by Lee Smolin
9. Michael Duff, Physics World, Dec. 2005.
10. www.damtp.cam.ac.uk/user/gr/public/qg_ss.html.
11. However, I am glad to report that it is not hard to find on the Web introductions to string theory that do not make distorted or exaggerated claims. Here are some examples: http://tena4.vub.ac.be/beyondstringtheory/index.html; http://www.sukidog.com/jpierre/strings/;http://en.wikipedia.org/wiki/M-theory.
12. S. Mandelstam, “The N-loop String Amplitude—Explicit Formulas, Finiteness and Absence of Ambiguities,” Phys. Lett. B, 277(1–2):82–88 (1992).
13. Here are a few examples: J. Barbon, hep-th/0404188, Eur. Phys. J., C33: S67–S74 (2004); S. Foerste, hep-th/0110055, Fortsch. Phys., 50:221–403 (2002); S. B. Giddings, hep-th/0501080; and I. Antoniadis and G. Ovarlez, hep-th/9906108. A rare example of a review with a careful and correct (for the time) discussion of the issue of finiteness is L. Alvarez-Gaume and M. A. Vazquez-Mozo, hep-th/9212006.
14. This is a paper by Andrei Marshakov (Phys. Usp., 45:915–54 (2002), hep-th/0212114). I apologize for the technical language, but perhaps the reader can see the point:
Unfortunately the ten-dimensional superstring pretending to be the most successful among existing string models is strictly defined, in general, only at tree and one-loop levels. Starting from the two-loop corrections to the scattering amplitudes all expressions in the perturbative superstring theory are really not defined. The reason for that comes from the well-known problems with supergeometry or integration over the “superpartners” of the moduli of complex structures. In contrast to the bosonic case where the integration measure is fixed by the Belavin-Knizhnik theorem, the definition of the integration measure over supermoduli (or, more strictly, the odd moduli of super-complex structures) is still an unsolved problem [88, 22]. The moduli spaces of the complex structures of Riemann surfaces are non compact, and the integration over such spaces requires special care and additional definitions. In the bosonic case, when the integrals over moduli spaces diverge, the result of integration in (3.14) is defined only up to certain “boundary terms” (the contributions of degenerate Riemann surfaces or the surfaces of lower genera (with less “handles”). In the superstring case one runs into more serious problems since the very notion of the “boundary of moduli space” is not defined. Indeed the integral over the Grassmann odd variables does not “know” what is the boundary term. This is the fundamental reason why the integration measure in fermionic string is not well-defined and depends on the “gauge choice” or the particular choice for the “zero modes” in the action (3.23). For two-loop contributions this problem can be solved “empirically” (see [88, 22]), but in the general setup the superstring perturbation theory is not mathematically well defined. Moreover, these are not problems of the formalism: the same obstacles arise in less geometrical approach of Green and Schwarz [91].
15. Here is an e-mail from Mandelstam, dated June 8, 2006:
With regard to my paper on the finiteness of the n-loop string amplitude, let me first remark that divergences can only occur where the moduli space degenerates. I examined the points of degeneracy associated with the “dilaton” divergence, with which string theorists have been concerned. I showed that the arguments previously applied to the one-loop amplitude can be extended to the n-loop amplitude, and also that the associated ambiguities in the definition of the integration contour over the even supermoduli can be resolved by using the unique prescription consistent with unitarity. I agree that this does not provide a mathematically rigorous proof of finiteness, but I believe it deals with the physical problems which could lead to infinities. I did not examine another source of infinities, known from the early days of dual models, namely the use of imaginary time. The factor exp(iEt), where E is the difference between the immediate and initial energies, can clearly diverge if one integrates over imaginary time. One believes on physical grounds that such infinities can be removed by analytic continuation to real time. This has been shown explicitly for the zero- and one-loop amplitude, and it has been shown that an analytic continuation leading to finiteness can be defined for the two-loop amplitude.
16. G. T. Horowitz and J. Polchinski, “Gauge/gravity duality,” gr-qc /0602037. To appear in Towards Quantum Gravity, ed. Daniele Oriti, Cambridge University Press.
17. http://golem.ph.utexas.edu/~distler/blog/archives/000404.html.
