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Problems such as how to cool a 27 km-circumference, 37,000 tonne ring of superconducting magnets to a temperature of 1.9 K using truck-loads of liquid helium are not the kind of things that theoretical physicists normally get excited about. It might therefore come as a surprise to learn that string theorists – famous lately for their belief in a theory that allegedly has no connection with reality – kicked off their main conference this year – Strings07 – with an update on the latest progress being made at the Large Hadron Collider (LHC) at CERN, which is due to switch on next May.

The possibility, however tiny, that evidence for string theory might turn up in the LHC’s 14 TeV proton–proton collisions was prominent among discussions at the five-day conference, which was held in Madrid in late June. In fact, the talks were peppered with the language of real-world data, particles and fields – particularly in relation to cosmology. Admittedly, string theorists bury these more tangible concepts within the esoteric grammar of higher-dimensional mathematics, where things like “GUT-branes”, “tadpoles” and “warped throats” lurk. However, Strings07 was clearly a physics event, and not one devoted to mathematics, philosophy or perhaps even theology.

But not everybody believes that string theory is physics pure and simple. Having enjoyed two decades of being glowingly portrayed as an elegant “theory of everything” that provides a quantum theory of gravity and unifies the four forces of nature, string theory has taken a bit of a bashing in the last year or so. Most of this criticism can be traced to the publication of two books: The Trouble With Physics by Lee Smolin of the Perimeter Institute in Canada and Not Even Wrong by Peter Woit of Columbia University in the US, which took string theory to task for, among other things, not having made any testable predictions. This provided newspaper and magazine editors with a great hook for some high-brow controversy, and some reviewers even went as far as to suggest that string theory is no more scientific than creationism (see “Stringing physics along”).

Some of the criticism is understandable. To most people, including many physicists, string theory does not appear to have told us anything new about how the world really works despite almost 40 years of trying. “Sadly, I cannot imagine a single experimental result that would falsify string theory,” says Sheldon Glashow of Harvard University, who shared the 1979 Nobel Prize for Physics for his role in developing the unified electroweak theory that forms the core of the Standard Model of particle physics. “I have been brought up to believe that systems of belief that cannot be falsified are not in the realm of science.”

String theory is certainly unprecedented in the amount of time a theoretical-physics research programme has been pursued without facing a clear experimental test. But while one can debate whether it has taken too long to get this far, string theory is currently best thought of as a theoretical framework rather than a well-formulated physical theory with the ability to make specific predictions. When viewed in this light, string theory is more like quantum field theory – the structure that combines quantum mechanics and special relativity – than the Standard Model, which is a particular field theory that has been phenomenally successful in describing the real world for the last 35 years or so.

String theory is a theory of the “DNA” of a universe, but we only get to study a single “life form” – our own local patch of space. It’s as though Gregor Mendel had only a single pea and a simple magnifying glass to work with, from which he was expected to discover the double helix and the four bases A, C, G and T. Leonard Susskind, Stanford University

Ed Witten of the Institute for Advanced Study (IAS) at Princeton University, who is widely regarded as the leading figure in string theory, admits that it is difficult for someone who has not worked on the topic to understand this distinction properly. “String theory is unlike any theory that we have dealt with before,” he says. “It’s incredibly rich and mostly buried underground. People just know bits and pieces at the surface or that they’ve found by a little bit of digging, even though this so far amounts to an enormous body of knowledge.”

Some critics also slam string theory for its failure to answer fundamental questions about the universe that only it, as our best working model of quantum gravity, can seriously address. Some of these questions, says David Gross of the University of California at Santa Barbara (UCSB) – who shared the 2004 Nobel prize for his work on quantum chromodynamics (QCD) – have been around since the days of quantum mechanics. “String theory forces us to face up to the Big Bang singularity and the cosmological constant – problems that have either been ignored until now or have driven people to despair,” he says.

Gross also thinks that many people expect string theory to meet unfairly high standards. “String theory is full of qualitative predictions, such as the production of black holes at the LHC or cosmic strings in the sky, and this level of prediction is perfectly acceptable in almost every other field of science,” he says. “It’s only in particle physics that a theory can be thrown out if the 10th decimal place of a prediction doesn’t agree with experiment.”

So what is stopping string theory from making the sort of definitive, testable predictions that would settle once and for all its status as a viable theory of nature? And why does the prospect of working on something that could turn out to be more fantasy than physics continue to attract hundreds of the world’s brightest students? After all, a sizable proportion of the almost 500 participants at Strings07 were at the very beginning of their careers. “I feel that nature must intend for us to study string theory because I just can’t believe that humans stumbled across something so rich by accident,” says Witten. “One of the greatest worries we face is that the theory may turn out to be too difficult to understand.”

