Stephen Hawking’s Scientific Legacy

Stephen Hawking died Wednesday morning, age 76. Plenty of memories and tributes have been written, including these by me:

• “Stephen Hawking’s Most Profound Gift to Physics,” in The New York Times — a piece concentrating on black hole evaporation and the information-loss puzzle.
• “Stephen Hawking Was Very Particular About His Tea,” in The Atlantic — more focused on our personal interactions and Hawking’s human side.

I can also point to my Story Collider story from a few years ago, about how I turned down a job offer from Hawking, and eventually took lessons from his way of dealing with the world.

• “What Would Stephen Hawking Do?“

Of course Hawking has been mentioned on this blog many times.

When I started writing the above pieces (mostly yesterday, in a bit of a rush), I stumbled across this article I had written several years ago about Hawking’s scientific legacy. It was solicited by a magazine at a time when Hawking was very ill and people thought he would die relatively quickly — it wasn’t the only time people thought that, only to be proven wrong. I’m pretty sure the article was never printed, and I never got paid for it; so here it is!

(If you’re interested in a much better description of Hawking’s scientific legacy by someone who should know, see this article in The Guardian by Roger Penrose.)

Stephen Hawking’s Scientific Legacy

Stephen Hawking is the rare scientist who is also a celebrity and cultural phenomenon. But he is also the rare cultural phenomenon whose celebrity is entirely deserved. His contributions can be characterized very simply: Hawking contributed more to our understanding of gravity than any physicist since Albert Einstein.

“Gravity” is an important word here. For much of Hawking’s career, theoretical physicists as a community were more interested in particle physics and the other forces of nature — electromagnetism and the strong and weak nuclear forces. “Classical” gravity (ignoring the complications of quantum mechanics) had been figured out by Einstein in his theory of general relativity, and “quantum” gravity (creating a quantum version of general relativity) seemed too hard. By applying his prodigious intellect to the most well-known force of nature, Hawking was able to come up with several results that took the wider community completely by surprise.

By acclimation, Hawking’s most important result is the realization that black holes are not completely black — they give off radiation, just like ordinary objects. Before that famous paper, he proved important theorems about black holes and singularities, and afterward studied the universe as a whole. In each phase of his career, his contributions were central.

The Classical Period

While working on his Ph.D. thesis in Cambridge in the mid-1960’s, Hawking became interested in the question of the origin and ultimate fate of the universe. The right tool for investigating this problem is general relativity, Einstein’s theory of space, time, and gravity. According to general relativity, what we perceive as “gravity” is a reflection of the curvature of spacetime. By understanding how that curvature is created by matter and energy, we can predict how the universe evolves. This may be thought of as Hawking’s “classical” period, to contrast classical general relativity with his later investigations in quantum field theory and quantum gravity.

Around the same time, Roger Penrose at Oxford had proven a remarkable result: that according to general relativity, under very broad circumstances, space and time would crash in on themselves to form a singularity. If gravity is the curvature of spacetime, a singularity is a moment in time when that curvature becomes infinitely big. This theorem showed that singularities weren’t just curiosities; they are an important feature of general relativity.

Penrose’s result applied to black holes — regions of spacetime where the gravitational field is so strong that even light cannot escape. Inside a black hole, the singularity lurks in the future. Hawking took Penrose’s idea and turned it around, aiming at the past of our universe. He showed that, under similarly general circumstances, space must have come into existence at a singularity: the Big Bang. Modern cosmologists talk (confusingly) about both the Big Bang “model,” which is the very successful theory that describes the evolution of an expanding universe over billions of years, and also the Big Bang “singularity,” which we still don’t claim to understand.

Hawking then turned his own attention to black holes. Another interesting result by Penrose had shown that it’s possible to extract energy from a rotating black hole, essentially by bleeding off its spin until it’s no longer rotating. Hawking was able to demonstrate that, although you can extract energy, the area of the event horizon surrounding the black hole will always increase in any physical process. This “area theorem” was both important in its own right, and also evocative of a completely separate area of physics: thermodynamics, the study of heat.

Thermodynamics obeys a set of famous laws. For example, the first law tells us that energy is conserved, while the second law tells us that entropy — a measure of the disorderliness of the universe — never decreases for an isolated system. Working with James Bardeen and Brandon Carter, Hawking proposed a set of laws for “black hole mechanics,” in close analogy with thermodynamics. Just as in thermodynamics, the first law of black hole mechanics ensures that energy is conserved. The second law is Hawking’s area theorem, that the area of the event horizon never decreases. In other words, the area of the event horizon of a black hole is very analogous to the entropy of a thermodynamic system — they both tend to increase over time.

Black Hole Evaporation

Hawking and his collaborators were justly proud of the laws of black hole mechanics, but they viewed them as simply a formal analogy, not a literal connection between gravity and thermodynamics. In 1972, a graduate student at Princeton University named Jacob Bekenstein suggested that there was more to it than that. Bekenstein, on the basis of some ingenious thought experiments, suggested that the behavior of black holes isn’t simply like thermodynamics, it actually is thermodynamics. In particular, black holes have entropy.

Like many bold ideas, this one was met with resistance from experts — and at this point, Stephen Hawking was the world’s expert on black holes. Hawking was certainly skeptical, and for good reason. If black hole mechanics is really just a form of thermodynamics, that means black holes have a temperature. And objects that have a temperature emit radiation — the famous “black body radiation” that played a central role in the development of quantum mechanics. So if Bekenstein were right, it would seemingly imply that black holes weren’t really black (although Bekenstein himself didn’t quite go that far).

