String Theory

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Physics has spent a century running on two rulebooks that cannot both be final. General relativity governs stars, galaxies, and spacetime itself; quantum mechanics governs everything small; each has passed every test set for it, and where they meet — inside a black hole, at the universe’s first instant — the combined calculations collapse into infinities. String theory is the longest-running attempt to write the one rulebook beneath the two. Its proposal fits in a sentence: the elementary constituents of nature are not point particles but minute one-dimensional strings, and the different particles — electron, photon, quark — are different modes of vibration of the same string, as one violin string sounds many notes. One kind of thing, vibrating differently, would be everything.

What made the theory irresistible to its advocates arrived uninvited. Among a string’s vibrational modes there is always a massless particle of spin two — exactly the properties required of the graviton, the conjectured quantum of gravity. A string theory cannot be written without it. Every direct attempt to quantize gravity had drowned in infinities; the string’s slight extension softens the mathematics, and gravity falls out as a by-product. The prize that could not be won head-on arrived unasked.

Origins: the dual resonance model

The origin was humbler. In the summer of 1968 Gabriele Veneziano, a young theorist visiting CERN, went looking for a formula to describe the strong nuclear force and found that a piece of eighteenth-century mathematics, the Euler beta function, met his requirements exactly. His “dual resonance model” was an immediate success, and only over the following years was it recognized as the physics of a vibrating string — betrayed by its spectrum, an infinite ladder of harmonics. Veneziano has described the preparatory collaboration with Marco Ademollo, Hector Rubinstein, and Miguel Virasoro at the Weizmann Institute; the discovery that the Euler beta function was an exact realization of duality came to Veneziano alone, first on a boat from Haifa to Venice, then at CERN in July 1968 before submission to Il Nuovo Cimento. By the Vienna conference that August the paper was already widely known and mentioned in several summary talks; it was, in Veneziano’s later account, “an instant hit.”

As a theory of the strong force it failed. It insisted on a massless spin-two particle the nuclear world has no use for, on extra dimensions of space, and at first on a particle faster than light. In 1974 Joël Scherk and John Schwarz proposed the reversal on which the whole field now rests: the embarrassing spin-two particle was the graviton, the theory had stumbled at the nucleus because it was really a theory of all forces, and the strings were not nuclear-sized but twenty orders of magnitude smaller — near the Planck length, around 10⁻³⁵ metres. The strong force went to quantum chromodynamics instead, and for a decade almost nobody followed them.

The two revolutions

The field’s two “revolutions” are dated to the year. In 1984 Michael Green and Schwarz showed the theory could be reconciled with the handedness of the weak interactions — the anomaly cancellation that had prevented consistent superstring theories — and hundreds of physicists moved in. Within a year there were five distinct consistent superstring theories, an awkward surplus for a candidate theory of everything. Type I, type IIA, type IIB, and two heterotic variants (with gauge groups SO(32) and E₈×E₈) each had distinct string content, and the embarrassment of riches intensified the question of which, if any, described the actual world.

In 1995 Edward Witten argued that the five are different limits of a single eleven-dimensional theory he named M-theory, linked by dualities under which apparently different theories describe the same physics. These dualities — S-duality relating strong and weak coupling regimes, T-duality connecting theories on geometrically different background spaces — showed that the five theories were not rivals but faces of one object. The equations of M-theory itself have never been written down. The argument was laid out in Witten’s March 1995 paper; as David Simmons-Duffin has observed, “Witten could make these arguments without writing down the equations of M-theory, which is impressive but left many questions unanswered.” Thirty years on, its existence is a conjecture argued from its shadows.

Branes, compactification, and the hidden dimensions

The strings need more room than the world appears to offer. The mathematics is consistent only in ten spacetime dimensions — eleven for M-theory — and the dimensions beyond the familiar four are held to be compactified: curled up on themselves in intricate shapes called Calabi–Yau manifolds, at scales smaller than an atom, hidden from view not by distance but by size. The idea generalizes a proposal Kaluza and Klein made in the 1920s. The compactification is not just geometrical tidying: the shape of the hidden dimensions determines the spectrum of particles and forces in the four-dimensional theory, so every distinct Calabi–Yau shape yields a different effective physics. (The history of extra dimensions’ deeper cultural career — from Zöllner’s spiritualist experiments through Hinton and Ouspensky — belongs to the spacetime article, which owns that thread.)

Alongside the strings proper, the 1995 revolution brought into focus a richer cast of extended objects: p-branes, generalized membranes of p dimensions propagating through spacetime according to the rules of quantum mechanics. Joseph Polchinski’s work established that D-branes — branes on which the endpoints of open strings are constrained to lie — are dynamical objects that carry charge, and that D-brane configurations at strong coupling are indistinguishable from black holes. This D-brane insight directly seeded the most significant concrete result the theory has produced.

