The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next

by Lee Smolin

  What I really meant by that is that we still don’t know the answer as to what string theory is and whether it’s the final theory or there is something missing in it and we seem to be faced with the necessity of deep conceptual changes . . . especially as to the nature of space and time. But, far from being an argument that we should stop doing string theory—it’s failed, it’s over—this is a wonderful period.

  5. J. Polchinski, talk given at the 26th SLAC Summer Institute on Particle Physics, 1998, hep-th/9812104.

  6. http://motls.blogspot.com/2005/09/why-no-new-einstein-ii.html.

  7. Lisa Randall, “Designing Words,” in Intelligent Thought: Science Versus the Intelligent Design Movement, ed. John Brockman (New York: Vintage, 2006).

  1. The Five Great Problems in Theoretical Physics

  1. John Stachel, “How Did Einstein Discover Relativity?” http://www.aip.org/history/einstein/essay-einstein-relativity.htm. I should note that some philosophers of science regard general relativity as at least partly a constructive theory; for the purposes of this discussion it is a principle theory because it describes how space, time, and motion are to be described, whatever matter the universe contains.

  2. The Beauty Myth

  1. The reader should note that my telling of this story simplifies it a great deal to make a point. There were other crucial experiments, which had to do with light moving through flowing water or the effect on observations of starlight of the relative motion of Earth and the star. Einstein was also not the only one who realized that the right answer involved embracing the principle of relativity; so did the great French mathematician and physicist Henri Poincaré.

  3. The World As Geometry

  1. I should confess that this is not how Nordström solved the problem. But he might have. This was the way adopted by later proponents of extra dimensions and it is an improvement over what Nordström did.

  2. There is a caveat, which is that this applies only to observations that take place in small regions of space over small intervals of time. If you fall far enough to see that the strength of the gravitational field changes, you can distinguish gravity from acceleration.

  3. An expert might prefer the more precise notion of inertia here, but I have found that this confuses lay readers.

  4. Except of course, in the case of dark matter and dark energy, as we have seen.

  5. Quoted in Hubert F. M. Goenner, On the History of Unified Field Theories (1914–1933), p. 30. http://relativity.livingreviews.org/Articles/lrr-2004-2/index.html (2004).

  6. Ibid., pp. 38–39.

  7. Ibid., p. 39.

  8. Ibid., p. 35.

  9. Quoted in Abraham Pais, Subtle Is the Lord (New York: Oxford Univ. Press, 1982), p. 330.

  10. Ibid., p. 332.

  11. Ibid.

  12. Ibid., p. 334.

  4. Unification Becomes a Science

  1. Those readers who are interested to learn more may read about gauge symmetries in chapter 4 of my 1997 book, The Life of the Cosmos (New York: Oxford University Press).

  2. Although we won’t need it, some readers may want to know more about how the gauge principle works. Here is the key idea: Usually the operations that define a symmetry have to be done to the whole system. To show that an object is symmetric under rotation, you have to rotate the whole object at once. You can’t rotate only part of a ball. But there are special cases in which the symmetry works even if you apply it to a part of the system. Such symmetries are called local symmetries. This seems counterintuitive; how could it work? It turns out—and this is the hard thing to explain without math—that it works if the various parts of the system act on one another with certain forces. These are the gauge forces.

  3. Again, the history is more complicated than my summary. The Yang-Mills theories were actually first discovered in the 1920s context of the higher-dimensional unified theories but appear to have been forgotten, leading to their rediscovery by Chen Ning Yang, Robert Mills, and others in the 1950s.

  4. The main theme of The Life of the Cosmos was the implications of this change.

  5. From Unification to Superunification

  1. Y. Nomura and B. Tweedie, hep-ph/0504246.

  2. P. Frampton, e-mail (used with permission).

  6. Quantum Gravity: The Fork in the Road

  1. Einstein, “Approximate Integration of the Field Equations of Gravitation,” Sitzungsberichte der Preussische Akadamie der Wissenschaften (Berlin, 1916), pp. 688–96. For the early history of quantum gravity, see John Stachel, introduction and comments to Part V, Conceptual Foundations of Quantum Field Theory, ed. Tian Yu Cao (Cambridge, U.K.: Cambridge University Press, 1999).

  2. W. Heisenberg and W. Pauli, “Zur Quantendynamik der Wellenfelder,” Zeit. für Physik, 56:1–61 (1929), p. 3.

  3. M. P. Bronstein, “Quantization of gravitational waves,” Zh. Eksp. Teor. Fix. 6 (1936), p. 195. For more information about Bronstein, see Stachel in Conceptual Foundations, and also G. Gorelik, “Matvei Bronstein and Quantum Gravity: 70th Anniversary of the Unsolved Problem,” Physics-Uspekhi, 48:10 (2005).

