To get string theory, you need only four physics assumptions

With just a handful of assumptions, string theory stands alone.

Based on the idea that all subatomic particles are made up of vibrating strings of energy, string theory is a candidate for a “theory of everything” that could merge disparate branches of physics under one unifying framework. It’s long been a controversial idea, with some scientists embracing it and others arguing that evidence for it is lacking.

A team of physicists reports a new detail that doesn’t settle the debate, but does suggest that string theory is unique. Given just four basic physics assumptions, string theory is the only possible option for a theory of everything, theoretical physicist Clifford Cheung and colleagues report in a paper accepted to Physical Review Letters.

String theory has garnered skepticism, most famously centering on the issue that its predictions thus far have not been testable — and may never be. Without experimental evidence, physicists will never be able to claim that string theory actually describes the real world. But “you can actually ask a question that’s the next best thing,” says Cheung, of Caltech. “Given things we view as conservative or well-established principles, how unique or inevitable is string theory?”

The work is part of “a recent wave of interest in understanding what is special about string theory,” says theoretical physicist Andrea Guerrieri of City St George’s, University of London, who was not involved with the research. To dig into that question, researchers employ a strategy known as “bootstrapping.” Rather than starting from a proposed theory, physicists begin from basic assumptions and follow them through to determine the features of possible theories, figuratively pulling themselves by their bootstraps.

Cheung and colleagues focused on a quantity that a theory of everything, such as string theory, could be expected to predict, called scattering amplitudes. These are mathematical expressions that can be used to determine the probability that two particles will interact with one another in a particular way.

In the new study, the researchers explored what types of scattering amplitudes are possible. Without any assumptions, a vast swath of scattering amplitudes could be correct. By adding in different assumptions, the researchers attempted to bootstrap their way to string theory’s predicted scattering amplitudes, without relying on the premise that the universe is made of strings.

Two of the assumptions Cheung and colleagues make are generally well-accepted by physicists. One, known as unitarity, comes from quantum mechanics, and it essentially means that the probabilities of all possible options in any given situation must add up to 100 percent. Another is Lorentz invariance, a principle of Einstein’s special theory of relativity, implies that the laws of nature are the same regardless of where you are in the universe or what speed you’re traveling at.

Another, less established condition, is that physics is well-behaved at extremely high energies, a realm where some theories stop working — namely, general relativity, the theory that describes gravity. Finally, a technical assumption, called “minimal zeroes,” selects the simplest possible version of the scattering amplitude, bypassing more complex ones.

Based on their assumptions, the researchers landed on two possible scattering amplitudes, called the Veneziano and Virasoro-Shapiro amplitudes. Lo and behold: Those are the amplitudes predicted by string theory.

“It’s very surprising that they could derive this in such a clean fashion,” says theoretical physicist Yu-tin Huang of National Taiwan University in Taipei. Although some physicists may have had the intuition that string theory would be special in this way, “believing it is true versus [being] able to show mathematically that it’s true is different.”

The result doesn’t mean string theory is correct. One of the assumptions could be wrong, for example. But playing with such assumptions is one way of exploring potential theories, Guerrieri says.

This method of investigation flips the script for theoretical physics, Cheung says. “Usually we write down some beautiful theory; we think about some deep idea.” And then, at the end, physicists calculate something that might be measurable in an experiment. “This is exactly the reversal of that.”