The Sacred, Spherical Cows of Physics
Early in their training, many physics students come across the idea of spherical cows. Cows in the real world—even at their most plump and well-fed—are hardly spherical, and this makes it tricky to calculate things like, say, how their volume or surface area scales with their height. But students learn that these numbers are easy to calculate if they assume the cow is a perfect sphere, or in other words, that it has spherical symmetry. The lesson: Hard problems become easier when certain underlying (though approximate) symmetries are enforced.1
The lessons of the spherical cow don’t end with the undergraduate classroom, though. They extend to the very forefront of physics. The theoretical physics community of the 1980s and 1990s was split by debates over the reality of symmetries similar to, but much more complex than, the spherical cow. String theorists argued for a single, unified mathematical description of reality that relied on certain symmetries, but had almost no experimental support. Other physicists argued that the role of a theory was to predict and explain experiment, and not to pursue mathematical structures for their own sake—no matter how beautiful they might be. The warring factions began to reconcile in the last decade with the realization that some of the sophisticated tools that string theorists had built could be applied in unexpected ways to other problems, and could even help make sense of real data.
Late in 2013, the latest chapter in the history of symmetry in physics began to unfold, when two theoretical physicists unveiled a new calculation tool called the “amplituhedron.” The amplituhedron is an exotic, flat-faceted geometric object that lives in an abstract, mathematical space of many dimensions. It can quickly yield answers that have up until now taken hundreds of pages of calculation. Most intriguingly, its power derives not just from making some symmetries old symmetries. In doing so, it may point the way to changing how we think about space and time.