  4. Richard P. Feynman, What Do You Care What Other People Think? (New York: W. W. Norton, 1988), p. 91.

  5. In fact this is a general property of systems bound together by gravity, such as stars and galaxies. All these are systems that cool down when energy is put in. This fundamental difference between systems with and without gravity has proved to be a big stumbling block for many attempts to unify physics.

  7. Preparing for a Revolution

  1. G. Veneziano, “Construction of a Crossing-Symmetric Regge-Behaved Amplitude for Linearly Rising Regge Trajectories,” Nuovo Cim., 57 A:190–97 (1968).

  2. http://www.edge.org/3rd_culture/susskind03/susskind_index.html.

  3. P. Ramond, “Dual theory for free fermions,” Phys. Rev. D, 3(10):2415–18 (1971).

  4. Another particularly influential paper was “Quantum Dynamics of a Massless Relativistic String,” by P. Goddard, J. Goldstone, C. Rebbi, and C. Thorn, Nucl. Phys., 56:109–35 (1973).

  5. J. Scherk and J. H. Schwarz, “Dual Models for Non-Hadrons,” Nucl. Phys. B, 81(1):118–44 (1974).

  6. T. Yoneya, “Connection of Dual Models to Electrodynamics and Gravi-dynamics,” Prog. Theor. Phys., 51(6):1907–20 (1974).

  8. The First Superstring Revolution

  1. J. H. Schwarz, interviewed by Sara Lippincott, July 21 and 26, 2000, http://oralhistories.library.caltech.edu/116/01/Schwarz_0H0.pdf.

  2. M. B. Green and J. H. Schwarz, “Anomaly Cancellations in Supersymmetric D=10 Gauge Theory and Superstring Theory,” Phys. Lett. B, 149 (1–3):117–22 (1984).

  3. Schwarz interview.

  4. Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: Univ. of Chicago Press, 1962).

  5. S. Mandelstam, “The N-loop String Amplitude—Explicit Formulas, Finiteness and Absence of Ambiguities,” Phys. Lett. B, 277(1–2):82–88 (1992).

  6. P. Candelas et al., “Vacuum Configurations for Superstrings,” Nucl. Phys. B, 258(1):46–74 (1985).

  7. A. Strominger, “Superstrings with Torsion,” Nucl. Phys. B, 274(2): 253–84 (1986).

  8. In P.C.W. Davies and Julian Brown, eds., Superstrings: A Theory of Everything (Cambridge, U.K.: Cambridge Univ. Press, 1988), pp. 194–95.

  9. Sheldon L. Glashow and Ben Bova, Interactions: A Journey Through the Mind of a Particle Physicist (New York: Warner Books, 1988), p. 25.

  10. L. Smolin, “Did the Universe Evolve?” Class. Quant. Grav., 9(1): 173–91 (1992).

  9. Revolution Number Two

  1. E. Witten, “String Theory Dynamics in Various Dimensions,” hep-th/9503124; Nucl. Phys. B, 443:85–126 (1995).

  2. C. M. Hull and P. K. Townsend, “Unity of Superstring Dualities,” hep-th/9410167; Nucl. Phys. B, 438:109–37 (1994).

  3. J. Polchinski, “Dirichlet Branes and Ramond-Ramond Charges,” Phys. Rev. Lett., 75(26):4724–27 (1995).

  4. J. Maldacena, “The Large N Limit of Superconformal Field Theorie
s and Supergravity,” hep-th/9711200; Adv. Theor. Math. Phys., 2:231–52 (1998); Int. J. Theor. Phys., 38:1113–33 (1999).

  5. A. M. Polyakov, “A Few Projects in String Theory,” hep-th/9304146.

  6. B. de Wit, J. Hoppe, and H. Nicolai, “On the Quantum-Mechanics of Supermembranes,” Nucl. Phys. B, 305(4):545–81 (1988).

  7. T. Banks, W. Fischler, S. Shenker, and L. Susskind, “M-Theory as a Matrix Model: A Conjecture,” Phys. Rev. D, 55(8):5112–28 (1997).

  10. A Theory of Anything

  1. The supernova observations were made by Saul Perlmutter and collaborators at Lawrence Berkeley Laboratory and Robert Kirschner and colleagues in the High-Z Supernova Search Team.

  2. E. Witten, “Quantum Gravity in de Sitter Space,” hep-th/0106109. Witten continues, “This last statement is not very surprising given the classical no go theorem. For, in view of the usual problems in stabilizing moduli, it is hard to get de Sitter space in a reliable fashion at the quantum level given that it does not arise classically.”