18. Irving Janis, Victims of Groupthink: A Psychological Study of Foreign-Policy Decisions and Fiascoes (Boston: Houghton Mifflin, 1972), p. 9. Of course, the phenomenon is much older. John Kenneth Galbraith, the influential economist, called it “conventional wisdom.” He meant by this “opinions that, while not necessarily well founded, are so widely held among the rich and influential that only the rash and foolish will endanger their careers by dissenting from them.” (From a book review in the Financial Times, Aug. 12, 2004.)
19. Irving Janis, Crucial Decisions: Leadership in Policymaking and Crisis Management (New York: Free Press, 1989), p. 60.
20. http://oregonstate.edu/instruct/theory/grpthink.html.
21. Another example is the erroneous proof of the nonexistence of hidden variables in quantum theory, published by John von Neumann in 1932 and widely cited for three decades before the quantum theorist David Bohm found a hidden variables theory.
17. What Is Science?
1. See Paul Feyerabend, Killing Time: The Autobiography of Paul Feyerabend (Chicago: Univ. of Chicago Press, 1996).
2. See, for example, Karl Popper, The Logic of Scientific Discovery (New York: Routledge, 2002).
3. Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: Univ. of Chicago Press, 1962).
4. Imre Lakatos, Proofs and Refutations (Cambridge, U.K.: Cambridge Univ. Press, 1976).
5. Leonard Susskind, in defending the validity of anthropic reasoning, has labeled its critics Popperazzi, for invoking the need for some means of falsification. But it is one thing to accept the critiques of Popper holding that falsification is only part of the story of how science works, and quite another to advocate the acceptance on scientific grounds of a theory that makes no unique or specific predictions by which it might be either falsified or confirmed. In this regard, I am proud to be a Popperazzo.
6. Alexander Marshack, The Roots of Civilization: The Cognitive Beginnings of Man’s First Art, Symbol, and Notation (New York: McGraw-Hill, 1972).
7. D. H. Wolpert and W. G. Macready, No Free Lunch Theorems for Search, Technical Report, Santa Fe Institute, SFI-TR-95-02-010.
8. Richard P. Feynman, “What Is Science?” The Physics Teacher, Sept. 1969.
18. Seers and Craftspeople
1. Quoted in Simon Singh, “Even Einstein Had His Off Days,” New York Times, Jan. 2, 2005.
2. See, for example, Mara Beller, Quantum Dialogue: The Making of a Revolution (Chicago: Univ. of Chicago Press, 1999).
3. Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: Univ. of Chicago Press, 1962).
4. A. Einstein to R. A. Thorton, unpublished letter dated Dec. 7, 1944 (EA 6-574). Einstein Archive, Hebrew University, Jerusalem. Quoted in Don Howard, “Albert Einstein as a Philosopher of Science,” Physics Today, Dec. 2005.
5. T. Jacobson and L. Smolin, “Nonperturbative Quantum Geometries,” Nucl. Phys. B, 299:295–345 (1988).
6. See, for example, L. Crane, “Clock and Category: Is Quantum Gravity Algebraic?” gr-qc/9504038; J. Math. Phys., 36:6180–193 (1995).
7. See, for example, F. Markopoulou, “An Insider’s Guide to Quantum Causal Histories,” hep-th/9912137; Nucl. Phys. B, Proc. Supp., 88(1): 308–13 (2000).
8. Seth Lloyd, Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos (New York: Alfred A. Knopf, 2006).
9. I have here to again emphasize that I am talking only about people with good training all the way through to a PhD. This is not a discussion about quacks or people who misunderstand what science is.
10. L. Smolin, “On the Nature of Quantum Fluctuations and Thei
r Relation to Gravitation and the Principle of Inertia,” Class. Quant. Grav., 3:347–59 (1986).
11. Julian Barbour, The End of Time: The Next Revolution in Physics (New York: Oxford Univ. Press, 2001).
12. D. Finkelstein, “Past-Future Asymmetry of the Gravitational Field of a Point Particle,” Phys. Rev., 110: 965–67 (1958).
