Crossing a wormhole: reality or science fiction? - Polytechnique Insights (2024)

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 oth­erside?

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 worm­holeopen.

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. 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 oneother.

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 yearsold.

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 intime.

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 beingweak.

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.