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ZAHVALNICE *Odlucio sam da pokuam da napiem jednu -popularnu knjigu o prostoru i vremenu poto (sam 1982. odrao na Lebovoj katedri na )Harvardu niz predavanja. Vec je postojao /prilican broj knjiga o ranoj Vaseljeni i crnim ,rupama, u rasponu od veoma dobrih, kao to -je Vajnbergovo delo Prva tri minuta, do veoma.rdavih, koje necu pominjati. No, doao sam do/zakljucka da se nijedna od njih ne bavi uistinu-pitanjima koja su mene uputila ka izucavanju -kosmologije i kvantne teorije. Odakle potice 0Vaseljena? Kako je i zato pocela? Da li ce se ,okoncati i, ako do toga dode, kako ce se to .odigrati? Postoje pitanja koja su od interesa .za sve nas. Ali moderna nauka postala je tako %tehnicka, da je samo veoma mali broj ,strucnjaka kadar da se razabere u matematici*koja se tu koristi. No, osnovne zamisli o 0nastanku i sudbini Vaseljene mogu se izloiti i*bez matematike, na nacin koji je dostupan ,ljudima bez naucnog obrazovanja. Upravo sam +ja to pokuao da ucinim u ovoj knjizi. Na .citaocu je da prosudi koliko sam u tome uspeo.+Neko mi je kazao da cu, kad god uvedem neku,jednacinu u knjigu, prepoloviti broj njenih %kupaca. Odlucio sam stoga da potpuno +izostavim sve jednacine. No, na kraju sam, &ipak odstupio od ove odluke, navevi +znamenitu Ajntajnovu jednacinu, E = mc2. (Nadam se da ovaj prizor nije prestravio 'polovinu mojih potencijalnih citalaca. /Izuzme li se to to sam imao nesrecu da obolim(od amiotroficke lateralne skleroze, ili -motoricke neuronske bolesti, bio sam srecan u&gotovo svim drugim pogledima. Pomoc i 1podrka koje su mi pruili moja supruga Dejn .i deca Robert, Lusi i Timi omogucile su mi da )vodim prilicno normalan ivot i da imam +uspenu karijeru. Takode sam imao srece u .tome da se opredelim za teorijsku fiziku, zato/to je ova vezana iskljucivo za umni rad. Moja.bolest se, dakle, u ovom pogledu nije pokazala#kao ozbiljan hendikep. Uz to, moje .kolege-naucnici takode su mi bez izuzetka biliod velike pomoci. /U prvoj, 'klasicnoj' fazi moje karijere kolege 1sa kojima sam najvie saradivao bili su Roder (Penrouz, Robert Geroc, Brendon Karter i 0Dord Elis. Zahvalan sam im na pomoci koju su,mi pruili, kao i na radu koji smo zajedno )obavili. Ova faza izloena je u knjizi, )Makrokosmicko ustrojstvo prostorvremena, )koju smo Elis i ja napisali 1973. Ne bih -savetovao citaoce ove knjige da konsultuju to-delo radi daljnjih informacija: ono je veoma .tehnicko i sasvim necitljivo. Nadam se da sam .od tada naucio kako da piem na nacin koji jelake shvatljiv. ,U drugoj, 'kvantnoj' fazi mog rada, koja je .pocela 1974, glavni saradnici bili su mi Gari /Gibson, Don Pejd i Dim Hartl. Veoma sam im /zahvalan, ba kao i studentima-istraivacima,.na velikoj pomoci koju su mi pruili, kako u -fizickom tako i u teorijskom smislu. Obaveza .da budem na visini sa studentima predstavljala0je veliki podsticaj i sprecila me je, nadam se, ,da se ne zaglibim u rutinski univerzitetski ivot. ,Znacajnu pomoc u pisanju ove knjige pruio ,mi je Brajan Vit, jedan od mojih studenata. ,Dobio sam zapaljenje pluca 1985, poto sam )napisao prvu verziju. Morao sam da budem -podvrgnut traheostomskoj operaciji koja mi je+uskratila sposobnost govorenja, to mi je ,gotovo sasvim onemogucilo optenje. Mislio &sam tada da necu biti kadar da knjigu 'privedem kraju. Brajan mi je, medutim, *pomogao ne samo da je preradim, nego i da -savladam jedan komunikacioni program koji se 3naziva 'ivo sredite' i koji mi je poklonio Volt0Voltos, iz kompanije 'Words Plus', u Sanivejlu, .Kalifornija. Pomocu ovog programa ne samo to,mogu da piem knjige i naucne radove, nego ,sam u stanju i da optim sa ljudima pomocu -jednog sintesajzera govora koji sam dobio na *dar od kompanije 'Speech Plus', takode iz 0Sanivejla, Kalifornija. Ovaj sintesajzer i mali -licni racunar montirao je na moja invalidska ,kolica Dejvid Mejsn. Sistem je predstavljao 1istinsko poboljanje. U stvari, sada uspenije (obavljam optenje nego pre no to sam izgubio glas. 0Veliki broj ljudi koji su videli ranije verzije *izneli su niz predloga kako da poboljam *knjigu. Ovo se pre svega odnosi na Pitera +Guzardija, moga urednika u izdavackoj kuci -'Bantam Books', koji mi je poslao stranice i -stranice komentara i pitanja vezanih za mesta-koja su mu se cinila nedovoljno objanjena. +Moram priznati da sam bio prilicno rasrden -kada sam primio njegov dugacak spisak stvari 0koje je valjalo promeniti, ali sada je jasno da (je bio sasvim u pravu. Uveren sam da je $njegovo insistiranje na neprekidnom -doterivanju rukopisa urodilo boljom knjigom. Takode sam veoma zahvalan mojim /asistentima, Kolinu Vilijemsu, Dejvidu Tomasu i-Rejmondu Laflemu; mojim sekretaricama Dudi 2Feli, En Ralf, Ceril Bilington i Sju Mejsi; kao i 2ekipi mojih negovateljica i bolnicarki. Nita od -svega ovoga ne bi bilo moguce bez finansijske0podrke mojim istraivanjima, kao i pokrivanja/medicinskih trokova, za ta su se postarali (koled Gonvil i Kiz, Savez za naucna i *inenjerska izucavanja, kao i zadubine 0Leverhulm, Mek Artur, Nafild i Ralf Smit. Svima njima dugujem zahvalnost. Stiven Hoking 20. oktobar 1987. UVOD -Mi ivimo nae svakodnevne ivote, gotovo /uopte ne razumevajuci svet. I ne pomiljamo 0na maineriju koja tvori Suncevu svetlost to -omogucuje postojanje ivota, na gravitaciju /to nas prikiva za Zemlju koja bi nas inace u ,trenu izbacila put kosmosa, ili na atome iz (kojih smo sazdani i od cije stabilnosti .zavisimo na temeljan nacin. Izuzmu li se deca /(koja jo ne znaju dovoljno da ne postavljaju (vana pitanja), tek se retki medu nama 0udubljuju u odgonetanje velikih tajni: zato je-priroda upravo ovakva kakva je; odakle potice,kosmos i da li je oduvek postojao; da li ce *vreme jednoga dana poceti da tece unazad, .tako da ce posledice prethoditi uzrocima; ili ,da li ima konacnih granica onome to ljudi +mogu da znaju? Postoje cak i deca - ja sam -sreo neku od njih - koja ele da znaju kako 0izgleda jedna crna rupa; koji je najmanji delic +materije; zato pamtimo prolost, a ne i .buducnost; kako to da je danas, naizgled, red,-ako je prethodno bio haos; i zato, postoji Vaseljena? +U naem drutvu i dalje je uobicajeno da /roditelji i ucitelji odgovaraju na ova pitanja -sleganjem ramenima ili pozivanjem na nejasno .upamcena religijska uputstva. Neki se osecaju *nelagodno kada se nadu suoceni sa ovakvim .stvarima, zato to one tako ivo docaravaju $ogranicenja ljudske moci shvatanja. /Ali u temelju najveceg dela filozofije i nauke *stoje upravo takva pitanja. Sve veci broj *odraslih spreman je da se upusti u ovakva ,razmiljanja, iz kojih se povremeno izrode -fantasticni odgovori. Podjednako udaljeni od &atoma i zvezda, mi proirujemo nae .istraivacke vidike da bismo obuhvatili kako +ono to je veoma malo, tako i ono to je veoma veliko. .U prolece 1974, oko dve godine pre no to se *kosmicka sonda 'Viking' spustila na Mars, +prisustvovao sam jednom skupu u Engleskoj, .pod okriljem Kraljevskog drutva iz Londona, -na kome su se razmatrala pitanja traganja za 'vanzemaljskim ivotom. Za vreme pauze %zapazio sam da se u susednoj dvorani +odravao jedan znatno veci skup, kome sam *se iz radoznalosti pridruio. Uskoro sam 'shvatio da prisustvujem jednom drevnom ,obredu, primanju novih clanova u Kraljevsko 0drutvo, koje predstavlja jednu od najstarijih .naucnih organizacija na planeti. U prvom redu,+jedan mladic u invalidskim kolicima sasvim /lagano je upisivao svoje ime u knjigu na cijoj -se prvoj strani nalazio potpis Isaka Njutna. )Kada je konacno zavrio, sa svih strana /razlegao se gromki pljesak. Stiven Hokin je vectada predstavljao legendu. &Hoking je sada profesor matematike na .Lukasovoj katedri Kembridskog univerziteta. )Oglaava se sa istog mesta odakle su to 1nekada cinili Njutn, a kasnije i P. A. M. Dirak, -dvojica slavnih istraivaca veoma velikog i +veoma malog. On je svakako njihov dostojan ,nastavljac. Hokingova prva knjiga namenjena ,nestrucnjacima viestruko je zanimljiva za -laicku publiku. Ona ne samo to se odlikuje .irokim tematskim repertoarom, nego i prua -uvid u nacin na koji dejstvuje autorov um. U -njoj se nahode lucidna otkrovenja o granicnim.podrucjima fizike, astronomije, kosmologije i hrabrosti. ,Ovo je takode knjiga o Bogu... ili moda o %odsustvu Boga. Rec Bog ispunjava ove +stranice. Hoking se otiskuje u traganje za -odgovorom na Ajntajnovo znamenito pitaje o ,tome da li je Bog imao bilo kakav izbor pri +stvaranju Vaseljene. On pokuava, kako to /sam nedvosmisleno tvrdi, da dokuci Boji um. A,to cini tim neocekivaniji zakljucak do koga -dolazi, bar za sada: Vaseljena bez granica u -prostoru, bez pocetka ili kraja u vremenu, i #bez icega to bi Tvorac tu radio. Karl Segan Univerzitet Kornel, Itaka, Njujork 1. NAA SLIKA VASELJENE .Jednom prilikom neki poznati naucnik (kau da/je to bio Bertrand Rasel) drao je predavanje ,iz astronomije. Objanjavao je kako Zemlja /krui oko Sunca i kako Sunce, sa svoje strane,+krui oko sredita ogromnog skupa zvezda )koji se naziva naa Galaksija. Na kraju .predavanja, u dnu sale ustala je jedna onia ,stara gospoda i rekla: "Sve to to ste nam 1ispricali obicna je besmislica. Svet je, zapravo,/ravna ploca koja se nalazi na ledima dinovske,kornjace." Na naucnikovim usnama pojavio se /nadmocni smeak pre no to je uzvratio: "A na)cemu stoji kornjaca?" "Veoma ste pametni -mladicu, veoma pametni", odgovorila je stara *gospoda. "Ali kornjace se pruaju sve do kraja!" ,Predstava o Vaseljeni kao o beskrajnom nizu /kornjaca mnogima bi izgledala smeno, ali zbog*cega smatramo da smo u ovom pogledu bolje )upuceni u stvar? ta, u stvari, znamo o ,Vaseljeni i kako to znamo? Odakle Vaseljena ,potice i kuda ide? Da li je Vaseljena imala ,pocetak, a ako jeste, ta je onda bilo pre -njega? Kakva je priroda vremena? Da li ce se -ikada okoncati? Najnovija dostignuca na polju'fizike, to su ih delimicno omogucile -fantasticne nove tehnologije, nagovetavaju -odgovore na neka od ovih pitanja sa kojima se%odavno suocavamo. Ti odgovori ce nam ,jednoga dana izgledati podjednako ocigledni /kao to nam je ocigledno da Zemlja krui oko -Sunca ili podjednako smeni kao to nam je .smena zamisao o kuli kornjaca. Tek ce vreme 1(ma ta ono bilo) pokazati ta ce biti od ovogadvoga. *Jo 340. godine pre nove ere, starogrcki 2filozof Aristotel naao se u prilici da u svojoj /knjizi, O nebu, izloi dva valjana razloga za +verovanje da je Zemlja okrugla kugla, a ne +ravna ploca. Prvo, uvideo je da pomracenje *Meseca izaziva Zemlja koja se nade izmedu -njega i Sunca. Zemljina senka na Mesecu uvek 0je bila kruna, to je moglo da se dogodi samo.ako Zemlja ima oblik lopte. Da je Zemlja bila 1ravna ploca, senka bi bila izduena i elipticna,*osim ako bi se pomracenje dogadalo uvek u ,vreme kada bi se Sunce nalazilo tacno ispod 0sredita ploce. Drugo, stari Grci su sa svojih (putovanja znali da se zvezda severnjaca ,pojavljuje nie na nebu posmatrana sa juga )nego kada se gleda sa severnih podrucja. -(Buduci da se zvezda severnjaca nalazi iznad *severnog pola, ona bi stajala tacno povrh ,glave posmatraca koji bi se tu nahodio, ali )nekome ko je na polutaru izgledalo bi da -pociva na samom obzorju. Na osnovu razlike u (prividnom poloaju zvezde severnjace u /Egiptu i Grckoj Aristotel je doao do procene ,da obim Zemlje iznosi 400.000 stadija. Nije /tacno poznato koliko je iznosila duina jednog,stadija, ali verovatno se kretala negde oko 0200 jardi, to znaci da je Aristotel doao do +dvostruko vece vrednosti od one za koju mi .danas pouzdano znamo. Stari Grci su znali i za0treci razlog koji je nalagao da Zemlja mora biti.okrugla: zato bi se, inace, najpre pojavila -jedra iznad morskog obzorja, a tek onda trup broda? .Aristotel je smatrao da je Zemlja nepomicna, a+da se Sunce, Mesec, planete i zvezde krecu +krunim orbitama oko nje. Verovao je u to 0zato to je osecao, iz misticnih razloga, da se0Zemlja nalazi u sreditu Vaseljene, kao i da je-kruno kretanje najsavrenije. Ovu zamisao &Ptolemej je u drugom stolecu nove ere ,razradio u jedan celovit kosmoloki model. ,Zemlja je tu pocivala u sreditu, optocena -nizom od osam sfera na kojima su se nalazili ,Mesec, Sunce, zvezde i pet planeta poznatih ,u to vreme: Merkur, Venera, Mars, Jupiter i /Saturn (Ilus. 1.1). Same planete kretale su se %manjim krunim orbitama spojenim sa +odgovarajucim sferama, kako bi se pruilo *objanjenje za njihove prilicno sloene ,putanje koje su uocene na nebu. Na krajnjoj (spoljnoj sferi nalazile su se takozvane -zvezde-nekretnice koje su stalno zadravale ,isti medusoban poloaj, ali su sve zajedno ,kruile nebom. Ono to se nalazilo iza te %poslednje sfere ostajalo je prilicno .neodredeno, ali zacelo nije predstavljalo deo vidljive Vaseljene covecanstva. *Ptolemejev sistem obezbedivao je prilicno -pouzdan nacin predvidanja poloaja nebeskih 0tela. Ali da bi ove poloaje tacno predskazao, ,Ptolemej je morao da pode od pretpostavke da*se Mesec krece putanjom koja ga povremeno -dovodi dvostruko blie Zemlji nego u drugim ,prilikama. Odavde je proishodilo da Mesec u %odredenim trenucima treba da izgleda +dvostruko veci nego inace! Ptolemej je bio /svestan ovog nedostatka, ali to nije osujetilo (rasprostranjeno, premda ne i sveopte, (prihvatanje njegovog modela. Ovaj model *prihvatila je hricanska crkva kao sliku .Vaseljene koja je u skladu sa Svetim Pismom i 'cija je glavna prednost u tome to je %ostavljala obilje prostora iza sfere "zvezda-nekretnica za raj i pakao. /Jedan jednostavniji model izloio je, medutim,11514. godine poljski svetenik Nikola Kopernik. ,(U pocetku, moda iz straha da ga crkva ne )proglasi jeretikom, Kopernik je anonimno (obznanjivao svoj model.) Prema njegovoj +zamisli, u sreditu je nepomicno pocivalo ,Sunce, a Zemlja i planete kretale su se oko /njega krunim orbitama. Prolo je skoro puno *stolece pre no to je ova ideja ozbiljno 'shvacena. A onda su dvojica astronoma, /Nemac Johan Kepler i Italijan Galileo Galilej, (pocela da javno podravaju Kopernikovu /teoriju, uprkos cinjenici da se orbite koje je )ona predvidala nisu sasvim podudarale sa $nalazima posmatranja. Smrtni udarac .Aristotelovoj i Ptolemejevoj teoriji zadat je -1609. Te godine Galilej je poceo da posmatra )nocno nebo upravo pronadenim teleskopom. 1Usredsredivi se na planetu Jupiter, Galilej je +ustanovio da oko nje krui nekoliko malih /satelita ili meseca. Ovo je znacilo da ne mora .ba sve da krui oko Zemlje, kao to su to 2smatrali Aristotel i Ptolemej. (I dalje je, razume*se, bilo moguce verovati da Zemlja pociva (nepomicno u sreditu Vaseljene i da se +Jupiterovi meseci krecu izuzetno sloenim /putanjama oko nje, stvarajuci, privid da krue+oko Jupitera. Kopernikova teorija bila je, -medutim, znatno jednostavnija.) U isto vreme /Johan Kepler je preinacio Kopernikovu teoriju, +izloivi zamisao da se planete krecu ne .krunim, nego elipticnim orbitama (elipsa je (izdueni krug). Predvidanja su se sada +konacno poklopila sa nalazima posmatranja. )to se Keplera ticalo, elipticne orbite ,predstavljale su samo ad hoc hipotezu, i to /prilicno odbojnu, buduci da su elipse ocigledno,bile nesavrenije od krugova. Ustanovivi 0gotovo slucajno da se elipticne orbite slau sa-nalazima posmatranja, on ih nikako nije mogao-usaglasiti sa svojom idejom da magnetne sile 'nagone planete da krue oko Sunca. Do +objanjenja se dolo tek znatno kasnije, *1687, kada je Njutn objavio svoju knjigu, .Philosophiae Naturalis Principia Mathematica, )verovatno najznacajnije pojedinacno delo 1koje je ikada objavljeno u fizici. U ovoj knjizi ,Njutn ne samo da je izloio teoriju o tome -kako se tela krecu u prostoru i vremenu, nego+je i pruio sloene matematicke postupke /neophodne da se izvri analiza ovih kretanja. .Pored toga, Njutn je tu postavio zakon opte %gravitacije, prema kome svako telo u /Vaseljeni privlaci svako drugo telo silom koja 2je tim snanija to su ta tela masivnija i to 0su medusobno blia. Ista ta sila bila je uzrok -padanja predmeta na tle. (Prica o tome da je +Njutna nadahnula jabuka koja mu je pala na /glavu gotovo izvesno je apokrifna. Sve to je -sam Njutn ikada kazao o tome bilo je da je na)pomisao o sili tee doao dok je sedeo ('zadubljen u razmiljanja o padu jedne +jabuke'.) Njutn je potom pokazao da, prema ,ovom zakonu, gravitacija nagoni Mesec da se .krece elipticnom orbitom oko Zemlje, a Zemlju /i ostale planete da elipticnim putanjama krue oko Sunca. (Kopernikov model odbacio je Ptolemejeve -nebeske sfere, a sa njima i zamisao o tome da)Vaseljena ima fizicke granice. Buduci da +zvezde-nekretnice nisu, kako je izgledalo, *menjale svoje poloaje, izuzev u pogledu $kruenja nebeskim svodom izazvanog .okretanjem Zemlje oko vlastite ose, postalo je-prirodno pretpostaviti da su ove zvezde tela ,slicna naem Suncu, ali znatno udaljenija. /Njutn je shvatio da bi, prema njegovoj teoriji ,gravitacije, zvezde trebalo da se medusobno .privlace, to je znacilo da ne mogu u osnovi 'ostati nepomicne. Zar se onda nece sve %sunovratiti jedne ka drugima u nekom *trenutku? U jednom pismu iz 1609. godine, ,upucenom Ricardu Bentliju, takode jednom od (vodecih mislilaca tog vremena, Njutn je .ustvrdio da bi se to uistinu dogodilo kada bi *postojao konacan broj zvezda razmeten u %nekom konacnom prostoru. No, ako bi, )nastavio je on, postojao beskonacan broj /zvezda razmeten manje ili vie jednoobrazno 'u beskonacnom prostoru, do ovoga ne bi +dolo, zato to u tom slucaju ne bi bilo ,nikakve sredinje tacke ka kojoj bi se one sunovracale. *Ovo je dobar primer zamke u koju se moe *upasti pri razmiljanju o beskonacnom. U +beskrajnoj Vaseljeni, svaka tacka se moe +smatrati sreditem, zato to se sa svake ,njene strane prua beskrajno mnogo zvezda. 