13. Antony Valentini, Pilot-Wave Theory of Physics and Cosmology (Cambridge, U.K.: Cambridge Univ. Press, in press).
14. Here is part of a letter from the National Science Foundation to University of Notre Dame physicist James Cushing in 1995, rejecting his proposal to support his work on foundations of quantum theory:
The subject under consideration, the rival Copenhagen and causal [Bohm] interpretations of the quantum theory, has been discussed for many years and in the opinion of several members of the Physics Division of the NSF, the situation has been settled. The causal interpretation is inconsistent with experiments which test Bell inequalities. Consequently . . . funding . . . a research program in this area would be unwise.
The remarkable thing about this letter is that it contains an elementary mistake, as it was by then well understood by experts that the causal interpretation is fully consistent with the experiments that test the Bell inequalities. By the way, Cushing had been a successful elementary-particle physicist before switching his interests to the foundations of quantum theory, but this did not prevent the NSF from cutting off his funding.
15. D. Deutsch, Proc. Roy. Soc. A, 400:97–117 (1985).
16. David Deutsch, The Fabric of Reality: The Science of Parallel Universes and Its Implications (London: Penguin, 1997).
17. P. W. Shor, “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” quant-ph/9502807.
18. A. Valentini, “Extreme Test of Quantum Theory with Black Holes,” astro-ph/041250s.
19. Alexander Grothendieck, Récoltes et Semailles, 1986, English translation by Roy Lisker, www.grothendieck-circle.org, chapter 2.
19. How Science Really Works
1. There is an unfortunate exception to this, which is when a professor is frightened by his younger self and has renounced his youthful risk-taking spirit in favor of scientific conservatism. Reminding someone like this of a younger self is generally not a good idea.
2. See, for example, “A Study on the Status of Women Faculty in Science at MIT,” vol. XI, no. 4, March 1999, available online at http://web.mit.edu/fnl/women/women.html. More information on issues on women in science is available from the American Physical Society at http://www.aps.org/educ/cswp/ and from the committee on Faculty Diversity at Harvard University at http://www.aps.org/educ/cswp/.
3. James Glanz, “Even Without Evidence, String Theory Gains Influence,” New York Times, March 13, 2001.
4. Gary Taubes, Nobel Dreams: Power, Deceit and the Ultimate Experiment (New York: Random House, 1986), pp. 254–55.
5. Isador Singer, from an interview published online at http://www.abel-prisen.no/en/prisvinnere/2004/interview_2004_1.html.
6. Alain Connes, interview available at www.ipm.ac.ir/IPM/news/connes-interview.pdf.
Acknowledgments
A book starts with an idea, and the credit for this one goes to John Brockman for perceiving that I wanted to do something more than write an obscure academic monograph on the relationship between democracy and science. That is one topic of this book, but, as he foresaw, the argument is much more powerful when developed in the context of a specific scientific controversy. I am indebted to him and to Katinka Matson for their continuing support and for inviting me into the community that comprises the third culture. By offering me a context that goes beyond my specialization, they changed my life.
No writer has had a better editor than Amanda Cook, and the extent to which anything good here is due to her guidance and interventions is embarrassing to admit. Sara Lippincott finished the job with an elegance and precision any writer would kill for. It was an honor to work with both of them. Holly Bemiss, Will Vincent, and everyone at Houghton Mifflin took care of this book with enthusiasm and skill.
Over the last decades, many colleagues have taken their time to educate me about string theory, supersymmetry, and cosmology. Among them, I am especially grateful to Nima Arkani-Hamed, Tom Banks, Michael Dine, Jacques Distler, Michael Green, Brian Greene, Gary Horowitz, Clifford Johnson, Renata Kallosh, Juan Maldacena, Lubos Motl, Hermann Nicolai, Amanda Peet, Michael Peskin, Joe Polchinski, Lisa Randall, Martin Rees, John Schwarz, Steve Shenker, Paul Steinhardt, Kellogg Stelle, Andrew Strominger, Leonard Susskind, Cumrun Vafa, and Edward Witten for their time and patience. If we still disagree, I hope it is clear that this book is not a final statement but a carefully structured argument, intended as a contribution to an ongoing conversation that has been undertaken with respect and out of admiration for their efforts. If the world turns out to be eleven-dimensional and supersymmetric, I will be the first to applaud their triumph. But for the present, I thank them in advance for allowing me to explain why, after a great deal of thought, I no longer believe this is likely.