Irresistible appeal

In some ways, string theory looks like a victim of its own success. It did not seek to bridge the two pillars of modern physics – quantum mechanics and Einstein’s general theory of relativity – while simultaneously unifying gravity with the three other basic forces in nature: electromagnetism, the strong and the weak forces. Rather, string theory began life in 1970 when particle physicists realized that a model of the strong force that had been proposed two years earlier to explain a plethora of experimentally observed hadrons was actually a theory of quantum-mechanical strings (see timeline below).

Sheldon Glashow

In this early picture, the quarks inside hadrons appear as if they are connected by a tiny string with a certain tension, which meant that the various different types of hadrons could be neatly organized in terms of the different vibrational modes of such 1D quantum strings. Although this model was soon superseded by QCD – a quantum field theory that treats particles as being pointlike rather than string-like – it soon became clear that the stringy picture of the world was hiding something altogether more remarkable than mere hadrons.

String theory is different to religion because of its utility in mathematics and quantum field theory, and because it may someday evolve into a testable theory (aka science). Sheldon Glashow, Boston University

One of several problems with the initial hadronic string model was that it predicted the existence of massless “spin-2” particles, which should have been turning up all over the place in experiments. These correspond to vibrations of strings that are connected at both ends, as opposed to the “open” strings the harmonics of which described various hadrons. But in 1974 John Schwarz of the California Institute of Technology and others (see timeline below) showed that these closed loops have precisely the properties of gravitons: hypothetical spin- 2 particles that crop up when you try to turn general relativity, a classical theory in which gravity emerges from the curvature of space–time, into a quantum field theory like the Standard Model. Although the fundamental string scale had to be some 10²⁰ orders of magnitude smaller than originally proposed to explain the weakness of the gravitational force, string theory immediately presented a potential quantum theory of gravity.

“Quantum field theories don’t allow the existence of gravitational forces,” says Leonard Susskind of Stanford University, who in 1970 was one of the first to link hadrons with strings. “String theory not only allows gravity, but gravity is an essential mathematical consequence of the theory. The sceptics say big deal; the string theorists say BIG DEAL!”

String theory succeeds where quantum field theory fails in this regard because it circumvents the shortdistance interactions that can cause calculations of observable quantities to diverge and give meaningless results. In the Standard Model – which is based on the gauge symmetry or gauge group SU(3) × SU(2) × U(1), where SU(3) is QCD and SU(2) × U(1) the unified electroweak theory – elementary particles interact by exchanging particles called gauge bosons. For instance, photons mediate the electromagnetic interaction, which is described by the original and most successful field theory of all time: quantum electrodynamics (QED), which was developed by Feynman and others in the 1940s.

Pictorially, these interactions take place where and when the space–time histories or “world lines” of pointlike particles intersect, and the simplest of such Feynman diagrams corresponds to the classical limit of the quantum theory. Provided the strength of the underlying interaction – which is described by the coupling constant of the theory, or the fine-structure constant in the case of QED – is weak, theorists can calculate the probabilities that certain physical processes occur by adding up all the quantum “loop” corrections to the basic underlying diagram (see “Why can’t string theory predict anything?” in part 2 of this article).

Hidden dimensions

When trying to incorporate gravity into the Standard Model, however, such “perturbative expansions” of the theory (which amount to power series in the coupling constant) go haywire. This stems from the fact that Newton’s gravitational constant is not dimensionless like, say, the fine-structure constant. As a result, gravitons – which arise from quantizing the space–time metric in general relativity – lead to point-like interactions with infinite probabilities. String theory gets round this by replacing the 1D paths traced out by point-like particles in space–time with 2D surfaces swept out by strings. As a result, all the fundamental interactions can be described topologically in terms of 2D “world sheets” splitting and reconnecting in space–time. The probability that such interactions occur is given by a single parameter – the string tension – and the shortdistance divergences never arise. “String theory grew up as the sum of the analogue of Feynman diagrams in 2D,” says Michael Green of Cambridge University in the UK. “But working out the rules of 2D perturbation theory is only the start of the problem.”

This is because perturbation theory only works if space–time has some rather otherworldly properties, one of which is supersymmetry. While the strings in the initial hadronic theory were bosonic (i.e. their vibrations corresponded to particles such as photons that have integer values of spin in units of Planck’s constant), the world is mostly made up of fermions – particles such as electrons and protons, which have half-integer spins. In the mid-1970s Schwarz and others realized that the only way string theory could accommodate fermions was if every bosonic string vibration has a supersymmetric fermionic counterpart, which corresponds to a particle with exactly the same mass (and vice versa). String theory is thus shorthand for superstring theory, and one of the main goals of the LHC is to find out whether such supersymmetric particles actually exist.

Pretty weird

The other demand that string theory places on space–time is a seemingly ridiculous number of dimensions. The original bosonic theory, for example, only respects Lorentz invariance – an observed symmetry of space–time that states there is no preferred direction in space – if it is formulated in 26 dimensions. Superstrings require a more modest 10 dimensions: nine of space and one of time. But in order to explain the fact that there are only three spatial dimensions, string theorists have to find ways to deal with the additional six, which is usually done by “compactifying” the extra dimensions at very small scales.