AdS/CFT: the holographic correspondence

The theory’s most-cited concrete achievement is a 1997 conjecture of Juan Maldacena’s: a gravitational universe with negatively curved geometry is exactly equivalent to a particle theory without gravity defined on that universe’s boundary — the deep world rendered, without loss, on its own surface. The paper, “The Large N Limit of Superconformal Field Theories and Supergravity”, became the most cited in high-energy physics, accumulating more than 16,000 citations in its first twenty years. The equivalence carries a philosophical sting: if a ten-dimensional world with gravity and a four-dimensional world without it are the same world, neither description is fundamental, and spacetime itself may be emergent.

The correspondence has delivered working science beyond its home domain. String-theoretic counting reproduced exactly the entropy formula for certain idealized black holes; AdS/CFT gave nuclear physicists a tractable model of the quark–gluon plasma — the ratio of shear viscosity to entropy density predicted by the correspondence was confirmed at the Relativistic Heavy Ion Collider at Brookhaven in 2008; and the same framework has been applied to condensed matter problems, including aspects of the superfluid-to-insulator transition. Whatever the strings’ standing as physics, the mathematics has earned its keep.

Mirror symmetry, born as two string descriptions of the hidden dimensions, handed mathematicians correct answers to century-old counting problems in enumerative geometry — the number of curves on a Calabi–Yau manifold — before they could derive them by conventional means. The mathematical return on the investment has been genuine and independent of the question of physical truth.

The landscape and the multiverse

What the theory has never done is pick out this world. Each way of curling the hidden dimensions yields a different vacuum — a different roster of particles and forces — and the standard estimate of the possibilities is 10⁵⁰⁰. Leonard Susskind embraced the resulting “landscape”: if every vacuum is realized somewhere in a multiverse, then observers necessarily find themselves in one of the rare universes compatible with observers — an anthropic argument with a respectable precedent in Steven Weinberg’s 1987 treatment of the cosmological constant. (The full multiverse map, with its inflationary mechanisms and typology, is handled in the multiverse article.) Peter Woit answered that a framework able to accommodate 10⁵⁰⁰ different versions of physics predicts none of them; the landscape, in his account, is not a prediction but an admission.

The critique era

The empirical ledger, after more than fifty years, is blank, and both sides know it. In 2002 Witten judged supersymmetry — the theory’s expected partner symmetry — to lie within reach of the Large Hadron Collider, and its discovery to be the realistic route to showing that string theory has something to do with nature. The collider ran; the superpartners did not come. By 2012 one of supersymmetry’s own architects, Mikhail Shifman, was calling on colleagues to abandon “developing contrived baroque-like aesthetically unappealing modifications” of supersymmetry and “start thinking and developing new ideas.” The miss wounds string theory without falsifying it — superpartners can always be heavier than the last search — and that very flexibility is the critics’ deepest charge.

Woit’s Not Even Wrong and Lee Smolin’s The Trouble with Physics, both 2006, pressed the case at book length. Smolin added that the theory never absorbed relativity’s hardest lesson — that spacetime is no fixed stage — and that its dominance starves the alternatives. In 2014 George Ellis and Joseph Silk argued in Nature that exempting such theories from experimental verification undermines science itself. The 2015 Munich meeting of physicists and philosophers — convened at Ludwig Maximilian University partly in response to Ellis and Silk’s challenge — grappled with whether non-empirical virtues could legitimately support a theory absent any experimental test. As David Gross reported at the opening session, fundamental physics faced a problem “dire enough to call for outsiders’ perspectives.” The meeting did not reach consensus but produced one useful clarification: Gross, a Nobel laureate inside the program, acknowledged that Richard Dawid’s criteria for non-empirical confirmation were good for justifying continued work, not for claiming validation.

The defense, at full strength, runs differently: string theory is the only known candidate for quantum gravity that has passed its own consistency checks. Dawid identified three non-empirical arguments circulating among practitioners — the no-alternatives argument, a meta-inductive argument from the Standard Model’s own formative period, and the unexpected explanatory interconnections the theory has forged. He concedes the risk: “it opens the floodgates.” No resolution has been reached. More than fifty years after Veneziano’s formula, the theory’s physical truth is simply undetermined — not confirmed, not refuted, and not yet confirmable.