To address this problem seriously, you need to look beyond general relativity itself, since Einstein’s theory is purely “classical” — it doesn’t incorporate the insights of quantum mechanics. Hawking knew that Russian physicists Alexander Starobinsky and Yakov Zel’dovich had investigated quantum effects in the vicinity of black holes, and had predicted a phenomenon called “superradiance.” Just as Penrose had showed that you could extract energy from a spinning black hole, Starobinsky and Zel’dovich showed that rotating black holes could emit radiation spontaneously via quantum mechanics. Hawking himself was not an expert in the techniques of quantum field theory, which at the time were the province of particle physicists rather than general relativists. But he was a quick study, and threw himself into the difficult task of understanding the quantum aspects of black holes, so that he could find Bekenstein’s mistake.

Instead, he surprised himself, and in the process turned theoretical physics on its head. What Hawking eventually discovered was that Bekenstein was right — black holes do have entropy — and that the extraordinary implications of this idea were actually true — black holes are not completely black. These days we refer to the “Bekenstein-Hawking entropy” of black holes, which emit “Hawking radiation” at their “Hawking temperature.”

There is a nice hand-waving way of understanding Hawking radiation. Quantum mechanics says (among other things) that you can’t pin a system down to a definite classical state; there is always some intrinsic uncertainty in what you will see when you look at it. This is even true for empty space itself — when you look closely enough, what you thought was empty space is really alive with “virtual particles,” constantly popping in and out of existence. Hawking showed that, in the vicinity of a black hole, a pair of virtual particles can be split apart, one falling into the hole and the other escaping as radiation. Amazingly, the infalling particle has a negative energy as measured by an observer outside. The result is that the radiation gradually takes mass away from the black hole — it evaporates.

Hawking’s result had obvious and profound implications for how we think about black holes. Instead of being a cosmic dead end, where matter and energy disappear forever, they are dynamical objects that will eventually evaporate completely. But more importantly for theoretical physics, this discovery raised a question to which we still don’t know the answer: when matter falls into a black hole, and then the black hole radiates away, where does the information go?

If you take an encyclopedia and toss it into a fire, you might think the information contained inside is lost forever. But according to the laws of quantum mechanics, it isn’t really lost at all; if you were able to capture every bit of light and ash that emerged from the fire, in principle you could exactly reconstruct everything that went into it, even the print on the book pages. But black holes, if Hawking’s result is taken at face value, seem to destroy information, at least from the perspective of the outside world. This conundrum is the “black hole information loss puzzle,” and has been nagging at physicists for decades.

In recent years, progress in understanding quantum gravity (at a purely thought-experiment level) has convinced more people that the information really is preserved. In 1997 Hawking made a bet with American physicists Kip Thorne and John Preskill; Hawking and Thorne said that information was destroyed, Preskill said that somehow it was preserved. In 2007 Hawking conceded his end of the bet, admitting that black holes don’t destroy information. However, Thorne has not conceded for his part, and Preskill himself thinks the concession was premature. Black hole radiation and entropy continue to be central guiding principles in our search for a better understanding of quantum gravity.

Quantum Cosmology

Hawking’s work on black hole radiation relied on a mixture of quantum and classical ideas. In his model, the black hole itself was treated classically, according to the rules of general relativity; meanwhile, the virtual particles near the black hole were treated using the rules of quantum mechanics. The ultimate goal of many theoretical physicists is to construct a true theory of quantum gravity, in which spacetime itself would be part of the quantum system.

If there is one place where quantum mechanics and gravity both play a central role, it’s at the origin of the universe itself. And it’s to this question, unsurprisingly, that Hawking devoted the latter part of his career. In doing so, he established the agenda for physicists’ ambitious project of understanding where our universe came from.

In quantum mechanics, a system doesn’t have a position or velocity; its state is described by a “wave function,” which tells us the probability that we would measure a particular position or velocity if we were to observe the system. In 1983, Hawking and James Hartle published a paper entitled simply “Wave Function of the Universe.” They proposed a simple procedure from which — in principle! — the state of the entire universe could be calculated. We don’t know whether the Hartle-Hawking wave function is actually the correct description of the universe. Indeed, because we don’t actually have a full theory of quantum gravity, we don’t even know whether their procedure is sensible. But their paper showed that we could talk about the very beginning of the universe in a scientific way.

Studying the origin of the universe offers the prospect of connecting quantum gravity to observable features of the universe. Cosmologists believe that tiny variations in the density of matter from very early times gradually grew into the distribution of stars and galaxies we observe today. A complete theory of the origin of the universe might be able to predict these variations, and carrying out this program is a major occupation of physicists today. Hawking made a number of contributions to this program, both from his wave function of the universe and in the context of the “inflationary universe” model proposed by Alan Guth.

Simply talking about the origin of the universe is a provocative step. It raises the prospect that science might be able to provide a complete and self-contained description of reality — a prospect that stretches beyond science, into the realms of philosophy and theology. Hawking, always provocative, never shied away from these implications. He was fond of recalling a cosmology conference hosted by the Vatican, at which Pope John Paul II allegedly told the assembled scientists not to inquire into the origin of the universe, “because that was the moment of creation and therefore the work of God.” Admonitions of this sort didn’t slow Hawking down; he lived his life in a tireless pursuit of the most fundamental questions science could tackle.