Physicists Found String Theory Without Even Looking for It

Physicists searching for a better understanding of quantum gravity stumbled upon something unexpected: the defining signatures of string theory.

Imagine slicing an apple into smaller and smaller pieces. First you would reach molecules, then atoms, and eventually the subatomic particles inside them, including protons, quarks, and gluons. According to string theory, however, nature may continue even deeper. At scales far smaller than a proton, the universe could be built from tiny vibrating strings.

Originally developed in the 1960s, string theory attempts to solve one of the biggest unsolved problems in physics: combining quantum mechanics with general relativity. Quantum mechanics explains the behavior of matter and energy at extremely small scales, while general relativity describes gravity and the structure of the cosmos on the largest scales. Physicists have struggled for decades to merge the two frameworks because the mathematics tends to break down when gravity is treated quantum mechanically.

String theory offers a possible solution by replacing pointlike particles with microscopic strings. Different vibrations of these strings would produce all known particles, including the graviton, a hypothetical particle believed to carry gravity. The theory also predicts the existence of at least 10 dimensions, rather than the four dimensions humans experience in everyday life.

One of the biggest challenges is testing the theory directly. The energies needed to probe strings experimentally are so enormous that researchers would need a particle accelerator roughly the size of a galaxy.

A New Bootstrap Approach to String Theory

Unable to test string theory directly, physicists are turning to alternative methods. One increasingly popular strategy is known as the “bootstrap” approach. Instead of beginning with a complete theory, scientists start with a few broad assumptions about how nature should behave and see what mathematical structures emerge.

In a new paper called “Strings from Almost Nothing,” accepted for publication in Physical Review Letters, researchers from Caltech, New York University, and Institut de Fisica d’Altes Energies in Barcelona used this method to explore particle interactions at extremely high energies. Starting from only a small number of assumptions about scattering behavior, they unexpectedly recovered the defining features of string theory.

“The strings just fell out,” says Clifford Cheung, professor of theoretical physics and director of the Leinweber Forum for Theoretical Physics at Caltech. “We didn’t start with any assumptions about strings at all, but then the solution contained the cornerstone signatures of strings.”

Cheung explains that the work does not count as experimental proof of string theory, but the result is still significant because the assumptions could have produced many possible mathematical outcomes. Instead, the equations led to a unique structure matching string theory.

The Infinite Spectrum of Particles

One of the most important signatures that emerged is called the string spectrum. In the late 1960s, Italian physicist Gabriele Veneziano at CERN discovered a mathematical function describing a seemingly endless sequence of particles produced in collider experiments. These particles appeared in an ordered pattern with steadily increasing masses and spins.

“At Veneziano’s time, particle colliders were seeing this spray of junk come out of the collisions, particles of different masses. It was fascinating, and nobody had any idea what was going on. Veneziano wrote down a function to describe all the masses, revealing an infinite tower of particles,” Cheung says.

Scientists later realized that this particle spectrum resembles the harmonic vibrations of a musical string. A violin string, for example, produces a fundamental note along with a series of higher harmonics. String theory proposes that particles arise from similar vibrational patterns.

The connection between string theory and gravity became clearer in 1974 when Caltech physicist John Schwarz and French physicist Joël Scherk recognized that the theory naturally included gravity itself.

“Like all particle physicists in that era, we had no prior interest in gravity. String theories are well-behaved at very high energies, unlike Einstein’s general theory of relativity, which survives as a low-energy approximation. Therefore, even though much was not yet understood, we were very excited that some version of string theory could provide a unified quantum theory of everything,” Schwarz says.

In string theory, each vibrational mode corresponds to a different particle. A photon can emerge from an open string vibrating in a fundamental mode, while a graviton may arise from a closed string vibrating in a similar way.

Why Quantum Gravity Becomes Unstable

The new study focused on scattering amplitudes, mathematical tools used to predict the outcomes of particle collisions. At extremely high energies near the Planck scale, calculations based on general relativity begin producing infinities that make no physical sense.

“If you take general relativity and scatter at very high energies at the so-called Planck scale—that is roughly 19 orders of magnitude greater than a proton’s mass—you get a result that makes no sense. Everything completely breaks down,” Cheung says.

String theory avoids this problem through a property called ultrasoftness. At very high energies, interactions become smoother and less violent, preventing the equations from diverging toward infinity.

“In a string theory framework, as you increase the energy transfer between particles, you will see a swift fall off in the probability that the particles will scatter. It’s like the particles don’t even want to scatter off one another, but rather pass freely,” Cheung says. “The scattering amplitudes don’t go to infinity. It’s better behaved.”

The researchers used this ultrasoft behavior as one of their core assumptions. They also assumed a property called “minimal zeros,” which limits the number of special points where scattering probabilities vanish.

“Remarkably, consistency requires scattering amplitudes not only to interact but also to not interact at special kinematic points called ‘zeros.’ The assumption of ‘minimal zeros’ demands the sparsest number of such vanishing points mathematically allowed by the equations,” Cheung says.

From only these assumptions, the researchers demonstrated mathematically that the resulting solutions naturally reproduced the central features of string theory, including its characteristic spectrum of particles and interaction strengths.

“The precise details of string theory emerged automatically, including the infinite tower of massive spinning particles that form the ‘harmonics’ of the string that the theory is famous for,” says co-author Grant N. Remmen (PhD ’17), the James Arthur Postdoctoral Fellow at New York University.

Reviving an Old Physics Idea

Cheung compares the bootstrap method to solving a sudoku puzzle. Starting with only a handful of rules, researchers search for the one solution that satisfies every condition.

“The deep irony is that this bootstrap idea that we’re pursuing now with modern tools and modern ideas is super retro. It’s an old idea,” Cheung explains. “The original discovery of the Veneziano spectrum, and John Schwarz’s work, took a similar approach. They didn’t start with string theory models, but rather the solutions came out of basic principles.”

Cheung also credits earlier pioneers of the bootstrap concept, including Caltech physicist Steven Frautschi and UC Berkeley physicist Geoffrey Chew. In the 1960s, they developed bootstrap methods in particle physics and uncovered early hints of the same infinite particle spectrum later linked to string theory.

“The bootstrap idea had become obsolete, but now people like Cliff are reviving and modernizing it,” says Hirosi Ooguri, the Fred Kavli Professor of Theoretical Physics and Mathematics at Caltech and the Kent and Joyce Kresa Leadership Chair of the Division of Physics, Mathematics and Astronomy. “We now have a better understanding of the basic assumptions we can make, as well as stronger techniques for translating these assumptions into properties of scattering amplitudes and other observables.”

Reference: “Strings from almost nothing” by Clifford Cheung, Grant N. Remmen, Francesco Sciotti and Michele Tarquini” Accepted, Physical Review Letters.
DOI: 10.1103/cw4p-cqh7

The study received support from the US Department of Energy, the Walter Burke Institute for Theoretical Physics, the Leinweber Forum for Theoretical Physics, the James Arthur Postdoctoral Fellowship at New York University, and the Next Generation EU. Additional authors include Francesco Sciotti of Institut de Fisica d’Altes Energies in Barcelona and Michele Tarquini, a graduate student at Caltech.

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