String Theory: When Physics Breaks the Boundaries of Four-Dimensional Spacetime

The Origins of String Theory: Two Incompatible Theories

Since the early 20th century, theoretical physics has rested on two pillars. General relativity (theory formulated by Einstein describing gravity as a curvature of spacetime caused by mass and energy), developed by Albert Einstein (1879-1955), describes the behavior of massive objects on a large scale. Quantum mechanics (physical theory describing the behavior of matter and energy at subatomic scales, where quantum effects dominate), developed by Niels Bohr (1885-1962) and Werner Heisenberg (1901-1976), governs the infinitely small world of elementary particles. The problem is that these two theories are mutually incompatible: applying quantum mechanics to gravity produces infinite divergences (mathematical result of division by zero or a physical quantity that diverges to infinity, signaling a limit of the theory's validity), signaling a deep gap in our understanding of physical reality. It was to bridge this gap that string theory was born.

What is String Theory?

In the 1960s, Gabriele Veneziano (born 1942) discovered that the Euler beta function (mathematical function introduced by Euler in the 18th century, reappearing unexpectedly in the description of strong interactions) surprisingly well described certain interactions between hadrons (composite particles made of quarks, subject to the strong interaction, such as protons, neutrons, and mesons). In 1970, Yoichiro Nambu (1921-2015), Holger Bech Nielsen (born 1941), and Leonard Susskind (born 1940) realized that this formula described one-dimensional vibrating objects: strings. In 1974, John Schwarz (born 1941) and Joël Scherk (1946-1980) realized that the vibration spectrum naturally included a state corresponding to the properties of the graviton, making string theory a serious candidate for a quantum theory of gravity.

The Core of the Theory: From Particles to Vibrating Strings

The Fundamental Idea

Instead of conceiving elementary particles as zero-dimensional geometric points, string theory describes them as tiny one-dimensional vibrating objects. These strings, whose length is on the order of the Planck length (fundamental length of quantum gravity, approximately 1.616 × 10⁻³⁵ meters, far beyond any current direct detection capability) \(\ell_P \approx 1.616 \times 10^{-35}\) m, appear point-like at all accessible energy scales. An electron, a quark, a photon, or a graviton would be different manifestations of the same vibrating entity, like a violin string producing different notes depending on its mode of vibration.

The Mathematical Necessity of Extra Dimensions

A consistent string theory in only four dimensions is impossible: tachyons (hypothetical particle whose squared mass would be negative, implying faster-than-light propagation and instability of the quantum vacuum) and anomalies (quantum anomaly referring to the violation of a classical symmetry upon quantization, making the theory mathematically inconsistent) inevitably break the theory's coherence. The bosonic string theory (first consistent formulation of string theory, describing only bosonic strings without supersymmetry, requiring 26 spacetime dimensions) requires 26 dimensions; superstring theories (extension of string theory incorporating supersymmetry, describing both bosonic and fermionic strings in a 10-dimensional spacetime) integrating supersymmetry (symmetry linking bosons and fermions in a quantum field theory, postulating the existence of a supersymmetric partner for each known particle) require 10; the M-theory (theoretical framework proposed by Edward Witten in 1995, unifying the five superstring theories and 11-dimensional supergravity into a single 11-dimensional theory) by Edward Witten (born 1951) demands 11. This number is not arbitrary: it is imposed by the internal consistency of the mathematics.

Hidden Dimensions: Where Are They?

The Compactification Mechanism

If spacetime has 10 or 11 dimensions, why do we only perceive 4? The answer is compactification (process by which the extra dimensions of spacetime would be curled up on themselves at a scale so small that they remain inaccessible to any direct observation): the extra dimensions would be curled up on themselves at the Planck scale, imperceptible to our senses and instruments. Imagine a garden hose seen from afar: it looks like a one-dimensional line, but hides a circular dimension invisible to the distant observer. The extra dimensions would work analogously, in far more complex geometries.

