String theory has spent decades as one of physics’ most debated ideas, celebrated by some as the best candidate for a “theory of everything,” dismissed by others as an untestable mathematical fantasy. Now, a team of physicists from Caltech, New York University, and Institut de Fisica d’Altes Energies in Barcelona may have added a genuinely surprising chapter to that debate. They were not trying to prove string theory. They were not even looking for it. But there it was, sitting at the end of their equations.
Their study, titled “Strings from Almost Nothing,” has been accepted for publication in Physical Review Letters. The core finding is striking: starting from just two basic assumptions about how particles behave at extreme energies, the mathematics naturally and uniquely produced the defining signatures of string theory, with no strings assumed to begin with.
A Problem That Has Haunted Physics for Decades
To understand why this matters, it helps to know what string theory was originally trying to solve. Physics rests on two extraordinarily successful but deeply incompatible frameworks. Quantum mechanics governs the behaviour of matter and energy at the smallest scales, the world of atoms, electrons, and quarks. General relativity, Einstein’s masterwork, describes gravity and the large-scale structure of the universe. Both theories work brilliantly within their own domains. The trouble starts when you try to use them together.
When physicists attempt to apply quantum mechanics to gravity, specifically when calculating how particles scatter at energies near the Planck scale (roughly 19 orders of magnitude greater than a proton’s mass), the equations break down completely. The results spiral into mathematical infinities that carry no physical meaning.
“If you take general relativity and scatter at very high energies at the so-called Planck scale, you get a result that makes no sense. Everything completely breaks down,” says Clifford Cheung, professor of theoretical physics and director of the Leinweber Forum for Theoretical Physics at Caltech, and the study’s lead author.
String theory was developed as a mathematical cure for exactly this problem. The idea, which first emerged in the 1960s, proposes that the fundamental building blocks of reality are not point-like particles but incredibly tiny vibrating strings, roughly a billion billion times smaller than a proton. Different vibrational modes of these strings produce different particles. A photon, for instance, arises from an open string vibrating in its fundamental mode. The graviton, the hypothetical particle believed to carry gravity, would emerge from a closed vibrating string. Because strings are extended objects rather than points, they naturally smear out interactions in a way that prevents the infinities from appearing.
There is, however, one enormous catch. Testing string theory directly would require a particle collider roughly the size of a galaxy. That experiment will never happen. So for decades, string theory has remained a mathematically elegant but experimentally unreachable idea.
What the Bootstrap Approach Actually Is
Since direct experiments are off the table, physicists have been looking for other ways to probe the theory’s validity. One increasingly powerful method is the “bootstrap” approach, a technique with roots going back to the 1960s work of Caltech physicist Steven Frautschi and UC Berkeley physicist Geoffrey Chew, who coined the name after the phrase “pulling oneself up by one’s bootstraps.”
The idea is deceptively simple. Instead of starting with a complete theory and testing its predictions, you start with a small number of things you believe must be true about nature, broad physical principles, and then ask: what mathematical structures are forced to exist by these principles alone? What laws emerge?
Cheung compares it to solving a sudoku puzzle. You are given a handful of rules about how numbers can be placed in a grid. From those rules alone, one unique solution exists. You did not design the solution. The constraints found it for you.
“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.”
Two Assumptions, One Unexpected Answer
For this study, the team began with two assumptions about how particles scatter during high-energy collisions, and only two.
The first assumption is called ultrasoftness. In string theory, as the energy of a collision increases toward the Planck scale, the probability of particles actually scattering drops sharply rather than diverging toward infinity. The interaction softens. The particles, in a sense, stop wanting to collide and instead pass through each other freely. The researchers took this behaviour as a starting condition, not because they assumed strings, but because this kind of softening is precisely what any well-behaved theory of quantum gravity would need.
The second assumption is called minimal zeros. Scattering amplitudes, the mathematical expressions describing collision probabilities, have special points where the probability vanishes entirely. These are called zeros. The team assumed there should be as few of these vanishing points as mathematically possible. Nothing more complicated than that.
“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 these two assumptions alone, the team rigorously worked through the mathematics. What emerged was not ambiguous. The equations pointed to one solution and one solution only, and that solution was string theory.
“The strings just fell out,” Cheung says. “We didn’t start with any assumptions about strings at all, but then the solution contained the cornerstone signatures of strings.”
The Infinite Tower of Particles
Among the most important features that emerged from the calculations was the string spectrum, one of string theory’s most distinctive fingerprints. This spectrum was first identified in the late 1960s by Italian theoretical physicist Gabriele Veneziano at CERN, who wrote down a mathematical function describing an unusual pattern in particle collider data. Particles of different masses were appearing in collisions in a strangely ordered sequence, with mass and spin increasing in precise, regular steps, an infinite tower of states, one stacked upon the next.
At the time, nobody had any idea what to make of it. Physicists eventually realised that the pattern resembles the harmonic vibrations of a string. When you pluck a violin string, you do not get a single note; you get the fundamental tone and a series of overtones, each a higher harmonic of the first. String theory proposes that particles arise in the same way as harmonics of vibrating strings at the quantum scale.
Co-author Grant N. Remmen, the James Arthur Postdoctoral Fellow at New York University, summarised the result plainly: “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.”
This was not put in by hand. It fell out of the two starting assumptions.
What This Does and Does Not Mean
It is important to be precise about what this study claims and what it does not. This is not experimental proof of string theory. No particle has been detected. No string has been observed. The energies needed to test string theory directly remain impossibly far beyond current technology.
What the study does show is something more subtle but still significant: when you start from the minimal conditions that any workable theory of quantum gravity would need to satisfy, string theory is not just one possible answer among many; it appears to be the only answer the mathematics allows.
“Though the work does not amount to experimental evidence for string theory, it is very suggestive from the theoretical viewpoint, since the general assumptions could have yielded infinite solutions, but they yielded only one,” Cheung says.
Hirosi Ooguri, the Fred Kavli Professor of Theoretical Physics and Mathematics at Caltech, who was not an author on the paper, also noted the method’s broader value. Beyond validating string theory’s internal consistency, the bootstrap approach can help physicists think more clearly about what assumptions would need to be abandoned if string theory turns out to be wrong. “If string theory is not true, and we want to find another model, then what basic assumptions do we need to remove?” Ooguri says.
An Old Idea, Revived With Modern Tools
There is something quietly fitting about the method at the centre of this research. The bootstrap approach was considered cutting-edge in the 1960s, then gradually fell out of fashion as other tools took over. Frautschi and Chew’s early bootstrap work in particle physics had already hinted at the same infinite tower of particles later formalised by Veneziano. Decades passed. The approach was largely set aside.
Now it is back; rebuilt with modern mathematical techniques and applied to one of the deepest open problems in physics.
“The bootstrap idea had become obsolete, but now people like Cliff are reviving and modernising it,” Ooguri says. “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.”
The study received funding 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.
The paper “Strings from Almost Nothing” is accepted for publication in Physical Review Letters (DOI: 10.1103/cw4p-cqh7).
