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3D illustration tunnel or wormhole, tunnel that can connect one universe with another. Abstract speed tunnel warp in space, wormhole or black hole, scene of overcoming the temporary space in cosmos
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Crossing a wormhole: reality or science fiction?

Guillaume Bossard
Guillaume Bossard
Lecturer in physics at École Polytechnique (IP Paris)

Worm­holes make for good sci­ence-fic­tion as ways for faster-than-light-speed trav­el between two extreme­ly dis­tant points in the uni­verse. In real­i­ty, how­ev­er, Einstein’s the­o­ry of gen­er­al rel­a­tiv­i­ty shows that it would not be pos­si­ble for mat­ter to actu­al­ly cross these “tun­nels through space”. But physi­cists are still con­sid­er­ing whether that hypoth­e­sis is false: quan­tum effects could play a role in refut­ing this hypoth­e­sis. Nev­er­the­less, recent research is help­ing sci­en­tists bet­ter under­stand how worm­holes could exist in a quan­tum the­o­ry of grav­i­ta­tion. And, in doing so, it may help solve Hawking’s famous “infor­ma­tion para­dox”.1

Are black holes “space portals”?

Worm­holes are usu­al­ly rep­re­sent­ed as a cylin­droid con­nect­ing two sheets (or planes) of the uni­verse – i.e., a tun­nel between two black holes. In the clas­si­cal descrip­tion of gen­er­al rel­a­tiv­i­ty (which neglects quan­tum effects), it is impos­si­ble to cross a worm­hole with­out invok­ing exot­ic effects such as time trav­el. Fur­ther­more, if a worm­hole con­nects two black holes and those black holes pull every­thing near them into them (even light!), then sure­ly it would be impos­si­ble to pass through a worm­hole while escap­ing the force of grav­i­ty on the oth­er side? 

To explain this, physi­cists the­o­rised that “strong” quan­tum effects are at play. Indeed, recent work by Juan Mal­da­ce­na (Insti­tute of Advanced Study, Prince­ton) and Xiao-Liang Qi (Stan­ford Uni­ver­si­ty)2, goes some way in con­firm­ing this hypoth­e­sis. The duo used a very sim­pli­fied mod­el to show that it is pos­si­ble to con­struct “neg­a­tive ener­gy” quan­tum states that pro­duce a worm­hole that can be trav­elled through. Neg­a­tive ener­gy (which, inci­den­tal­ly is thought to be respon­si­ble for the accel­er­at­ed expan­sion of the uni­verse) is the ener­gy that oppos­es the force of grav­i­ty and, as such, would keep the “mouth” of a worm­hole open.

Quantum effects

What is most phys­i­cal­ly inter­est­ing in Mal­da­ce­na and Qi’s hypoth­e­sis is not so much the pos­si­bil­i­ty of worm­holes we could cross, but rather its rela­tion­ship to the “infor­ma­tion para­dox” put for­ward by Stephen Hawk­ing – a very active area of research34!

A black hole is formed when a very mas­sive star dies and its resid­ual core has a mass three times that of our Sun. 

A black hole is formed when a very mas­sive star dies and its resid­ual core has a mass three times that of our Sun. Black holes of this size are so dense that they curve the struc­ture of space-time around them to such an extent that noth­ing can escape, not even light. But Hawk­ing pre­dict­ed in 1974 that, even though black holes absorb every­thing, they could some­how them­selves emit par­ti­cles in the form of radi­a­tion (this is known as the “Hawk­ing radi­a­tion”)5. These par­ti­cles are cre­at­ed by so-called “quan­tum events” at the edge of the black hole (its “event hori­zon” or “point of no return”). 

Accord­ing to quan­tum the­o­ry, the vac­u­um of emp­ty space is not a true vac­u­um, but con­tains “vir­tu­al par­ti­cles”: pairs made up of a sub­atom­ic par­ti­cle and its antipar­ti­cle (an elec­tron and a positron, for exam­ple). These par­ti­cles may briefly come into exis­tence in a ran­dom quan­tum fluc­tu­a­tion, before anni­hi­lat­ing one other.

The sit­u­a­tion is quite dif­fer­ent at the event hori­zon, how­ev­er. Here, one of the pair might fall into the black hole while the oth­er escapes and becomes a real par­ti­cle. This process draws (grav­i­ta­tion­al) ener­gy from the black hole, which reduces its effec­tive mass. The black hole then slow­ly evap­o­rates, while Hawk­ing radi­a­tion streams from its sur­face. This radi­a­tion is extreme­ly weak, and in the­o­ry, a black hole of one solar mass would take 1058 bil­lion years to evap­o­rate com­plete­ly – and the uni­verse is not even 14 bil­lion years old.