  3. S. Kachru, R. Kallosh, A. Linde, and S. Trivedi, “De Sitter Vacua in String Theory,” hep-th/0301240.

  4. See, for example, T. Hertog, G. T. Horowitz, and K. Maeda, “Negative Energy Density in Calabi-Yau Compatifications,” hep-th/0304199, Jour. High Energy Phys., 0305:60(2003).

  11. The Anthropic Solution

  1. L. Susskind, “The Anthropic Landscape of String Theory,” hep-th/0302219.

  2. S. Weinberg, “Anthropic Bound on the Cosmological Constant,” Phys. Rev. Lett., 59(22):2607–10 (1987).

  3. L. Smolin, “Did the Universe Evolve?” Class. Quant. Grav., 9(1): 173–91 (1992).

  4. Weinberg, “Living in the Multiverse,” hep-th/0511037.

  5. From a recent survey by Seed Magazine on the relationship between the anthropic principle and the proliferation of string theories; http://www.seedmagazine.com/news/2005/12/surveying_the_landscape.

  6. E. J. Copeland, R. C. Myers, and J. Polchinski, “Cosmic F- and D-Strings,” Jour. High Energy Phys., Art. no. 013, June 2004.

  7. M. Sazhin et al., “CSL-1: Chance Projection Effect or Serendipitous Discovery of a Gravitational Lens Induced by a Cosmic String?” Mon. Not. R. Astron. Soc., 343:353–59 (2003).

  8. N. Arkani-Hamed, G. Dvali, and S. Dimopoulos, “The Hierarchy Problem and New Dimensions at a Millimeter,” Phys. Lett. B, 429:263–72 (1998).

  9. L. Randall and R. Sundrum, “An Alternative to Compactification,” hep-th/9906064; Phys. Rev. Lett., 83:4690–93 (1999).

  12. What String Theory Explains

  1. In technical terms, supersymmetry implies that there is a timelike or lightlike killing field on the spacetime geometry. It implies the existence of a symmetry in time, because (in technical language) the supersymmetry algebra closes on the Hamiltonian. Another way to say this is that supersymmetry requires a killing spinor, which implies a null or timelike killing vector.

  2. E. D’Hoker and D. H. Phong, Phys. Lett. B, 529:241–55 (2002); hep-th/0110247.

  3. D. Friedan, “A Tentative Theory of Large Distance Physics,” hep-th/0204131.

  4. D. Karabali, C. Kim, and V. P. Nair, Phys. Lett. B, 434:103–9 (1998); hep-th/9804132; R. G. Leigh, D. Minic, and A. Yelnikov, hep-th/0604060. For the application to 3+1 dimensions, see L. Freidel, hep-th/0604185.

  5. In The Road to Reality (2005), Roger Penrose argued that most of the compactified spaces that extra dimensions curl up into will quickly collapse to singularities. To show this, he applied to the spacetime backgrounds of these string theories the theorems he and Hawking developed showing that general relativity predicts singularities in cosmological solutions. As far as I know, his arguments stand. They hold only at the classical level of approximation, but this is the only approximation in which we can study the time evolution of spacetime backgrounds in string theory. Therefore, Penrose’s result is as reliable as the arguments that convince string theorists of the existence of the landscape of string theories.

  6. Quoted in Amanda Gefter, “Is String Theory in Trouble?” New Scientist, Dec. 17, 2005.

  13. Surprises from the Real World

  1. It is often the case that surprising experimental results are not confirmed when other experimentalists repeat the experiment. This does not mean someone is being dishonest. Experiments on the edge of what is possible are almost always hard to replicate, and it is typically difficult to separate noise from a meaningful signal. Often it takes many years and many attempts by different people before all the sources of error in a new kind of experiment are understood and eliminated.

  2. Expressed in terms of R, the cosmological constant is equal to 1/R2.

  3. K. Land and J. Magueijo, “Examination of Evidence for a Preferred Axis in the Cosmic Radiation Anisotropy,” Phys. Rev. Lett., 95:071301 (2005).

  4. Ibid.

  5. M. Milgrom, “A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis,” Astrophys. Jour., 270(2): 365–89 (1983).

  6. More information about MOND and the data supporting it, plus references, is available at www.astro.umd.edu/~ssm/mond/.

  7. J. D. Anderson et al., “Study of the Anomalous Acceleration of Pioneer 10 and 11,” gr-qc/0104064.

  8. M. T. Murphy et al., “Further Evidence for a Variable Fine Structure Constant from Keck/HIRES QSO Absorption Spectra,” Mon. Not. Roy. Ast. Soc., 345:609–38 (2003).

