Effective Spacetime: Understanding Emergence in Effective Field Theory and Quantum Gravity

Over the past few years, “emergence” has become an increasingly popular buzzword in physics. The term captures something important. In condensed-matter physics, for example, objects that are not fundamental entities, such as phonons, rotons, and Cooper pairs, still give the “right” higher-level descriptions. But as soon as we move away from the obvious cases, the notion of emergence is exasperatingly fuzzy. Is thermodynamics emergent from statistical mechanics? Is classical physics emergent from quantum mechanics? If phonons are emergent, are protons or, for that matter, photons? Particularly in an area like quantum gravity, where we have no well-established theory to start with, discussions can quickly become frustrating.

Karen Crowther is a philosopher at the University of Geneva. Philosophers are good at clarifying fuzzy concepts, so one might hope that her new book Effective Spacetime: Understanding Emergence in Effective Field Theory and Quantum Gravity might offer some clarity. Sadly, part of Crowther’s conclusion seems to be that emergence is as fuzzy in philosophy as in physics—“a vast and thorny thicket,” as she puts it. But the philosophers’ discussions that Crowther details in her book offer some interesting new insights into how physicists might think about the question.

This book, definitely written for philosophers, would not be an appropriate place to learn about quantum gravity. Rather than attempt to survey the field, Crowther has picked out a few particular research programs, some popular and some obscure, to illustrate her points. String theory is almost entirely missing, but a quarter of a chapter is devoted to an idiosyncratic approach called “quantum causal histories” that has inspired perhaps 20 papers in 17 years.

Physicists will be frustrated by misstatements and misunderstandings. For instance, in an early discussion of quantum mechanics, Crowther writes that “a system described by any initial state will naturally evolve into a superposition,” a statement that means about as much as “any number can naturally be written as the sum of other numbers.” Readers in general will be frustrated by the frequent typos: Examples include recurring references to “p. xxx” with no page numbers inserted and “1032” for 10³².

The acknowledgments thank several philosophers, many of them with some expertise in physics, but I can’t help but think the book would have been better if the author had spent more time talking to physicists actually working on quantum gravity; they might have warned against drawing broad conclusions from what is very much a work in progress. And of course the book is already out of date, as any book on quantum gravity will inevitably be. In particular, Crowther just missed one of the most fascinating cases of emergence in quantum gravity, the early indications that spacetime could emerge from quantum entanglement.

But a physicist who is willing to put up with some frustration (“No! That’s not what a Gaussian fixed point means!”) may find some interesting ways to look at the universe. I was especially taken by Crowther’s emphasis on “autonomy,” the independence of emergent low-energy theories from details of the high-energy degrees of freedom. As Crowther stresses, that autonomy is familiar both from effective field theory, in which the high-energy degrees of freedom merely renormalize low-energy coupling constants, and from second-order phase transitions, for which theories with vastly different fundamental degrees of freedom can lie in the same universality class. She rightly warns researchers in quantum gravity that there may be many different “quantum theories of gravity” with the same low-energy limits.

I also enjoyed discussions of the subtle relationship between emergence and reduction, whether “not predictable in principle” is really very different from “not predictable in practice,” and the role of “higher organizing principles” such as patterns of symmetry breaking.

For a reader who wants to learn about quantum gravity, or even about the emergence of spacetime in particular approaches to quantum gravity, I can’t recommend Effective Spacetime. But for a physicist who would like to see intriguingly different perspectives on some of the important abstract questions we deal with in quantum gravity, it’s an interesting read.