THE ORI­GINS OF EN­TAN­GLE­MENT

Al­bert Ein­stein re­vealed the phe­nom­e­non of ‘spooky ac­tion at a dis­tance’ – iron­i­cally while try­ing to ar­gue away the weird­ness of quan­tum the­ory, writes ROBYN ARIANRHOD.

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IT ALL BE­GAN IN OC­TO­BER 1927, at the Fifth Solvay Congress in Brus­sels. It was Louis de Broglie’s first congress, and he had been “full of plea­sure and cu­rios­ity” at the prospect of meet­ing Ein­stein, his teenage idol. Now 35, de Broglie hap­pily re­ported: “I was par­tic­u­larly struck by his mild and thought­ful ex­pres­sion, by his gen­eral kind­ness, by his sim­plic­ity, and by his friend­li­ness.”

Back in 1905, Ein­stein had helped pi­o­neer quan­tum the­ory with his revo­lu­tion­ary dis­cov­ery that light has the char­ac­ter­is­tics of both a wave and a par­ti­cle. Niels Bohr later ex­plained this as “com­ple­men­tar­ity”: de­pend­ing on how you ob­serve light, you will see ei­ther wave or par­ti­cle be­hav­iour. As for de Broglie, he had taken Ein­stein’s idea into even stranger ter­ri­tory in his 1924 PHD the­sis: if light waves could be­have like par­ti­cles, then per­haps par­ti­cles of mat­ter could also be­have like waves! Af­ter all, Ein­stein had shown that en­ergy and mat­ter were in­ter­change­able, via E=mc2.

Ein­stein was the first to pub­licly sup­port de Broglie’s bold hy­poth­e­sis. By 1926, Er­win Schrödinger had de­vel­oped a math­e­mat­i­cal for­mula to de­scribe such “mat­ter waves”, which he pic­tured as some kind of rip­pling sea of smeared-out par­ti­cles. But Max Born showed that Schrödinger’s waves are, in ef­fect, “waves of prob­a­bil­ity”. They en­code the sta­tis­ti­cal like­li­hood that a par­ti­cle will show up at a given place and time based on the be­hav­iour of many such par­ti­cles in re­peated ex­per­i­ments. When the par­ti­cle is ob­served, some­thing strange ap­pears to hap­pen. The wave­func­tion “col­lapses” to a sin­gle point, al­low­ing us to see the par­ti­cle at a par­tic­u­lar po­si­tion.

Born’s prob­a­bil­ity wave also fit­ted neatly with Werner Heisen­berg’s re­cently pro­posed “un­cer­tainty prin­ci­ple”. Heisen­berg had con­cluded that in the quan­tum world it is not pos­si­ble to ob­tain ex­act in­for­ma­tion about both the po­si­tion and the mo­men­tum of a par­ti­cle at the same time. He imag­ined the very act of mea­sur­ing a quan­tum par­ti­cle’s po­si­tion, say by shin­ing a light on it, gave it a jolt that changed its mo­men­tum, so the two could never be pre­cisely mea­sured at once.

When the world’s lead­ing physi­cists gathered in Brus­sels in 1927, this was the strange state of quan­tum physics.

The of­fi­cial photograph of the par­tic­i­pants shows 28 be­suited, sober-look­ing men, and one equally se­ri­ous wo­man, Marie Curie. But fel­low physi­cist Paul Ehren­fest’s pri­vate photo of in­tel­lec­tual ad­ver­saries Bohr and Ein­stein cap­tures the spirit of the con­fer­ence: Bohr looks in­tensely thought­ful, hand on his chin, while Ein­stein is lean­ing back look­ing re­laxed and dreamy. This gen­tle, contemplative pic­ture be­lies the depth of the fa­mous clash be­tween these two in­tel­lec­tual ti­tans – a clash that hinged on the ex­tra­or­di­nary con­cept of quan­tum en­tan­gle­ment.

