SO HOW BIG IS SPACE?

There is no big­ger em­pir­i­cal ques­tion in astro­physics than how big space is. CATHAL O’CON­NELL pro­vides a brief his­tory of ideas about the size and shape of the uni­verse.

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IN ONE SENSE the edge of the uni­verse is easy to mark out: it’s the dis­tance a beam of light could have trav­elled since the be­gin­ning of time. Any­thing be­yond is im­pos­si­ble for us to ob­serve, and so out­side our so­called ‘ob­serv­able uni­verse’.

You might guess that the dis­tance from the cen­tre of the uni­verse to the edge is sim­ply the age of the uni­verse (13.8 bil­lion years) mul­ti­plied by the speed of light: 13.8 bil­lion light years.

But space has been stretch­ing all this time; and just as an air­port walk­way ex­tends the stride of a walk­ing pas­sen­ger, the mov­ing walk­way of space ex­tends the stride of light beams. It turns out that in the 13.8 bil­lion years since the be­gin­ning of time, a light beam could have trav­elled 46.3 bil­lion light years from its point of ori­gin in the Big Bang. If you imag­ine this beam trac­ing a ra­dius, the ob­serv­able uni­verse is a sphere whose di­am­e­ter is dou­ble that: 92.6 bil­lion light years.

“Since noth­ing is faster than light, ab­so­lutely any­thing could in prin­ci­ple hap­pen out­side the ob­serv­able uni­verse,” says An­drew Lid­dle, an as­tronomer at the Univer­sity of Ed­in­burgh. “It could end and we’d have no way of know­ing.”

But we have good rea­sons to sus­pect the en­tire Uni­verse (cap­i­talised now to dis­tin­guish from the merely ob­serv­able uni­verse) goes on a lot fur­ther than the part we can ob­serve – and that it is pos­si­bly in­fi­nite.

So how can we know what goes on be­yond the ob­serv­able uni­verse?

Imag­ine a bac­terium swim­ming in a fish­bowl. How could it know the true ex­tent of its seem­ingly in­fi­nite world? Well, dis­tor­tions of light from the cur­va­ture

“Space is big. You just won’t be­lieve how vastly, hugely, mind- bog­glingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.”

Dou­glas Adams, Hitch­hik­ers Guide to the Galaxy

of the glass might give it a clue. In the same way, the cur­va­ture of the uni­verse tells us about its ul­ti­mate size.

“The ge­om­e­try of the uni­verse can be of three dif­fer­ent kinds,” says Robert Trotta, an as­tro­physi­cist at Im­pe­rial Col­lege Lon­don. It could be closed (like a sphere), open (like a sad­dle) or flat (like a ta­ble). The closed ge­om­e­try would mean the Uni­verse is fi­nite, while the other two would mean the Uni­verse is, the­o­ret­i­cally, in­fi­nite.

The key to mea­sur­ing its cur­va­ture is the cos­mic mi­crowave back­ground (CMB) ra­di­a­tion – a wash of light given out by the fire­ball of plasma that per­vaded the uni­verse 400,000 years af­ter the Big Bang. It’s our snap­shot of the uni­verse when it was very young and about 1,000 times smaller than it is to­day.

Just as an­cient ge­og­ra­phers once used the curvi­ness of the Earth’s hori­zon to work out the size of our planet, astronomers are us­ing the curvi­nesss of the CMB at our cos­mic hori­zon to es­ti­mate the size of the uni­verse.

The key is to use satel­lites to mea­sure the tem­per­a­ture of dif­fer­ent fea­tures in the CMB. The way these fea­tures dis­tort across the CMB land­scape is used to cal­cu­late its ge­om­e­try. “So de­ter­min­ing the size and ge­ometr, of the Uni­verse helps us de­ter­mine what hap­pened right af­ter its birth,” Trotta says.

Since the late 1980s, three gen­er­a­tions of satel­lites have mapped the CMB with ever im­prov­ing res­o­lu­tion, gen­er­at­ing bet­ter and bet­ter es­ti­mates of the uni­verse’s cur­va­ture. The lat­est data, re­leased in March 2013, came from the Euro­pean Space Agency’s Planck tele­scope. It es­ti­mated the cur­va­ture to be com­pletely flat, at least to within a mea­sure­ment cer­tainty of plus or mi­nus 0.4%.