'Znatno kasnije se uvidelo da je jedino ,ispravno uzeti u obzir konacnu situaciju, u ,kojoj sve zvezde padaju jedna prema drugoj, /a zatim se zapitati kako bi se stvari promenile)ako bi se izvan tog podrucja dodalo jo )zvezda prilicno ravnomerno razmetenih. $Prema Njutnovom zakonu, ove dodatne -zvezde ne bi, u proseku, uopte delovale na -one prvobitne, tako da bi se ove sunovracale )podjednako brzo. Moemo dodavati koliko .hocemo zvezda, ali one bi sve kolabirale jedna)u drugu. Sada znamo da je nemoguce imati -beskonacni staticni model Vaseljene u kome je!gravitacija uvek privlacna sila. *Okolnost da niko nije doao na pomisao o 2tome da se Vaseljena iri ili saima predstavlja.zanimljiv pokazatelj o optoj misaonoj klimi .pre dvadesetog stoleca. Vladalo je uverenje da$je Vaseljena ili oduvek postojala u *nepromenjenom obliku, ili da je nastala u ,nekom konacnom vremenu u prolosti u manje -ili vie slicnom obliku u kome je mi vidimo -danas. Ovo je delimicno mogla biti posledica *sklonosti ljudi da veruju u vecne istine, .odnosno utenosti pomisli da ce, iako ce oni $ostariti i umreti, Vaseljena ostati nepromenjena. +Cak ni oni koji su shvatili da iz Njutnove .teorije gravitacije proishodi da Vaseljena ne -mora da bude staticna nisu doli na pomisao 1da se ona moda iri. Umesto toga, pokuali su*da preoblikuju teoriju time to su uveli *pretpostavku da gravitaciona sila postaje ,odbojna na veoma velikim udaljenostima. Ovo /nije znacajnije uticalo na njihova predvidanja 0kretanja planeta, ali je doputalo da ostane u *ravnotei razmetaj zvezda u beskrajnom 0prostoru, u smislu da su se privlacne sile medu -oblinjim zvezdama javljale kao protivtea -odbojnim silama dalekih zvezda. Mi, medutim, +danas smatramo da bi takva ravnotea bila -nestabilna: ako bi se zvezde u nekom podrucju0samo malo medusobno pribliile, privlacna sila ,medu njima postala bi snanija i odnela bi (prevagu nad odbojnim silama, tako da bi .zvezde nastavile da se primicu jedne drugima. &Sa druge strane, ukoliko bi se zvezde /medusobno malo udaljile, prevagu bi odnele sile2odbijanja, to bi dovelo do daljeg razilaenja. ,Postoji jo jedna zamerka modelu beskrajne -staticne Vaseljene, koja se obicno pripisuje ,nemackom filozofu Hajnrihu Olbersu. On je o 0ovoj teoriji pisao 1823. U stvari, jo su neki +Njutnovi savremenici ukazali na problem, a .Olbersov tekst cak nije bio ni prvi u kome se 0izlau uverljivi argumenti protiv nje. No, taj /tekst je prvi postao ire poznat. Tekoca se (ogledala u tome to bi se u beskrajnoj -staticnoj Vaseljeni gotovo svaka linija vida *okoncala na povrini neke zvezde. Odavde *proishodi da bi celo nebo trebalo da bude +podjednako blistavo kao Sunce. Cak i nocu. .Olbersov protivargumenat glasio je da svetlost(sa dalekih zvezda priguuje apsorpcija (materije koja se nalazi u meduzvezdanom /prostoru. No, da je to posredi, ova materija bi&se jednom zagrejala, postavi i sama -podjednako sjajna kao i zvezde. Jedini nacin +da se izbegne zakljucak da celo nocno nebo .treba po sjajnosti da bude ravno Suncu bio je .da se pretpostavi da zvezde nisu vecno sijale,&vec da su se upalile u nekom konacnom 2vremenu u prolosti. U tom slucaju ili jo nije %moralo doci do zagrevanja materije u .meduzvezdanom prostoru ili svetlost sa dalekih0zvezda jo nije morala stici do nas. A ovo nas .suocava sa sledecim pitanjem: ta je to to #uopte dovodi do paljenja zvezda? +O problemu pocetka Vaseljene vodile su se, .razume se, rasprave jo znatno ranije. Prema !izvesnom broju ranih kosmologa i -judejsko-hricansko-muslimanskoj tradiciji, ,Vaseljena je nastala u jednom konacnom i ne -narocito dalekom vremenu u prolosti. Jedan ,od argumenata u prilog ovakvom pocetku bilo /je uverenje da je neophodno imati 'prvi uzrok' )da bi se objasnilo postojanje Vaseljene. '(Unutar Vaseljene neki dogadaj se uvek )objanjavao kao posledica nekog drugog, .ranijeg dogadaja, ali postojanje Vaseljene se ,moglo rastumaciti na ovaj nacin samo ako je *ona imala nekakav pocetak.) Drugi argumet 3izloio je sveti Augustin u svojoj knjizi Boija 0drava. On je istakao da civilizacija napreduje*i da mi pamtimo ko je ucinio ovo delo ili /usavrio onu tehniku. Stoga covek, a moda i -sama Vaseljena, nisu morali da postoje odvec /dugo. Sveti Augustin je prihvatio da se, prema ''Knjizi Postanja', stvaranje Vaseljene *odigravalo oko 5000. godine pre nove ere. -(Zanimljivo je da to nije predaleko od kraja -poslednjeg ledenog doba, koje se okoncalo oko(deset hiljada godina pre nove ere, kada )arheolozi smatraju da su uistinu udareni temelji civilizacije.) 0Aristotelu i vecini ostalih grckih filozofa, sa )druge strane, nije se dopadala zamisao o *stvaranju, zato to je ona podrazumevala -boanski upliv. Oni su stoga smatrali da su .ljudska rasa i svet oko nje postojali i da ce /postojati vecito. Mislioci starog sveta vec su +razmotrili argument o napredovanju koji je -prethodno opisan, uzvrativi tim povodom da +su se periodicno javljali potopi ili druge -nesrece koji su nas svaki put iznova vracali na pocetak civilizacije. *O pitanjima da li Vaseljena ima pocetak u )vremenu i da li je ogranicena u prostoru 0kasnije je opseno raspravljao filozof Imanuel #Kant u svom monumentalnom (i veoma $opskurnom) delu Kritika cistog uma, +objavljenom 1781. On je ova pitanja nazvao -antinomije (odnosno, protivurecnosti) cistog (razuma, zato to je smatrao da postoje *podjednako valjani razlozi za verovanje u -tezu da Vaseljena ima pocetak, kao i antitezu,da je ona oduvek postojala. Njegov argumenat.u korist teze bio je da bi, ukoliko Vaseljena -nema pocetak, pre bilo kog dogadaja postojalo(beskrajno razdoblje, to je on smatrao )besmislenim. Argumenat u korist antiteze ,glasio je da bi, ako Vaseljena ima pocetak, .onda pre njega postojalo beskrajno razdoblje, /tako da nije jasno zato bi Vaseljena pocela u,nekom posebnom trenutku? U stvari, ono to 0Kant navodi u prilog tezi i antitezi u osnovi je)isti argument. Obe tvrdnje temelje se na ,precutnoj pretpostavci da se vreme prua u *beskraj unazad, bez obzira na to da li je *Vaseljena oduvek postojala. Kao to cemo ,videti, medutim, pojam vremena besmislen je -pre pocetka Vaseljene. Na ovo je prvi ukazao /sveti Augustin. Na pitanje: 'ta je Bog radio 0pre no to je stvorio Vaseljenu?' Augustin nije,uzvratio: 'Pripremao je pakao za ljude koji )postavljaju takva pitanja.' Umesto toga, -kazao je da je vreme svojstvo Vaseljene koju +je Bog stvorio, tako da nije postojalo pre njenog pocetka. -U doba kada je vecina ljudi verovala u to da #je Vaseljena u sutini staticna i .nepromenljiva, pitanje da li ona ima ili nema .pocetak pripadalo je, zapravo, metafizici ili (teologiji. Zapaene pojave mogle su se )podjednako lako objasniti teorijom da je ,Vaseljena oduvek postojala i teorijom da je $stavljena u pokret u nekom konacnom -vremenu na takav nacin da je izgledalo da je -vecno postojala. Ali 1929. godine Edvin Habl -doao je do temeljnog nalaza da se udaljene /galaksije, ma kuda pogledali, brzo udaljuju od /nas. Drugim recima, Vaseljena se iri. Ovo je *znacilo da su u ranijim vremenima nebeska /tela bila medusobno blia. U stvari, postojao 0je, kako izgleda, trenutak, pre otprilike deset 0ili dvadeset hiljada miliona godina, kada su se -sva nalazila tacno na istom mestu i kada je, -stoga, gustina Vaseljene bila beskrajna. Ovo )otkrice konacno je uvelo pitanje pocetka Vaseljene na podrucju nauke. -Iz Hablovih posmatranja proishodilo je da je -postojao trenutak, nazvan Veliki Prasak, kada)je Vaseljena bila infinitezimalno mala i .beskrajno gusta. Pod takvim uslovima otkazali &bi svi zakoni nauke, pa, dakle, i sve .mogucnosti da se predvidi buducnost. Ako je i +bilo nekih zbivanja pre ovog trenutka, ona -nisu ni na koji nacin uticala na ono to se -dogada u sadanjem vremenu. Postojanje ovih .zbivanja moe se prenebreci zato to ona ne *bi imala nikakvih posmatrackih posledica. -Moglo bi se, dakle, reci da vreme pocinje sa .Velikim Praskom, u smislu da se ranija vremena-naprosto ne mogu definisati. Treba, medutim, (istaci da je ovaj pocetak vremena veoma .razlicit od onih koja su prethodno razmatrana.+U nepromenljivoj Vaseljeni pocetak vremena -jeste neto to mora da uvede neki entitet -izvan Vaseljene; ne postoji fizicka nunost -tog pocetka. Moglo bi se zamisliti da je Bog .stvorio Vaseljenu u doslovce bilo kom trenutku.prolosti. Sa druge strane, ako se Vaseljena 3iri, moda postoje fizicki razlozi koji nalau 1pocetak. No, i dalje bi se moglo zamisliti da je )Bog stvorio Vaseljenu u trenutku Velikog .Praska, ili cak posle toga, na takav nacin da 0izgleda kao da je postojao Veliki Prasak, ali bi-bilo besmisleno pretpostaviti da je ona bila -stvorena pre Velikog Praska. Vasiona koja se 2iri ne iskljucuje tvorca, ali postavlja granice )u pogledu toga kada je on mogao da obavi svoj posao! /Da bi se moglo razgovarati o prirodi Vaseljene 0i raspravljati o tome da li ona ima pocetak ili ,kraj, valja prethodno razjasniti ta je to .naucna teorija. Najjednostavnije bi bilo reci &da teorija nije nita drugo do model .Vaseljene, ili nekog njenog ogranicenog dela, .kao i niz pravila koja dovode u vezu svojstva )modela sa posmatrackim nalazima do kojih .dolazimo. Ona postoji jedino u naim umovima +i nema nikakvu drugu stvarnost (ma ta to +znacilo). Jedna teorija je valjana ukoliko +zadovoljava dva zahteva: ona mora tacno da +opie veliku klasu posmatrackih nalaza na )osnovu modela koji sadri samo nekoliko (proizvoljnih elemenata i mora da prui &pouzdana predvidanja vezana za ishode -buducih posmatranja. Na primer, Aristotelova .teorija da je sve sazdano od cetiri elementa -(zemlje, vazduha, vatre i vode - bila je .dovoljno jednostavna da zadovolji prvi uslov, 0ali nije pruala nikakva pouzdana predvidanja. ,Nasuprot tome, Njutnova teorija gravitacije .temeljila se na jo jednostavnijem modelu, u ,okviru koga su se tela medusobno privlacila +silom koja je bila upravo srazmerna jednom *njihovom svojstvu koje je nazvano masa, a ,obrnuto srazmerna kvadratu udaljenosti medu -njima. No, ona je predvidala kretanje Sunca, -Meseca i planeta uz visok stepen pouzdanosti i tacnosti. )Svaka teorija na podrucju fizike uvek je )provizorna, u smislu da predstavlja samo )hipotezu: ona se, naime, nikada ne moe *dokazati. Bez obzira na to koliko se puta .ishodi opita slau sa nekom teorijom, nita (vam ne jemci da joj naredni ishodi nece 0protivureciti. Sa druge strane, jedna teorija se)moe opovrci ustanovljenjem samo jednog 0nalaza koji nije u saglasnosti sa onim to ona 0predvida. Kao to je istakao filozof nauke Karl-Poper, valjana teorija odlikuje se svojstvom .da iz nje proishodi izvestan broj predvidanja &koja bi se u nacelu mogla opovrci ili .krivotvoriti posmatrackim nalazima. Svaki put +kada se pokae da su ishodi novih opita u *skladu sa predvidanjima date teorije, ona +ostaje na snazi i nae poverenje u nju se )povecava; ali kada se pokae da su nova *posmatranja nesaglasna teoriji, nju valja 1odbaciti ili preinaciti. Ili bi bar tako trebalo )postupiti, premda uvek moete dovesti u .sumnju strucnu pozvanost osobe koja je vrila posmatranje. -U praksi se, medutim, najcece dogada da se (postavi nova teorija koja je, u stvari, +produetak prethodne. Primera radi, veoma ,precizna posmatranja planete Merkur ukazala *su na malu razliku izmedu njenog stvarnog .kretanja i predvidanja koja su proishodila iz +Njutnove teorije gravitacije. Ajntajnova *opta teorija relativnosti predvidala je ,kretanje koje se sasvim malo razlikovalo od -onoga na koje je ukazivala Njutnova teorija. +Okolnost da su se Ajntajnova predvidanja +poklopila sa posmatrackim nalazima, dok to /nije bio slucaj sa Njutnovim, predstavljala je ,jednu od kljucnih potvrda nove teorije. Mi, .medutim, i dalje koristimo Njutnovu teoriju za+sve prakticne potrebe zato to su razlike /izmedu njenih predvidanja i onih to proishode/iz opte relativnosti veoma male u situacijama-sa kojima se mi najcece srecemo. (Njutnova 0teorija odlikuje se i jednom velikom prednocu:&ona je znatno jednostavnija za rad od Ajntajnove!) -Krajnji cilj nauke jeste da se dode do jedne )jedinstvene teorije koja bi opisala celu (Vaseljenu. Pristup za koji se, medutim, -opredeljuje vecina naucnika pretpostavlja da .se problem razdvoji u dva dela. Prvo, postoje )zakoni koji nam govore kako se Vaseljena &menja s vremenom. (Ukoliko znamo kako +Vaseljena izgleda u bilo kom trenutku, ovi %zakoni fizike govore nam kako ce ona *izgledati bilo kada u buducnosti.) Drugo, +postoji pitanje pocetnog stanja Vaseljene. +Neki ljudi smatraju da bi nauka trebalo da *bude usredsredena samo na prvi deo: prema +njihovom uverenju, pitanje pocetnog stanja /predstavlja stvar metafizike ili religije. Oni +tvrde da je Bog, buduci svemoguc, mogao da /zapocne Vaseljenu na bilo koji nacin. Moda je*stvarno tako, ali u tom slucaju takode je +mogao da njen potonji razvoj ucini potpuno -proizvoljnim. No, kako izgleda, on se radije +opredelio za to da se Vaseljena razvija na (veoma pravilan nacin saglasan odredenim 'zakonima. Upravo stoga izgleda potpuno *razlono pretpostaviti da takode postoje 'zakoni koji upravljaju njenim pocetnim stanjem. .Pokazuje se da je veoma teko doci do teorije.koja bi opisala celu Vaseljenu. Stoga problem +razdvajamo na manje odeljke i nastojimo da /postavimo niz delimicnih teorija. Svaka od ovih.delimicnih teorija opisuje i predvida izvesnu +ogranicenu klasu posmatranja, zanemarujuci 0dejstva drugih svojstava ili ih predstavljajuci .jednostavnim nizovima brojeva. Nije iskljuceno.da je ovaj pristup potpuno pogrean. Ako sve +u Vaseljeni zavisi od svega drugog na neki (temeljni nacin, moe se pokazati da je ,nemoguce doci do potpunog reenja zasebnim *izucavanjem delova problema. No, u svakom 'slucaju, na ovaj nacin smo ostvarivali 0napredak u prolosti. Klasican primer ponovo je.Njutnova teorija gravitacije, koja nam govori ,da gravitaciona sila izmedu dva tela zavisi *samo od jedne njihove velicine, mase, pri )cemu je potpuno svejedno od cega se tela -sastoje. Uopte, naime, nije potrebno imati /teoriju o ustrojstvu i sastavu Sunca i planeta $da bi se izracunale njihove orbite. (Dananji naucnici opisuju Vaseljenu iz ,perspektive dve osnovne delimicne teorije - 0opte teorije relativnosti i kvantne mehanike. (One predstavljaju ogromna intelektualna /postignuca prve polovine naeg stoleca. Opta1teorija relativnosti opisuje gravitacionu silu i %makrokosmicko ustrojstvo Vaseljene - &ustrojstvo, naime, u rasponu od svega 1nekoliko milja do milion miliona miliona miliona *milja (jedinica iza koje se prua niz od .dvadeset cetiri nule), koliko iznosi velicina *Vaseljene dostupne posmatranjima. Kvantna -mehanika, sa druge strane, usredsredena je na*pojave izuzetno malih razmera, oko jednog -milionitog milionitog dela inca. Na alost, +poznato je da su ove dve teorije medusobno ,nesaglasne - one ne mogu obe biti ispravne. ,Jedno od glavnih pregnuca savremene fizike, (kao i sredinja tema ove knjige, jeste -traganje za novom teorijom koja bi obuhvatila&obe ove delimicne teorije. Posredi je /takozvana kvantna teorija gravitacije. Mi jo )ne raspolaemo takvom teorijom i sva je +prilika da je jo daleko dan kada cemo je +konacno imati, ali zato su nam vec poznata ,mnoga svojstva koja ona mora da poseduje. U +narednim poglavljima videcemo da smo vec u *prilicnoj meri upuceni u predvidanja koja 'moraju da proishode iz kvantne teorije gravitacije. .Ukoliko ste, dakle, uvereni da Vaseljena nije .proizvoljna, vec da njome upravljaju odredeni (zakoni, na kraju cete morati da spojite /delimicne teorije u jednu celovitu objedinjenu +teoriju koja ce opisivati sve u Vaseljeni. ,Postoji, medutim, jedan temeljni paradoks u +traganju za ovakvom celovitom objedinjenom /teorijom. Prethodno izloene zamisli o naucnim-teorijama zasnivaju se na pretpostavci da smo)mi razumna bica slobodna da prema elji *posmatraju Vaseljenu i da izvlace logicne 0zakljucke iz onoga to vide. U takvoj situaciji,razlono je pretpostaviti da se jo vie *moemo pribliiti zakonima koji vladaju .Vaseljenom. Ukoliko, medutim, uistinu postoji .celovita objedinjena teorija, ona bi, takode, )verovatno odredila naa delanja. Drugim .recima, sama teorija odredila bi ishod naeg 0traganja za njom! Ali zato bi ona odredila da ,mi dodemo do ispravnih zakljucaka na osnovu ,nalaza i posmatranja? Zar ona u podjednakoj +meri ne bi mogla da odredi da mi dodemo do 0pogrenih zakljucaka? Ili da uopte ne dodemo do zakljucaka? (Jedini odgovor koji ja mogu dati na ova (pitanja temelji se na Darvinovom nacelu -prirodnog odabiranja. Zamisao pociva na tome 0da ce se u bilo kojoj populaciji organizama to*se sami razmnoavaju javiti varijacije u (genetskom materijalu koje ce dovesti do )nastanka razlicitih jedinki. Ove razlike .pretpostavljaju da su neke jedinke vicnije od +drugih da dolaze do ispravnih zakljucaka o ,svetu to ih okruuje, da bi potom delale +saglasno tim zakljuccima. Te jedinke imaju .vie izgleda da preive i ostave potomstvo, 0tako da ce njihov nacin ponaanja i miljenja &odneti prevagu. Nesumnjivo je da je u .prolosti ono to nazivamo inteligencijom i (naucnim otkricem donosilo preimucstvo u -pogledu opstanka. No, nije sasvim izvesno da 0je to i dalje slucaj: naa naucna otkrica lako .nas sve mogu unititi - pa cak ako do toga i +ne dode, na nae izglede na opstanak lako (moe da nema nikakvog uticaja celovita .objedinjena teorija. Pod uslovom, medutim, da *se Vaseljena razvijala na pravilan nacin, %moemo pretpostaviti da ce razumske ,sposobnosti koje nam je podarilo odabiranje "vredeti i u traganju za celovitom +objedinjenom teorijom, te da nas tako nece navesti na pogrene zakljucke. )S obzirom na okolnost da su se delimicne )teorije kojima vec raspolaemo pokazale .dovoljne za dolaenje do tacnih predvidanja u.svim okolnostima osim onih krajnjih, traganje -za celovitom objedinjenom teorijom Vaseljene -teko da bi se moglo opravdati u prakticnom *pogledu. (Valja, medutim, primetiti da se .slicnim argumentima moglo pribeci i u slucaju .kako relativnosti, tako i kvantne mehanike, a +ove teorije pruile su nam kako nuklearnu /energiju, tako i mikroelektronsku revoluciju!) *Postavljanje celovite objedinjene teorije *moglo bi, dakle, da ne doprinese opstanku /nae vrste. Moda cak ne bi ni na koji nacin -uticalo na nacin ivota. Ali jo od osvita 1civilizacije ljudi se nisu zadovoljavali time da .vide dogadaje kao nepovezane i neobjanjive. )Umesto toga, upirali su se da proniknu u )skriveni poredak sveta. Mi danas i dalje )ceznemo da dokucimo zbog cega smo ovde i ,odakle poticemo. Najdublja ed covecanstva +za znanjem predstavlja dovoljno opravdanje /za nastavak naih traganja. A cilj koji imamo (pred sobom nije nita manje do potpuno &opisivanje Vaseljene u kojoj ivimo. 