AT THE CONGRESS, Bohr pre­sented his view of quan­tum me­chan­ics for the first time. Dubbed the Copen­hagen in­ter­pre­ta­tion, in hon­our of Bohr’s home city, it com­bined his own idea of par­ti­cle-wave com­ple­men­tar­ity with Born’s prob­a­bil­ity waves and Heisen­berg’s un­cer­tainty prin­ci­ple.

Most of the at­ten­dees read­ily ac­cepted this view, but Ein­stein was per­turbed. It was one thing for groups of par­ti­cles to be ruled by chance; in­deed Ein­stein had ex­plained the jit­tery mo­tion of pollen in ap­par­ently still wa­ter (dubbed Brow­n­ian mo­tion) by in­vok­ing the ran­dom group be­hav­iour of wa­ter mol­e­cules. In­di­vid­ual mol­e­cules, though, would still be ruled by New­ton’s laws of mo­tion; their ex­act move­ments could in prin­ci­ple be cal­cu­lated.

By con­trast, the Copen­hagen the­ory held that sub­atomic par­ti­cles were ruled by chance.

Ein­stein be­gan his at­tack in the time-hon­oured tra­di­tion of re­duc­tio ad ab­sur­dum – ar­gu­ing that the log­i­cal ex­ten­sion of quan­tum the­ory would lead to an ab­surd out­come.

Af­ter sev­eral sleep­less nights, Bohr found a flaw in Ein­stein’s logic. Ein­stein did not re­treat: he was sure he could con­vince Bohr of the ab­sur­dity of this strange new the­ory. Their de­bate flowed over into the Sixth Solvay Congress in 1930, and on un­til Ein­stein felt he fi­nally had the pieces in place to check­mate Bohr at

01 Niels Bohr and Al­bert Ein­stein at the Fifth Solvay Congress.

the sev­enth congress in 1933. Two weeks be­fore that, how­ever, Nazi per­se­cu­tion forced Ein­stein to flee to the United States. The planned check­mate would have to wait.

When it came, it was de­cep­tively sim­ple. In 1935 at Princeton, Ein­stein and two col­lab­o­ra­tors, Boris Podol­sky and Nathan Rosen, pub­lished what be­came known as the Ein­stein-podol­sky-rosen para­dox, or EPR for short. Podol­sky wrote up the thought ex­per­i­ment in a math­e­mat­i­cal form, but let me il­lus­trate it with jelly­beans.

Sup­pose you have a red and a green jelly­bean in a box. The box seals off the jelly­beans from all oth­ers: tech­ni­cally speak­ing, the pair form an “iso­lated sys­tem”, and they are “en­tan­gled” in the sense that the colour of one jelly­bean gives in­for­ma­tion about the other. You can see this by ask­ing a friend to close her eyes and pick a jelly­bean at ran­dom. If she picks red, you know the re­main­ing sweet is green.

This is key to EPR: by know­ing the colour of your friend’s jelly­bean, you can know the colour of your own with­out “dis­turb­ing” it by look­ing at it. But in try­ing to by­pass the sup­posed ob­server-ef­fect in this way, EPR had also in­ad­ver­tently un­cov­ered the strange idea of “en­tan­gle­ment”. The term was coined by Schrödinger af­ter he read the EPR pa­per .

So now ap­ply this tech­nique to two elec­trons. In­stead of a colour, each one has an in­trin­sic prop­erty called “spin”. Imag­ine some­thing like the spin axis of a gy­ro­scope. If two elec­trons are pre­pared to­gether in the lab so that they have zero to­tal spin, then the prin­ci­ple of con­ser­va­tion of an­gu­lar mo­men­tum means that if one of the elec­trons has its spin axis up, the other elec­tron’s axis must be down. The elec­trons are en­tan­gled, just as the jelly­beans were.