The ex­treme flat­ness of the uni­verse sup­ports the the­ory of cos­mic in­fla­tion. This the­ory holds that in a frac­tion of a sec­ond (10− 36 sec­ond to be pre­cise) just af­ter its birth, the uni­verse in­flated like a bal­loon, ex­pand­ing many or­ders of mag­ni­tude while stretch­ing and flat­ten­ing its sur­face fea­tures.

Per­fect flat­ness would mean the uni­verse is in­fi­nite, though the plus or mi­nus 0.4% mar­gin of er­ror means we can’t be sure. It might still be fi­nite but very big. Us­ing the Planck data, Trotta and his col­leagues worked out the min­i­mum size of the ac­tual Uni­verse would have to be at least 250 times greater than the ob­serv­able uni­verse.

The next gen­er­a­tion of te­le­scopes should im­prove on the data from the Planck tele­scope. Whether they will give us a de­fin­i­tive an­swer about the size of the uni­verse re­mains to be seen. “I imag­ine that we will still treat the uni­verse as very nearly flat and still not know well enough to rule out open or closed for a long time to come,” says Charles Ben­net, head of the new CLASS ar­ray of mi­crowave te­le­scopes in Chile.

As it turns out, ow­ing to back­ground noise there are fun­da­men­tal lim­its to how well we can ever mea­sure the cur­va­ture, no mat­ter how good the te­le­scopes get. In July 2016, physi­cists at Ox­ford worked out we can­not pos­si­bly mea­sure a cur­va­ture be­low about 0.01%. So we still have a ways to go, though mea­sure­ments so far, and the ev­i­dence from in­fla­tion the­ory, has most physi­cists weigh­ing to­ward the view the uni­verse is prob­a­bly in­fi­nite. An im­pas­sioned mi­nor­ity, how­ever, have had a se­ri­ous prob­lem with that.

GET­TING RID OF IN­FIN­ITY, the great Bri­tish physi­cist Paul Dirac said, is the most im­por­tant chal­lenge in physics. “No in­fin­ity has ever been ob­served in na­ture,” notes Columbia Univer­sity as­tro­physi­cist Janna Levin in her 2001 mem­oir How the Uni­verse got its Spots. “Nor is in­fin­ity tol­er­ated in a sci­en­tific the­ory.”

So how come physi­cists keep al­low­ing that the uni­verse it­self may be in­fi­nite? The idea goes back to the found­ing fathers of physics. New­ton, for ex­am­ple, rea­soned that the uni­verse must be in­fi­nite based on his law of grav­i­ta­tion. It held that ev­ery­thing in the

We will need to know more about what went down in the first split- sec­ond of the uni­verse. Per­haps grav­i­ta­tional waves will be the an­swer, a way to ‘ hear’ the vi­bra­tions of the big bang it­self.

uni­verse at­tracted ev­ery­thing else. But if that were so, even­tu­ally the uni­verse would be pulled to­wards a sin­gle point, in the way that a star even­tu­ally col­lapses un­der its own weight. This was at odds with his firm be­lief the uni­verse had al­ways ex­isted. So, he fig­ured, the only ex­pla­na­tion was in­fin­ity – the equal pull in all di­rec­tions would keep the uni­verse static, and eter­nal.

Al­bert Ein­stein, 250 years later at the start of the 20th cen­tury, sim­i­larly en­vi­sioned an eter­nal and in­fi­nite uni­verse. Gen­eral rel­a­tiv­ity, his the­ory of the uni­verse on the grand­est scales, plays out on an in­fi­nite land­scape of space­time.

Math­e­mat­i­cally speak­ing, it is eas­ier to pro­pose a uni­verse that goes on for­ever than to have to deal with the edges. Yet to be in­fi­nite is to be un­real – a hy­per­bole, an ab­sur­dity.

In his short story The Li­brary of Ba­bel, Ar­gen­tinian writer Jorge Luis Borges imag­ines an in­fi­nite li­brary con­tain­ing ev­ery pos­si­ble book of ex­actly 410 pages: “…for ev­ery sen­si­ble line of straight­for­ward state­ment, there are leagues of sense­less ca­coph­o­nies, ver­bal jum­bles and in­co­her­ences.” Be­cause there are only so many pos­si­ble ar­range­ments of let­ters, the pos­si­ble num­ber of books is lim­ited, and so the li­brary is des­tined to re­peat it­self.

