A Geometric Theory of Everything

    Modern physics began with a sweeping unification: in 1687 Isaac Newton showed that the existing jumble of disparate theories describing everything from planetary motion to tides to pendulums were all aspects of a universal law of gravitation. Unification has played a central role in physics ever since. In the middle of the 19th century James Clerk Maxwell found that electricity and magnetism were two facets of electromagnetism. One hundred years later electromagnetism was unified with the weak nuclear force governing radioactivity, in what physicists call the electroweak theory.

This quest for unification is driven by practical, philosophical and aesthetic considerations. When successful, merging theories clarifies our understanding of the universe and leads us to discover things we might otherwise never have suspected. Much of the activity in experimental particle physics today, at accelerators such as the Large Hadron Collider at CERN near Geneva, involves a search for novel phenomena predicted by the unified electroweak theory. In addition to predicting new physical effects, a unified theory provides a more aesthetically satisfying picture of how our universe operates. Many physicists share an intuition that, at the deepest level, all physical phenomena match the patterns of some beautiful mathematical structure.

The current best theory of nongravitational forces—the electromagnetic, weak and strong nuclear force—was largely completed by the 1970s and has become familiar as the Standard Model of particle physics. Mathematically, the theory describes these forces and particles as the dynamics of elegant geometric objects called Lie groups and fiber bundles. It is, however, somewhat of a patchwork; a separate geometric object governs each force. Over the years physicists have proposed various Grand Unified Theories, or GUTs, in which a single geometric object would explain all these forces, but no one yet knows which, if any, of these theories is true.

And an even deeper unification problem faces today’s physicists. In a fully unified theory, gravity and matter should also combine naturally with the other forces, all as parts of one mathematical structure—a Theory of Everything. Since the 1980s string theory, the dominant research program in theoretical particle physics, has been an attempt to describe gravity and the Standard Model using elaborate constructs of strings and membranes vibrating in many spacetime dimensions.

But string theory is not the only effort. An alternative, loop quantum gravity, uses a more minimal framework, closer to that of the Standard Model [see “Atoms of Space and Time,” by Lee Smolin; Scientific American, January 2004]. Building on its insights, one of us (Lisi) proposed a new unified theory in 2007. The basic idea is to extend Grand Unified Theories and include gravity as part of a consistent geometric framework. In this unified field theory, called E8 theory, all forces and matter are described as the twisting of a single geometric object.

All new ideas must endure a trial by fire, and this one is no exception. Many physicists are skeptical—and rightly so. The theory remains incomplete. But even in this early stage of development, it unveils some of the beautiful structures in play at the deepest levels of nature, and it makes predictions for new particles that the Large Hadron Collider might find. Although physicists are not yet at the culmination of our centuries-long quest for unity, E8 theory is an important step on that journey.

Every Fiber of Our Being

To describe E8 theory, we first need to set out the widely accepted geometric principles that govern all known forces and particles. Geometry is the study of shape, but in the case of fundamental physics, you might wonder: shape of what? Plato thought elements such as earth and air were associated with little cubes and octahedra. Similarly, in modern physics, the geometric objects associated with elementary particles are perfect, smooth shapes, existing outside our space yet connected to it. We cannot see these shapes directly, but we see their effects.