2. PROSTOR I VREME 0Nae sadanje zamisli o kretanju nebeskih tela1vode poreklo od Galileja i Njutna. Pre njih ljudi,su verovali Aristotelu koji je tvrdio da je .prirodno stanje tela mirovanje, odnosno da se *ono krece samo pod dejstvom neke sile ili ,podsticaja. Odavde je proishodilo da teko 0telo treba da pada bre od lakog, zato to ce %biti snanije privlaceno ka Zemlji. 1Iz aristotelovske tradicije takode je sledilo da -se do svih zakona koji upravljaju Vaseljenom .moe doci iskljucivo razmiljanjem: provera -kroz posmatranja uopte nije bila potrebna. &Niko pre Galileja nije mario za to da 0neposredno proveri da li tela razlicite teine ,uistinu padaju razlicitim brzinama. Postoji &prica o tome da je Galilej pokazao da +Aristotelovo uverenje nije ispravno na taj 0nacin to je pustio dva tela nejednake teine ,sa krivog tornja u Pizi. Epizoda je po svoj 6prilici izmiljena, ali Galilej je ipak ucinio neto0slicno: pustio je da se niz jednu glatku kosinu 0kotrljaju lopte razlicite teine. Situacija je /slicna onoj kada tela padaju okomito, ali ovde +je lake vriti posmatranje buduci da su )posredi manje brzine. Galilejeva merenja (pokazala su da je svako telo povecavalo )brzinu istom stopom, bez obzira na svoju /teinu. Na primer, ako pustite neku loptu niz -kosinu koja se sputa po jedan metar svakih (deset predenih metara, onda ce se lopta &kretati brzinom od oko jednog metra u (sekundi posle prve sekunde, dva metra u .sekundi posle druge sekunde, i tako dalje, bez0obzira na to koliko je teka. Razume se, olovo .ce padati bre od pera, ali to je samo stoga -to otpor vazduha usporava pero. Ukoliko se -puste da padnu dva tela na koja ne dejstvuje -mnogo otpor vazduha, kao to su, na primer, .dva olovna predmeta razlicite teine, ona ce padati istom brzinom. +Galilejeva merenja iskoristio je Njutn kao #osnovu za svoje zakone kretanja. U /Galilejevim ogledima, kako se telo kotrlja niz )kosinu na njega uvek dejstvuje ista sila 0(njegova teina), to za posledicu ima njegovo)stalno ubrzavanje. Ovo je pokazalo da se (stvarno dejstvo neke sile uvek ogleda u %promeni brzine tela, a ne u njegovom (pokretanju, kako se prethodno smatralo. ,Odavde je takode proishodilo da kad na telo /ne dejstvuje nikakva sila, ono ce nastaviti da *se krece pravolinijski istom brzinom. Ova ,zamisao prvi put je eksplicitno izloena u &Njutnovom delu Principia Mathematica, +objavljenom 1687, i poznata je kao Njutnov 0prvi zakon. Prema njemu, telo ce ubrzavati, ili /menjati brzinu, stopom koja je srazmerna sili. 0(Primera radi, ukoliko je sila dvostruko jaca i (ubrzanje je dvostruko vece.) Isto tako, )ubrzanje je manje to je veca masa (ili 1kolicina materije). (Ista sila koja dejstvuje na *telo dvostruko vece mase proizvece samo -polovinu prethodnog ubrzanja.) Kod automobila*se najcece srecemo sa primerom koji ovo 1ilustruje: to je motor jaci, vece je ubrzanje, .ali to su kola tea, ubrzanje je srazmerno manje sa istim motorom. )Pored zakona kretanja, Njutn je otkrio i ,zakon koji opisuje gravitacionu silu, prema +kome svako telo privlaci svako drugo silom -koja je srazmerna masi svakog od njih. Shodno.tome, sila koja dejstvuje izmedu dva tela bice)dvostruko jaca ukoliko se jednom od njih )(recimo, telu A) masa udvostruci. Ovo je 0upravo ono to bi se i ocekivalo, buduci da bi )se novo telo A moglo zamisliti kao da se -sastoji od dva tela prvobitne mase. Svako od 1njih privlacilo bi telo B prvobitnom silom. Prema.tome, ukupna sila izmedu tela A i tela B bice )dvostruko jaca od prvobitne sile. A ako, -recimo, jedno od tela stekne dvostruku masu, .a drugo trostruku, onda ce sila postati est -puta jaca. Odavde je sasvim jasno zato sva .tela padaju istom brzinom: telo dvostruko vece.teine bice privlaceno dvostruko vecom silom )gravitacije nadole, zato to mu je masa 'dvostruka veca. Prema Njutnovom drugom (zakonu, ova dva dejstva ce se medusobno .potpuno potrti, tako da ce ubrzanje biti isto u svim slucajevima. ,Njutnov zakon gravitacije takode nam govori *da je sila tee tim slabija to su tela )medusobno udaljenija. Prema ovom zakonu, -gravitaciono privlacenje neke zvezde iznosice-tacno jednu cetvrtinu privlacenja neke druge,)slicne zvezde koja se nalazi na polovini )udaljenosti prve. Ovaj zakon veoma tacno *predvida orbite Zemlje, Meseca i planeta. )Ukoliko bi zakon nalagao da gravitaciono 0privlacenje bre opada sa udaljenocu, orbite .planeta ne bi bile elipticne, vec bi spiralno *vodile ka Suncu. Ako bi ovo opadanje bilo *sporije, gravitaciono privlacenje dalekih (zvezda odnelo bi prevagu nad Zemljinim. /Kljucna razlika u zamislima Aristotela s jedne 0strane i Galileja i Njutna sa druge ocitovala se/u tome to je Aristotel verovao u povlaceno *stanje mirovanja, u kome bi se svako telo 0nalo kada na njega ne bi dejstvovali neka sila0ili podsticaj. tavie, on je smatrao da se i )Zemlja nalazi u stanju mirovanja. Ali iz .Njutnovih zakona je proishodilo da ne postoji .jedinstveni standard mirovanja. Podjednako bi /se moglo reci da se telo A nalazi u mirovanju, -dok se telo B krece stalnom brzinom u odnosu 0na telo A, kao i da telo B miruje, dok se telo A(krece. Primera radi, ako se za trenutak -zanemare okretanja Zemlje oko vlastite ose i .njeno kruenje oko Sunca, moglo bi se kazati /da se naa planeta nalazi u stanju mirovanja, (a da se jedan voz na njoj krece u smeru .severa brzinom od devedeset milja na cas, ba.kao to bi se moglo kazati da voz miruje dok .se Zemlja krece na jug istom brzinom. Ukoliko 0bi se izvrili opiti sa kretanjem tela u vozu, .pokazalo bi se da svi Njutnovi zakoni i dalje *ostaju na snazi. Na primer, igraci stonog ,tenisa u vozu ustanovili bi da se loptica u +svemu pokorava Njutnovim zakonima ba kao +da se sto nalazi pokraj pruge. Prema tome, 0nema nacina da se kae da li se voz ili Zemlja nalaze u stanju kretanja. ,Nepostojanje apsolutnog standarda mirovanja /znacilo je da nema nacina da se odredi da li se*dva dogadaja koja se zbivaju u razlicitim &vremenima odigravaju na istom mestu u /prostoru. Primera radi, pretpostavimo da naa ,ping pong loptica u vozu skakuce gore dole, -potpuno uspravno, udarivi pri tom dva puta 'istu tacku na stolu u razmaku od jedne .sekunde. Nekome ko stoji kraj pruge izgledalo /bi da su se ova dva odbijanja od stola odigrala-na razdaljini od oko 40 metara, zato to bi -voz prevalio tu udaljenost u jednoj sekundi. "Nepostojanje apsolutnog mirovanja +pretpostavljalo je, dakle, da se, protivno *Aristotelovom uverenju, ne moe odrediti .apsolutni poloaj u prostoru nekog dogadaja. 2Poloaji, zbivanja i udaljenosti izmedu njih bili0bi razliciti za osobu u vozu i osobu koja stoji .kraj pruge, a ni po cemu se jedan poloaj ne bi mogao pretpostaviti drugome. *Njutna je veoma zabrinjavalo ovo odsustvo /apsolutnog poloaja, ili apsolutnog prostora, 0kako je bio nazvan, zato to se nije slagalo sa-njegovom idejom o apsolutnom Bogu. U stvari, %on je odbio da prihvati nepostojanje /apsolutnog prostora, iako je ono proishodilo iz.njegovih zakona. Mnogi su ga kritikovali zbog 0ovog iracionalnog uverenja, a najglasniji je bio.biskup Berkeli, filozof koji je smatrao da su 0svi materijalni predmeti, kao i prostor i vreme,+samo opsena i privid. Kada je znameniti dr +Donson doznao za Berkelijevo miljenje, -uzviknuo je: "Evo kako ga pobijam!" i udario nogom o jedan veliki kamen. ,I Aristotel i Njutn verovali su u apsolutno .vreme. Smatrali su, naime, da je bespogovorno -moguce izmeriti interval izmedu dva dogadaja,-odnosno da bi ovo vreme bilo isto bez obzira ,na to ko ga meri, pod uslovom da se koristi &dobar casovnik. Vreme je bilo potpuno +zasebno i nezavisno od prostora. Za vecinu 0ljudi ovo bi bilo zdravorazumsko stanovite. Pa.ipak, mi smo morali da promenimo naa videnja0prostora i vremena. Iako su, kako izgleda, nae+zdravorazumske predstave sasvim na mestu sa0stvarima kao to su jabuke ili planete koje se )krecu srazmerno lagano, one potpuno gube .valjanost kada su posredi stvari koje se krecu(brzinom svetlosti ili sasvim blizu nje. )Cinjenicu da se svetlost krece konacnom, ,premda veoma velikom brzinom prvi je otkrio ,1676. godine danski astronom Ole Kristensen &Remer. On je uocio da vremena zalaska +Jupiterovih meseca iza velike planete nisu -pravilna, protivno ocekivanjima zasnovanim na(okolnosti da meseci krue oko Jupitera *postojanom brzinom. Kako Zemlja i Jupiter $krue oko Sunca, javlja se promena -udaljenosti medu njima. Remer je uocio da do -pomracenja Jupiterovih meseca dolazi kasnije 2to smo mi udaljeniji od Jupitera. On je izloio+pretpostavku da je razlog ovome to to je .svetlosti potrebno due da stigne do nas kada+smo udaljeniji. Njegova merenja varijacija .udaljenosti Zemlje od Jupitera nisu, medutim, -bila odvec precizna, tako da je proracunao da0brzina svetlosti iznosi 140.000 milja u sekundi,.dok mi danas znamo da ona, u stvari, dostie *186.000 milja u sekundi. Pa ipak, Remerov .podvig, koji se ogledao ne samo u tome to je&dokazao da se svetlost krece konacnom *brzinom, nego i u tome to je izmerio tu .brzinu, bio je izuzetan, buduci da je do njega-dolo jedanaest godina pre no to je Njutn *objavio svoje delo Principia Mathematica. (Valjana teorija o prostiranju svetlosti +postavljena je tek 1865, kada je britanski *fizicar Dejms Maksvel uspeo da objedini /delimicne teorije koje su do tada koricene da/bi se opisale sile elektriciteta i magnetizma. +Maksvelove jednacine predvidale su da se u )kombinovanom elektromagnetnom polju mogu .javiti talasni poremecaji, kao i da bi se oni *prostirali nepromenljivom brzinom, slicno ,talasicima na povrini mirne vode. Ukoliko *duina tih talasa (razdaljina izmedu dva 1susedna brega) iznosi metar ili vie, onda je tu#posredi ono to mi danas nazivamo .radio-talasima. Manje talasne duine poznate ,su kao mikrotalasi (nekoliko centimetara) i .infracrveni talasi (nekoliko desetohiljaditih -delova centimetra). Talasna duina vidljive .svetlosti iznosi izmedu cetrdeset i osamdeset 0milionitih delova centimetra. Jo manje talasne'duine poznate su kao ultraljubicasta )svetlost, rendgenski zraci i gama-zraci. $Maksvelova teorija predvidala je da .radio-talasi ili svetlosni talasi treba da se +krecu nepromenljivom brzinom. Ali Njutnova 'teorija odbacila je ideju o apsolutnom .mirovanju, tako da, ako je svetlost trebalo da)se krece nepromenljivom brzinom, onda je 0valjalo ustanoviti u odnosu na ta treba meriti,tu nepromenljivu brzinu. Stoga je izloena *pretpostavka o postojanju jedne supstance )nazvane 'eter' za koju se smatralo da se ,prostire svuda, cak i u 'praznom' prostoru. -Svetlosni talasi trebalo je da se krecu kroz -eter isto kao to zvucni talasi putuju kroz %vazduh, te bi se tako njihova brzina 'odredivala u odnosu na eter. Razliciti ,posmatraci, koji se krecu u odnosu na eter, 0videli bi kako svetlost ide ka njima razlicitim /brzinama, ali bi zato brzina svetlosti u odnosu+na eter ostala nepromenljiva. U konkretnom +slucaju, kako se Zemlja krece kroz eter na +svom kruenju oko Sunca, brzina svetlosti ,merena u smeru Zemljinog kretanja kroz eter 2(dakle, prilikom pribliavanja izvoru svetlosti) ,trebalo bi da bude veca od brzine svetlosti 'merene pod pravim uglom u odnosu na to *kretanje (dakle, kada se ne pribliavamo /izvoru). Godine 1887, Albert Majklson (koji je -kasnije postao prvi Amerikanac koji je dobio +Nobelovu nagradu za fiziku) i Edvard Morli 0izveli su veoma precizan ogled u Kejzovoj koli/primenjene nauke u Klivlendu. Oni su uporedili /brzinu svetlosti u smeru Zemljinog kretanja sa .brzinom svetlosti koja dolazi pod pravim uglom.u odnosu na Zemljino kretanje. Na svoje veliko)iznenadenje, ustanovili su da su ove dve brzine u dlaku iste. (Izmedu 1887. i 1905. preduzeto je vie +pokuaja, medu kojima je najpoznatiji bio -onaj holandskog fizicara Henrika Lorenca, da /se objasni ishod Majklson-Morlijevog ogleda iz (perspektive pretpostavke da se predmeti +saimaju, a casovnici usporavaju prilikom *kretanja kroz eter. Medutim, u znamenitom (tekstu iz 1905. jedan do tada nepoznati (cinovnik vajcarskog patentnog zavoda, 0Albert Ajntajn, istakao je da je cela zamisao &o eteru nepotrebna, pod uslovom da se +odustane od ideje o apsolutnom vremenu. Do -slicnog zakljucka doao je nekoliko nedelja *kasnije vodeci francuski matematicar Anri -Poankare, koji je ovom problemu pristupio iz 'matematickog ugla. Danas se Ajntajnu /pripisuje u zaslugu nova teorija, ali znacajan ,obol njenom postavljanju dao je i Poankare. 0Temeljni postulat teorije relativnosti, kako je )ona nazvana, bio je da bi zakoni prirode .trebalo da budu isti za sve posmatrace koji se.slobodno krecu, bez obzira na njihovu brzinu. ,Ovo je vailo za Njutnove zakone kretanja, (ali sada su ovom idejom obuhvacene jo +Maksvelova teorija i brzina svetlosti: svi *posmatraci trebalo bi da mere istu brzinu -svetlosti, bez obzira na to kojom se brzinom (krecu. Ova jednostavna zamisao imala je +izuzetne posledice. Moda je najpoznatija )medu njima istovetnost mase i energije - #velicina obuhvacenih Ajntajnovom )znamenitom jednacinom, E = mc2 (gde je E +energija, m masa, a c brzina svetlosti). S &obzirom na jednakost energije i mase, )energija koju neko telo dobija kretanjem +dovece do povecanja njegove mase. Drugim -recima, to ce oteati povecanje brzine. Ovo -dejstvo dolazi do izraaja tek kod objekata %koji se krecu brzinom sasvim bliskom 0svetlosnoj. Na primer, pri brzini koja dostie *deset odsto svetlosne, masa nekog objekta +samo je 0,5 odsto veca od normalne, dok je .pri devedeset odsto brzine svetlosti masa tela,vie nego dvostruko veca od normalne. Kako .se neki objekat pribliava brzini svetlosti, +masa mu se jo bre povecava, tako da je +potrebno sve vie energije da bi on dalje -ubrzavao. Telo, zapravo, uopte ne moe da -dostigne brzinu svetlosti, buduci da bi mu u 'tom trenutku masa postala beskrajna, a /shodno jednakosti mase i energije za to bi bila-potrebna beskrajna kolicina energije. Upravo -je ovo razlog to je svaki normalan objekat +zauvek ogranicen relativnocu na kretanja 0brzinama niim od svetlosne. Jedino svetlost i .ostali talasi koji nemaju stvarnu masu mogu dase krecu brzinom svetlosti. .Podjednako znacajna posledica relativnosti bio.je nacin na koji je ona revolucionisala nae *zamisli o prostoru i vremenu. U Njutnovoj +teoriji, ukoliko je jedan impuls svetlosti +upucen sa jednog mesta na drugo, razliciti .posmatraci sloili bi se o trajanju njegovog /kretanja (buduci da je vreme apsolutno), ali se,ne bi uvek saglasili oko toga koliki je put .preao (buduci da prostor nije apsolutan). S .obzirom na to da je brzina svetlosti naprosto 0razdaljina koju je impuls prevalio podeljena sa -utroenim vremenom, razliciti posmatraci bi 3merili razlicite brzine svetlosti. U relativnosti, 0naprotiv, svi posmatraci, moraju se sloiti oko+toga kojom se brzinom svetlost krece. Oni, .medutim, jo ne postiu saglasnost oko toga 1koju je razdaljinu svetlost prevalila, tako da i /dalje moraju meriti razlicito utroeno vreme. *(Ovo utroeno vreme nije nita drugo do +brzina svetlosti o kojoj se svi posmatraci )slau pomnoena sa razdaljinom koju je 'svetlost prevalila, o kojoj ne postoji 1saglasnost.) Drugim recima, teorija relativnosti -oznacila je kraj ideje o apsolutnom vremenu! *Kako izgleda, svaki posmatrac mora da ima +vlastitu meru vremena, odredenu casovnikom -koji ima uza se, odnosno istovetni casovnici *koje imaju razliciti posmatraci ne moraju nuno da budu u saglasnosti. .Svaki posmatrac moe da upotrebi radar da bi ,odredio gde se i kada zbio neki dogadaj, na .taj nacin to bi uputio impuls svetlosti ili ,radio-talase. Jedan deo talasa dati dogadaj *odraava natrag i posmatac meri vreme za -koje se vratio ovaj odjek. Vreme dogadaja se (potom ustanovljava kao polovina vremena &proteklog izmedu upucivanja impulsa i 'primanja odjeka, dok je mesto dogadaja )polovina vremena utroenog na dvosmerno +putovanje pomnoena sa brzinom svetlosti. ,(Dogadaj u ovom smislu jeste neto to se ,zbiva u jednoj odredenoj tacki prostora i u $nekom odredenom vremenu.) Ova ideja 1prikazana je na ilustraciji 2.1. koja predstavlja$primer prostorvremenskog dijagrama. ,Primenjujuci ovaj postupak, posmatraci koji -se krecu jedan u odnosu na drugoga pripisace .razlicita vremena i poloaje istom dogadaju. (Merenje nekog odredenog posmatraca nije /tacnije od merenja bilo kog drugog, ali sva su (merenja povezana. Svaki posmatrac moe .precizno da ustanovi koje ce vreme i poloaj .pripisati dogadaju bilo koji drugi posmatrac, -pod uslovom da zna njegovu relativnu brzinu. %Danas koristimo upravo ovaj metod za -precizno merenje razdaljina, buduci da smo u -stanju da vreme merimo tacnije nego duine. 0U stvari, metar se definie kao razdaljina koju)svetlost prevali za 0,000000003335640952 (sekunde, mereno cezijumskim casovnikom. .