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.


A black hole as imag­ined by NASA, the Amer­i­can space agency. ‘Maybe God just doesn’t like us­ing hugely dif­fer­ent kinds of things’ BILL UN­RUH On why ev­ery­thing in the uni­verse seems to be con­nected

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