Stephen Hawk­ing's fi­nal sci­en­tific pa­per re­leased

The Guardian Australia - - World News - Ian Sam­ple Sci­ence ed­i­tor

Stephen Hawk­ing’s fi­nal sci­en­tific pa­per has been re­leased by physi­cists who worked with the late cos­mol­o­gist on his ca­reer-long ef­fort to un­der­stand what hap­pens to in­for­ma­tion when ob­jects fall into black holes.

The work, which tack­les what the­o­ret­i­cal physi­cists call “the in­for­ma­tion para­dox”, was com­pleted in the days be­fore Hawk­ing’s death in March. It has now been writ­ten up by his col­leagues at Cam­bridge and Har­vard uni­ver­si­ties and posted on­line.

Mal­colm Perry, a pro­fes­sor of the­o­ret­i­cal physics at Cam­bridge and a coau­thor on the pa­per, Black Hole En­tropy and Soft Hair, said the in­for­ma­tion para­dox was “at the cen­tre of Hawk­ing’s life” for more than 40 years.

The ori­gins of the puz­zle can be traced back to Al­bert Ein­stein. In 1915, Ein­stein pub­lished his the­ory of gen­eral rel­a­tiv­ity, a tour-de-force that de­scribed how grav­ity arises from the space­time-bend­ing ef­fects of mat­ter, and so why the plan­ets cir­cle the sun. But Ein­stein’s the­ory made im­por­tant pre­dic­tions about black holes too, no­tably that a black hole can be com­pletely de­fined by only three fea­tures: its mass, charge, and spin.

Nearly 60 years later, Hawk­ing added to the pic­ture. He ar­gued that black holes also have a tem­per­a­ture. And be­cause hot ob­jects lose heat into space, the ul­ti­mate fate of a black hole is to evap­o­rate out of ex­is­tence. But this throws up a prob­lem. The rules of the quan­tum world de­mand that in­for­ma­tion is never lost. So what hap­pens to all the in­for­ma­tion con­tained in an ob­ject – the na­ture of a moon’s atoms, for in­stance – when it tum­bles into a black hole?

“The dif­fi­culty is that if you throw some­thing into a black hole it looks like it dis­ap­pears,” said Perry. “How could the in­for­ma­tion in that ob­ject ever be re­cov­ered if the black hole then dis­ap­pears it­self ?”

In the lat­est pa­per, Hawk­ing and his col­leagues show how some in­for­ma­tion at least may be pre­served. Toss an ob­ject into a black hole and the black hole’s tem­per­a­ture ought to change. So too will a prop­erty called en­tropy, a mea­sure of an ob­ject’s in­ter­nal dis­or­der, which rises the hot­ter it gets.

The physi­cists, in­clud­ing Sasha Haco at Cam­bridge and An­drew Stro­minger at Har­vard, show that a black hole’s en­tropy may be recorded by pho­tons that sur­round the black hole’s event hori­zon, the point at which light can­not es­cape the in­tense grav­i­ta­tional pull. They call this sheen of pho­tons “soft hair”.

“What this pa­per does is show that ‘soft hair’ can ac­count for the en­tropy,” said Perry. “It’s telling you that soft hair re­ally is do­ing the right stuff.”

It is not the end of the in­for­ma­tion para­dox though. “We don’t know that Hawk­ing en­tropy ac­counts for ev­ery­thing you could pos­si­bly throw at a black hole, so this is re­ally a step along the way,” said Perry. “We think it’s a pretty good step, but there is a lot more work to be done.”

Days be­fore Hawk­ing died, Perry was at Har­vard work­ing on the pa­per with Stro­minger. He was not aware how ill Hawk­ing was and called to give the physi­cist an up­date. It may have been the last sci­en­tific ex­change Hawk­ing had. “It was very dif­fi­cult for Stephen to com­mu­ni­cate and I was put on a loud­speaker to ex­plain where we had got to. When I ex­plained it, he sim­ply pro­duced an enor­mous smile. I told him

we’d got some­where. He knew the fi­nal re­sult.”

Among the un­knowns that Perry and his col­leagues must now ex­plore are how in­for­ma­tion as­so­ci­ated with en­tropy is phys­i­cally stored in soft hair and how that in­for­ma­tion comes out of a black hole when it evap­o­rates.

“If I throw some­thing in, is all of the in­for­ma­tion about what it is stored on the black hole’s hori­zon?” said Perry. “That is what is re­quired to solve the in­for­ma­tion para­dox. If it’s only half of it, or 99%, that is not enough, you have not solved the in­for­ma­tion para­dox prob­lem.

“It’s a step on the way, but it is def­i­nitely not the en­tire an­swer. We have slightly fewer puz­zles than we had be­fore, but there are def­i­nitely some per­plex­ing is­sues left.”

Marika Tay­lor, pro­fes­sor of the­o­ret­i­cal physics at Southamp­ton Uni­ver­sity and a former stu­dent of Hawk­ing’s, said: “Un­der­stand­ing the mi­cro­scopic ori­gin of this en­tropy – what are the un­der­ly­ing quan­tum states that the en­tropy counts? – has been one of the great chal­lenges of the last 40 years.

“This pa­per pro­poses a way to un­der­stand en­tropy for as­tro­phys­i­cal black holes based on sym­me­tries of the event hori­zon. The au­thors have to make sev­eral non-triv­ial as­sump­tions so the next steps will be to show that these as­sump­tions are valid.”

Juan Mal­da­cena, a the­o­ret­i­cal physi­cist at Ein­stein’s alma mater, the In­sti­tute for Ad­vanced Stud­ies in Prince­ton, said: “Hawk­ing found that black holes have a tem­per­a­ture. For or­di­nary ob­jects we un­der­stand tem­per­a­ture as due to the mo­tion of the mi­cro­scopic con­stituents of the sys­tem. For ex­am­ple, the tem­per­a­ture of air is due to the mo­tion of the mol­e­cules: the faster they move, the hot­ter it is.

“For black holes, it is un­clear what those con­stituents are, and whether they can be as­so­ci­ated to the hori­zon of a black hole. In some phys­i­cal sys­tems that have spe­cial sym­me­tries, the ther­mal prop­er­ties can be cal­cu­lated in terms of these sym­me­tries. This pa­per shows that near the black hole hori­zon we have one of these spe­cial sym­me­tries.”

Pho­to­graph: Murdo Ma­cleod for the Guardian

Stephen Hawk­ing.

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