(Razlog za ovaj poseban broj jeste to to on /odgovara istorijskoj definiciji metra odredenoj-dvema oznakama na jednoj narocitoj ipki od +platine koja se cuva u Parizu.) Isto tako, +moemo da koristimo jednu pogodniju, novu *jedinicu duine koja se naziva svetlosna *sekunda. Ona se jednostavno definie kao *razdaljina koju svetlost prevali u jednoj (sekundi. U teoriji relativnosti mi sada +odredujemo razdaljinu jedinicama vremena i .brzinom svetlosti, odakle automatski sledi da .ce svaki posmatrac ustanoviti da svetlost ima +istu brzinu (prema definciji, 1 metar puta $0,000000003335640952 sekunde). Nema ,nikakve potrebe za uvodenjem ideje o eteru, -cije se postojanje u svakom slucaju ne moe .otkriti, kako je to pokazao Majklson-Morlijev /ogled. Teorija relativnosti, medutim, primorava)nas da iz temelja izmenimo nae ideje o &prostoru i vremenu. Moramo prihvatiti +cinjenicu da vreme nije potpuno odvojeno i ,nezavisno od prostora, vec da je povezano sa.njim i da obrazuje jednu celinu koja se nazivaprostorvreme. .Okolnost da se poloaj jedne tacke u prostoru#moe opisati trima brojevima, ili (koordinatama, predstavlja dobro poznatu .stvar. Primera radi, moe se reci da je neka ,tacka u sobi udaljena sedam stopa od jednog -zida, tri stope od drugog i da se nalazi pet .stopa iznad poda. Isto se tako moe odrediti .da je neka tacka na datoj geografskoj duini 0i geografskoj irini, kao i na datoj nadmorskoj0visini. Sasvim se slobodno mogu upotrebiti bilo (koje tri pogodne koordinate, premda one .imaju samo ogranicen raspon vanosti. Teko .da bi se poloaj Meseca odredivao jedinicama .milja severno i zapadno od Pikadili Sirkusa i *jedinicama stopa nadmorske visine. Umesto )toga, odredio bi se preko udaljenosti od /Sunca, udaljenosti od ravni orbitiranja planeta,i ugla izmedu linije koja povezuje Mesec sa *Suncem i linije koja spaja Sunce sa nekom ,oblinjom zvezdom, kakva je Alfa Kentaura. /No, cak ni ove koordinate ne bi bile od velike 0koristi pri opisivanju poloaja Sunca u naoj 3Galaksiji ili poloaja nae Galaksije u lokalnoj /grupi galaksija. U stvari, svekolika Vaseljena -mogla bi se opisati posredstvom niza odlomaka-koji se preklapaju. Kod svakog odlomka moe /se upotrebiti razliciti skup od tri koordinate )kojim bi se odredio poloaj neke tacke. /Jedan dogadaj je neto to se zbiva u jednoj %odredenoj tacki u prostoru i u nekom 'odredenom vremenu. On se, dakle, moe /odrediti sa cetiri broja ili koordinate. Izbor *koordinata ponovo je proizvoljan; mogu se 'primeniti bilo koje tri dobro odredene +prostorne koordinate i bilo koja vremenska ,mera. U relativnosti nema, zapravo, razlike +izmedu prostornih i vremenskih koordinata, /ba kao to nema ni razlike izmedu bilo koje ,dve prostorne koordinate. Moe se odabrati -novi skup koordinata u kome, na primer, prva -prostorna koordinata predstavlja kombinaciju .stare prve i druge prostorne koordinate. Tako,-recimo, umesto da merimo poloaj neke tacke ,na Zemlji u miljama severno od Pikadilija i 'miljama zapadno od Pikadilija, mogu se .upotrebiti milje severoistocno od Pikadilija, +odnosno milje severozapadno od Pikadilija. 0Slicno tome, u relativnosti, moe se primeniti ,nova vremenska koordinata koja bi bila zbir .starog vremena (u sekundama) i udaljenosti (u -svetlosnim sekundama) severno od Pikadilija. )Cesto je od pomoci razmiljati o cetiri +koordinate nekog dogadaja kao o odrednicama!koje fiksiraju njegov poloaj u %cetvorodimenzionom prostoru nazvanom $prostorvreme. Nemoguce je zamisliti -cetvorodimenzioni prostor. Meni licno cak je 0teko da predocim sebi i trodimenzioni prostor!#Lako je, medutim, crtati dijagrame .dvodimenzionih prostora, kakva je, na primer, 'povrina Zemlje. (Povrina Zemlje je .dvodimenziona zato to poloaj neke tacke na,njoj moe biti odreden dvema koordinatama, .geografskom irinom i geografskom duinom.) +Ja cu nacelno koristiti dijagrame u kojima *vreme raste nagore, a jedna od prostornih ,dimenzija je prikazana vodoravno. Druge dve -prostorne dimenzije su prenebregnute ili je, ponekad, jedna od njih oznacena $perspektivom. (Posredi su takozvani /prostorvremenski dijagrami, kao to je onaj na0ilustraciji 2.1). Na primer, na ilustraciji 2.2 #vreme se meri nagore u godinama, a (udaljenost du linije od Sunca do Alfe +Kentaura prikazana je vodoravno u miljama. #Putanje Sunca i Alfe Kentaura kroz ,prostorvreme date su kao uspravne linije sa .leve i desne strane dijagrama. Zrak svetlosti )sa Sunca krece se dijagonalnom linijom i ,potrebne su mu oko cetiri godine da prevali put od Sunca do Alfe Kentaura. *Kao to smo videli, Maksvelove jednacine -predvidaju da brzina svetlosti treba da bude 0svuda ista, bez obzira na brzinu izvora, to je-i potvrdeno preciznim merenjima. Odavde sledi+da ako u nekom datom trenutku bude odaslat .jedan impuls svetlosti iz neke date tacke, on 1ce se, kako vreme protice, iriti u obliku lopte3svetlosti ciji su velicina i poloaj nezavisni od ,brzine izvora. Posle jednog milionitog dela -sekunde poluprecnik svetlosne lopte iznosice -300 metara; posle dva milionita dela sekunde .on ce dostici 600 metara; i tako dalje. Stvar -ce u svemu nalikovati talasima koji se ire (mirnom povrinom vode na koju je bacen 'kamen. Talasi se ire u koncentricnim ,krugovima koji postaju sve veci s prolaskom ,vremena. Ako se zamisli trodimenzioni model +koji se sastoji od dvodimenzione povrine /vode i jedne dimenzije vremena, ireci talasi 0obrazovali bi kupu ciji se vrh nalazi na mestu i(u vremenu gde je, odnosno kada je kamen 0pogodio vodu (Ilus. 2.3). Slicno tome, svetlost )koja se iri od nekog dogadaja obrazuje (trodimenzionu kupu u cetvorodimenzionom ,prostorvremenu. Ova kupa se naziva svetlosna(kupa buducnosti dogadaja. Na isti nacin 'moemo nacrtati i drugu kupu, nazvanu 0svetlosna kupa prolosti, koja predstavlja niz ,dogadaja sa kojih je jedan impuls svetlosti .kadar da stigne do nekog datog dogadaja (Ilus.2.4). -Svetlosne kupe prolosti i buducnosti nekog ,dogadaja P dele prostorvreme u tri podrucja *(Ilus. 2.5). Apsolutna buducnost dogadaja +predstavlja podrucje unutar svetlosne kupe &buducnosti dogadaja P. To je niz svih *dogadaja do kojih moe doci pod uticajem +onoga to se zbilo u P. Do zbivanja izvan (svetlosne kupe dogadaja P ne mogu stici 2signali sa P zato to nita nije u stanju da se -krece bre od svetlosti. Na njih, dakle, ne /moe uticati ono to se zbiva u P. Apsolutna +prolost dogadaja P jeste podrucje unutar +svetlosne kupe prolosti. To je skup svih /dogadaja sa kojih signali to se krecu brzinom1svetlosti ili ispod nje mogu stici do P. Posredi .je, dakle, skup svih dogadaja koji mogu imati .uticaj na ono to se zbiva u P. Ako neko zna )ta se zbiva u nekom odredenom trenutku 'svuda u podrucju koje se nalazi unutar /svetlosne kupe prolosti dogadaja P, mogao bi /da predvidi ta ce se odigrati u P. Preostalo &podrucje prostorvremena ne pripada ni 0buducoj ni proloj svetlostnoj kupi dogadaja P.,Zbivanja iz tog podrucja ne mogu uticati na *dogadaj P, niti on moe uticati na njih. *Primera radi, ako bi se dogodilo da Sunce ,prstane da sija uprvo u ovom casu, to ne bi ,imalo uticaja na zbivanja na Zemlji u istom -trenutku, zato to bi se ona nalazila izvan .svetlosne kupe dogadaja gaenja Sunca (Ilus. .2.6). Mi bismo o tome doznali tek kroz neto )vie od osam minuta, koliko je potrebno .svetlosti da prevali put od Sunca do nas. Tek -tog bi se trenutka dogadaji na Zemlji nali *unutar svetlosne kupe buducnosti dogadaja .gaenja Sunca. Slicno tome, mi ne znamo ta ,se u ovom trenutku zbiva dalje u Vaseljeni: *svetlost koju vidimo sa dalekih galaksija /otisnula se sa njih pre mnogo miliona godina, a.u slucaju najudaljenijih objekata koje vidimo *svetlost se otisnula na svoj put pre osam *hiljada miliona godina. Shodno tome, kada ,bacimo pogled prema Vaseljeni, mi je vidimo kakva je bila u prolosti. -Ukoliko se zanemare gravitaciona dejstva, kao1to su ih prenebregli Ajntajn i Poankare 1905,&onda imamo posla sa posebnom teorijom !relativnosti. Za svaki dogadaj u (prostorvremenu moemo da sazdamo jednu *svetlosnu kupu (skup svih mogucih putanja ,svetlosti koju u prostorvremenu emituje taj /dogadaj), a buduci da je brzina svetlosti ista +kod svakog dogadaja i u svim pravcima, sve ,svetlosne kupe bice istovetne i sve ce biti .upravljene u istom pravcu. Ova teorija takode /nam govori da se nita ne moe kretati bre /od svetlosti. Odavde proishodi da putanja bilo +kog objekta kroz prostor i vreme mora biti (predstavljena linijom koja lei unutar .svetlosne kupe svakog dogadaja na njoj (Ilus. 2.7). )Posebna teorija relativnosti pokazala se -veoma uspena u objanjavanju okolnosti da #brzina svetlosti izgleda ista svim !posmatracima (kako je to pokazao -Majklson-Morlijev opit) i u opisivanju onoga -to se dogada kada se stvari krecu brzinama 0bliskim brzini svetlosti. Ona je, medutim, bila -nesaglasna sa Njutnovom teorijom gravitacije .koja je tvrdila da se tela medusobno privlace ,silom koja zavisi od razdaljine medu njima. -Ovo je znacilo da ako neko pomeri dalje jedno+od tela, sila kojom ono dejstvuje na drugo +istog trenutka bi se smanjila. Ili, drugim .recima, gravitaciona dejstva trebalo bi da se )krecu beskrajnom brzinom, umesto brzinom .svetlosti ili ispod nje, kako je to zahtevala +posebna teorija relativnosti. Ajntajn je -preduzeo vie bezuspenih pokuaja izmedu -1908. i 1914. da dode do teorije gravitacije 0koja bi bila saglasna sa teorijom relativnosti. +Konacno, 1915, postavio je teoriju koju mi ,danas nazivamo opta teorija relativnosti. .Ajntajn je doao na revolucionarnu zamisao -da gravitacija nije sila kao druge sile, vec )posledica cinjenice da prostorvreme nije -ravno, protivno prethodnom optem ubedenju: 1ono je zakrivljeno, ili 'savijeno', pod uticajem .rasporeda mase i energije u njemu. Tela poput %Zemlje nisu bila sazdana da se krecu /zakrivljenim orbitama pod dejstvom sile tee; (umesto toga, ona se krecu gotovo pravom 'putanjom u zakrivljenom prostoru, a ta +trajektorija naziva se geodezijska linija. .Geodezijska linija je najkraca (ili najdua) ,putanja izmedu dve oblinje tacke. Primera (radi, povrina Zemlje je dvodimenzioni -zakrivljeni prostor. Geodezijska linija se u 'slucaju Zemlje naziva veliki krug i on *predstavlja najkraci put izmedu dve tacke -(Ilus. 2.8). Buduci da je geodezijska linija 'najkraca putanja izmedu dva aerodroma, .upravo je to put na koji ce navigator uputiti -pilota. U optoj relativnosti, tela se uvek )krecu pravolinijski u cetvorodimenzionom ,prostorvremenu, ali nam svejedno izgleda da $idu zakrivljenim putanjama u naem *trodimenzionom prostoru. (Ovo nalikuje na &posmatranje aviona koji prelece preko 0brdovitog predela. Iako on leti pravolinijski u -trodimenzionom prostoru, njegova senka klizi -zakrivljenom putanjom po dvodimenzionom tlu.)-Masa Sunca zakrivljuje prostorvreme na takav /nacin da, iako se Zemlja krece pravolinijski u (cetvorodimenzionom prostorvremenu, nama )izgleda da ona putuje krunom orbitom u *trodimenzionom prostoru. U stvari, orbite )planeta koje predvida opta relativnost ,gotovo su potpuno istovetne sa onima na koje&ukazuje Njutnova teorija gravitacije. ,Medutim, u slucaju Merkura, koji je, buduci 0planeta najblia Suncu, izloen najsnanijem -gravitacionom dejstvu, te stoga ima prilicno 0iduenu orbitu, opta relativnost predvida da .bi velika poluosa elipse trebalo da se okrece (oko Sunca brzinom od oko jedan stepen u .deset hiljada godina. Iako je ovo sasvim mala .vrednost, ona je bila uocena jo pre 1915. i )posluila je kao jedna od prvih potvrda /Ajntajnove teorije. Poslednjih godina radarom)su izmerena jo manja odstupanja orbita -drugih planeta od predvidanja proisteklih iz $Njutnovog zakona; za ova odstupanja "ustanovljeno je da su saglasna sa #predvidanjima opte relativnosti. 0I svetlosni zraci se moraju drati geodezijske /linije u prostorvremenu. Okolnost da je prostor-zakrivljen i ovde znaci da svetlost ostavlja *utisak kao da se ne krece pravolinijski u .prostoru. Opta relativnost usitinu predvida &zakrivljavanje svetlosti pod dejstvom +gravitacionog polja. Primera radi, teorija .predvida da ce svetlosne kupe tacaka u blizini*Sunca biti malo nagnute unutra usled mase *nae zvezde. Ovo znaci da ce svetlost sa +neke daleke zvezde koja prode pokraj Sunca -biti skrenuta za jedan mali ugao, to ce za -posledicu imati da nekom posmatracu na Zemlji)izgleda da se ta zvezda nalazi na drugom 1mestu (Ilus. 2.9). Razume se, ako bi svetlost sa -date zvezde uvek prolazila pokraj Sunca, onda2ne bismo bili u stanju da kaemo da li je dolo -do skretanja svetlosti ili se zvezda uistinu -nalazi tamo gde je mi vidimo. Kako, medutim, *Zemlja krui oko Sunca, razlicite zvezde *izgleda kao da zalaze iza njega, pri cemu /dolazi do skretanja njihove svetlosti. One tako,menjaju svoj relativan poloaj u odnosu na druge zvezde. -Normalno je veoma teko uociti ovaj efekat, (zato to svetlost sa Sunca onemogucuje ,posmatranje zvezda koje se pojavljuju blizu +njega na nebu. To je, medutim, ipak moguce (uciniti za vreme pomracenja Sunca, kada *Mesec zaprecava svetlost sa nae zvezde. -Ajntajnovo predvidanje skretanja svetlosti .nije se moglo odmah proveriti 1915, buduci da /je u jeku bio prvi svetski rat, tako da je tek +1919. jedna britanska ekspedicija, koja je &pratila pomracenje iz Zapadne Afrike, .pokazala da svetlost uistinu biva skrenuta pod,dejstvom Sunca, ba kao to je teorija to -predvidala. Ovaj dokaz jedne nemacke teorije ,koji su ostvarili britanski naucnici bio je )pozdravljen kao cin pomirenja dve zemlje 0posle rata. Ima stoga ironije u okolnosti da su /potonja ispitivanja fotografija snimljenih pri )toj ekspediciji pokazala da su postojale ,greke velike kao i efekti koje je valjalo 2izmeriti. Zabeleeni nalazi predstavljali su puku2srecu ili slucaj dobijanja eljenih ishoda, to +nipoto nije bilo retko u istoriji nauke. .Skretanje svetlosti bilo je, medutim, pouzdano+i precizno potvrdeno vecim brojem kasnijih posmatranja. 0Iz opte relativnosti takode je proishodilo da ,vreme treba da tece sporije u blizini nekog /masivnog tela kakva je Zemlja. To je stoga to/postoji odnos izmedu energije svetlosti i njene/ucestalosti (odnosno, broja talasa svetlosti u *sekundi): to je veca energija, via je .ucestalost. Kako se svetlost krece nagore kroz/Zemljino gravitaciono polje, ona gubi energiju,.pa joj se tako i ucestalost smanjuje. (Drugim -recima, povecava se duina intervala izmedu (dva susedna brega talasa.) Nekome ko se 0nalazi na velikoj visini izgledalo bi da se sve -dole zbiva nekako usporenije. Ovo predvidanje$provereno je 1962. pomocu dva veoma -precizna casovnika koja su postavljena na vrh.i dno jednog vodotornja. Ustanovljeno je da je/casovnik na dnu, koji je bio blii tlu, iao $sporije, sasvim u skladu sa optom -relativnocu. Razlika u brzini casovnika na /raznim visinama iznad Zemlje danas ima i veliki&prakticni znacaj, s obzirom na razvoj -izuzetno preciznih navigacionih sistema koji 0se temelje na signalima sa satelita. Ukoliko bi -se prenebregla predvidanja koja proishode iz .opte relativnosti, izracunati poloaj neke *tacke mogao bi da bude pogrean za vie milja! *Njutnovi zakoni kretanja oznacili su kraj +zamisli o apsolutnom poloaju u prostoru. -Teorija relativnosti odbacila je i apsolutno 'vreme. Razmotrimo slucaj dva blizanca. /Zamislimo da jedan od njih ode da ivi na vrhu+neke planine, dok drugi rei da ostane na -nivou mora. Ako bi se ponovo sreli, jedan bi 0bio stariji od drugoga. U ovom slucaju razlika u.starosti bila bi veoma mala, ali bi se znatno .povecala ako bi jedan od blizanaca otiao na +dugo putovanje kosmickim brodom koji bi se .kretao brzinom sasvim bliskom svetlosnoj. Kada0bi se vratio, bio bi znatno mladi od brata koji -je ostao na Zemlji. Ova situacija poznata je #kao paradoks blizanaca, ali ona je )paradoksalna samo ako se negde u zaumlju )krije predrasuda o apsolutnom vremenu. U ,teoriji relativnosti ne postoji jedinstveno -apsolutno vreme, vec svaka jedinka ima svoje -licno merenje vremena koje zavisi od toga gdese nalazi i kako se krece. ,Pre 1915, za prostor i vreme se smatralo da .predstavljaju nepromenljive arene u kojima se -zbivaju dogadaji, ali i na koje ne utice ono 1to se u njima odigrava. Ovo je vailo cak i u 0slucaju posebne teorije relativnosti. Tela su se4kretala, sile su privlacile i odbijale, ali vreme i /prostor naprosto su nastavljali da postoje, ne .trpeci nikakav uticaj. Bilo je stoga prirodno -zakljuciti da su prostor i vreme beskonacni. +Situacija je, medutim, sasvim razlicita iz 1perspektive opte teorije relativnosti. Prostor ,i vreme sada su dinamicka svojstva: kada se ,neko telo krece ili neka sila dejstvuje, to /utice na zakrivljenost prostora i vremena ba &kao to, sa svoje strane, ustrojstvo .prostorvremena utice na nacin na koji se tela /krecu i sile dejstvuju. Prostor i vreme ne samo)to vre uticaj na sve to se zbiva u ,Vaseljeni, nego i trpe uticaj svega to se +odigrava u njoj. Ba kao to se ne moe -govoriti o dogadajima u Vaseljeni bez pojmova+prostora i vremena, isto je tako u optoj .relativnosti besmisleno govoriti o prostoru i !vremenu izvan granica Vaseljene. *U potonjim decenijama, ovo novo shvatanje ,prostora i vremena revolucionisalo je nae .videnje Vaseljene. Stara zamisao o sutinski *nepromenljivoj Vaseljeni koja je mogla da *postoji i da nastavi da postoji unedogled &zamenjena je predstavom o dinamicnoj, 0irecoj Vaseljeni koja je, kako izgleda, pocela+pre nekog konacnog vremena i koja se moe (okoncati posle nekog konacnog vremena u &buducnosti. Ova revolucija predmet je -narednog poglavlja. A godinama kasnije ona ce+takode predstavljati polazite mog rada u 1teorijskoj fizici. Roder Penrouz i ja pokazali &smo da iz Ajntajnove opte teorije /relativnosti proishodi da Vaseljena mora imati pocetak i, moda, kraj. 3. VASELJENA KOJA SE IRI *Ukoliko se baci pogled prema nebu za neke .vedre noci bez mesecine, sva je prilika da ce /najsjajnija tela na njemu biti planete Venera, )Mars, Jupiter i Saturn. Videce se takode +veoma veliki broj zvezda, koje su prilicno ,slicne naem Suncu, ali su na znatno vecoj ,udaljenosti od nas. Neke od ovih nepomicnih )zvezda, medutim, kao da ipak sasvim malo .menjaju medusobni poloaj kako Zemlja krui &oko Sunca: one, zapravo, uopte nisu -nepomicne! Do ovoga dolazi stoga to su nam /one srazmerno blizu. Prilikom kruenja Zemlje /oko Sunca mi ih vidimo iz razlicitih poloaja .spram zaleda udaljenijih zvezda. Ovo je srecna%okolnost, zato to nam omogucuje da (neposredno izmerimo razdaljinu koja nas ,razdvaja od tih zvezda: to su, naime, one 3blie, to vie izgleda da se pomeraju. Najblia )zvezda, ciji je naziv Proksima Kentaura, /nalazi se, kako je ustanovljeno, na udaljenosti0od oko cetiri svetlosne godine (svetlosti sa nje+potrebne su oko cetiri godine da stigne do -Zemlje), odnosno od oko dvadeset tri miliona -miliona milja. Vecina ostalih zvezda koje su /vidljive golim okom nalazi se na razdaljini od +nekoliko stotina svetlosnih godina od nas. -Poredenja radi, od naeg Sunca razdvaja nas .pukih osam svetlosnih minuta! Vidljive zvezde ,izgledaju razmetene po celom nocnom nebu, ,ali su posebno usredsredene u jednom pojasu ,koji nazivamo Mlecni Put. Jo 1750. godine 0neki astronomi su izloili zamisao o tome da bi.se izgled Mlecnog Puta mogao objasniti ukoliko)bi se vecina vidljivih zvezda nalazila u /konfiguraciji diskolikog oblika, ciji je jedan /vid spiralna galaksija. Samo nekoliko decenija /kasnije, astronom ser Vilijem Herel potvrdio "je ispravnost ove ideje mukotrpno /katalogizujuci poloaje i udaljenosti velikog $broja zvezda. No, bez obzira na to, ,pretpostavka je bila potpuno prihvacena tek pocetkom ovog stoleca. +Nae moderne predstave o Vaseljeni poticu -tek iz 1924, kada je americki astronom Edvin -Habl pokazao da naa Galaksija nije jedina. -Postoje, zapravo, jo mnoge druge, a izmedu (njih se pruaju ogromni potezi praznog ,prostora. Da bi ovo dokazao, on je morao da .odredi udaljenost ovih drugih galaksija, koje *su toliko daleko da odista, za razliku od ,oblinjih zvezda, izgleda da su nepomicne. -Habl je zbog toga bio prinuden da se koristi 'posrednim metodima merenja razdaljina. )Prividni sjaj jedne zvezde zavisi od dva .cinioca: od kolicine svetlosti koju ona zraci .