Calabi-Yau Manifolds

To preserve supersymmetry in four dimensions, these hidden dimensions must form precise geometric structures: Calabi-Yau manifolds (compact complex manifold of real dimension 6 (or complex dimension 3), admitting a Ricci-flat metric, whose geometry determines the physical properties of particles in superstring theories), named after mathematicians Eugenio Calabi (1923-2023) and Shing-Tung Yau (born 1949). There are potentially between \(10^{500}\) and \(10^{272,000}\) distinct configurations, each generating a universe with different physical laws. This abundance, the landscape (space of all possible consistent physical theories arising from the compactification of string theory, representing a vast set of universes with different physical laws), raises a major criticism: if the theory describes an almost infinite number of universes, what is its predictive power for ours? Leonard Susskind (born 1940) responds by invoking the anthropic principle (principle according to which our universe seems fine-tuned to allow life because, without this fine-tuning, no observer would be there to notice it) and the multiverse (cosmological concept postulating the existence of a vast number of distinct universes, each with potentially different physical constants and laws).

The 1984 Revolution and the Five Theories

The First Superstring Revolution

In 1984, Michael Green (born 1946) and John Schwarz (born 1941) showed that certain quantum anomalies (quantum anomaly referring to the violation of a classical symmetry upon quantization, making the theory mathematically inconsistent) canceled out exactly in 10-dimensional superstring theories, triggering a massive influx of researchers into this field. Five consistent theories emerged: Type I (10-dimensional superstring theory whose gauge symmetry group is SO(32), containing only oriented open and closed strings), Types IIA and IIB (10-dimensional superstring theories containing only closed strings, with two non-chiral (IIA) or chiral (IIB) supersymmetries), and heterotic SO(32) and E8×E8 (hybrid theories combining bosonic strings in one sector and superstrings in the other, with SO(32) or E8×E8 symmetry groups). Their coexistence seemed incompatible with the ambition of a single, fundamental theory.

The Second Revolution and M-Theory

In 1995, Edward Witten (born 1951) settled the matter: these five theories and 11-dimensional supergravity (theory of gravity incorporating supersymmetry in 11 dimensions, appearing as a low-energy limit of M-theory) are merely facets of a deeper theory, M-theory (M for "Mother," "Mystery," "Membrane," or "Matrix"). At 11 dimensions, it extends the concept of strings to higher-dimensional objects, p-branes (extended objects with p spatial dimensions naturally appearing in superstring theories, generalizing the concept of strings (1-branes) to higher-dimensional membranes), including 2-branes (two-dimensional spatially extended object in string theory, analogous to a two-dimensional membrane moving through spacetime) and 5-branes (five-dimensional spatially extended object in M-theory, playing a fundamental role in the dualities between different superstring theories), unified by relations of duality (mathematical equivalence between two seemingly different physical theories, allowing problems in one to be solved using the tools of the other).

Main Versions of String Theory and Their Characteristics

N.B.:
The symmetry groups in the table are Lie groups governing fundamental interactions. The \(E_8 \times E_8\) group is remarkable because it contains all the symmetries of the Standard Model of particle physics. D-branes (objects where open strings attach) were introduced by Joseph Polchinski (1954-2018) in 1995.

Why Is String Theory Criticized?

Despite its mathematical elegance, string theory faces three major criticisms within the scientific community. The first, and most radical, is the complete absence of verifiable predictions through experiment. Strings are so small (Planck scale) that no particle accelerator, even in the future, will ever be able to observe them directly.

The second criticism concerns what physicists call the string landscape (colossal set of mathematical solutions compatible with string theory, estimated at 10 to the power of 500 possible universes). This term refers to the astronomical number of possible universes (about \(10^{500}\) different solutions) allowed by the theory. For its detractors, this landscape makes the theory non-falsifiable: any observation can be justified a posteriori by choosing the right solution.

Finally, some scientists, such as Sabine Hossenfelder (1976–) or Peter Woit (1956–), denounce a speculative drift in fundamental physics. According to them, string theory has dominated quantum gravity research for over four decades, at the expense of other approaches (loop quantum gravity, non-commutative geometry) that might be more promising. The lack of experimental progress since the 1980s thus fuels an epistemological unease: mathematical beauty alone is not enough to make a physical theory.

Key Takeaways

String theory proposes replacing point-like particles with tiny vibrating strings and predicts the existence of the graviton (hypothetical particle, quantum messenger of the gravitational force). It naturally unifies gravity and quantum physics, but at the cost of adding 6 to 7 extra dimensions, curled up at an infinitely small scale in complex geometric structures called Calabi-Yau manifolds (compact complex manifold of real dimension 6 (or complex dimension 3), admitting a Ricci-flat metric, whose geometry determines the physical properties of particles in superstring theories). However, its greatest challenge remains the lack of experimental evidence.

FAQ: Everything You Need to Know About String Theory