“To call them extra dimensions is a misnomer in some sense because everything is granular at the Planck [string] scale,” says Green. “Because they are defined quantum mechanically, they should be thought of as some kind of internal space–time structure.” Indeed, while the job of string theorists would be much easier if the universe was 10D and not 4D, the fact that strings have six extra dimensions into which they can vibrate can account for the otherwise mysterious intrinsic properties of elementary particles, such as their spins and charges.

Box: Strings in context

1968

Gabriele Veneziano discovers that the Euler “beta function” brings order to the measured scattering amplitudes of different types of hadrons.

1970

Leonard Susskind, Yoichiro Nambu and Holger Neilsen independently identify Veneziano’s amplitudes with solutions to a quantum-mechanical theory of 1D bosonic strings.

1971

Claud Lovelace realizes string theory requires 26 dimensions; Yuri Gol’fand and Eugeny Likhtman discover supersymmetry in 4D; John Schwarz, André Neveu and Pierre Ramond realize that string theory requires supersymmetry to accommodate fermions as well as bosons; Gerard ‘t Hooft shows that electroweak unification proposed by Steven Weinberg in 1967 is “renormalizable”, thus making gauge theories physically viable.

1973

Julius Wess and Bruno Zumino develop supersymmetric quantum field theories; David Gross, Frank Wilczek and David Politzer discover asymptotic freedom and so establish QCD; combined with electroweak theory, the Standard Model is established.

1974

Schwarz and Joel Scherk (and, independently, Tamiaki Yoneya) realize that string theory contains gravitons, and propose a unified framework of quantum mechanics and general relativity; Sheldon Glashow and Howard Georgi propose grand unification of the Standard Model forces via the symmetry group SU(5).

1976

Stephen Hawking claims that quantum mechanics is violated during the formation and decay of a black hole; mathematicians reveal Calabi–Yau spaces.

1978

Eugène Cremmer, Bernard Julia and Scherk construct 11D supergravity, which incorporates supersymmetry in general relativity.

1981

Schwarz and Michael Green formulate Type I superstring theory; Georgi and Savas Dimopoulos propose the supersymmetric extensions of the Standard Model.

1982

Green and Schwarz develop Type II superstring theory; Andrei Linde and others invent modern inflationary theory from which the multiverse follows.

1983

The discovery of W and Z bosons at CERN seals a decade of success for the Standard Model; Ed Witten and Luis Alvarez-Gaumé show that the gauge anomalies cancel in Type IIB superstring theory.

1984

Green and Schwarz show that the anomalies in Type I theory cancel if the theory is 10D and has either SO(32) or E₈ × E₈ gauge symmetry; T duality is discovered.

1985

Gross, Jeff Harvey, Ryan Rohm and Emil Martinec construct heterotic string theory; Philip Candelas, Andrew Strominger, Gary Horowitz and Witten find a way of compactifying the extra six dimensions using Calabi–Yau spaces.

1987

Weinberg uses anthropic reasoning to place a bound on the cosmological constant.

1994

Susskind proposes the holographic principle by extending work done by ‘t Hooft.

1995

Paul Townsend and Chris Hull, and Witten, propose that Type IIA theory is the weak-coupling limit of 11D “M-theory”; Polchinski discovers D-branes; Witten and others conjecture that all five string theories are linked by dualities, some of which are facilitated by D-branes.

1996

Witten and Polchinski discover that Type I theory and SO(32) heterotic theory are linked by S-duality; Witten and Petr Hořava show E₈ × E₈ is the low-energy limit of M-theory; Strominger and Cumrun Vafa derive the Bekenstein–Hawking black-hole entropy formula using string theory; Susskind and others propose a candidate for M-theory called Matrix theory.

1997

Juan Maldacena discovers the equivalence between string theory and quantum field theory (AdS/CFT duality), thus providing an exact manifestation of the holographic principle.

1998

The experimental discovery of the accelerating expansion of the universe suggests a small, positive vacuum expectation value in the form of a cosmological constant; Lisa Randall and Raman Sundrum propose braneworld scenarios as an alternative to compactification.

1999

Gia Dvali and Henry Tye propose brane-inflation models.

2003

The KKLT paper shows that supersymmetry can be broken to produce a small, positive vacuum expectation value using flux compactification to deal with extra dimensions; Susskind coins the term “landscape” to describe the vast solution space implied by flux compactification, and invokes the anthropic principle and the multiverse to explain the cosmological constant; the KKLMMT paper extends KKLT to cosmology.

2004

Hawking admits he was wrong about black holes and concedes bet to John Preskill.

2005

String theory is mentioned in the context of RHIC quark–gluon plasma thanks to application of AdS/CFT, thereby returning the theory to its roots as a description of hadrons.