With jelly­beans, the colour of your friend’s cho­sen sweet is fixed, whether or not she ac­tu­ally ob­serves it. With elec­trons, by con­trast, un­til your friend makes her ob­ser­va­tion, quan­tum the­ory sim­ply says there is a 50% chance its spin is up, and 50% it is down.

The EPR at­tempt to strike at the heart of quan­tum the­ory now goes like this. Per­haps the spin of your friend’s elec­tron was in fact de­ter­mined be­fore she picked it out. How­ever, like a wa­ter­mark that can’t be de­tected un­til a spe­cial light is shone on it, the spin state is only re­vealed when she looks at it. Quan­tum spin, then, in­volves a “hid­den vari­able”, yet to be de­scribed by quan­tum the­ory. Al­ter­na­tively, if quan­tum me­chan­ics is cor­rect and com­plete, then the the­ory de­fies com­mon sense – be­cause as soon as your friend checks the spin of her elec­tron, your elec­tron ap­pears to re­spond in­stantly, be­cause if hers is “up” then yours will be “down”.

This is be­cause the cor­re­la­tion be­tween the two spins was built into the ex­per­i­ment when the elec­trons were first en­tan­gled, just as putting the two jelly­beans in a box en­sures the colour of your jelly­bean will be “op­po­site” that of your friend’s. The im­pli­ca­tions are pro­found. Even if your friend moved to the other side of the galaxy, your elec­tron would “know” that it must man­i­fest the op­po­site spin in the in­stant she makes her ob­ser­va­tion.

Of course, in­stant ac­tion vi­o­lated Ein­stein’s the­ory of rel­a­tiv­ity: noth­ing can travel faster than the speed of light. Hence Ein­stein dubbed this ab­surd propo­si­tion “spooky ac­tion at a dis­tance”.

But there was more. Spin is not the only prop­erty your friend could have cho­sen to ob­serve. What EPR showed, then, is that the phys­i­cal na­ture of your elec­tron seems to have no iden­tity of its own. Rather, it de­pends on how your friend chooses to ob­serve her elec­tron. As Ein­stein put it: “Do you re­ally be­lieve the Moon is there only when you look at it?” The EPR pa­per con­cluded: “No rea­son­able def­i­ni­tion of re­al­ity

could be ex­pected to per­mit this.” Ergo, the au­thors be­lieved, quan­tum the­ory had some se­ri­ous prob­lems.

BOHR WAS STUMPED by EPR. He ditched the idea that the act of mea­sure­ment jolted the state of the par­ti­cle. (In­deed, later ex­per­i­ments would show that un­cer­tainty is not solely the re­sult of an in­ter­fer­ing ob­server; it is an in­her­ent char­ac­ter­is­tic of par­ti­cles.)

But he did not aban­don the un­cer­tainty at the heart of quan­tum me­chan­ics. In­stead of try­ing to wres­tle with the real world im­pli­ca­tions, he con­cluded that we can only speak of what we ob­serve –at the be­gin­ning of the ex­per­i­ment and the end when your friend’s elec­tron is def­i­nitely “up”, say. We can­not speak about what hap­pens in be­tween.

Ein­stein and Bohr con­tin­ued to de­bate the is­sue for the rest of their lives. What they re­ally dis­agreed about was the na­ture of re­al­ity. Bohr be­lieved that na­ture was fun­da­men­tally ran­dom. Ein­stein did not. “God does not play dice with the uni­verse,” he de­clared.

Nev­er­the­less, Ein­stein knew that quan­tum the­ory ac­cu­rately de­scribed the re­sults of real as op­posed to thought ex­per­i­ments. So most physi­cists con­sid­ered that Bohr had won. They fo­cused on ap­ply­ing quan­tum the­ory, and ques­tions about the EPR para­dox and en­tan­gle­ment be­came a niche in­ter­est.

In 1950, Chien-shi­ung Wu and Irv­ing Sha­knov found oddly linked be­hav­iour in pairs of pho­tons. They didn’t know it at the time but it was the first real-world ob­ser­va­tion of quan­tum en­tan­gle­ment.