Frontier: the swampland program and the it-from-qubit turn

The decade since the LHC’s null supersymmetry results has not stalled the research programme; it has reoriented it. The swampland program, developed principally by Cumrun Vafa, maps the boundary between the string landscape and the vast outer territory of effective field theories that appear self-consistent but cannot be completed into a full quantum gravity theory. Vafa has argued that the swampland is in fact much larger than the landscape — that most low-energy theories one might write down are, in this sense, incompatible with consistent quantum gravity, even if they violate no apparent principle. The weak gravity conjecture and the distance conjecture are among the criteria proposed for diagnosing which theories fall outside. Critically, the KKLT construction of 2003 (Kachru, Kallosh, Linde, Trivedi), which was the principal mechanism for accommodating a small positive cosmological constant in the landscape, has come under sustained challenge: at Strings 2018 in Okinawa, Vafa argued it belongs in the swampland rather than the landscape, meaning it may not be viable at a fundamental quantum-gravity level. The debate is unresolved.

A second reorientation has come from quantum information. The Ryu–Takayanagi conjecture, extending the AdS/CFT correspondence, expresses the entropy of a bulk gravitational region in terms of a minimal surface in the boundary theory — an area formula reminiscent of the Bekenstein–Hawking formula — and connects directly to the structure of quantum entanglement. The programme loosely gathered under “it from qubit” proposes that spacetime geometry emerges from the pattern of entanglement in the boundary theory. The ER=EPR conjecture of Susskind and Maldacena (2013) goes further, proposing that pairs of entangled particles (EPR pairs) are connected by non-traversable wormholes (Einstein–Rosen bridges): that entanglement and geometry may be two aspects of the same thing. The conjecture remains speculative — a notable tension exists between the linearity of quantum mechanics and the geometry its superpositions would appear to imply — but it has driven an extensive programme linking quantum error correction, holography, and the emergence of spacetime. The quantum entanglement article handles the broader entanglement context.

Reception: vibration, higher dimensions, and the esoteric thread

What earns string theory a place in this encyclopedia is the shape of the proposal, not its standing — a shape this site cannot help reading in an older light. A single substance whose modes are all things; a visible world wrapped around dimensions hidden from sight; reality rendered as the surface-image of a deeper order: to anyone schooled in emanationist cosmology, where the many proceed as modes of the One, or in the Pythagorean cosmos, where the world is built the way music is built, the silhouette is immediately familiar.

The popular reception saw it at once. Brian Greene’s The Elegant Universe (1999) carried the vibrating cosmos to millions. Before it, Fritjof Capra’s The Tao of Physics (1975) and Gary Zukav’s The Dancing Wu Li Masters (1979) had trained a readership for whom “vibration” was a metaphysical word; the New Age adopted the vocabulary and kept it. Michio Kaku’s Hyperspace (1994) served as the popular bridge between the cultural appetite for extra dimensions — an appetite with a Victorian pedigree in Hinton and Ouspensky — and the contemporary physics of Calabi–Yau compactification. The spacetime article holds the fuller account of that reception history, from Zöllner’s spiritualist fourth-dimension experiments through the Theosophical hyperspace tradition; what matters here is how neatly the string imagery completed it.

The irony is genealogical. Capra built his physics-and-mysticism parallels not on strings but on the 1960s bootstrap program of Geoffrey Chew — the same S-matrix soil out of which Veneziano’s amplitude actually grew. The mystical reading and the mathematical theory are estranged siblings of one abandoned research program, which is much of why the language crossed over so easily. As Peter Woit has documented, Capra left the bootstrap physics intact through multiple editions of The Tao of Physics even after the Standard Model had superseded it — “a statement far from any relation to the reality that in 1983 the standard model was nearly universally accepted in the physics community, and the bootstrap theory was a dead idea.”

The physicists’ refusals of that crossing are on record by name. Murray Gell-Mann coined “quantum flapdoodle” for the genre; Jeremy Bernstein, reviewing Capra, objected to “accidental similarities of language” being offered as evidence of deep connection; Leon Lederman, in The God Particle, dismissed both Capra’s and Zukav’s books as elaborate extensions that entirely missed how theory and experiment are woven together. Their point survives contact with the house reading, and sharpens it. When Witten reaches for violins and harmonics, the music is pedagogy for a mathematical structure, not a kinship claim with vibrational metaphysics; and a theory whose own truth is undetermined has no confirmation to lend in any direction. The echo lives in the imagery — imagery the physicists chose for themselves — and the imagery is, for now, the whole of what is shared.

Daniele Amati described string theory, in a line Witten liked, as “part of 21st-century physics that fell by chance into the 20th century.” A quarter of the century in question has now run, and the verdict Amati’s line deferred belongs to the three-quarters that remain.

→ Related: Multiverse · Emanation · Pythagoras · Quantum Entanglement · Spacetime · Quantum Physics · Holographic Principle