If you keep splitting the apple into smaller and smaller pieces, you’ll eventually arrive at molecules, then atoms, and smaller particles within atoms such as protons, quarks, and gluons. But according to string theory, the journey doesn’t end there. On the scale of about one billionth of a proton, physicists propose that everything is made of incredibly tiny vibrating strings.
String theory first emerged in the 1960s as a potential solution to one of physics’ biggest problems. It is a combination of quantum mechanics, which governs the smallest particles, and general relativity, Einstein’s theory that explains gravity and the large-scale structure of the universe. Scientists have long struggled to integrate the two because when gravity is involved at the quantum scale, the equations often spiral toward mathematical infinity.
String theory offers a possible way around this problem. In this theory, all particles, including the hypothetical graviton that carries gravity, arise from various vibrations of tiny strings. Mathematics also requires strings to exist in at least 10 dimensions, rather than the four dimensions that humans experience.
One major hurdle remains. Directly testing string theory would require such extreme energies that researchers would need particle colliders the size of galaxies.
Bootstrap physics and string theory
Direct experiments are not possible with current technology, so physicists are looking for other methods. One promising strategy is known as the “bootstrap” approach. Rather than postulating a detailed theory from the beginning, scientists start with some broad principles that they believe nature must follow, and then determine what laws appear in nature.
In a new study titled “Strings from Almost Nothing,” which has been accepted for publication in Physical Review Letters, researchers from the California Institute of Technology, New York University, and the National Institute of Energy in Barcelona used this strategy to investigate the behavior of particles at very high energies. Starting from just a few assumptions about how particles scatter during collisions, we unexpectedly arrived at a core feature of string theory.
“The string just fell off,” says Clifford Chan, a professor of theoretical physics at the California Institute of Technology and director of the Rheinweber Forum for Theoretical Physics. “We didn’t start by making any assumptions about the string, but then the solution included the underlying signature of the string.”
Although the discovery does not provide experimental proof of string theory, the result is surprising because many different mathematical outcomes were possible, Cheung said. Instead, the calculations showed only one solution.
infinite particle tower
One of the most important features obtained from the calculation is known as the string spectrum. In the late 1960s, Italian theoretical physicist Gabriele Veneziano at CERN developed a mathematical function to describe the mysterious “towers” of particles seen in collider experiments. The particles emerged in a sequence in which their mass and spin increased in regular steps.
“In Veneziano’s time, particle bombarders were observing particles of different masses colliding and ejecting droplets of junk like this. It was fascinating, but no one knew what was going on. Veneziano wrote down a function that described all the masses, revealing an infinite tower of particles,” Zhang says.
Researchers later realized that this pattern resembled the overtones of a vibrating string. When you pluck a violin string, it produces a tonic tone and a series of overtones. String theory holds that particles arise from similar vibrational patterns.
In 1974, Caltech physicist John Schwartz and French physicist Joel Schaak realized that string theory could also include gravity. This discovery created one of the first meaningful connections between string theory and general relativity.
“Like all particle physicists at the time, we had no previous interest in gravity. Unlike Einstein’s general theory of relativity, which survived as a low-energy approximation, string theory works well at very high energies. So we were very excited that some version of string theory could provide a unified quantum theory of everything, even though there was still a lot we didn’t understand,” says Schwartz.
According to string theory, different modes of vibration produce different particles. For example, photons originate from an open string vibrating in its simplest mode, while gravitons are thought to originate from a closed, vibrating string.
Why does quantum gravity collapse?
The new study focused on scattering amplitude, a mathematical equation that describes the consequences of particle collisions. When scientists use general relativity to calculate collisions at very high energies, near the Planck scale, the calculations break down and produce infinity.
“If you use general relativity and scatter at very high energies on the so-called Planck scale (roughly 19 orders of magnitude greater than the mass of a proton), you get meaningless results. Everything breaks down completely,” Cheung says.
String theory avoids these infinities through a property called supersoftness. At very high energies, the strings effectively break up interactions and prevent violent movements that would normally cause equation breakdown.
“In the string theory framework, we see that as the energy transfer between particles increases, the probability that the particles will scatter decreases rapidly. It’s not like the particles even want to scatter from each other, but rather they pass freely through each other,” Cheung says. “The amplitude of the scattering doesn’t go to infinity. It works better that way.”
The researchers used this ultra-soft behavior as one of their starting assumptions. It also includes another condition called “minimum zero” that limits the number of points at which the scattering probability disappears.
“Surprisingly, achieving consistency requires not only that the scattering amplitudes interact, but also that they do not interact at a special kinematic point called ‘zero.’ “Assuming a ‘minimum zero’ requires the sparsest number of such vanishing points that are mathematically allowed in the equation,” says Cheung.
Using only these assumptions, the research team showed that the resulting mathematics naturally reproduces features of string theory, including the famous spectra of particles’ masses and spins.
“The precise details of string theory were automatically revealed, including the endless towers of giant rotating particles that form the theory’s famous string ‘overtones,'” says co-author Grant N. Lemen (PhD ’17), a James Arthur postdoctoral fellow at New York University.
Revive old ideas with modern tools
Cheung likens the bootstrap approach to solving a Sudoku puzzle. A few simple rules are provided at the beginning, which ultimately lead to a unique solution.
“The deep irony is that this bootstrapping idea that we’re pursuing now with modern tools and modern ideas is very retro. It’s an old idea,” Cheung explains. “A similar approach was taken with the original discovery of the Veneziano spectrum and with the work of John Schwartz. They did not start with string theory models, but rather solutions were derived from fundamental principles.”
The study also builds on earlier work by Caltech physicist Stephen Frautsky and UC Berkeley physicist Jeffrey Chu, who pioneered the bootstrap approach in particle physics in the 1960s. Their work provided some of the early hints of the infinite particle spectrum that was later linked to string theory.
“The idea of bootstrapping was outdated, but now people like Cliff are bringing it back and modernizing it,” says Hiroshi Oguri, the Fred Kavli Professor of Theoretical Physics and Mathematics and the Kent and Joyce Kulesa Leadership Chair in the Department of Physics, Mathematics, and Astronomy at Caltech. “We now have a better understanding of the fundamental assumptions that can be made and more powerful techniques to translate these assumptions into scattering amplitudes and other properties of observations.”
The study, “Strings from Almost Nothing,” was funded by the U.S. Department of Energy, the Walter Burke Institute for Theoretical Physics, the Reinweber Forum for Theoretical Physics, the James Arthur Postdoctoral Fellowship at New York University, and Next Generation EU. Additional authors include Francesco Ciotti of the Artes Energy Institute in Barcelona and Michele Tarchini, a graduate student at the California Institute of Technology.