(sjajnost) i od udaljenosti od nas. U slucaju -oblinjih zvezda, u prilici smo da izmerimo .njihov prividni sjaj i njihovu udaljenost, te (tako moemo da ustanovimo kolika im je *sjajnost. U tom slucaju, kada bismo znali ,sjajnost zvezda u drugim galaksijama, mogli )bismo da im izracunamo udaljenost na taj 3nacin to bismo im izmerili prividni sjaj. Habl je.uocio da izvesni tipovi zvezda uvek imaju istu-sjajnost kada se nalaze dovoljno blizu da to *moemo izmeriti; stoga, zakljucio je on, -ukoliko bismo pronali takve zvezde u nekoj /drugoj galaksiji, mogli bismo pretpostaviti da .imaju istu sjajnost, to bi nam omogucilo da .izracunamo udaljenost do te galaksije. Ako bi /nam to polo za rukom u slucaju vie zvezda u-istoj galaksiji i ukoliko bi nai proracuni .ukazivali uvek na istu udaljenost, onda bismo ,se sasvim mogli pouzdati u dobijene nalaze. &Na ovaj nacin Edvin Habl je ustanovio .udaljenosti devet galaksija. Mi danas znamo da/je naa Galaksija samo jedna od nekih stotinu +hiljada miliona koje se mogu videti pomocu +modernih teleskopa, pri cemu svaka od njih .sadri po priblino stotinu hiljada miliona 0zvezda. Ilustracija 3.1 pokazuje jednu spiralnu ,galaksiju koja izgleda upravo onako kako bi +nekom iz neke druge galaksije morao, prema /naem uverenju, izgledati na Mlecni Put. Mi ,ivimo u Galaksiji ciji precnik iznosi oko ,stotinu hiljada svetlosnih godina i koja se )lagano okrece; zvezde u njenim spiralnim -kracima naprave pun krug oko njenog sredita)jednom u svakih nekoliko stotina miliona *godina. Nae Sunce je samo obicna, uta /zvezda, prosecne velicine, koja se nalazi blizu/unutranje ivice jednog od spiralnih krakova. -Nema nikakve sumnje u to da smo prevalili dug,put od vremena Aristotela i Ptolemeja, kada /smo smatrali da je Zemlja sredite Vaseljene! /Zvezde se nalaze na toliko velikoj udaljenosti -da nam izgledaju samo kao tackice svetlosti. -Nismo u stanju da razaberemo njihovu velicinu'ili njihov oblik. Kako onda moemo da -razlikujemo pojedine tipove zvezda? U slucaju)ogromne vecine zvezda postoji samo jedno *osobeno svojstvo koje moemo da uocimo - .boja njihove svetlosti. Njutn je ustanovio da -ako svetlost sa Sunca prode kroz komad stakla,trougaonog oblika, nazvan prizma, ona ce se /razloiti na sastavne boje (njen spektar) kao ,kod duge. Ako usredsredimo teleskop na neku ,pojedinacnu zvezdu ili galaksiju, na slican ,nacin bismo dobili spektar njene svetlosti. .Razlicite zvezde imaju razlicite spektre, ali .relativni sjaj razlicitih boja uvek je sasvim .onakav kakav bi se ocekivao kod svetlosti to&je emituje neko telo u stanju crvenog 0usijanja. (U stvari, svetlost koju emituje neko .neprozirno telo u stanju crvenog usijanja ima +osoben spektar koji zavisi samo od njegove *temperature - takozvani termicki spektar. #Ovo znaci da moemo da ustanovimo +temperaturu zvezde na osnovu spektra njene 2svetlosti.) tavie, ustanovljava se da izvesne ,sasvim specificne boje nedostaju iz spektra ,zvezda, a te nedostajuce boje mogu varirati (od zvezde do zvezde. Buduci da znamo da -svaki hemijski elemenat apsorbuje osoben niz +veoma specificnih boja, poredenjem ovih sa ,onima koje nedostaju iz spektra neke zvezde +moemo tacno da odredimo koji su elementi prisutni u njenoj atmosferi. +Tokom dvadesetih godina ovog stoleca, kada .su astronomi poceli da ispituju spektre zvezda+u drugim galaksijama, ustanovili su neto .krajnje neobicno: javljali su se isti osobeni 0nizovi nedostajucih boja kao u naoj Galaksiji,0ali oni su svi bili pomereni u istom relativnom -iznosu prema crvenom kraju spektra. Da bismo *razumeli ta je ovo znacilo, moramo prvo 0objasniti Doplerov efekat. Kao to smo videli, 1vidljiva svetlost sastoji se od fluktuacija, ili -talasa, u elektromagnetnom polju. Ucestalost 2(ili broj talasa u sekundi) svetlosti izuzetno je 0visoka, dostiuci izmedu cetiri i sedam stotina,miliona miliona talasa u sekundi. Razlicite /ucestalosti svetlosti izgledaju naem oku kao 1razlicite boje, pri cemu se najnie ucestalosti *javljaju na crvenom kraju spektra, dok se +najvie javljaju na plavom kraju spektra. /Zamislite sada neki izvor svetlosti na stalnoj -udaljenosti od nas, kao to je neka zvezda, 1koji emituje talase svetlosti stalne ucestalosti.-Jasno je da ce ucestalost talasa koje primamo.odgovarati ucestalosti kojom su oni emitovani )(gravitaciono polje Galaksije ne bi bilo -dovoljno snano da ovde ima neki znacajniji /uticaj). Pretpostavimo sada da izvor svetlosti ,pocne da se krece ka nama. Kada se sa njega ,bude otisnuo naredni breg talasa, on ce nam 0biti blii, tako da ce vreme koje je tom bregu .talasa potrebno da stigne do nas biti krace od-vremena kada je zvezda bila stacionarna. Ovo *znaci da bi vreme izmedu dva brega talasa 2koji stiu do nas bilo krace, te bi stoga i broj ,talasa koje primamo svake sekunde (odnosno, (ucestalost) bila veca nego onda kada je /zvezda mirovala. Slicno tome, ukoliko se izvor .udaljuje od nas, ucestalost primljenih talasa /postace manja. U slucaju svetlosti, dakle, ovo +znaci da ce zvezde koje se udaljuju od nas 'imati spektralne linije pomerene prema -crvenom kraju spektra (crveni pomak), dok ce +one koje se krecu ka nama imati spektralne /linije pomerene ka plavom kraju spektra (plavi (pomak). Ovaj odnos izmedu ucestalosti i (brzine, koji se naziva Doplerov efekat, ,srecemo i u svakodnevnom ivotu. Sluajte %zvuk kola koja prolaze putem: dok se 2pribliavaju, zvuci motora izgledaju vii (to /odgovara vioj ucestalosti zvucnih talasa), a *kad pocnu da se udaljuju, onda im je zvuk 1nii. Svetlost ili radio-talasi ponaaju se na %slican nacin. Ovu okolnost koristi i ,saobracajna policija koja pomocu Doplerovog )efekta odreduje brzinu automobila na taj 0nacin to meri ucestalost impulsa radio-talasa odraenih sa njih. )U godinama posle pouzdanog ustanovljenja .postojanja drugih galaksija, Habl se posvetio 'katalogizovanju njihovih udaljenosti i )proucavanju spektara. U to vreme, vecina ,astronoma smatrala je da se galaksije krecu +sasvim nasumce, te se zato ocekivalo da ce ,se naci priblino podjednak broj crvenih i &plavih pomaka. Bilo je stoga prilicno *iznenadujuce kada se ustanovilo da se kod -velike vecine galaksija javlja crveni pomak: ,gotovo sve one su se udaljavale od nas! No, .jo je neobicnije delovao jedan drugi Hablov /nalaz koji je on objavio 1929: cak ni velicina #crvenog pomaka neke galaksije nije *nasumicna, vec je upravo srazmerna njenoj 0udaljenosti od nas. Ili, drugim recima, to je 1neka galaksija udaljenija, to se bre udaljava! *A ovo je znacilo da Vaseljena moda nije .staticna, kako su svi prethodno smatrali, vec 1da se nalazi u stanju brzog irenja; udaljenosti/izmedu razlicitih galaksija brzo se povecavaju./Otkrice da se Vaseljena iri predstavljalo je +jednu od velikih intelektualnih revolucija +dvadesetog stoleca. Kada se danas osvrnemo 1na celu stvar, uistinu je teko razabrati zato+niko nije ranije pomislio na tu mogucnost. /Njutn i ostali naucnici trebalo je da shvate da)bi staticna Vaseljena ubrzo pocela da se &saima pod dejstvom gravitacije. Ali 0pretpostavimo da se Vaseljena, naprotiv, iri. .Ukoliko bi ovo irenje bilo srazmerno sporo, (gravitaciona sila dovela bi na kraju do $njegovog zaustavljanja i do pocetka -saimanja. Ako se, medutim, Vaseljena iri (brzinom koja premaa odredenu kriticnu -vrednost, onda bi ona nastavila da se zauvek 0iri. Situacija pomalo nalikuje na onu kada se 0sa povrine Zemlje ispali uvis raketa. Ako joj +je brzina nedovoljna, gravitacija ce je na 'kraju zaustaviti i ona ce poceti da se -sunovraca natrag ka Zemlji. Sa druge strane, -ako je brzina rakete iznad odredene kriticne &vrednosti (oko sedam milja u sekundi) .gravitacija ne bi bila dovoljno snana da je .privuce natrag, te bi ona tako nastavila da se&zauvek udaljava od Zemlje. Ponaanje (Vaseljene moglo se predvideti na osnovu )Njutnove teorije gravitacije bilo kada u $devetnaestom, osamnaestom, pa cak i ,sedamnaestom veku. No, tako je snano bilo .verovanje u staticnu Vaseljenu da se zadralo/sve do dvadesetog stoleca. Cak je i Ajntajn, /kada je formulisao optu teoriju relativnosti -1915, bio u toj meri uveren da Vaseljena mora.biti staticna da je modifikovao svoju teoriju *kako bi ovo omogucio, uvevi u jednacine .takozvanu kosmoloku konstantu. Ajntajn je -zamislio jednu novu silu, 'antigravitaciju', 2koja, za razliku od ostalih sila, nije poticala ni-iz kakvog posebnog izvora, vec je bila utkana,u samu tvar prostorvremena. On je tvrdio da .prostorvreme ima usadenu tenju ka irenju, 0koja bi trebalo da se nalazi u tacnoj ravnotei,sa privlacnim dejstvom svekolike materije u )Vaseljeni, tako da je kao ishod nastajao (staticni kosmos. Samo je jedan fizicar, *izgleda, bio spreman da doslovno prihvati .optu relativnost; dok su Ajntajn i ostali +naucnici nastojali da pronadu nacine da se *izbegne predvidanje opte relativnosti o 'nestaticnoj Vaseljeni, ruski fizicar i .matematicar Aleksandar Fridman latio se posla da ovo objasni. +Fridman je postavio dve sasvim jednostavne )pretpostavke o Vaseljeni: da ona, naime, -izgleda istovetno ma u kom pravcu pogledali, .kao i da ovo ostaje na snazi bez obzira na to +odakle vrimo posmatranje. Samo na osnovu ,ove dve zamisli Fridman je pokazao da ne bi .trebalo ocekivati da Vaseljena bude staticna. ,U stvari, 1922, nekoliko godina pre otkrica -Edvina Habla, Fridman je predvideo upravo onoto ce Habl ustanoviti! -Pretpostavka da Vaseljena izgleda istovetno u%svim pravcima nesumnjivo ne odgovara /stvarnosti. Primera radi, kao to smo videli, *ostale zvezde u naoj Galaksiji obrazuju -upadljivu traku svetlosti preko nocnog neba, ,zvanu Mlecni Put. Ali ako panju posvetimo .udaljenim galaksijama, izgleda da ih ima manje,ili vie isti broj. Pokazuje se, dakle, da ,Vaseljena ipak izgleda uglavnom isto u svim *pravcima, ukoliko se posmatra u razmerama $koje odgovaraju razdaljinama izmedu -galaksija, odnosno ako se zanemare razlike u *manjim razmerama. Ovo je dugo smatrano za +dovoljnu potvrdu Fridmanove pretpostavke - 0kao gruba priblinost stvarne Vaseljene. Ali u -novije vreme jedno slucajno otkrice pokazalo +je da Fridmanova pretpostavka predstavlja, +zapravo, veoma tacan opis nae Vaseljene. ,Godine 1965, dva americka fizicara iz 'Bell .Telephone Laboratories' u Nju Derziju, Arno /Penzijas i Robert Vilson, isprobavali su jedan &veoma osetljiv mikrotalasni detektor. 2(Mikrotalasi su slicni svetlosnim talasima, ali im/ucestalost dostie samo deset hiljada miliona +talasa u sekundi.) Penzijas i Vilson su se ,zabrinuli kada su ustanovili da im detektor .belei izrazitiji um nego to je trebalo. 0Izgledalo je da taj um ne potice ni iz jednog ,posebnog pravca. U prvi mah, pronali su u -detektoru tragove pticjeg izmeta, to ih je &navelo da se daju u potragu za drugim /mogucim potekocama ove vrste, ali nita nije.otkriveno. Znali su da bi um koji potice iz /atmosfere bio snaniji kada detektor ne bi bio,upravljen pravo nagore, zato to svetlosni *zraci putuju kroz znatno deblju atmosferu ,kada stiu s male razdaljine iznad obzorja ,nego onda kada prispevaju pravo odozgo. No, .pokazalo se da je viak uma nepromenjen ma +u kom pravcu bio okrenut detektor, to je &znacilo da mora da potice negde izvan .atmosfere. um je uz to ostajao isti danju i -nocu, kao i preko cele godine, bez obzira na +to to se Zemlja okretala oko svoje ose i /kruila oko Sunca. Ovo je znacilo da zracenje &mora da dolazi odnekud izvan Suncevog /sistema, pa cak i izvan Galaksije, buduci da bi'inace variralo kako bi kretanje Zemlje +upravljalo detektor u razlicitim pravcima. *Danas znamo da je ovo zracenje na putu do )nas moralo da prevali svekoliku vidljivu +Vaseljenu, a kako izgleda da je ono isto u .svim pravcima, onda i Vaseljena mora biti ista(u svim pravcima, makar i samo u velikim 'razmerama. Sada nam je poznato da, bez +obzira na pravac iz koga potice, ovaj um ,nikada ne varira vie od jednog hiljaditog .dela, te su tako Penzijas i Vilson i nehotice ,doli do izuzetno tacne potvrde Fridmanove prve pretpostavke. +Priblino u isto vreme, dvojica americkih $fizicara sa oblinjeg Prinstonskog 0univerziteta, Bob Dajk i Dim Pibls, takode su -poceli da se zanimaju za mikrotalase. Oni su )ispitivali pretpostavku Dorda Gamova ,(nekadanjeg studenta Aleksandra Fridmana) +da je rana Vaseljena trebalo da bude veoma /topla i gusta, u stanju belog usijanja. Dajk i 1Pibls doli su do zakljucka da bismo mi i dalje .morali da budemo u stanju da vidimo sjaj rane +Vaseljene, buduci da bi svetlost iz njenih +veoma udaljenih delova trebalo da tek sada /stie do nas. irenje Vaseljene je, medutim, /nalagalo da ova svetlost ima tako veliki crveni+pomak da bi nam izgledala kao mikrotalasno 0zracenje. Dajk i Pibls su se upravo spremali da *krenu u potragu za ovim zracenjem kada su -Penzijas i Vilson culi za njihov rad i odmah /shvatili da u ruci vec imaju traenu potvrdu. /Penzijasu i Vilsonu je za ovo pripala Nobelova -nagrada 1978. (to nije bilo odvec poteno +prema Dajku i Piblsu, a da se i ne pominje Gamov). .Na prvi pogled, svi nalazi o tome da Vaseljena)izgleda istovetna bez obzira na to u kom -pravcu posmatrali kao da ukazuju na to da je &nae mesto u njoj posebno. Na osnovu .okolnosti da se sve galaksije udaljuju od nas ,moglo bi nam se uciniti da se mi nalazimo u /sreditu Vaseljene. Postoji, medutim, i jedno .alternativno objanjenje: Vaseljena bi mogla /izgledati ista u svim pravcima i iz svake druge,galaksije. Bila je to, kao to smo videli, &Fridmanova druga pretpostavka. Nemamo -naucnih dokaza ni u prilog ove pretpostavke, +ni protiv nje. Smatramo da je ona ispravna .samo na osnovu skromnosti: bilo bi to krajnje ,izuzetno kada bi Vaseljena izgledala ista u 'svim pravcima samo oko nas, a ne i oko *ostalih tacaka u Vaseljeni! U Fridmanovom ,modelu sve galaksije se medusobno udaljuju. 'Situacija odgovara balonu sa nacrtanim ,tackicama, koji se polako naduvava. Kako se /balon iri, razmak izmedu bilo koje dve tacke -se povecava, ali ne postoji tacka za koju se .moe reci da se nalazi u sreditu irenja. %tavie, to su tackice medusobno .razmaknutije, to ce se one i bre razmicati. *Slicno tome, u Fridmanovom modelu, brzina /kojom se bilo koje dve galaksije udaljuju jedna)od druge upravo je srazmerna udaljenosti )izmedu njih. Odavde je proishodilo da ce )crveni pomak jedne galaksije biti upravo .srazmeran njenoj udaljenosti od nas, ba kao .to je to Habl ustanovio. Uprkos uspenosti -Fridmanovog modela, kao i cinjenici da je on -predvidao nalaze Hablovih posmatranja, radovi.ovog fizicara ostali su uglavnom nepoznati na ,Zapadu sve dok do slicnih modela nisu 1935. 0godine doli americki fizicari Hauard Robertson-i britanski matematicar Artur Voker, koji su (preduzeli razradivanje Hablovog otkrica "jednoobraznog irenja Vaseljene. ,Iako je Fridman pronaao samo jedan model, -postoje, zapravo, tri razlicite vrste modela .koje su u saglasnosti sa njegove dve temeljne -pretpostavke. U prvoj vrsti (koju je Fridman ,pronaao), irenje Vaseljene srazmerno je *sporo, tako da ce gravitacono privlacenje /izmedu razlicitih galaksija dovesti do njegovog&usporavanja i konacnog zaustavljanja. -Galaksije bi tada stale da se krecu jedna ka /drugoj, a Vaseljena da se saima. Ilustracija ,3.2 prikazuje kako se udaljenost izmedu dve ,susedne galaksije menja sa protokom vremena.