  9. See, for example, E. Peik et al., “Limit on the Present Temporal Variation of the Fine Structure Constant,” Phys. Rev. Lett., 93(17):170801 (2004), and R. Srianand et al., “Limits on the Time Variation of the Electromagnetic Fine Structure Constant in the Low Energy Limit from Absorption Lines in the Spectra of Distant Quasars,” Phys. Rev. Lett., 92(12):121302 (2004).

  10. K. Greisen, “End to the Cosmic-Ray Spectrum?” Phys. Rev. Lett., 16(17):748–50 (1966), and G. T. Zatsepin and V. A. Kuzmin, “Upper Limit of the Spectrum of Cosmic Rays,” JETP Letters, 4:78–80 (1966).

  11. S. Coleman and S. L. Glashow, “Cosmic Ray and Neutrino Tests of Special Relativity,” Phys. Rev. B, 405:249–52 (1997); Coleman and Glashow, “Evading the GZK Cosmic-Ray Cutoff,” hep-ph/9808446.

  14. Building on Einstein

  1. G. Amelino-Camelia, “Testable Scenario for Relativity with Minimum-Length,” hep-th/0012238.

  2. João Magueijo, Faster Than the Speed of Light: The Story of a Scientific Speculation (New York: Perseus Books, 2003).

  3. Vladimir Fock, The Theory of Space, Time, and Gravitation (London: Pergamon Press, 1959).

  4. L. Friedel, J. Kowalski-Glikman, and L. Smolin, “2 + 1 Gravity and Doubly Special Relativity,” Phys. Rev. D., 69:044001 (2004).

  5. E. Livine and L. Friedel, “Ponzano-Regge Model Revisited III: Feynman Diagrams and Effective Field Theory,” hep-th/0502106; Class. Quant. Grav., 23:2021–62 (2006).

  6. Florian Girelli and Etera R. Livine, “Physics of Deformed Special Relativity,” gr-qc/0412079.

  15. Physics After String Theory

  1. A. Ashtekar, “New Variables for Classical and Quantum Gravity,” Phys. Rev. Lett., 57(18):2244–47 (1986).

  2. http://online.kitp.ucsb.edu/online/kitp25/witten/oh/10.html.

  3. This was not always the prevalent belief; credit for championing the role of causality should go to Roger Penrose, Rafael Sorkin, Fay Dowker, and Fotini Markopoulou.

  4. See, for example, R. Loll, J. Ambjørn, and J. Jurkiewicz, “The Universe from Scratch,” hep-th/0509010.

  5. See, for example, Alain Connes, Noncommutative Geometry (San Diego: Academic Press, 1994).

  6. O. Dreyer, “Background-Independent Quantum Field Theory and the Cosmological Constant Problem,” hep-th/0409048.

  7. See, for example, C. Rovelli, “Graviton Propagator from Background-Independent Quantum Gravity,” gr-qc/0508124.

  8. S. Hofmann and O. Winkler, “The Spectrum of Fluctuations in Singularity-free Inflationary Quantum Cosmology,” astro-ph/0411124.

  9. F. Markopoulou, “Towards gravity from the quantum,
” hep-th/0604120.

  10. S. O. Bilson-Thompson, “A Topological Model of Composite Preons,” hep-ph/0503213.

  11. S. O. Bilson-Thompson, F. Markopoulou, and L. Smolin, “Quantum Gravity and the Standard Model,” hep-th/0603022.

  12. Audiotapes of the discussions are available at http://www.perimeterinstitute.ca/activities/scientific/cws/evolving_laws/.

  16. How Do You Fight Sociology?

  1. www.cosmicvariance.com/2005/11/18/a-particle-physicists-perspective.

  2. Anonymous posting on http://groups.google.com/group/sci.physics.strings/ by String Theorist, Oct. 9, 2004.

  3. Guardian Unlimited, Jan. 20, 2005.

  4. To papers of mine questioning one or another result in string theory, I’ve received three responses in which the correspondent refers to the “strong” theory community. As in “while perturbative finiteness (or the Maldacena conjecture, or S-duality) may not have been proved, no one in the strong theory community believes that it could possibly be false.” Once might be a coincidence; thrice, and this is a classic Freudian slip. How much of the sociology of string theory is just the all-too-recognizable human desire to want to be part of the strongest group around?

  5. S. Kachru, R. Kallosh, A. Linde, and S. Trivedi, “De Sitter Vacua in String Theory,” hep-th/0301240.

  6. http://groups.google.com/group/sci.physics.strings/, April 6, 2004.

  7. L. Smolin, “Did the Universe Evolve?” Class. Quant. Grav., 9:173–91 (1992).

  8. www.imp.ac.ir/IPM/news/connes-interview.pdf (used with permission).