This is not a scholarly history, but I do tell stories, and several friends and colleagues gave generously of their time to help me tell true stories rather than perpetuating myths. Julian Barbour, Joy Christian, Harry Collins, John Stachel, and Andrei Starinets gave me detailed scholarly notes on the whole manuscript. The mistakes that remain are, of course, my responsibility alone, as are the consequences of choices made to make the book as accessible as possible. Corrections and further thoughts will be posted on a Web page connected to this book. Other friends and family who read the manuscript and offered very helpful criticisms included Cliff Burgess, Howard Burton, Margaret Geller, Jaume Gomis, Dina Graser, Stuart Kauffman, Jaron Lanier, Janna Levin, João Magueijo, Patricia Marino, Fotini Markopoulou, Carlo Rovelli, Michael Smolin, Pauline Smolin, Roberto Mangabeira Unger, Antony Valentini, and Eric Weinstein. Chris Hull, Joe Polchinski, Pierre Ramond, Jorge Russo, Moshe Rozali, John Schwarz, Andrew Strominger, and Arkady Tseytlin also helped to clarify specific facts and issues.
For many years my research was comfortably supported by the National Science Foundation, for which I remain very thankful. But I was extraordinarily fortunate to encounter someone who asked me, “What would you really like to do? What is your most ambitious and crazy idea?” Then, unexpectedly and generously, Jeffrey Epstein gave me the chance to try to make good on my answers, and for this I will always be deeply grateful.
This book is partly about the values that should govern a scientific community, and I was lucky to learn mine from some of those who pioneered the search for quantum spacetime: Stanley Deser, David Finklestein, James Hartle, Chris Isham, and Roger Penrose. I would not have gotten anywhere on that search were it not for the collaboration and support of Abhay Ashtekar, Julian Barbour, Louis Crane, Ted Jacobson, and Carlo Rovelli. I am also indebted to my recent collaborators Stephon Alexander, Mohammad Ansari, Olaf Dreyer, Jerzy Kowalski-Glikman, João Magueijo, and especially Fotini Markopoulou, for continual criticisms and challenges that keep me honest and block any temptation to take myself too seriously. It must also be said that our work would not make sense without the wider community of physicists, mathematicians, and philosophers who ignore academic fashion to devote themselves to work on the foundational problems in physics. This book is dedicated to them, above all.
My work and life would be impoverished without the support of friends who enabled me to both do science and come to understand its larger context. These include Saint Clair Cemin, Jaron Lanier, Donna Moylan, Elizabeth Turk, and Melanie Walker.
Each book is written with the spirit of a place. For my first two, these were New York and London. This book carries the spirit of Toronto; Pico Iyer calls it the city of the future, and I count myself lucky to know why. For welcoming an immigrant at the uncertain moment of September 2001, I have to thank above all Dina Graser but also Charlie Tracy Macdougal, Olivia Mizzi, Hanna Sanchez, and the guys at the
Outer Harbour Centreboard Club (if you didn’t see me out on the water much last spring, this is why!).
For inviting me here, I have to thank Howard Burton and Mike Lazaridis. I know of no greater act of vision and support for science than their founding of the Perimeter Institute for Theoretical Physics. For their faith in the future of science and their continuing devotion to the institute’s success, they deserve the highest praise that anyone who cares about science can give. I owe them enormous thanks for the opportunity they opened to me, both personally and scientifically.
For all the shared adventures and challenges of building that institute and community, all possible thanks to Clifford Burgess, Freddy Cachazo, Laurent Freidel, Jaume Gomis, Daniel Gottesman, Lucien Hardy, Justin Khoury, Raymond Laflamme, Fotini Markopoulou, Michele Mosca, Rob Myers, Thomas Thiemann, Antony Valentini, and others too numerous to name who risked their careers to contribute to this venture. And although it doesn’t need to be said, let me emphasize that every word of this book is my own view and reflects in no way any official or unofficial views of Perimeter Institute, its scientists, or its founders. On the contrary, this book has been made possible by my membership in a community of scientists who celebrate honest scientific disagreement and who know that lively discussion need not get in the way of friendship or mutual support in our efforts to do science. Were there many more places like Perimeter, I wouldn’t have felt the need to write this book.
Finally, to my parents, for their ongoing unconditional love and support, and to Dina, for everything that makes life a joy, which puts all that this book is about into its proper perspective.
Index
Page numbers in italics refer to figures.