+Ona pocinje na nuli, raste do maksimuma, a *zatim pada ponovo na nulu. U drugoj vrsti 0reenja, irenje Vaseljene je tako brzo da ga .gravitaciono privlacenje ne moe zaustaviti, .premda ga ipak malo usporava. Ilustracija 3.3 +prikazuje razdvajanje susednih galaksija u +ovom modelu. Ono pocinje na nuli, da bi se 'konacno galaksije medusobno udaljavale ,nekom postojanom brzinom. Konacno, postoji i+treca mogucnost u kojoj je brzina irenja %Vaseljene taman tolika da se izbegne +kolabiranje. U ovom slucaju, prikazanom na /ilustraciji 3.4, razmak izmedu galaksija takode,pocinje na nuli, da bi se zauvek povecavao. .No, brzina razmicanja galaksija neprekidno se )smanjuje, premda nikada ne pada na nulu. "Veoma vana posledica prve vrste $Fridmanovog modela jeste da u njemu +Vaseljena nije prostorno beskrajna, premda *prostor nema granica. Gravitacija je tako ,snana da je prostor zakrivljen oko samoga 2sebe, tako da prilicno nalikuje povrini Zemlje. )Ukoliko se neko krece u odredenom pravcu -povrinom Zemlje i ako ne naide ni na kakvu ,neprelaznu prepreku niti padne preko ivice, -konacno ce stici na mesto sa koga je krenuo. +U prvom Fridmanovom modelu sa prostorom je /upravo ovo slucaj, ali sa tri dimenzije umesto ,dve koliko ima na povrini Zemlje. Cetvrta -dimenzija, vreme, takode je konacna, ali ona (je poput crte sa dva kraja ili granice, *pocetkom i krajem. Kasnije cemo videti da +kada se dovedu u vezu opta relativnost i 'nacelo neodredenosti kvantne mehanike, )postaje moguce da i prostor i vreme budu 'konacni bez ikakvih ivica ili granica. .Zamisao da bi se mogla obici cela Vaseljena i )vratiti na polazno mesto od koristi je u .naucnoj fantastici, ali njen prakticni znacaj /je mali, buduci da se moe pokazati da bi pre -dolo do kolabiranja Vaseljene nego to bi ,neko stigao da je obide. Morali biste da se .krecete bre od svetlosti da biste stigli na -mesto odakle ste krenuli pre no to dode do 'kraja Vaseljene, a to nije doputeno! ,U prvoj vrsti Fridmanovog modela, u kome se *Vaseljena najpre iri, a potom kolabira, ,prostor je zakrivljen oko samoga sebe poput ,povrine Zemlje. On je tu stoga konacan. U )drugoj vrsti modela, u kome se Vaseljena -zauvek iri, prostor je zakrivljen na drugi 0nacin, slicno povrini sedla. Ovde je on stoga #beskonacan. Najzad, u trecoj vrsti /Fridmanovog modela, gde je brzina irenja tik .iznad kriticne granice, prostor je ravan (pa, dakle, ponovo beskonacan). )Ali koji Fridmanov model odgovara naoj .Vaseljeni? Da li ce Vaseljena jednom prestati .da se iri i poceti da se saima, ili ce se +zauvek iriti? Da bismo odgovorili na ovo 0pitanje, moramo znati sadanju brzinu irenja )Vaseljene, kao i njenu trenutnu prosecnu )gustinu. Ukoliko se gustina nalazi ispod -izvesne kriticne vrednosti, odredene brzinom 1irenja, gravitaciono privlacenje bice preslabo 0da zaustavi irenje. Ako je, pak, gustina iznad,kriticne granice, gravitacija ce zaustaviti (irenje u nekom trenutku u buducnosti, +izazvavi istovremeno pocetak kolabiranja Vaseljene. +Sadanju brzinu irenja moemo odrediti -merenjem brzina kojima se galaksije udaljuju (od nas, pomocu Doplerovog efekta. To je -moguce izvesti veoma precizno. Udaljenosti do&galaksija nisu, medutim, sasvim dobro /poznate, zato to smo u prilici samo posredno -da ih merimo. Sve to u ovom trenutku znamo /jeste da se Vaseljena iri za vrednost izmedu 05 i 10 odsto svakih hiljadu miliona godina. No, (jo neizvesnije stoje stvari u pogledu )trenutne prosecne gustine Vaseljene. Ako *zbrojimo mase svih zvezda koje moemo da &vidimo u naoj Galaksiji i u ostalim 'galaksijama, vrednost koju dobijamo ne (dostie ni jedan stoti deo one koja je 'neophodna da bi se zaustavilo irenje *Vaseljene, cak i u slucaju najnie stope -irenja. Naa Galaksija i ostale galaksije ,zasigurno, medutim, sadre velike kolicine ,'tamne materije' koju ne moemo neposredno ,videti, ali za koju znamo da mora postojati .zbog uticaja njenog gravitacionog privlacenja +na orbite zvezda u galaksijama. tavie, -vecina galaksija javlja se u jatima, tako da )se, na slican nacin, moe pretpostaviti (prisustvo novih kolicina tamne materije .izmedu galaksija u tim jatima po dejstvu koje .ona vri na njihovo kretanje. Kada se uzme u +obzir sva ova tamna materija, dobijamo tek +jednu desetinu kolicine neophodne da bi se *zaustavilo irenje. Ne moemo, medutim, -iskljuciti mogucnost da postoje i neki drugi $oblici materije, razmeteni gotovo +jednoobrazno po Vaseljeni, koje jo nismo -otkrili i koji bi ipak mogli podici prosecnu (gustinu Vaseljene do kriticne vrednosti 1neophodne da bi se irenje zaustavilo. Sadanji%nalazi ukazuju na to da ce Vaseljena 0verovatno nastaviti zauvek da se iri, ali sve 0u ta stvarno moemo biti sigurni jeste da cak,i ako dode do kolabiranja Vaseljene, ono se .nece dogoditi bar jo narednih deset hiljada +miliona godina, buduci da se ona vec iri -najmanje toliko vremena. Ovo, medutim, ne bi -trebalo mnogo da nas brine: u to vreme, osim +ako ne budemo preduzeli kolonizaciju izvan %Suncevog sistema, covecanstvo ce vec 0odavno izumreti, iceznuvi zajedno sa naim Suncem! -Svi Fridmanovi modeli imaju jedno zajednicko /svojstvo: u nekom trenutku u prolosti (negde ,pre izmedu deset i dvadeset hiljada miliona -godina) razdaljine izmedu susednih galaksija 0morale su biti ravne nuli. U tom trenutku, koji ,nazivamo Veliki Prasak, gustina Vaseljene i %zakrivljenost prostorvremena bile su *beskonacne. Buduci da matematicari nisu u ,stanju da operiu beskonacnim vrednostima, 1to znaci da opta teorija relativnosti (na kojoj*se temelje Fridmanovi modeli) predvida da ,postoji jedna tacka u povesti Vaseljene gde -ona sama gubi vanost. Ova tacka predstavlja)primer onoga to se u matematici naziva 2singularnost. U stvari, sve nae teorije u fizici#zasnovane su na pretpostavci da je ,prostorvreme jednoobrazno i gotovo ravno, te/stoga prestaju da vae u singularnosti Velikog,Praska, gde je zakrivljenost prostorvremena )beskrajna. Ovo znaci da cak i da je bilo ,dogadaja pre Velikog Praska, pomocu njih se *nije moglo odrediti ta ce se posle toga 1dogoditi, zato to bi predvidljivost otkazala u ,trenutku Velikog Praska. Slicno tome, ako - .kao to je uistinu slucaj - znamo jedino ono /to se zbivalo posle Velikog Praska, ne bismo 0mogli da odredimo ta se odigravalo pre njega. .to se nas tice, dogadaji pre Velikog Praska /nisu mogli imati nikakve posledice, te stoga ne-bi trebalo da sacinjavaju deo naucnog modela .Vaseljene. Zato bi trebalo da ih otklonimo iz ,modela i da uzmemo da vreme pocinje Velikim Praskom. 'Mnogim ljudima ne dopada se zamisao da 'vreme ima pocetak, verovatno zato to .podseca na boanski upliv. (Katolicka crkva, /naprotiv, prihvatila je model Velikog Praska i (1951. zvanicno je proglasila da je on u )saglasnosti sa Biblijom.) Javio se stoga &izvestan broj pokuaja da se izbegne .zakljucak da je postojao Veliki Prasak. Ideja /koja je dobila najvecu podrku bila je nazvana)teorija stacionarnog stanja. Ovu teoriju 1postavili su 1948. dvojica izbeglica iz Austrije +pod nacistickom okupacijom, Herman Bondi i .Tomas Gold, kao i Britanac Fred Hojl, koji je *sa njima radio na razvoju radara za vreme .rata. Zamisao se sastojala u tome da, kako se ,galaksije medusobno razuduju, u meduprostoru/dolazi do stalnog nastajanja novih iz materije -koja se neprekidno stvara. Vaseljena bi tako 1izgledala priblino ista u svim vremenima, kao i-u svim tackama prostora. Teorija stacionarnog&stanja nalagala je preinacenje opte -relativnosti kako bi se omogucilo neprekidno -stvaranje materije, ali tu je bila u pitanju -tako nizak obim (priblino jedna cestica po /kubnom kilometru godinje) da nije dolazila u /sukob sa nalazima opita. Posredi je bila dobra )naucna teorija u smislu opisanom u prvom +poglavlju: bila je jednostavna i iz nje su ,proishodila odredena predvidanja koja su se ,mogla proveriti posmatranjima. Jedno od tih 2predvidanja bilo je da broj galaksija ili slicnih .objekata u bilo kojoj datoj zapremini prostora*treba da bude isti bez obzira na to u kom %cemo pravcu i kada pogledati. Krajem *pedesetih i pocetkom ezdesetih godina u %Kembridu je jedna grupa astronoma, +predvodena Martinom Rajlom (koji je takode *saradivao sa Bondijem, Goldom i Hojlom na *radaru tokom rata), preduzela ispitivanje ,izvora radio-talasa koji dolaze iz kosmosa. ,Kembridska grupa je pokazala da se vecina (ovih radio-izvora morala nalaziti izvan .Galaksije (mnogi su od njih, zapravo, dovedeni,u vezu sa drugim galaksijama), kao i da ima -znatno vie slabih nego jakih izvora. Slabe .izvore su protumacili kao da su udaljeniji, a ,jake kao blie. Pokazalo se da po jedinici /zapremine prostora ima manje oblinjih izvora .nego udaljenijih. Ovo je moglo da znaci da se -nalazimo u sreditu jednog velikog podrucja ,Vaseljene u kome su izvori proredeniji nego .drugde. Alternativno, takode je bilo moguce da3su izvori bili brojniji u prolosti, u vreme kada /su se radio-talasi otisnuli na putovanje prema .nama, nego sada. Oba objanjenja kosila su se,sa teorijom stacionarnog stanja. tavie, +otkrice mikrotalasnog zracenja Penzijasa i .Vilsona iz 1965. isto je tako ukazivalo na to ,da je Vaseljena morala biti znatno guca u 0prolosti. Teoriju stacionarnog stanja valjalo je, dakle, napustiti. .Drugi pokuaj da se izbegne zakljucak kako je,morao postojati Veliki Prasak, pa, dakle, i ,pocetak vremena, potekao je 1963. od dvojice,ruskih naucnika, Jevgenija Lifica i Isaka /Kalatnikova. Prema njihovom miljenju, Veliki (Prasak mogao je predstavljati osobenost +jedino Fridmanovih modela, koji su i sami, )uostalom, bili tek aproksimacija stvarne -Vaseljene. Moda su, od svih modela koji su 1priblino odgovarali stvarnoj Vaseljeni, jedino *Fridmanovi sadrali singularnost Velikog )Praska. U Fridmanovim modelima sve su se ,galaksije medusobno direktno, udaljavale te *stoga nije iznenadujuce da su se jednom u /prolosti nalazile na istom mestu. U stvarnoj .Vaseljeni, medutim, galaksije se ne udaljavaju-jedna od druge samo direktno vec imaju i male-pobocne brzine. Prema tome, u stvarnosti, one/se, zapravo, nisu sve morale nalaziti na istom +mestu, vec samo veoma blizu jedne drugima. +Moda je u tom slucaju sadanje irenje )Vaseljene proisteklo ne iz singularnosti )Velikog Praska, vec iz jedne ranije faze *saimanja; kako je Vaseljena kolabirala, /cestice u njoj nisu se morale sve sudariti, vec3su se mimoile i razile, izazvavi na taj nacin/sadanje irenje Vaseljene. Kako bismo u tom -slucaju mogli da ustanovimo da li je stvarna .Vaseljena pocela Velikim Praskom? Ono to su 'Lific i Kalatnikov preduzeli bilo je /proucavanje modela Vaseljene koji su priblino/nalikovali Fridmanovim modelima, ali se u njima-vodilo racuna o nepravilnostima i nasumicnim -brzinama galaksija u stvarnoj Vaseljeni. Oni +su, dodue, pokazali da takvi modeli mogu -poceti Velikim Praskom, iako se galaksije ne .udaljuju uvek direktno jedna od druge, ali su *tvrdili da je tako neto moguce jedino u ,izvesnim izuzetnim modelima u kojima se sve )galaksije krecu na pravilan nacin. Prema -njihovom uverenju, buduci da je izgledalo da )postoji neuporedivo vie modela slicnih -Fridmanovima bez singularnosti Velikog Praska1nego onih sa njim, valjalo bi zakljuciti da ni u 1stvarnosti nije bilo Velikog Praska. Kasnije su, )medutim, uvideli da postoji jedna znatno -optija klasa modela slicnih Fridmanovima u -kojima se javljaju singularnosti i kod kojih ,galaksije ne moraju da se krecu ni na kakav ,poseban nacin. I tako, 1970. godine, oni su odustali od svoje zamisli. 0Rad Lifica i Kalatnikova bio je dragocen zato ,to je pokazao da je Vaseljena mogla imati .jednu singularnost, Veliki Prasak, ukoliko je +ispravna opta teorija relativnosti. Oni, /medutim, nisu dali odgovor na kljucno pitanje: 1predvida li opta relativnost da naa Vaseljena*mora imati Veliki Prasak, odnosno pocetak +vremena? Ovaj odgovor potekao je, medutim, .iz jednog potpuno drugacijeg pristupa, koji je/1965. ostvario britanski matematicar i fizicar /Roder Penrouz. Uzevi u obzir nacin na koji &se svetlosne kupe ponaaju u optoj -relativnosti, kao i cinjenicu da gravitacija +uvek dejstvuje privlacno, on je pokazao da )jedna zvezda koja kolabira pod vlastitom -gravitacijom biva zarobljena u podrucje cija +ce se povrina na kraju smanjiti do nulte (velicine. A buduci da se povrina ovog (podrucja smanjuje do nule, isto se mora /dogoditi i sa zapreminom. Svekolika materija u &zvezdi bila bi tada sabijena u nultoj &zapremini, tako da bi njena gustina i %zakrivljenost prostorvremena postali &beskonacni. Drugim recima, nastala bi "singularnost sadrana u podrucju 'prostorvremena poznatom kao crna rupa. -Na prvi pogled, Penrouzov nalaz kao da vai .samo za zvezde; on naizgled nita ne govori o(tome da li je svekolika Vaseljena imala *singularnost Velikog Praska u prolosti. *Medutim, u vreme kada je Penrouz postavio ,svoju teoremu, ja sam ocajnicki nastojao da +pronadem neki problem koji bi predstavljao (predmet moje doktorske disertacije. Dve +godine ranije postavili su mi dijagnozu da ,bolujem od amiotroficke lateralne skleroze, &poznatije kao Lu Gerigov sindrom, ili -motoricke neuronske bolesti, stavivi mi do /znanja da mi preostaje jo samo jedna ili dve ,godine ivota. Pod takvim okolnostima nije /izgledalo odvec svrhovito upustiti se u izradu .doktorske teze - naprosto, za nju vie nisam +imao dovoljno vremena. No, protekle su dve 'godine, a moje stanje nije se znatnije 3pogoralo. U stvari, sve je ilo prilicno dobro, +pa sam se cak i verio jednom veoma zgodnom +devojkom po imenu Dejn Vajld. Ali da bih (mogao da se oenim, bio mi je potreban +posao, a da bih dobio posao, trebalo je da doktoriram. &Godine 1965, doznao sam o Penrouzovoj -teoremi, prema kojoj svako telo koje podlegne*gravitacionom kolapsu mora na kraju da se .pretvori u singularnost. Iznenada sam shvatio #da ako se preokrene smer vremena u )Penrouzovoj teoremi, tako da kolabiranje 0postane irenje, proporcije teoreme i dalje bi )ostale na snazi pod uslovom da Vaseljena 'priblino odgovara jednom Fridmanovom ,modelu u velikim razmerama u ovom trenutku. (Penrouzova teorema pokazala je da svaka &kolabirajuca zvezda mora da zavri u (singularnosti; model sa obrnutim smerom %vremena pokazao je, pak, da je svaka ,fridmanovska Vaseljena koja se iri morala /poceti kao singularnost. Iz tehnickih razloga, ,Penrouzova teorema nalagala je da Vaseljena ,bude prostorno beskrajna. Mogao sam, dakle, "to upotrebiti da pokaem kako ce 1singularnosti biti jedino ako se Vaseljena iri $dovoljno brzo da izbegne prelazak u -kolabiranje (jer samo se kod tih Fridmanovih #modela javljao beskrajni prostor). *Tokom narednih nekoliko godina razvio sam %nove matematicke postupke kojima sam )uklonio ovaj i ostale tehnicke uslove iz /teorema to su dokazivale da se moraju javiti 0singularnosti. Konacni ishod bio je rad koji smo.Penrouz i ja zajedno objavili 1970. i koji je 'konacno dokazao da je morala postojati )singularnost Velikog Praska, pod jedinim +uslovom da je opta relativnost ispravna, -odnosno da Vaseljena stvarno sadri onoliko .materije koliko mi to registrujemo. Javilo se -mnogo protivljenja naem radu, delimicno od )strane Rusa, zbog njihovog marksistickog ,uverenja u naucni determinizam, a delimicno /od ljudi koji su smatrali da je cela zamisao o .singularnostima odbojna i da naruava lepotu )Ajntajnove teorije. Medutim, sa jednom !matematickom teoremom nema mnogo 1rasprave. I tako, konacno, na rad bio je opte-prihvacen i danas gotovo svi dre zasigurno .da je Vaseljena pocela singularnocu Velikog /Praska. Moda stoga ima ironije u okolnosti da+sada ja, poto sam u meduvremenu promenio 0miljenje, pokuavam da uverim ostale fizicare.da u pocetku Vaseljene u stvari nije postojala-singularnost - kao to cemo kasnije videti, ,ona moe da nestane poto se uzmu u obzir kvantna dejstva. -Videli smo u ovom poglavlju kako se, za manje.od pola stoleca, preobrazilo covekovo videnje .Vaseljene, koje se prethodno gradilo hiljadama0godina. Hablovo otkrice da se Vaseljena iri i 'uvidanje beznacajnosti nae planete u +ogromnosti Vaseljene bili su samo pocetak. .Kako su se eksperimentalni i teorijski radovi ,umnoavali, postajalo je sve jasnije da je *Vaseljena morala imati pocetak u vremenu, -sve dok to 1970. Penrouz i ja nismo dokazali &na osnovu Ajntajnove opte teorije *relativnosti. Ovaj dokaz pokazao je da je /opta relativnost, zapravo, nepotpuna teorija:(ona nam ne moe reci kako je Vaseljena 0pocela, zato to predvida da svi zakoni fizike,*kao i ona sama, vie ne vae na pocetku 0Vaseljene. Medutim, opta teorija relativnosti .i tvrdi da je samo delimicna teorija, tako da )ono to teorije o singularnosti uistinu -pokazuju jeste da je postojalo jedno vreme u ,veoma ranoj Vaseljeni kada je ona bila tako *mala da se tu vie nisu mogla zanemariti 'dejstva u malim razmerama druge velike -delimicne teorije dvadesetog stoleca, kvantne(mehanike. Pocetkom sedamdesetih godina, /dakle, bili smo prinudeni da nae traganje za &razumevanjem Vaseljene preusmerimo sa (teorije o izuzetno velikom na teoriju o )izuzetno malom. O ovoj teoriji, kvantnoj ,mehanici, bice odmah reci, kako bismo potom ,mogli da upravimo napore na povezivanje dve (delimicne teorije u jedinstvenu kvantnu teoriju gravitacije. 4. NACELO NEODREENOSTI *Uspeh naucnih teorija, a posebno Njutnove )teorije gravitacije, naveo je francuskog 'naucnika, markiza Laplasa, da pocetkom -devetnaestog stoleca ustvrdi da je Vaseljena .potpuno deterministicka. Laplas je smatrao da .postoji skup naucnih zakona koji bi trebalo da)nam omoguce da predvidimo sve to ce se +dogoditi u Vaseljeni, pod uslovom da znamo ,celokupno stanje Vaseljene u datom vremenu. +Primera radi, kada bismo znali poloaje i -brzine Sunca i planeta u nekom trenutku, tada'bismo pomocu Njutnovih zakona mogli da *izracunamo stanje Suncevog sistema u bilo )kom drugom vremenu. Determinizam izgleda 1prilicno ocigledan u ovom slucaju, ali Laplas je .otiao i korak dalje, ustvrdivi da postoje +slicni zakoni koji upravljaju svim ostalim 0oblastima, ukljucujuci tu i ljudsko ponaanje. ,Doktrini naucnog determinizma odlucno su se 3usprotivili mnogi autori koji su bili miljenja da-se ovim sputava sloboda Boga da uplivie na /svet, ali ona je ipak formalno ostala na snazi *u nauci sve do ranih godina ovog stoleca. %Jedan od prvih pokazatelja da ce ovo .uverenje morati da bude naputeno usledio je .kada je iz proracuna britanskih naucnika lorda3Rejlija i sera Dejmsa Dinsa proizilo da neki /topli objekat, ili telo, kakva je zvezda, mora 'da zraci energiju u beskonacnom obimu. .Saglasno zakonima u ciju se valjanost verovalo+u to vreme, jedno toplo telo trebalo je da .odailje elektromagnetne talase (kao to su /radio-talasi, vidljiva svetlost ili rendgenski *talasi) ravnomerno na svim ucestalostima. 1Primera radi, toplo telo trebalo bi da zraci istu*kolicinu energije na ucestalostima izmedu .jedan i dva miliona miliona talasa u sekundi, /kao i na ucestalostima izmedu dva i tri miliona,miliona talasa u sekundi. Buduci da je broj /talasa u sekundi neogranicen, to bi znacilo da (je ukupna energija zracenja beskonacna. .Da bi izbegao ovaj ocigledno besmislen ishod, -nemacki naucnik Maks Plank izloio je 1900. .godine zamisao da svetlost, rendgenski zraci i$ostali talasi ne bivaju emitovani u )proizvoljnom obimu, vec samo u odredenim *paketima koje je on nazvao kvantima. Osim (toga, svaki kvant ima odredenu kolicinu 'energije koja je tim veca to je veca *ucestalost talasa, tako da bi na dovoljno +visokoj ucestalosti emitovanje samo jednog -kvanta zahtevalo vie energije nego to je .uopte raspoloivo. Prema tome, zracenje na ,visokim ucestalostima bilo bi smanjeno, a i /stopa kojom telo gubi energiju bila bi konacna.