Compared to the unsolved mysteries of the universe, far less gets said about one of the most profound facts to have crystallized in physics over the past half-century: To an astonishing degree, nature is the way it is because it couldn’t be any different. “There’s just no freedom in the laws of physics that we have,” said Daniel Baumann, a theoretical physicist at the University of Amsterdam.

Since the 1960s, and increasingly in the past decade, physicists like Baumann have used a technique known as the “bootstrap” to infer what the laws of nature must be. This approach assumes that the laws essentially dictate one another through their mutual consistency — that nature “pulls itself up by its own bootstraps.” The idea turns out to explain a huge amount about the universe.

When bootstrapping, physicists determine how elementary particles with different amounts of “spin,” or intrinsic angular momentum, can consistently behave. In doing this, they rediscover the basic form of the known forces that shape the universe. Most striking is the case of a particle with two units of spin: As the Nobel Prize winner Steven Weinberg showed in 1964, the existence of a spin-2 particle leads inevitably to general relativity — Albert Einstein’s theory of gravity. Einstein arrived at general relativity through abstract thoughts about falling elevators and warped space and time, but the theory also follows directly from the mathematically consistent behavior of a fundamental particle.

“I find this inevitability of gravity [and other forces] to be one of the deepest and most inspiring facts about nature,” said Laurentiu Rodina, a theoretical physicist at the Institute of Theoretical Physics at CEA Saclay who helped to modernize and generalize Weinberg’s proof in 2014. “Namely, that nature is above all self-consistent.”

## How Bootstrapping Works

A particle’s spin reflects its underlying symmetries, or the ways it can be transformed that leave it unchanged. A spin-1 particle, for instance, returns to the same state after being rotated by one full turn. A spin-12 particle must complete two full rotations to come back to the same state, while a spin-2 particle looks identical after just half a turn. Elementary particles can only carry 0, 1/2, 1, 3/2 or 2 units of spin.

To figure out what behavior is possible for particles of a given spin, bootstrappers consider simple particle interactions, such as two particles annihilating and yielding a third. The particles’ spins place constraints on these interactions. An interaction of spin-2 particles, for instance, must stay the same when all participating particles are rotated by 180 degrees, since they’re symmetric under such a half-turn.

Interactions must obey a few other basic rules: Momentum must be conserved; the interactions must respect locality, which dictates that particles scatter by meeting in space and time; and the probabilities of all possible outcomes must add up to 1, a principle known as unitarity. These consistency conditions translate into algebraic equations that the particle interactions must satisfy. If the equation corresponding to a particular interaction has solutions, then these solutions tend to be realized in nature.

For example, consider the case of the photon, the massless spin-1 particle of light and electromagnetism. For such a particle, the equation describing four-particle interactions — where two particles go in and two come out, perhaps after colliding and scattering — has no viable solutions. Thus, photons don’t interact in this way. “This is why light waves don’t scatter off each other and we can see over macroscopic distances,” Baumann explained.