An in­fi­nite Uni­verse leads to sim­i­lar con­clu­sions. Be­cause there are only so many ways that atoms can be ar­ranged in space (even within a re­gion 93 bil­lion light years across), an in­fi­nite Uni­verse re­quires that there must be, out there, an­other huge re­gion of space iden­ti­cal to ours in ev­ery re­spect. That means an­other Milky Way, an­other Earth, an­other ver­sion of you and an­other of me.

Physi­cist Max Teg­mark, of the Mas­sachusetts In­sti­tute of Tech­nol­ogy, has run the num­bers. He es­ti­mates that, in an in­fi­nite Uni­verse, patches of space iden­ti­cal to ours would tend to come along about ev­ery 1010115 me­tres (an in­sanely huge num­ber, one with more ze­roes af­ter it than there are atoms in the ob­serv­able uni­verse). So no dan­ger of bump­ing into your twin self down at the shops; but still Levin does not ac­cept it: “Is it ar­ro­gance or logic that makes me be­lieve this is wrong? There’s just one me, one you. The uni­verse can’t be in­fi­nite.”

Levin was one of the first the­o­rists to ap­proach gen­eral rel­a­tiv­ity from a new per­spec­tive. Rather than think­ing about ge­om­e­try, which de­scribes the shape of space, she looked at its topol­ogy: the way it was con­nected.

All those as­sump­tions about flat, closed or open uni­verses were only valid for huge, spher­i­cal uni­verses, she ar­gued. Other shapes could be topo­log­i­cally ‘flat’ and still fi­nite.

“Your idea of a donut-shaped uni­verse is in­trigu­ing, Homer,” says Stephen Hawk­ing in a 1999 episode of The Simp­sons. “I may have to steal it.” Ac­tu­ally, the show’s writ­ers had al­ready stolen the idea from Levin—who pub­lished her anal­y­sis of a donut-shaped uni­verse in 1998.

A donut, she noted, ac­tu­ally had – “topo­log­i­cally speak­ing” – zero cur­va­ture be­cause the neg­a­tive cur­va­ture on the in­side is bal­anced by the pos­i­tive

cur­va­ture on the out­side. The (near) zero cur­va­ture mea­sured in the CMB was there­fore as con­sis­tent with a donut as with a flat sur­face.

In such a uni­verse, Levin re­alised, you might cross the cos­mos in a space­ship, the way sailors crossed the globe, and find your­self back where you started. This idea in­spired Aus­tralian physi­cist Neil Cor­nish, now based at Montana State Univer­sity, to think about how the very old­est light, from the CMB, might have cir­cum­nav­i­gated the cos­mos. If the donut uni­verse were be­low a thresh­old size, that would cre­ate a tell­tale sig­na­ture, which Cor­nish called “cir­cles in the sky”.

Alas, when CMB data came back from the Wilkin­son Mi­crowave Anisotropy Probe (WMAP) in 2001, no such sig­na­tures were found. That doesn’t rule out the donut the­ory en­tirely; but it does mean that the uni­verse, if it is a donut, is an aw­fully big one.

AT­TEMPTS TO DI­RECTLY prove or dis­prove the in­fin­ity of the uni­verse seem to lead us to a dead-end, at least with cur­rent tech­nol­ogy. But we might do it by in­fer­ence, Cor­nish be­lieves.

In­fla­tion the­ory does a com­pelling job of ex­plain­ing the key fea­tures of our uni­verse; and one of the off­shoots of in­fla­tion is the mul­ti­verse the­ory.

It’s the kind of the­ory that, when you first hear it, seems to have sprung from the mind of a sci­ence-fic­tion au­thor in­dulging in mind-ex­pand­ing sub­stances. Ac­tu­ally it was first pro­posed by in­flu­en­tial Stan­ford physi­cist An­drei Linde in the 1980s. Linde – to­gether with Alan Guth at MIT and Alexei Starobin­sky at Rus­sia’s Lan­dau In­sti­tute for The­o­ret­i­cal Physics – was one of the ar­chi­tects of in­fla­tion the­ory.

