“In the 1960s, the charismatic physicist Geoffrey Chew espoused a radical vision of the universe, and with it, a new way of doing physics. “
““Nature is as it is because this is the only possible nature consistent with itself,” he wrote at the time. He believed he could deduce nature’s laws solely from the demand that they be self-consistent.”
“Scientists since Democritus had taken a reductionist approach to understanding the universe, viewing everything in it as being built from some kind of fundamental stuff that cannot be further explained. “
“But Chew’s vision of a self-determining universe required that all particles be equally composite and fundamental. He conjectured that each particle is composed of other particles, and those others are held together by exchanging the first particle in a process that conveys a force. Thus, particles’ properties are generated by self-consistent feedback loops. Particles, Chew said, “pull themselves up by their own bootstraps.””
“Chew’s approach, known as the bootstrap philosophy, the bootstrap method, or simply “the bootstrap,” came without an operating manual. The point was to apply whatever general principles and consistency conditions were at hand to infer what the properties of particles (and therefore all of nature) simply had to be.”
“An early triumph in which Chew’s students used the bootstrap to predict the mass of the rho meson — a particle made of pions that are held together by exchanging rho mesons — won many converts.”
“But the rho meson turned out to be something of a special case, and the bootstrap method soon lost momentum. “
“The bootstrap languished for decades at the bottom of the physics toolkit. “
“But recently the field has been re-energized as physicists have discovered novel bootstrap techniques that appear to solve many problems. “
“As the new generation of bootstrappers explores this abstract theory space, they seem to be verifying the vision that Chew, now 92 and long retired, laid out half a century ago — but they’re doing it in an unexpected way. Their findings indicate that the set of all quantum field theories forms a unique mathematical structure, one that does indeed pull itself up by its own bootstraps, which means it can be understood on its own terms.”
“As physicists use the bootstrap to explore the geometry of this theory space, they are pinpointing the roots of “universality,” a remarkable phenomenon in which identical behaviors emerge in materials as different as magnets and water.”
“They are also discovering general features of quantum gravity theories, with apparent implications for the quantum origin of gravity in our own universe and the origin of space-time itself. “
“The bootstrap is technically a method for computing “correlation functions” — formulas that encode the relationships between the particles described by a quantum field theory. “
“These functions tell you essentially everything about the iron chunk. But they involve infinitely many terms riddled with unknown exponents and coefficients. They are, in general, onerous to compute. The bootstrap approach is to try to constrain what the terms of the functions can possibly be in hopes of solving for the unknown variables. “
“Most of the time, this doesn’t get you far. But in special cases, as the theoretical physicist Alexander Polyakov began to figure out in 1970, the bootstrap takes you all the way.”
“Polyakov, then at the Landau Institute for Theoretical Physics in Russia, was drawn to these special cases by the mystery of universality.”
“As condensed matter physicists were just discovering, when materials that are completely different at the microscopic level are tuned to the critical points at which they undergo phase transitions, they suddenly exhibit the same behaviors and can be described by the exact same handful of numbers. Heat iron to the critical temperature where it ceases to be magnetized, for instance, and the correlations between its atoms are defined by the same “critical exponents” that characterize water at the critical point where its liquid and vapor phases meet. These critical exponents are clearly independent of either material’s microscopic details, arising instead from something that both systems, and others in their “universality class,” have in common. Polyakov and other researchers wanted to find the universal laws connecting these systems. “And the goal, the holy grail of all that, was these numbers,” he said: Researchers wished to be able to calculate the critical exponents from scratch.”
“What materials at critical points have in common, Polyakov realized, is their symmetries: the set of geometric transformations that leave these systems unchanged. “
“He conjectured that critical materials respect a group of symmetries called “conformal symmetries,” including, most importantly, scale symmetry. Zoom in or out on, say, iron at its critical point, and you always see the same pattern: Patches of atoms oriented with north pointing up are surrounded by patches of atoms pointing downward; these in turn are inside larger patches of up-facing atoms, and so on at all scales of magnification. Scale symmetry means there are no absolute notions of “near” and “far” in conformal systems; if you flip one of the iron atoms, the effect is felt everywhere. “The whole thing organizes as some very strongly correlated medium,” Polyakov explained.”
“The world at large is obviously not conformal. The existence of quarks and other elementary particles “breaks” scale symmetry by introducing fundamental mass and distance scales into nature, against which other masses and lengths can be measured. Consequently, planets, composed of hordes of particles, are much heavier and bigger than we are, and we are much larger than atoms, which are giants next to quarks. Symmetry-breaking makes nature hierarchical and injects arbitrary variables into its correlation functions — the qualities that sapped Chew’s bootstrap method of its power.”
“The conformal bootstrap, like the original bootstrap more than a decade earlier, fell into disuse.”
“The lull lasted until 2008, when a group of researchers discovered a powerful trick for approximating solutions to Polyakov’s bootstrap equation for CFTs with three or more dimensions.”
“Uncovering the polyhedral structure representing all possible quantum field theories would, in a sense, unify quark interactions, magnets and all observed and imagined phenomena in a single, inevitable structure — a sort of 21st-century version of Geoffrey Chew’s “only possible nature consistent with itself.” But as Hartman, Simmons-Duffin and scores of other researchers around the world pursue this abstraction, they are also using the bootstrap to exploit a direct connection between CFTs and the theories many physicists care about most. “Exploring possible conformal field theories is also exploring possible theories of quantum gravity,” Hartman said.”
“The conformal bootstrap is turning out to be a power tool for quantum gravity research. “
“It’s far from clear whether our own universe holographically emerges from a conformal field theory in the way that AdS universes do, or if this is even the right way to think about it. The hope is that, by bootstrapping their way around the unifying geometric structure of possible physical realities, physicists will get a better sense of where our universe fits in the grand scheme of things — and what that grand scheme is. Polyakov is buoyed by the recent discoveries about the geometry of the theory space. “There are a lot of miracles happening,” he said. “And probably, we will know why.””