Stephen Hawking is gone, but he has left behind something incredibly precious: a knotty, frustrating puzzle, one that scientists will be wrestling with for years to come. Dr. Hawking’s puzzle is an important piece of perhaps the biggest question in physics today: How can we reconcile gravity with quantum mechanics?

The early years of the 20th century witnessed two incredible scientific revolutions. One was the theory of relativity. Led by Albert Einstein, physicists discarded the absolute space and time of Isaac Newton, and replaced it with a unified four-dimensional space-time continuum. It is the warps and wiggles of space-time, Einstein realized, that give rise to what you and I experience as the force of gravity.

The other revolution — even more profound than relativity — was quantum mechanics. When we examine the behavior of subatomic particles, we find they can’t be described in the clockwork language of classical physics. Instead, they appear as waves of probability, and the best we can do is calculate the chance that any particular measurement will return this or that result.

Gradually, everything we know about the physical world has been put under the umbrella of quantum mechanics. The behavior of matter, electricity and magnetism, and the subatomic forces at work inside the nuclei of atoms — all fit elegantly into the quantum paradigm.

The one exception is gravity. For both technical and conceptual reasons, Einstein’s vision of curved space-time has stubbornly resisted reconciliation with the rules of quantum mechanics. The search for a theory that would unify the two paradigms — a theory of “quantum gravity” — is perhaps the single most ambitious project in modern theoretical physics.

“Theoretical” is an important word here, as it is nearly impossible to do experiments that would directly reveal anything important about quantum gravity. Quantum mechanics reveals itself at the subatomic scale, where we are dealing with just a few elementary particles, while gravity becomes noticeable only when we collect astronomically large masses. There is no easily accessible situation in which both are important at the same time.

This is where Dr. Hawking comes in. When real experiments are elusive, one turns to thought experiments. And in the 1970s, Dr. Hawking described the mother of all thought experiments, one that still keeps physicists awake at night.

It starts with a black hole. According to Einstein’s relativity, a black hole is a region of space-time where gravity has become so strong that nothing can escape. But Dr. Hawking asked himself how quantum particles behave in the vicinity of such an object. After all, quantum mechanics is a theory of probabilities; maybe what’s impossible according to Einstein is possible in the quantum realm.

And indeed it is. Dr. Hawking’s calculations revealed, as he put it in his characteristically mischievous way, that “black holes ain’t so black.” They actually emit a steady, faint stream of particles, now known as Hawking radiation. These particles carry away bits of the mass of the hole, so that it will eventually disappear entirely, a phenomenon known as Hawking evaporation.

So here’s the thought experiment: Throw a book into the black hole. The book carries information. Perhaps that information is about physics, perhaps that information is the plot of a romance novel — it could be any kind of information. But as far as anyone knows, the outgoing Hawking radiation is the same no matter what went into the black hole. The information is apparently lost — where did it go?

Thus we have the “black hole information loss puzzle,” perhaps Dr. Hawking’s most profound gift to physics. At issue is the fate of the principle of the conservation of information. Without general relativity, quantum mechanics predicts that information is conserved; likewise, without quantum mechanics, general relativity predicts that information is conserved, even if some of it is hidden inside a black hole. It is therefore bothersome that putting the two theories together seems to lead to information just disappearing.

For a long time Dr. Hawking argued, against the intuition of most other leading physicists, that information was simply erased from the universe, and we would have to learn to deal with it. But eventually he changed his mind (something he always was admirably willing to do), conceding in 2004 that information was probably somehow retained in the outgoing radiation. The matter, however, is very far from settled.

Dr. Hawking’s information-loss thought experiment is the single biggest clue we have to how quantum gravity might operate. Even if we don’t have the full theory yet, we know a lot about quantum mechanics and a lot about gravity. Together those are enough to convince us that Hawking radiation is real, even if it has never been directly observed. This means that any eventual theory of quantum gravity will have to explain either how information somehow escapes from black holes or how it is destroyed.

Black-hole radiation and the information-loss puzzle were certainly not Dr. Hawking’s only contributions to modern physics. Back on the firmer ground of classical relativity, he proved a number of fundamental theorems about the behavior of black holes and the expansion of the universe. On the more speculative side, Dr. Hawking and the physicist James Hartle proposed a candidate for the “wave function of the universe,” the quantum state describing all of reality. In between, Dr. Hawking found time to make contributions to deep questions like the origin of structure in the universe and whether it is possible to build a time machine. (It’s not, he argued.)

He did all of this, of course, in addition to reaching a broad popular audience and sharing with it his passion for physics and the mysteries of the universe. Dr. Hawking was an extraordinarily influential scientist, as well as a courageous and determined human being. He has left us a lot to think about.

**Sean Carroll** is a theoretical physicist at the California Institute of Technology and the author of *The Big Picture: On the Origins of Life, Meaning, and the Universe Itself*.