How to imagine a black hole
Find something on Earth that’s analogous. Like a bathtub
VANCOUVER— Bill Unruh looks quite normal, although there is more than a suggestion of mischief in his flashing eyes and rumbling laugh. A spiky white beard and rounded frame evoke memories of a middle- aged Peter Ustinov. Then Unruh talks. About cosmic processes that will take zillions of times longer than the current age of the universe, already a not-insignificant 13.7 billion years old. About experiments that would work only at a few thousandths of a degree above absolute zero, already minus 273 C. About an object accelerating so fast it heats up — “ fast” being the acceleration from gravity when falling multiplied by 10 followed by 20 zeros. Such matters are stock-intrade for theoretical physicists like the 60- year- old Unruh, a professor at the University of British Columbia. As is an office so shambolic with papers, books and teaching aids that there’s hardly any spot to lower your foot safely. Unruh begins musing about the black hole lurking in bathtubs everywhere, causing a visitor to mentally check out escape routes. But this turns out to be simply an example of the classic kind of “ thought” experiment in which Albert Einstein delighted.
It also provides a glimpse into the creative and intuitive thought processes of today’s scientific explorers of Einstein’s legacy.
Real black holes ( as opposed to the bathtub variety) are the most violent and one of the least understood features of today’s universe, with gravitational forces so immense that not even light can escape their pull. A German scientist used Einstein’s general theory of relativity to predict the possibility of black holes 90 years ago. Einstein himself then tried to prove that such bizarre objects couldn’t exist, a skepticism widely shared among physicists until the 1960s. By 1967, however, when Unruh, a Manitoba native, arrived at Princeton University for his graduate studies, the tide had changed. That year John Wheeler, the celebrated Princeton cosmologist who became Unruh’s PhD supervisor, coined the term “ black hole.” “The Russians were calling them frozen stars. Black holes certainly caught on more,” says Unruh with a chuckle.
Black holes are high profile in Einstein’s legacy because they are one of the very few places where the effects of quantum theory and general relativity are both important.
Quantum theory rules the domain of the very small; relativity is Einstein’s highly successful theory of gravity, which rules the cosmic domain. Many researchers believe that delving into the abyss of black holes is the most promising path to marrying these two concepts into a much- sought Theory of Everything. With radio telescopes and Xray satellites, astronomers can infer the presence of dustshrouded black holes at the centre of many galaxies, including our own Milky Way. The monster black holes pack a mass equal to millions or even billions of suns into a space no bigger than the solar system. They are born when the core of a massive, rapidly rotating star collapses under its own weight, shooting out jets of material at nearly the speed of light. Collisions between lumps of this material produce the most powerful explosions in the universe since the Big Bang, accompanied by a dazzling flash of light called a gamma- ray burst.
Yet astronomers can’t actually photograph a black hole, much less run experiments there. So experts like Unruh are instead thinking of analogues — processes to study here on Earth as away of deciphering some of the mysteries of the unattainable black holes themselves. Unruh is a world- recognized expert, responsible for predicting and explaining one of the two kinds of exotic radiation associated with black holes. He modestly calls it “ acceleration radiation,” although other scientists often say “ Unruh radiation.” The second kind is Hawking radiation, named after Stephen Hawking, the iconic English physicist confined to a wheelchair. The two kinds of radiation most likely form a seamless web. If you were lowered toward a black hole ( with a very strong rope around your waist), you’d first detect Hawking radiation as an infinitesimally small rise in temperature locally. The closer you got to the black hole’s outer boundary — called the event horizon — the higher the temperature would rise, because of your acceleration under the intense gravitational pull. Near the event horizon everything is Unruh radiation.
“ Nobody has a good idea where one turns into the other,” says Unruh.
Neither kind of radiation has ever been observed directly. Hawking radiation has attracted the most attention because it allows energy to escape from the black hole as particles. This energy leakage implies that black holes aren’t really entirely black and also aren’t eternal and will eventually evaporate. In the case of a sun- sized black hole, “ eventually” is calculated to be 1066 years, which is 10 followed by 65 zeros.
Controversies abound. One made headlines briefly in July 2004 when Hawking himself famously recanted his long- held view that black holes would destroy any information inside them as they slowly evaporated. The question is far from esoteric. For many physicists the idea that information can never be destroyed, like energy, is a sacred and immutable law. If that’s wrong, then those physicists believe much of the edifice of modern physics will have to be rebuilt. Unruh isn’t in that camp. “ I myself do not believe there is any problem at all with black holes destroying information,” he notes in an email. But how to test what actually happens in black holes?
