andrade, Doubleday (1964).

  4. The quote from Susskind can be found in Scientific American 305, pp80–83 (July 2011).

  5. The quote from Schwarz is in Gravity, Unification, and the Superstring, at p47 of The Birth of String Theory, ed. Cappelli, Andrea et al, Cambridge University Press (2012).

  6. Peskin’s quote is on p786 of the classic textbook An Introduction to Quantum Field Theory by Peskin and Daniel Schroeder, Westview Press (1995). I am taking the liberty of assigning the quote to the senior author of the book!

  7. Green is quoted on p136 of Superstrings: A Theory of Everything? ed. P. Davies, Cambridge University Press (1988).

  8. Weinberg’s quote is on p223 of Superstrings: A Theory of Everything? ed. P. Davies, Cambridge University Press (1988).

  9. The paper ‘Vacuum Configurations for Superstrings’ by Candelas et al. is in Nuclear Physics B:258, pp.46–74 (1985).

  10. The number 473 800 776 comes from the Kreuzer-Skarke classification in Adv.Theor.Math.Phys. 4 pp1209-1230 (2002), arXiv:hep-th/0002240.

  11. Witten is quoted on p96 of Superstrings: A Theory of Everything? ed. P. Davies, Cambridge University Press (1988).

  12. The paper by Bergshoeff et al. is Physics Letters B:189 pp75–78 (1987).

  13. The paper by Duff et al. is Physics Letters B:191 pp70–74 (1987).

  14. Duff’s comment is from his 2015 paper ‘M-history without the M’, arXiv:1501.04098.

  Chapter 6

  1. At the time of writing, all the talks for the Strings conferences for the past decade or so can be found online on the various conference webpages.

  Chapter 8

  1. Maldacena’s paper is Int.J.Theor.Phys. 38 pp1113–1133 (1999), arXiv:hep-th/9711200.

  2. I thank Jeff Harvey for permission to include the words of the ‘Maldacena’.

  3. I have taken the expression for the anomalous dimension of the Konishi operator from the paper arXiv:1202.5733.

  4. I particularly thank Andrei Starinets for advice on the historical parts of this chapter, and Dam Son for permission to include the text of the quoted email.

  5. The quote from Kenneth Wilson is taken from a 2002 interview with the History of Recent Science and Technology Project, currently hosted at http://authors.library.caltech.edu/5456/1/hrst.mit.edu/hrs/renormalization/Wilson/index.htm.

  Chapter 9

  1. Peter Goddard’s comment can be found amidst his recollections in his 2008 article From Dual Models to String Theory, arXiv:0802.3249.

  2. I thank Sheldon Glashow for permission to include his verse.

  3. Greg Moore’s essay Physical Mathematics and the Future is currently available on his website at http://www.physics.rutgers.edu/gmoore/PhysicalMathematicsAndFuture.pdf.

  4. Hardy’s 1940 essay A Mathematician’s Apology is widely available and its full text can be found online.

  5. Robbins’ recollections appear in New College: A History, ed. J. Buxton and P. Williams (New College, 1979).

  Chapter 10

  1. A review of the cluster soft excess and the possible axionic explanation of it can be found in Angus et al., Soft X-ray Excess in the Coma Cluster from a Cosmic Axion Background, JCAP 1409 09:026 (2014), arXiv:1312.3947.

  Chapter 11

  1. The comment on the Thorne/Hawking bet comes from chapter 6 of Stephen Hawking’s A Brief History of Time (Bantam, 1989).

  2. The paper by Strominger and Vafa is Microscopic Origin of the Bekenstein-Hawking Entropy, Physics Letters B379 pp.99–104, (1996).

  3. A useful reference on subleading logarithmic corrections to black hole entropy is Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions by Ashoke Sen, JHEP04 156 (2013), arXiv:1205.0971.

  Chapter 12

  1. Ecclesiastes 1:9–10 is quoted in the King James Version of the Bible.

  2. Nobel Dreams: Power, Deceit and the Ultimate Experiment by Gary Taubes (Microsoft Press, 1988) is an accessible popular account of the discovery of the W and Z bosons.

  3. The OED records the first use of ‘scientist’ as by William Whewell in 1834: some ingenious gentleman proposed that, by analogy with artist, they might form scientist, and added that there could be no scruple in making free with this termination when we have such words as sciolist, economist, and atheist – but this was not generally palatable.’

  Chapter 13

  1. Feynman’s opinion on philosophy can be found on p232 of Surely You’re Joking, Mr Feynman?, Vintage (1992).

  2. Max Born’s words can be found in the text of his 1954 Nobel Prize lecture, available from the website of the Nobel foundation, www.nobelprize.org.

  Further Reading and General References

  Essentially all technical papers on the subject since 1992 are available on the electronic e-print, http://arxiv.org.

  An accessible book for learning general physics is

  The Theoretical Minimum: What You Need to Know to Start Doing Physics, Leonard Susskind and George Hrabovsky, Basic Books (2014).

  Popular books on string theory are

  The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Brian Greene, Norton, 2nd edition 2010.

  The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, Brian Greene, Vintage, 2011.

  The Little Book of String Theory, Steven Gubser, Princeton University Press, 2010.

  Semi-technical accounts of string theory include

  Superstrings: A Theory of Everything?, Paul Davies and Julian Brown (editors), Cambridge University Press (1992).

&n
bsp; A Brief History of String Theory: From Dual Models to M-Theory, Dean Rickles, Springer (2014).

  The Birth of String Theory, Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo di Vecchia, Cambridge University Press (2012).

  String Theory and the Scientific Method, Richard Dawid, Cambridge University Press (2014).

  The most accessible books for those who want to learn string theory at a technical level are

  Basic Concepts of String Theory, Ralph Blumenhagen, Dieter Lüst and Stefan Theisen, Springer (2012).

  A First Course in String Theory, Barton Zwiebach, Cambridge University Press (2009).

  Lectures on String Theory, David Tong, arXiv:0908.0333.

  Criticisms of string theory can be found in:

  The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, Lee Smolin, Mariner Books (2007).

  Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law, Peter Woit, Basic Books (2007).

  Peter Woit also maintains a well-curated blog of the same name, Not Even Wrong, at http://www.math.columbia.edu/woit/wordpress/, covering a wide range of topics in physics and mathematics.

  Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth, Jim Baggott, Pegasus, 2014.

  Books on alternatives to string theory include

  Three Roads To Quantum Gravity, Lee Smolin, Basic Books (2002).

  Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory, Carlo Rovelli and Francesca Vidotto, Cambridge University Press (2014).