Inextricable links

This evap­o­ra­tion also pos­es anoth­er dif­fi­cult the­o­ret­i­cal prob­lem, relat­ed to “quan­tum entan­gle­ment” (a process by which par­ti­cles become inex­tri­ca­bly linked). The par­ti­cles emit­ted by the Hawk­ing radi­a­tion are entan­gled with the quan­tum state describ­ing the black hole. But if the black hole ends up evap­o­rat­ing com­plete­ly – and thus dis­ap­pears – there would be no black hole quan­tum state with which Hawk­ing radi­a­tion par­ti­cles can entan­gle. So, accord­ing to quan­tum the­o­ry, it should be pos­si­ble to have a sit­u­a­tion in which a par­ti­cle would be absorbed by the black hole while its antipar­ti­cle would “evap­o­rate”.

To over­come this appar­ent para­dox, most the­o­rists believe that Hawk­ing radi­a­tion is max­i­mal­ly entan­gled with the black hole only dur­ing the first part of its evap­o­ra­tion (rough­ly its “half-life”). In the sec­ond part, the black hole would emit radi­a­tion entan­gled with the radi­a­tion emit­ted in the first moments of its life. Once it has evap­o­rat­ed, the quan­tum entan­gle­ment would there­fore only occur between par­ti­cles radi­at­ed at dis­tinct moments in time.

Semi-classical states 

The chal­lenge for physi­cists is to pro­vide a quan­ti­ta­tive expla­na­tion for these ideas using a quan­tum the­o­ry of grav­i­ta­tion. The so-called semi-clas­si­cal approach (so called because it describes the mat­ter in and around black holes using quan­tum the­o­ry, but describes grav­i­ty using Einstein’s clas­si­cal the­o­ry), con­sid­ers quan­tum effects as being weak.

No one has been able to pro­vide a sat­is­fac­to­ry descrip­tion of this phe­nom­e­non. Accord­ing to Mal­da­ce­na and Qi, the expla­na­tion lies in the idea that when a black hole is young, the clas­si­cal descrip­tion of Hawk­ing radi­a­tion holds. With time, how­ev­er, new semi-clas­si­cal states, involv­ing a worm­hole that links the black hole to the radi­a­tion it emit­ted in its ear­ly days, become more impor­tant. As the black hole evap­o­rates, these new states even­tu­al­ly end up includ­ing worm­holes out­side the black hole. These new worm­holes describe the quan­tum entan­gle­ment between the ear­ly and late-stage radiation.

Final­ly, these worm­holes are vir­tu­al and there is no ques­tion of tra­vers­ing them, but they play an impor­tant role in describ­ing the phe­nom­e­non of black hole evap­o­ra­tion. Even if their mod­els are very sim­pli­fied, researchers can now accu­rate­ly describe that the entan­gle­ment entropy – which mea­sures the rate of entan­gle­ment between the radi­a­tion and the black hole – fol­lows the so-called Page curve6, in a way that resolves Hawk­ing’s infor­ma­tion paradox.

Interview by Isabelle Dumé
1https://​jour​nals​.aps​.org/​p​r​/​a​b​s​t​r​a​c​t​/​1​0​.​1​1​0​3​/​P​h​y​s​R​e​v​.​48.73
2https://​arx​iv​.org/​a​b​s​/​1​8​0​4​.​00491
3https://​arx​iv​.org/​a​b​s​/​1​9​1​1​.​12333
4https://​arx​iv​.org/​a​b​s​/​1​9​1​1​.​11977
5https://​www​.nature​.com/​a​r​t​i​c​l​e​s​/​2​4​8​030a0
6https://​jour​nals​.aps​.org/​p​r​l​/​a​b​s​t​r​a​c​t​/​1​0​.​1​1​0​3​/​P​h​y​s​R​e​v​L​e​t​t​.​7​1​.3743

Contributors

Guillaume Bossard

Guillaume Bossard

Lecturer in physics at École Polytechnique (IP Paris)

Guillaume Bossard's research includes various aspects of string theory and theories of supergravity. He studies black holes and quantum corrections to low energy gravitation, as well as mathematical aspects of duality symmetries. He defended his thesis on non-renormalisation theorems in quantum supersymmetric field theory at the Laboratoire de Physique théorique et des Hautes Energies of the Université Pierre et Marie Curie (now Paris Sorbonne) in 2007. After a postdoctoral fellowship at the Max-Planck Institute for Gravitational Physics in Potsdam, Germany, he joined the CNRS in the theoretical physics centre of the École Polytechnique where he is a member of the String Theory team since 2010.