+Kvantna hipoteza sasvim je dobro objasnila -izmerenu kolicinu emitovanog zracenja toplih )tela, ali njen uticaj na deterministicku *doktrinu bio je shvacen tek 1926, kada je $jedan drugi nemacki naucnik, Verner 'Hajzenberg, formulisao svoje znamenito *nacelo neodredenosti. Da bi se predvideli /buduci poloaj i brzina neke cestice, potrebno,je tacno izmeriti njen sadanji poloaj i -brzinu. Ocigledni nacin da se to ucini jeste 0osvetliti cesticu. Cestica ce razbiti jedan deo *talasa svetlosti, to ce ukazati na njen ,poloaj. No, poloaj cestice nece se moci )tacnije odrediti nego to iznosi razmak ,izmedu dva brega svetlosnog talasa, tako da 0je potrebno koristiti svetlost kratkih talasnih +duina da bi se precizno odredio poloaj ,cestice. Prema Plankovoj kvantnoj hipotezi, ,medutim, ne moe se upotrebiti proizvoljno /mala kolicina svetlosti; valja uzeti bar jedan *kvant. Ovaj kvant ce poremetiti cesticu i (promeniti njenu brzinu na nacin koji ne ,moemo predvideti. tavie, to tacnije *merimo poloaj, to treba koristiti krace -talasne duine svetlosti, pa je tako veca i +energija jednog kvanta. A time ce i brzina -cestice biti u vecoj meri poremecena. Drugim -recima, to tacnije pokuavate da izmerite ,poloaj cestice, to manje precizno moete /izmeriti njenu brzinu i obrnuto. Hajzenberg je ,pokazao da proizvod neodredenosti poloaja -cestice, neodredenosti brzine cestice i mase (cestice ne moe biti manji od odredene &velicine koja je poznata kao Plankova (konstanta. Ovo ogranicenje ne zavisi od /nacina na koji pokuavate da izmerite poloaj,ili brzinu cestice, kao ni od tipa cestice. #Hajzenbergovo nacelo neodredenosti .predstavlja temeljno, neumitno svojstvo sveta./Nacelo neodredenosti izvrilo je veoma vaan +uticaj na na nacin videnja sveta. Cak ni +sada, posle vie od pedeset godina, mnogi 0filozofi jo nisu postali svesni ovog uticaja, (tako da je on i dalje predmet ozbiljnih .kontroverzi. Nacelo neodredenosti oznacilo je .kraj Laplasovog sna o jednoj teoriji nauke, o ,jednom modelu Vaseljene koji bi bio potpuno ,deterministicki: sasvim je izvesno da se ne +mogu tacno predvidati buduci dogadaji, ako .se ne moe precizno izmeriti cak ni trenutno 1stanje Vaseljene! I dalje moemo zamiljati da .postoji skup zakona koji potpuno determiniu +dogadaje nekom natprirodnom bicu kadrom da (posmatra sadanje stanje Vaseljene, ne -remeteci ga pri tom. Ovakvi modeli Vaseljene *nisu, medutim, od velikog interesa za nas *obicne smrtnike. Izgleda prikladnije ovde +primeniti nacelo ekonomicnosti poznato kao &Okamova otrica i njome odrezati sva -svojstva teorije koja se ne mogu posmatrati. (Ovakav pristup omogucio je Hajzenbergu, *Ervinu redingeru i Polu Diraku da tokom *dvadesetih godina ovog veka preformuliu -mehaniku u jednu novu teoriju koja je dobila ,naziv kvantna mehanika i koja se temelji na .nacelu neodredenosti. U ovoj teoriji, cestice 'vie nemaju zasebne i sasvim odredene /poloaje i brzine koji se ne mogu posmatrati. +Umesto toga, one imaju kvantno stanje koje ,predstavlja kombinaciju poloaja i brzine. (Uopteno govoreci, kvantna mehanika ne *predvida jedinstven i odreden ishod nekog .posmatranja. Naprotiv, ona predvida veci broj .razlicitih mogucih ishoda i govori nam o tome /kakvi su izgledi svakog od njih. Drugim recima,,ukoliko se preduzme isto merenje na velikom /broju slicnih sistema, koji su svi zapoceli na .isti nacin, ustanovice se da ce ishod merenja -biti A u izvesnom broju slucajeva, B u nekom %drugom broju i tako dalje. Moguce je .predvideti priblian broj puta kada ce ishod 1biti A ili B, ali se ne moe predvideti poseban ,rezultat nekog pojedinacnog merenja. Kvantna+mehanika, dakle, uvodi neizbean elemenat ,nepredvidljivosti ili nasumicnosti u nauku. *Ajntajn se ovome veoma protivio, uprkos ,vanoj ulozi koju je sam odigrao u razvoju *ove zamisli. On je, naime, dobio Nobelovu (nagradu upravo za doprinos postavljanju +kvantne teorije. No, Ajntajn nikada nije ,prihvatio ideju da Vaseljenom vlada slucaj; )njegovo gledanje na ovu stvar saeto je /iskazano u znamenitoj recenici: 'Bog se ne igra-kockicama.' Vecina drugih naucnika, medutim, -bila je spremna da prihvati kvantnu mehaniku /zato to se ona savreno slagala sa nalazima ,opita. I odista, bila je to izuzetno uspela /teorija, koja stoji u temelju gotovo svekolike *moderne nauke i tehnologije. Ona upravlja -ponaanjem tranzistora i integrisanih kola, /koji predstavljaju kljucne delove elektronskih -uredaja kao to su televizori i racunari, a .pociva u osnovi i moderne hemije i biologije. &Jedina podrucja fizike u koja kvantna *mehanika jo nije prikladno uvedena jesu 'gravitacija i makrokosmicko ustrojstvo Vaseljene. -Iako se svetlost sastoji od talasa, Plankova )kvantna hipoteza govori nam o tome da se +ona u izvesnim pogledima ponaa kao da je /sazdana od cestica: svetlost, naime, moe biti.emitovana ili apsorbovana samo u paketima, ili-kvantima. Isto tako, iz Hajzenbergovog nacela(neodredenosti proishodi da se cestice u -izvesnim pogledima ponaaju kao talasi: one $nemaju odreden poloaj, vec bivaju #'razmazane' uz izvesnu verovatnocu &razmetaja. Teorija kvantne mehanike *zasnovana je na jednom potpuno novom tipu -matematike koji vie ne objanjava stvarni .svet iz perspektive cestica i talasa; iz ovog (ugla mogu biti opisana samo posmatranja /sveta. Postoji, stoga, dvojstvo izmedu talasa i-cestica u kvantnoj mehanici: za neke svrhe od*koristi je o cesticama razmiljati kao o +talasima, dok je, pak, za druge od koristi )talase smatrati za cestice. Jedna vana *posledica ove okolnosti jeste da se moe $posmatrati ono to je dobilo naziv )interferencija izmedu dva skupa talasa i .cestica. Drugim recima, bregovi jedne skupine -talasa mogu da se poklapaju sa doljama druge ,skupine. Dve skupine talasa mogu da se tako *medusobno potru, umesto da udruene daju 1snaniji talas, kao to bi se ocekivalo (Ilus. .4.1). Poznati primer interferencije u slucaju .svetlosti jesu boje koje se cesto mogu videti )kod mehurova od sapunice. Njih izazivaju +odrazi svetlosti sa dva kraja tanke vodene (opne koja obrazuje mehur. Bela svetlost )sastoji se od svetlosnih talasa mnotva 3razlicitih talasnih duina, ili boja. Kod izvesnih.talasnih duina bregovi talasa odraenih sa -jedne strane opne od sapunice poklopice se sa.doljama odraenim sa druge strane. Boje koje 'odgovaraju tim talasnim duinama bice -odsutne iz odraene svetlosti, koja ce tako izgledati kao da je raznobojna. +Do interferencije moe doci i kod cestica &usled dvojnosti koju je uvela kvantna )mehanika. Znameniti primer u ovom smislu 1jeste takozvani ogled sa dva proreza (Ilus. 4.2).-Zamislite jedan paravan sa dva uska, uporedna-proreza. Sa jedne strane paravana stavlja se -izvor svetlosti neke odredene boje (odnosno, ,neke odredene talasne duine). Najveci deo .svetlosti zaustavice se na paravanu, ali mala %kolicina ce ipak proci kroz proreze. *Pretpostavimo sada da postavimo platno sa )suprotne strane paravana u odnosu na onu .gde se nalazi izvor svetlosti. Do svih tacaka 1na platnu stizace talasi koji su proli kroz dva+proreza. Medutim, razdaljina koju svetlost +mora da prede od izvora do platna kroz dva /proreza bice razlicita. Ovo znaci da talasi iz .proreza nece biti u fazi jedni sa drugima kada)stignu do platna: na nekim mestima ce se &medusobno potrti, dok ce se na drugim 0ojacati. Ishod ove okolnosti jeste osobena arasvetlih i tamnih pruga. ,Veoma je zanimljivo to da se dobija potpuno /ista vrsta pruga ako se izvor svetlosti zameni *izvorom cestica, kao to su elektroni sa ,odredenom brzinom (u smislu da odgovarajuci 1talasi imaju odredenu duinu). Ovo izgleda jo -neobicnije zbog okolnosti da ako postoji samo*jedan prorez, onda se ne dobijaju nikakve (pruge, vec samo jednoobrazni razmetaj *elektrona preko platna. Stoga bi se moglo *pomisliti da ce se otvaranjem jo jednog *proreza samo povecati broj elektrona koji )udaraju u svaku tacku platna, ali, usled *interferencije, time se zapravo ovaj broj &smanjuje na izvesnim mestima. Kada bi -elektroni bili upuceni kroz proreze jedan po +jedan, ocekivalo bi se da svaki prode kroz +jedan ili kroz drugi prorez, te bi se tako /ponaali kao da je prorez kroz koji prolaze u *stvari jedini - to bi dalo jednoobrazan -razmetaj na platnu. U stvarnosti, medutim, -cak i onda kada se elektroni upucuju jedan po*jedan, pruge se i dalje pojavljuju. Svaki *elektron, dakle, mora da prolazi kroz oba proreza u isto vreme! -Pojava interferencije medu cesticama bila je )od kljucnog znacaja za nae razumevanje -ustrojstva atoma, osnovnih jedinica hemije i )biologije i gradivnih opeka od kojih smo 0sazdani kako mi, tako i sve to nas okruuje. .Pocetkom stoleca smatralo se da atomi prilicno.nalikuju na planete koje krue oko Sunca, sa %elektronima (cesticama sa negativnim -naelektrisanjem) koje krue oko sredinjeg 0jezgra to nosi pozitivan elektricni naboj. Za +privlacnost izmedu pozitivnog i negativnog .elektriciteta pretpostavljalo se da zadrava ,elektrone na orbitama na isti nacin na koji (gravitaciono privlacenje izmedu Sunca i ,planeta zadrava ove na njihovim orbitama. .Nevolja sa ovakvim videnjem stvari ogledala se/u tome to su zakoni mehanike i elektriciteta,'pre kvantne mehanike, predvidali da ce +elektroni postepeno gubiti energiju i tako -poceti da se spiralno sunovracuju ka jezgru, +da bi se na kraju sudarili sa njim. Ovo je 'znacilo da bi atomi, odnosno svekolika .materija, trebalo da brzo kolabiraju u stanje -veoma visoke gustine. Do delimicnog reenja ,ovog problema doao je danski naucnik Nils .Bor 1913. On je izloio zamisao da elektroni 0moda nisu u stanju da orbitiraju na bilo kojoj/udaljenosti od sredinjeg jezgra, vec samo na -sasvim odredenim razdaljinama. Ako se takode ,pretpostavi da samo jedan ili dva elektrona ,mogu da krue na nekoj od ovih razdaljina, )onda se time reava problem kolabiranja *atoma, zato to elektroni ne bi mogli da %poniru dublje od orbita sa najmanjim /udaljenostima i energijama koje bi popunjavali.$Ovaj model objasnio je sasvim dobro $ustrojstvo najjednostavnijeg atoma, .vodonika, kod koga samo jedan elektron krui 0oko jezgra. Ali nije bilo jasno kako se on moe4proiriti i na sloenije atome. tavie, zamisao/o ogranicenom nizu doputenih orbita izgledala+je veoma proizvoljna. Nova teorija kvantne +mehanike reila je ovu potekocu. Ona je /pokazala da se elektron koji krui oko jezgra 1moe shvatiti kao talas, cija duina zavisi od ,njegove brzine. Kod izvesnih orbita njihove 'duine odgovarale bi celom broju (kao -suprotnom decimalnom broju) talasnih duina 0elektrona. Kod tih orbita breg talasa nalazio bi,se na istom mestu kod svakog kruga, to bi 'dovelo do zbrajanja talasa: ove orbite ,odgovarale bi Borovim doputenim orbitama. $Medutim, kod orbita cije duine ne /predstavljaju ceo broj talasnih duina, svaki +breg bio bi ranije ili kasnije potrt nekom 0doljom prilikom kruenja elektrona; ove orbite ne bi bile doputene. $Zgodan nacin da se predoci dvojnost &talas-cestica jeste takozvani zbir po .istorijama na koji je ukazao americki naucnik .Ricard Fajnmen. Prema ovoj zamisli, smatra se (da cestica nema samo jednu istoriju ili -putanju u prostorvremenu, kao to bi to bio /slucaj u klasicnoj, nekvantnoj teoriji. Umesto *toga, veruje se da se ona krece od A do B )svim mogucim putanjama. Uz svaku putanju 'vezana su dva broja: jedan predstavlja *velicinu talasa, a drugi poloaj ciklusa *(odnosno, da li je na bregu ili u dolji). -Verovatnoca prevaljivanja razdaljine izmedu A+i B ustanovljava se zbrajanjem talasa svih /putanja. Uopteno govoreci, ukoliko se uporedi,skup susednih putanja, faze ili poloaji u .ciklusu veoma ce se razlikovati. Ovo znaci da /ce se talasi koji stoje u vezi sa tim putanjama,gotovo savreno medusobno potrti. Medutim, ,kod nekih skupova susednih putanja nece doci.do velikih varijacija izmedu faza. Ove putanje)odgovaraju Borovim doputenim orbitama. %Na osnovu ovih zamisli, izloenih u (konkretnom matematickom obliku, bilo je ,srazmerno lako izracunati doputene orbite /kod sloenijih atoma, pa cak i molekula, koji +se sastoje od veceg broja atoma to ih na /okupu dre elektroni na orbitama oko vie od /jednog jezgra. Buduci da ustrojstvo molekula i )njihove medusobne reakcije predstavljaju -temelj svekolike hemije i biologije, kvantna #mehanika nam u nacelu omogucuje da -predvidamo gotovo sve to nas okruuje, do $samih granica koje postavlja nacelo #neodredenosti. (U praksi, medutim, /izracunavanja kod sistema koji sadre vie od/nekoliko elektrona toliko su sloena da ih ne moemo izvesti.) 1Ajntajnova opta teorija relativnosti upravlja*makrokosmickim ustrojstvom Vaseljene. Ona +spada u takozvane klasicne teorije; drugim $recima, ona ne uzima u obzir nacelo ,neodredenosti kvantne mehanike, kao to bi .to trebalo, ukoliko eli da bude saglasna sa /ostalim teorijama. Razlog to ona ne dovodi do+neslaganja sa nalazima posmatranja lei u ,tome to su sva gravitaciona polja koja mi +normalno iskuujemo veoma slaba. Medutim, 0teoreme o singularnosti, o kojima je ranije bilo*reci, ukazuju na to da gravitaciono polje *treba da postane veoma snano u najmanje 0dve situacije: kod crnih rupa i Velikog Praska. *Kod takvih snanih polja dejstva kvantne 'mehanike postaju vana. Prema tome, u -izvesnom smislu, klasicna opta relativnost predvida vlastito zakazivanje, -nagovetavajuci postojanje tacaka beskrajne ,gustine, ba kao to i klasicna (odnosno, 'nekvantna) mehanika predvida sopstveno )zakazivanje, govoreci o tome da ce atomi ,kolabirati do beskrajne gustine. Mi jo ne -raspolaemo celovitom, koherentnom teorijom .koja objedinjuje optu relativnost i kvantnu *mehaniku, ali nam je zato poznat izvestan &broj svojstava koja ona treba da ima. ,Posledice koje ce ta svojstva imati po crne -rupe i Veliki Prasak bice opisane u narednim (poglavljima. Nakratko cemo se, medutim, -vratiti skoranjim nastojanjima da se nae ,razumevanje ostalih sila prirode objedini u jedinstvenu kvantnu teoriju. &5. ELEMENTARNE CESTICE I SILE PRIRODE /Aristotel je verovao da se svekolika materija u.Vaseljeni sastoji od cetiri osnovna elementa: &zemlje, vazduha, vatre i vode. Na ove .elemente deluju dve sile: gavitacija, tenja -zemlje i vode da tonu, i levitacija, tenja (vazduha i vatre da se diu. Ova podela 1sadrine Vaseljene na materiju i sile jo je i danas na snazi. $Aristotel je smatrao da je materija &neprekidna, odnosno da se jedan komad +materije moe deliti na sve manje i manje ,delove bez ikakvih granica: nikada se ne bi .dolo do delica materije koji se dalje ne bi /mogao deliti. Nekolicina Grka, kao to je bio .Demokrit, verovala je, medutim, da je materija'zrnastog ustrojstva, odnosno da je sve -sazdano od velikog broja raznih vrsta atoma. '(Rec atom na grckom znaci 'nedeljiv'.) /Suceljavanje ova dva stanovita nastavilo se i#u potonjim stolecima, bez stvarnih .argumenata u prilog bilo koje strane, sve dok /1803. britanski hemicar i fizicar Don Dalton (nije ukazao na to da se cinjenica da se %hemijska jedinjenja uvek kombinuju u %odredenim srazmerama moe objasniti -narocitim grupisanjem atoma kojim se dobijaju.jedinice nazvane molekuli. No, rasprava izmedu1dve kole miljenja konacno je reena u korist,atomista tek pocetkom ovog stoleca. Jedan od(vanih fizickih dokaza ovde je pruio +Ajntajn. U jednom radu objavljenom 1905, ,samo nekoliko nedelja pre znamenite posebne 1teorije relativnosti, Ajntajn je istakao da se 'ono to se naziva Braunovo kretanje - -nepravilno, nasumicno kretanje malih cestica 0praine u nekoj tecnosti - moe objasniti kao 'dejstvo atoma vode koji se sudaraju sa cesticama praine. -U to vreme vec se javilo podozrenje da atomi,0zapravo, nisu nedeljivi. Nekoliko godina ranije,4profesor sa koleda Triniti u Kembridu, D. D.&Tomson, pokazao je da postoje cestice *materije, nazvane elektroni, cija je masa ,preko hiljadu puta manja od mase najlakeg /atoma. Naprava koju je on koristio prilicno je #nalikovala na katodnu cev modernog *televizora: jedno metalno vlakno u stanju -crvenog usijanja odailjalo je elektrone, a ,kako su oni imali negativno naelektrisanje, -moglo se koristiti elektricno polje da bi se )ubrzali prema narocitom ekranu optocenom -fosforom. Kada bi elektroni udarili u ekran, *nastajali bi bleskovi svetlosti. Ubrzo je -shvaceno da ovi elektroni moraju poticati iz .unutranjosti samih atoma, a 1911. britanski ,fizicar Ernest Raderford konacno je pokazao /da atomi materije imaju unutranje ustrojstvo:.oni se sastoje od izuzetno majunog jezgra sa.pozitivnim naelektrisanjem, oko koga orbitira )izvestan broj elektrona. Zakljucio je to (analizujuci nacin na koji alfa-cestice, +odnosno cestice sa pozitivnim nabojem koje ,emituju radioaktivni atomi, skrecu prilikom sudara sa atomima. *U prvi mah se smatralo da se jezgro atoma (sastoji od elektrona i razlicitog broja *pozitivno naelektrisanih cestica nazvanih 0protoni, od grcke reci koja znaci 'prvi', buduci-da se verovalo da su to temeljne jedinice iz ,kojih je sazdana svekolika materija. Godine +1932, medutim, jedan Raderfordov kolega sa .Kembrida, Dejms Cedvik, otkrio je da se u *jezgru nalazi jo jedna cestica, nazvana )neutron, koja ima gotovo istu masu kao i -proton, ali ne i elektricni naboj. Cedvik je -dobio Nobelovu nagradu za ovo otkrice, kao i )zvanje upravnika koleda Gonvil i Kiz u 'Kembridu (istog onog na kome ja sada ,predajem). Kasnije je dao ostavku na zvanje &upravnika, zbog neslaganja sa ostalim ,profesorima. Dolo je, naime, do estokog 'spora na koledu kada je grupa mladih /profesora koja se vratila iz rata izglasala da -mnogi stari profesori izgube katedre koje su *dugo drali. No, sve je ovo bilo pre mog .vremena. Ja sam doao u koled 1965, sasvim -na kraju ovog neprijatnog razdoblja, ali i u ,vreme kada je jedan slican spor nagnao jo -jednog dobitnika Nobelove nagrade, ser Nevila!Mota, da takode podnese ostavku. ,Sve do pre dvadesetak godina smatralo se da 1su protoni i neutroni 'elementarne' cestice, ali /onda su ogledi u kojima su se protoni sudarali 0sa drugim protonima ili elektronima pri velikim /brzinama pokazali da se oni, u stvari, sastoje 0od jo manjih cestica. Fizicar sa Kalteha Marej*Gel-Man nazvao je ove cestice kvarkovi, a ,1969. dobio je Nobelovu nagradu za svoj rad ,na njima. Naziv 'kvarkovi' uzet je iz jedne +zagonetne recenice Demsa Dojsa: 'Three .quarks for Muster Mark!' Rec quark trebalo bi 0da se izgovara kao quart (kvort), s tim to je ,na kraju, k a ne, t, ali se obicno izgovara #tako da se rimuje sa, lark (lark). .Postoji vie razlicitih varijeteta kvarkova: -smatra se da ima najmanje est 'ukusa' koje .nazivamo gore, dole, cudno, armantno, dno i 1vrh. Svaki ukus javlja se u tri 'boje', crvenoj, -zelenoj i plavoj. (Treba naglasiti da su ovi ,termini samo puke oznake: kvarkovi su znatno0manji od talasne duine vidljive svetlosti, te "tako ne mogu imati nikakvu boju u -uobicajenom smislu. Stvar je naprosto u tome &da su, kako izgleda, moderni fizicari &matovitiji u nadevanju naziva novim .cesticama i pojavama - oni se, naime, vie ne)ogranicavaju na grcki!) Jedan proton ili 0neutron sastoje se od tri kvarka razlicite boje.