Guth and Starobin­sky’s orig­i­nal ideas had in­fla­tion pe­ter­ing out in the first split sec­ond af­ter the big bang; Linde, how­ever, had it go­ing on and on, with new uni­verses sprout­ing off like an ever­last­ing gin­ger root.

Linde has since showed that “eter­nal in­fla­tion” is prob­a­bly an in­evitable part of any in­fla­tion model. This eter­nal in­fla­tion, or mul­ti­verse, model is at­trac­tive to Linde be­cause it solves the great­est mys­tery of all: why the laws of physics seem fine-tuned to al­low our ex­is­tence.

The strength of grav­ity is just enough to al­low sta­ble stars to form and burn, the elec­tro­mag­netic and nu­clear forces are just the right strength to al­low atoms to form, for com­plex mol­e­cules to evolve, and for us to come to be.

In each newly sprouted uni­verse these con­stants get as­signed ran­domly. In some, grav­ity might be so strong that the uni­verse rec­ol­lapses im­me­di­ately af­ter its big bang. In oth­ers, grav­ity would be so weak that atoms of hy­dro­gen would never con­dense into stars or gal­ax­ies. With an in­fi­nite num­ber of new uni­verses sprout­ing into and out of ex­is­tence, by chance one will pop up that is fit for life to evolve.

The mul­ti­verse the­ory has its crit­ics, no­tably an­other co-founder of in­fla­tion the­ory, Paul Stein­hardt. who told Sci­en­tific Amer­i­can in 2014: “Sci­en­tific ideas should be sim­ple, ex­plana­tory, pre­dic­tive. The in­fla­tion­ary mul­ti­verse as cur­rently un­der­stood ap­pears to have none of those prop­er­ties.” Mean­while Paul Davies at the Univer­sity of Ari­zona wrote in The New York Times that “in­vok­ing an in­fin­ity of un­seen uni­verses to ex­plain the un­usual fea­tures of the one we do see is just as ad hoc as in­vok­ing an un­seen cre­ator”.

But in an­other sense the mul­ti­verse is the sim­pler of the two in­fla­tion mod­els. In a few lines of equa­tions, or just a few sen­tences of speech, the mul­ti­verse gives us a mech­a­nism to ex­plain the ori­gin of our uni­verse, just as Charles Dar­win’s the­ory of nat­u­ral se­lec­tion ex­plained the ori­gin of species. As Max Teg­mark puts it: “Our judg­ment there­fore comes down to which we find more wasteful and in­el­e­gant: many worlds or many words.”

To set­tle the is­sue, we will need to know more about what went down in the first split-sec­ond of the uni­verse. Per­haps grav­i­ta­tional waves will be the an­swer, a way to ‘hear’ the vi­bra­tions of the big bang it­self. Whether in­fi­nite or fi­nite, stand-alone or one of an end­less mul­ti­tude, the uni­verse is surely a mind­bend­ing place.

Which brings us back to The Hitch­hiker’s Guide to the Galaxy: “If there’s any real truth, it’s that the en­tire mul­ti­di­men­sional in­fin­ity of the Uni­verse is al­most cer­tainly be­ing run by a bunch of ma­ni­acs.” CATHAL O’CON­NELL is a sci­ence writer, with a back­ground in physics, based in Mel­bourne.

IMAGES 01 NASA / Getty Images 02 ESA and the Planck Col­lab­o­ra­tion 03 Me­hau Ku­lyk / Getty Images 04 An­drei Linde

Uni­ver­sal ge­om­e­try: the uni­verse could be closed like sphere, open like a sad­dle or flat like a ta­ble. The first op­tion would make it fi­nite; the other two, in­fi­nite.

Snap­shot of the baby uni­verse: the cos­mic mi­crowave back­ground (CMB) as ob­served by the Planck ob­ser­va­tory. Just as ge­og­ra­phers once used the curve of the hori­zon to work out the size of Earth, astronomers are us­ing fea­tures in the CMB to es­ti­mate the curvi­ness and hence, the the size of the uni­verse.

One ring the­ory to rule them all: CMB data doesn’t rule out a donut-shape, but it would be an aw­fully big one. 03

In­fi­nite va­ri­ety: in the the eter­nal in­fla­tion model, new uni­verses sprout off like an ever­last­ing gin­ger root.

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