Later, David Bohm re­alised Wu and Sha­knov’s dis­cov­ery was an op­por­tu­nity to take en­tan­gle­ment out of the realm of thought ex­per­i­ments and into the lab. Fol­low­ing Bohm, in 1964 John Bell trans­lated the two EPR al­ter­na­tives into a math­e­mat­i­cal re­la­tion­ship that could be tested. But it was left to other ex­per­i­menters – most fa­mously Alain As­pect in 1981 – to carry out the tests.

Ein­stein’s hopes of find­ing hid­den vari­ables that would take the un­cer­tainty out of quan­tum the­ory were dashed. There seemed no es­cap­ing the bizarre con­se­quences of EPR and the re­al­ity of en­tan­gle­ment.

But does this also mean “spooky ac­tion at a dis­tance” is real? En­tan­gle­ment in elec­trons has been demon­strated at dis­tances of a kilo­me­tre or two. But so far that’s too short a dis­tance to know if fasterthan-light in­ter­ac­tions be­tween them were in­volved. Things may soon be­come clearer: at the time of writ­ing, Chi­nese sci­en­tists have just an­nounced the suc­cess­ful trans­mis­sion of en­tan­gled pho­tons from an or­bit­ing satel­lite over dis­tances of more than 1,200 km.

On the other hand, some physi­cists have re­cently taken up Ein­stein’s side of the ar­gu­ment. For in­stance, in 2016 Bengt Nordén, of Chalmers Univer­sity in Swe­den, pub­lished a pa­per en­ti­tled, “Quan­tum en­tan­gle­ment: facts and fic­tion – how wrong was Ein­stein af­ter all?” Against Bohr’s bet­ter judge­ment, such physi­cists are once again ask­ing about the mean­ing of re­al­ity, and won­der­ing what is caus­ing the weird phe­nom­e­non of en­tan­gle­ment.

Some even sug­gest that some­thing like a “worm­hole” – a tun­nel in space­time be­tween two widely sep­a­rated black holes, a con­se­quence of gen­eral rel­a­tiv­ity the­ory first de­duced by Ein­stein and Rosen – may be the mech­a­nism un­der­ly­ing en­tan­gle­ment. The myth­i­cal faster-than-light tachyon is an­other pos­si­ble con­tender.

But nearly ev­ery­one agrees that what­ever is go­ing on be­tween en­tan­gled par­ti­cles, ex­per­i­menters can only com­mu­ni­cate their ob­ser­va­tions of en­tan­gled par­ti­cles at light speed or less.

En­tan­gle­ment is no longer a philo­soph­i­cal cu­rio: not only are physi­cists us­ing it to en­crypt in­for­ma­tion and re­ly­ing on it to un­der­pin the de­sign of to­mor­row’s quan­tum com­put­ers, they are once again grap­pling with the hard ques­tions about the na­ture of re­al­ity that en­tan­gle­ment raises.

Ninety years af­ter the Fifth Solvay Congress, Ein­stein’s thought ex­per­i­ments con­tinue to drive sci­ence on­wards. ROBYN ARIANRHOD is a se­nior ad­junct re­search fel­low at the School of Math­e­mat­i­cal Sciences at Monash Univer­sity.

IMAGES 01 Amer­i­can In­sti­tute Of Physics / Getty Images

Some even sug­gest that some­thing like a ‘ worm­hole’ – a tun­nel in space­time be­tween two widely sep­a­rated black holes, a con­se­quence of gen­eral rel­a­tiv­ity the­ory first de­duced by Ein­stein and Rosen – may be the mech­a­nism un­der­ly­ing en­tan­gle­ment.

An ob­server sees elec­tron A as “spin up”. Elec­tron B must now be “spin down”. The change in elec­tron B oc­curs in­stan­ta­neously. An en­tan­gled pair of elec­trons

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