String theory is a mathematical description of nature that requires space to possess several additional dimensions beyond the ordinary three. These extra dimensions, too small to be noticed in ordinary life, can take on many possible shapes or geometries (artistically represented here) that can influence the properties of the universe and subatomic particles. Credits: O. Knill and E. Slavkovsky
Scientists seeking the secrets of the universe would like to create a model that shows how all of nature’s forces and particles fit together. It would be nice to do it with Legos. But maybe it would be better to connect everything with strings.
Not literal strings, of course, but little rings or shards of vibrating energy. And the “fit together” must be mathematical, not via appropriately shaped pieces of plastic. For decades now, many physicists have pursued the hope that equations involving a particularly small “string” could provide the theory capable of solving nature’s ultimate subatomic mysteries.
String theory, as it is called, has acquired a kind of confusing cultural consensus, appearing on popular television shows such as THE Big Bang TheoryAND NCIS. Among physicists, reaction to the theory has been mixed. After several promising discoveries in the 1980s and 1990s, strings fell out of favor for failing to deliver on their promises. Among these was to provide the correct way to include gravity in the quantum theory of subatomic particles. Another was revealing the mathematics that would demonstrate that the multiple fundamental forces of nature are simply different children of a single unified force. Promises still not kept.
However, since string theory retreated from the limelight, a sizable group of string devotees have been working to tie all the loose ends together. Success remains elusive, but concrete progress has been made. The questions plaguing physicists not only about the smallest bits of matter but also about the properties of the entire universe may yet yield to the efforts of string theorists.
“Many of the unsolved problems in particle physics and cosmology are deeply intertwined,” write physicists Fernando Marchesano, Gary Shiu and Timo Weigand in 2024 Annual review of nuclear and particle science. String theory may provide the path to solving these problems.
The equations of reality
One of the main approaches in this research is to understand whether string theory can explain what is known as the Standard Model of particle physics. Developed in the latter part of the 20th century, the Standard Model provides a sort of directory listing all of nature’s fundamental particles. Some provide the building blocks of matter; others transmit forces between material particles, determining their behavior.
It’s pretty simple to draw a graph showing those particles. 12 points are needed for material particles: six quarks and six leptons. Four points are needed for force particles (collectively known as bosons) plus one point for the Higgs boson, a particle needed to explain why some particles have mass. But the math behind the graph is unfathomably complex, a combination of equations that make the hieroglyphs seem self-explanatory.
These equations work great to explain the results of virtually all behavior in particle physics. But the Standard Model cannot represent the entire history of the universe. “Despite the Standard Model’s incredible success in describing observed particle physics down to currently accessible energy scales, there are compelling arguments as to why it is incomplete,” Marchesano and collaborators write.
For one thing, its equations do not include gravity, which has no place in the Standard Model table. And the mathematics of the Standard Model leaves many questions unanswered, such as why some particles have the precise masses that they do. The Standard Model’s mathematics also does not include the mysterious dark matter that lurks within and between galaxies, nor does it explain why empty space is imbued with a form of energy that causes the universe to expand at an accelerating rate.
Some physicists who study these problems believe that string theory can help, since a string version of the Standard Model will contain additional calculations that could explain its flaws. In other words, if string theory were correct, the Standard Model would be just a segment of the complete mathematical description of reality provided by string theory. The problem is that string theory describes many different versions of reality. This is because strings exist in a realm with multiple dimensions of space beyond the ordinary three. Kind of like The Twilight Zone on steroids.
String theorists admit that daily life goes well in a three-dimensional world. Therefore, the extra dimensions of the string world must be too small to notice: they must shrink, or “compact,” to submicroscopic dimensions. It’s like the way an ant living on a vast sheet of paper would perceive a two-dimensional surface without ever realizing that the paper has a third, very small dimension.
Not only must the extra dimensions of string theory shrink, but they can also shrink into countless different configurations, or geometries, of the vacuum of space. One of these possible geometries could be the right form of restricted dimensions to explain the properties of the Standard Model.
“Standard model…features, questions, and puzzles can be reformulated in terms of the geometry of extra dimensions,” Marchesano and collaborators write.
Because the mathematics of string theory can be expressed in many different forms, theorists must explore multiple possible avenues to find the most fruitful formulation. So far, string approaches have been found that describe many features of the Standard Model. But to explain each feature different vacuum compaction geometries are needed. The challenge, Marchesano and colleagues point out, is to find a geometry for the vacuum that combines all these features simultaneously, while also incorporating features that describe the known universe.
Successful compaction of extra dimensions, for example, would produce a vacuum in space that would contain just the right amount of “dark energy,” the source of the universe’s accelerated expansion. And candidates for cosmic dark matter should also appear in string mathematics. In fact, a whole additional set of particles of force and matter emerges from the string equations involving a mathematical property called supersymmetry. “Almost all string theory models that resemble the Standard Model exhibit supersymmetry at the compactification scale,” Marchesano and his coauthors write.
Versions of string theory containing supersymmetric particles go by the nickname “superstring theory.” It has long been suspected that such “superparticles” constitute the dark matter of the universe. But attempts to detect them in space or create them in particle accelerators have so far been unsuccessful.
As for gravity, particles that carry gravitational force appear naturally in the mathematics of string theory – one of the great attractions of the theory to begin with. But the fact that many formulations of string theory include gravity does not say which formulation provides the correct description of the real world.
Tests are possible
If string theory were correct, the fundamental particles of nature would not be the zero-dimensional point objects of the standard theory. Instead, different particles would arise from different modes of vibration of a one-dimensional string, a ring, or a fragment with ends attached to multidimensional space objects called branes. Such strings would be roughly smaller than an atom to the extent that an atom is smaller than the solar system. Very small, with no feasible way to detect them directly. The amount of energy needed to probe such small flakes is far beyond the reach of any practical technology.
But if string theory could explain the Standard Model, it would also contain other features of reality that would be accessible to experiments, such as types of particles not included in the Standard Model map. “String constructions realizing the Standard Model always contain additional sectors… on an energy scale that could be tested in the near future,” Marchesano and colleagues write.
Ultimately, string theory remains a promising candidate for putting together all the pieces of the cosmic puzzle. If it worked, scientists could finally unlock the mysteries of how quantum physics’ relationship to gravity and the properties of particles and forces in nature are all deeply linked. “String theory,” Marchesano and colleagues write, “has all the ingredients to help us understand this profound connection.”
10.1146/knowable-112124-2
Tom Siegfried is a science journalist from Avon, Ohio. His book The number of heavenson the history of the multiverse, was published in 2019 by Harvard University Press.
This article originally appeared in Knowable magazinea journalistic effort independent of Annual Reviews. Sign up for the newsletter.