Enter Unruh’s idea of a “ dumb hole,” the result of a gedanken, or “thought,” experiment. He explains:
“ Dumb comes from deaf- anddumb, so [ it is] a hole that is not able to speak rather than a hole that is not able to emit light like a black hole. This is a sonic analogue. Imagine a waterfall where, as the water falls over the edge, it accelerates. Eventually the water is flowing faster than sound can travel through the water. At that point where the velocity of the water is just equal to the velocity of sound, sound trying to get out is pulled back in just as fast as it’s trying to get out. So you have a surface that’s just like in a black hole where light can never escape, except here you have a surface where sound can never escape.” No such waterfall exists in nature, of course, but Unruh says it should be possible to come up with a lab experiment where some fluid was accelerating faster than the speed of sound, creating a “ dumb hole.” He pauses and his eyes twinkle mischievously:
“ In fact, you do it every day that you take a bath.”
Yikes. Shades of Calvin in the comic strip, fearing he and Hobbes would be sucked down the bathtub drain. Not quite. It turns out that Unruh is not talking about sound but about the surface waves formed in a bathtub as the water drains. “As the water gets shallow enough, eventually the water flowing out the plug hole is going faster than these waves can travel and you get the analogue of a black hole in your bathtub. The interesting thing is because the water is always swirling as it goes out of the bathtub, that’s actually an analogue to a rotating black hole,” he says.
It gets weirder. Unruh explains that rotating black holes feature a “ very interesting” wave amplification, first described by the renowned British mathematician Sir Roger Penrose. Similar patterns seem to appear in the water right next to the tub drain.
“ I think the thing that initially triggers those patterns is exactly the equivalent of the Penrose process. So we’re getting some of the really interesting blackhole physics occurring in your bathtub,” he says. The beauty of the bathtub analogy is that the surface waves are described by exactly the same equations as the waves in a black hole. So there should be a bathtub equivalent of the Hawking radiation from black holes. The drawback is that the radiation would show up as a temperature increase of something like one- trillionth of a degree Celsius. Unruh grins. “ Most of us have baths in warmer water than that, so in the bathtub you could never actually measure this thermal radiation.”
Yet the inconveniently warm bathwater does not mean that this particular gedanken experiment has proven a dead end. In the two decades after Unruh first suggested “dumb holes,” other physicists have proposed different sonic analogues of black holes, using exotic materials such as liquid helium and the ultra-cold Bose-Einstein condensates, where thousands of individual molecules act as if they were one. Investigators hope such systems could be used to verify Hawking radiation and then unlock mysteries of both the radiation and of black holes.
Right now there’s no general agreement on what causes Hawking radiation or where it is created. And detecting it directly is impossible with current, or even foreseeable, instruments. Here’s why:
Physicists calculate that the temperature increase from Hawking radiation depends on the size of the black hole, with smaller holes producing a bigger temperature boost.
Yet, says Unruh, for that effect to stand out from background radiation, which floods the universe, requires a black hole roughly a millionth the mass of our sun. But the black hole at the centre of the Milky Way has an estimated mass of 3.7 million suns, and even midget black holes are 10 times the sun’s mass. Which explains why Unruh never stopped thinking about possible “ dumb hole” analogues here on Earth. The speed-ofsound waterfall, helium and condensate system have so far proven too daunting to construct. So this summer Unruh floated the idea of an electronic counterpart to a black hole, developed in conjunction with Ralf Schützhold, a former UBC research associate now at the Dresden University of Technology in Germany.
Their proposal was taken seriously enough to be published in one of the leading physics journals and written up in the monthly magazine Physics Today. The electronic apparatus would generate a much higher Hawking temperature than any of the sonic analogues and also be simpler to build. But it would still require a special hollow tube, called a waveguide, at least a kilometre long filled with some unknown conducting material that is kept at just above absolute zero.
Explains Unruh: “Then you have to shine this very, very high- powered laser along it in order to excite the material in the waveguide to change the velocity of light inside. It’s probably more expensive than anybody would really want to spend just on the off- chance that it worked.” Such is the lot of a theoretical physicist trying to understand black holes and possibly succeed in unifying quantum theory and general relativity. After more than three decades of mental heavy lifting, investigators aren’t much closer to being able to test many of their ideas.
Yet Unruh is upbeat about prospects in his field. “One of the amazing things that physics has discovered in the last 20 years is that almost everything seems to be connected to everything else, not through some physical influence but [ because] they all get described by very, very similar mathematics. So there seems to be a universality of the mathematical description that occurs in many different fields of physics.” Unruh isn’t sure whether these parallels say something about the limited mathematical vocabulary used to describe natural phenomena or indicate something truly fundamental about the world.
“ Maybe God just doesn’t like using hugely different kinds of things,” he says. “ He wants to keep using the same kinds of ideas in many, many different aspects of the world.”
Bill Unruh, a theoretical physicist at the University of British Columbia, has spent 30 years investigating black holes. When he wanted ideas, he looked in his bathroom.
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