-Proton sadri dva kvarka gore i jedan kvark 0dole, dok neutron sadri dva dole i jedan gore.(Moguce je stvoriti cestice sacinjene od .ostalih kvarkova (neobicni, armantni, dno i +vrh), ali sve one imaju znatno vecu masu i %veoma se brzo raspadaju na protone i neutrone. (Danas znamo da ni atomi, a ni protoni i 0neutroni u njima, nisu nedeljivi. Pitanje stoga )glasi: 'ta su onda stvarne elementarne ,cestice, osnovne gradivne opeke iz kojih je +sve sazdano?' Buduci da je talasna duina (svetlosti znatno veca od razmera atoma, (nema nikakve nade da cemo na uobicajeni (nacin 'osmotriti' delove atoma. Ovde je +potrebno koristiti neto sa znatno manjom )talasnom duinom. Kao to smo videli u 'prethodnom poglavlju, kvantna mehanika .govori nam da su sve cestice, zapravo, talasi,.kao i da to je veca energija cestica, to je *manja duina odgovarajucih talasa. Prema ,tome, najbolji odgovor koji moemo dati na +nae pitanje zavisi od toga koliko visoku -energiju cestice imamo na raspolaganju, zato ,to ovaj cinilac odreduje koliko cemo male -razmere moci da vidimo. Ove energije cestica (obicno se mere jedinicom koja se naziva )elektron volt. (Kod Tomsonovih ogleda sa )elektronima videli smo da je on koristio +elektricno polje da bi ubrzavao elektrone. -Energija koju elektron dobija od elektricnog .polja od jednog volta poznata je kao elektron .volt.) U devetnaestom stolecu, kada je jedina /energija cestica za koju su ljudi znali kako da+je koriste bila niska energija od nekoliko ,elektron volti to su je stvarale hemijske /reakcije kao to je gorenje, smatralo se da su)atomi najmanje jedinice. U Raderfordovom /ogledu, alfa-cestice imale su energiju koja je .dostizala na milione elektron volti. U novije $vreme naucili smo kako da koristimo .elektromagnetna polja da bismo dobili energije.cestica najpre od vie miliona, a potom i na +hiljade miliona elektron volti. I tako smo +doznali da se cestice za koje smo pre samo -dvadeset godina smatrali da su 'elementarne' 0sastoje, zapravo, od jo manjih cestica. Moe -li se za ove ispostaviti, kako idemo ka jo 0viim energijama, da se sastoje od jo manjih +cestica? To je svakako moguce, ali postoje .izvesni teorijski razlozi za verovanje da smo 2vec doli - ili smo im sasvim blizu - do krajnjihgradivnih opeka prirode. *Pomocu dvojnosti talas-cestica, o cemu je +bilo reci u prethodnom poglavlju, sve se u 0Vaseljeni, racunajuci tu svetlost i gravitaciju,.moe opisati iz perspektive cestica. Cestice *imaju jedno svojstvo koje se naziva spin. .Jedan od nacina da se predoci ovaj spin jeste -da se cestice zamisle kao male cigre koje se %okrecu oko svoje ose. Ovo poredenje, .medutim, moe da stvori pogrenu predstavu, &buduci da nas kvantna mehanika uci da +cestice nemaju neku odredenu osu. Ono to -nam spin cestica zapravo govori jeste to kako.cestica izgleda iz raznih pravaca. Cestica sa -spinom 0 odgovara tacki: ona izgleda ista iz -svih pravaca (Ilus. 5.1 i). Sa druge strane, -cestica sa spinom 1 odgovara streli: ona ima 6razlicit izgled iz razlicitih pravaca (Ilus. 5.1 ii), +odnosno izgleda ista samo ako se okrene za ,ceo krug (360 stepeni). Cestici sa spinom 2 /odgovara dvostrana strela (Ilus. 5.1 iii): ona .izgleda ista ako se okrene za pola kruga (180 /stepeni). Slicno tome, cestice sa vecim spinom *izgledaju iste ako se okrenu za srazmerno 'manji deo punoga kruga. Sve ovo deluje 0prilicno normalno, ali izuzetna je cinjenica da .postoje cestice koje ne izgledaju isto ako se +okrenu samo za jedan krug: potrebno ih je, *naime, okrenuti dva puna kruga! Za ovakve 'cestice kae se da imaju spin od 1/2. (Sve poznate cestice u Vaseljeni mogu se /podeliti u dve skupine: cestice sa spinom 1/2, ,od kojih se sastoji materija u Vaseljeni, i ,cestice sa spinom 0, 1 i 2, koje, kako cemo +videti, stoje u osnovi sila to dejstvuju *izmedu cestica materije. Cestice materije -pokoravaju se onome to se naziva Paulijevo /nacelo iskljucenja. Ovo nacelo otkrio je 1925. 1austrijski fizicar Volfgang Pauli, za ta mu je *1945. pripala Nobelova nagrada. On je bio 0arhetip teorijskog fizicara: za njega se pricalo+da je cak i samo njegovo prisustvo u nekom &gradu imalo za posledicu propast svih -prakticnih opita koji se tu vre! Paulijevo *nacelo iskljucenja kae da dve istovrsne *cestice ne mogu postojati u istom stanju, /odnosno one ne mogu imati isti poloaj i istu *brzinu u okviru meda koje odreduje nacelo /neodredenosti. Nacelo iskljucenja je od kljucne-vanosti zato to objanjava zbog cega ne /dolazi do kolabiranja cestica materije u stanje/veoma velike gustine pod dejstvom sila to ih /stvaraju cestice sa spinom 0, 1 i 2: da cestice.materije imaju prakticno iste poloaje, onda 0bi morale da imaju razlicite brzine, to znaci .da se ne bi dugo zadrale na istom mestu. Da (je svet stvoren bez nacela iskljucenja, *kvarkovi ne bi obrazovali zasebne, sasvim *odredene protone i neutrone. Niti bi ovi, ,zajedno sa elektronima, obrazovali zasebne, *sasvim odredene atome. Svi bi kolabirali, (obrazujuci uglavnom jednoobraznu, gustu 'supu'. ,Do ispravnog razumevanja elektrona i drugih -cestica sa spinom od 1/2 dolo je tek 1928, /kada je Pol Dirak, koji je kasnije postao ef -katedre za matematiku na Kembridu (iste one+koju je nekada Njutn drao i koju ja sada +drim), postavio svoju znamenitu teoriju. .Dirakova teorija bila je prva koja se slagala &kako sa kvantnom mehanikom, tako i sa &optom teorijom relativnosti. Ona je .matematicki objanjavala zato elektron ima /spin od 1/2, odnosno zato ne izgleda isti ako+ga okrenete samo jedan krug, a izgleda ako -ga okrenete dva kruga. Ova teorija takode je .predvidala da elektron treba da ima parnjaka: -antielektron ili pozitron. Otkrice pozitrona 01932. potvrdilo je Dirakovu teoriju i dovelo do -toga da on dobije Nobelovu nagradu za fiziku *1933. Mi danas znamo da svaka cestica ima +anticesticu sa kojom moe da se potre. (U $slucaju cestica koje nose energiju, /anticestice su iste kao i same cestice.) Sasvim*je moguce da postoje citavi antisvetovi i /antiljudi sazdani od anticestica. Medutim, ako ,vam se dogodi da sretnete antiverziju samoga,sebe, nipoto se nemojte rukovati! Obojica 0cete nestati u silnom blesku svetlosti. Pitanje +zbog cega izgleda da ima neuporedivo vie -cestica nego anticestica oko nas izuzetno je -vano i ja cu se na njega vratiti kasnije u ovom poglavlju. -U kvantnoj mehanici smatra se da se sile ili $medudejstva izmedu cestica materije ,odigravaju posredstvom cestica ciji je spin 0celi broj 0, 1 ili 2. Dogada se, zapravo, to da 1cestica materije, kao to je elektron ili kvark,/emituje cesticu koja nosi silu. Posledica ovog (emitovanja jeste promena brzine cestice *materije. Cestica koja nosi silu potom se +sudara sa nekom drugom cesticom materije i *biva apsorbovana. Ovaj sudar menja brzinu 0druge cestice, ba kao da je dolo do dejstva 'neke sile izmedu dve cestice materije. /Vano svojstvo cestica koje nose silu jeste to,da se one ne pokoravaju nacelu iskljucenja. *Ovo znaci da ne postoji granica u pogledu ,broja cestica koje mogu biti razmenjene, te -su tako one u stanju da proizvedu jaku silu. +Ako, medutim, cestice koje nose silu imaju -veliku masu, onda je teko proizvoditi ih i -razmenjivati na velikim udaljenostima. Stoga (ce sile koje one nose imati samo kratak -domet. Sa druge strane, ako cestice koje nose+silu nemaju vlastitu masu, te sile ce biti -dalekodometne. Cestice koje nose silu i koje &se razmenjuju medu cesticama materije 0nazivaju se virtuelne cestice, zato to se, za *razliku od 'stvarnih', ne mogu neposredno )otkriti detektorom cestica. Mi, medutim, -znamo da one postoje zato to im se dejstva +mogu meriti: one tvore silu izmedu cestica /materije. Cestice sa spinom 0, 1 ili 2 postoje 'pod izvesnim okolnostima i kao stvarne -cestice, kada se neposredno mogu meriti. One -se onda pojavljuju u obliku za koji bi jedan 0klasicni fizicar rekao da je talas; posredi mogu,biti svetlosni ili gravitacioni talasi. Oni )ponekad mogu biti emitovani kada cestice ,materije stupaju u medudejstvo, razmenjujuci*pri tom virtuelne cestice koje nose silu. .(Primera radi, elektroodbojna sila izmedu dva 'elektrona dovodi do razmene virtuelnih *fotona, koji se nikada ne mogu neposredno -otkriti; ali ako jedan elektron prode pokraj &drugoga, moe se dogoditi da dode do %odvajanja stvarnih fotona, koje onda $registrujemo kao svetlosne talase.) 0Cestice koje nose silu mogu se podeliti u cetiri*vrste, prema snazi sile koju nose i prema +cesticama sa kojima stupaju u medudejstvo. +Treba, medutim, istaci da je ova podela na -cetiri vrste samo uslovna; ona je pogodna za /postavljanje delimicnih teorija, ali moda ne ,odgovara dubljim slojevima stvarnosti. Osim ,toga, vecina fizicara se nada da ce doci do *objedinjene teorije koja ce objasniti sve 'cetiri sile kao razlicite vidove jedne ,jedinstvene sile. Za mnoge je ovo, zapravo, ,osnovni zadatak savremene fizike. Nedavno su0preduzeti uspeni pokuaji da se objedine tri 0od cetiri vrste sila - o cemu ce podrobnije biti,reci u ovom poglavlju. Pitanje objedinjenja /jedine preostale sile, gravitacije, ostavicemo za kasnije. -Prva vrsta je gravitaciona sila. Ova sila je .univerzalna, odnosno svaka cestica oseca silu )tee vec u zavisnosti od svoje mase ili 1energije. Gravitacija je ubedljivo najslabija od .cetiri sile; ona je toliko slaba da bi ostala )potpuno nezapaena kada ne bi imala dva 'posebna svojstva: dejstvuje na velikim -udaljenostima i uvek je privlacna. Ovo znaci )da se veoma slabe gravitacione sile medu -pojedinacnim cesticama u dva velika tela, kao)to su, na primer, Zemlja i Sunce, mogu 5sabrati u prilicno jaku silu. Ostale tri sile su ili (kratkodometne, ili ponekad privlacne, a -ponekad odbojne, te tako tee da se potiru. %Prema videnju gravitacionog polja iz -perspektive kvantne mehanike, za nosioca sile,izmedu dve cestice materije smatra se jedna .cestica sa spinom 2, koja se naziva graviton. ,On nema sopstvenu masu, tako da je sila koju-nosi dalekodometna. Gravitaciona sila izmedu .Sunca i Zemlje pripisuje se razmeni gravitona -medu cesticama koje sacinjavaju ova dva tela./Iako su razmenjene cestice virtuelne, one i te ,kako proizvode merljiva dejstva medu kojima /je najistaknutije orbitiranje Zemlje oko Sunca!-Stvarni gravitoni tvore ono to bi klasicni -fizicari nazvali gravitacionim talasima. Ovi 0talasi su izuzetno slabi, tako da do danas jo uopte nisu registrovani. *Narednu vrstu predstavlja elektromagnetna ,sila koja stupa u dejstvo sa naelektrisanim 2cesticama, kao to su elektroni ili kvarkovi, ali/ne i sa cesticama bez naelektrisanja, kao to )su gravitoni. Ona je znatno snanija od /gravitacione sile: elektromagnetna sila izmedu 0dva elektrona snanija je od gravitacione sile /milion miliona miliona miliona miliona miliona 0miliona puta (jedinica iza koje se prua niz od+cetrdeset dve nule). Postoje, medutim, dve &vrste elektricnog naboja: pozitivan i ,negativan. Sila izmedu dva pozitivna naboja .dejstvuje odbojno, ba kao i sila izmedu dva *negativna naboja, ali je zato sila izmedu *pozitivnog i negativnog naboja privlacna. 1Jedno veliko telo, kao to je Zemlja ili Sunce, /sadri priblino podjednak broj pozitivnih i ,negativnih naboja. Privlacne i odbojne sile %izmedu pojedinacnih cestica stoga se )medusobno gotovo potiru, tako da postoji )veoma malo ciste elektromagnetne sile. U +malim razmerama atoma i molekula, medutim, "elektromagnetne sile preovladuju. ,Elektromagnetno privlacenje izmedu negativno%naelektrisanih elektrona i pozitivno 'naelektrisanih protona u jezgru nagoni -elektrone da orbitiraju oko atomskog jezgra, .ba kao to gravitaciono privlacenje nagoni +Zemlju da krui oko Sunca. Smatra se da u *zaledu elektromagnetne sile stoji razmena .velikog broja virtuelnih cestica bez mase, sa /spinom 1, koje se nazivaju fotoni. Fotoni koji .se razmenjuju predstavljaju, dakle, virtuelne )cestice. Medutim, kada elektron prede sa 0jedne doputene orbite na drugu, bliu jezgru,,dolazi do oslobadanja energije i emitovanja ,stvarnog fotona - koji ljudsko oko moe da 0registruje kao vidljivu svetlost, ukoliko on ima"odgovarajucu talasnu duinu. Ovo 0registrovanje vri i detektor fotona, kakav je ,fotografski film. Isto tako, ako se stvarni +foton sudari sa atomom, on moe da izbaci .neki elektron sa orbite blie jezgru na neku 0udaljeniju. Tom prilikom biva utroena energija'fotona, te on tako postaje apsorbovan. .Trecu vrstu predstavlja slaba nuklearna sila, +koja stoji u osnovi radioaktivnosti i koja ,dejstvuje na sve cestice materije sa spinom /1/2, ali ne i na one sa spinom 0, 1 ili 2, kao 0to su fotoni i gravitoni. Prava priroda slabe -nuklaearne sile shvacena je tek 1967, kada su/Abdus Salam sa londonskog koleda Imperijal i ,Stiven Vajnberg sa Harvarda nezavisno jedan 0od drugoga postavili teorije koje su objedinile +ovu vrstu medudejstava sa elektromagnetnom /silom, ba kao to je stotinak godina ranije -Maksvel objedinio elektricitet i magnetizam. +Prema ovim teorijama, pored fotona postoje .jo tri cestice sa spinom 1, koje se zajedno .nazivaju masivni vektorski bozoni i koje nose *slabu silu. Ovi bozoni dobili su naziv W+ -(izgovara se 've plus'), W- (izgovara se 've 1minus') i Z0 (izgovara se 'zed nula') i svaki od +njih ima masu od oko 100 GeV (gigaelektron /volti, ili hiljadu miliona elektron volti). Iz *Vajnberg-Salamove teorije proishodi jedno )svojstvo poznato kao spontano razbijanje -simetrije. Ono, naime, to je izgledalo kao ,izvestan broj potpuno razlicitih cestica na ,niskim energijama pokazuje se, zapravo, kao 1isti tip cestice, samo u razlicitim stanjima. Na -visokim energijama sve ove cestice se slicno /ponaaju. Efekat prilicno nalikuje ponaanju 0kuglice na tocku ruleta. Pri velikim energijama .(kada se tocak brzo okrece) kuglica se ponaa#u osnovi na samo jedan nacin - ona )neprekidno krui. Ali kada tocak uspori .okretanje, energija kuglice se smanjuje i ova 'konacno pada u jedan od trideset sedam -odeljaka na tocku. Drugim recima, pri niskim -energijama postoji trideset sedam razlicitih 0stanja u kojima se javlja kuglica. Ako bismo, iz/nekog razloga, bili u stanju da vidimo kuglicu .jedino pri niskim energijama, doli bismo do .zakljucka da, zapravo, postoji trideset sedam razlicitih tipova kuglica! -U Vajnberg-Salamovoj teoriji, pri energijama +viim od 100 GeV tri nove cestice i foton 0ponaali bi se na slican nacin. Ali pri niim .energijama cestica, koje se javljaju u vecini .normalnih situacija, dolazi do razbijanja ove /simetrije izmedu cestica. W+, W- i Z0 stekli bi1vece mase, to bi uslovilo da sile koje oni nose+budu sasvim kratkodometne. U vreme kada su /Salam i Vajnberg izloili svoju teoriju, malo 0fizicara im je verovalo, a akceleratori cestica 1nisu bili dovoljno snani da domae energije od,100 GeV neophodne da bi se proizvele stvarne+W+, W- i Z0 cestice. Medutim, tokom naredne+decenije predvidanja ove teorije na niim *energijama bila su u toj meri saglasna sa -nalazima opita da su, 1979. Salam i Vajnberg .dobili Nobelovu nagradu za fiziku, zajedno sa .eldonom Gleouom, takode sa Harvarda, koji 'je postavio slicnu objedinjenu teoriju .elektromagnetne i slabe nuklearne sile. Odbor ,za dodelu Nobelove nagrade bio je poteden ,neugodnosti da je pogreio kada su 1983. u &CERN-u (Evropskom centru za nuklearna -istraivanja) konacno otkrivena tri masivna &partnera fotona, sa tacno predvidenim /masama i ostalim svojstvima. Karlo Rubija, koji/je predvodio ekipu od nekoliko stotina fizicara1to su doli do ovog otkrica, takode je, 1984, ,dobilo Nobelovu nagradu, zajedno sa Simonom .van der Merom, inenjerom iz CERN-a, koji je ,sazdao sistem za uskladivanje antimaterije, 0to je tom prilikom bio upotrebljen. (Veoma je ,teko steci uvaavanje u eksperimentalnoj /fizici ovih dana, osim ako vec niste na vrhu!) .Cetvrtu vrstu predstavlja jaka nuklearna sila )koja dri na okupu kvarkove u protonu i .neutronu, ba kao i proton i neutron zajedno +u jezgru atoma. Veruje se da ovu silu nosi *jedna cestica sa spinom 1, nazvana gluon, ,koja stupa u dejstvo jedino sa samom sobom i-sa kvarkovima. Jaka nuklearna sila ima jedno -neobicno svojstvo koje se naziva ogranicenje -('confinement'): ona uvek povezuje cestice u -takve kombinacije koje nemaju boju. Ne moe /se izdvojeno imati pojedinacni kvark, zato to,bi on imao boju (crvenu, zelenu ili plavu). (Umesto toga, jedan crveni kvark mora da (bude 'uetom' gluona povezan sa jednim *zelenim i jednim plavim kvarkom (crveno + .zeleno + plavo = belo). Ovakva trojka obrazuje'jedan proton ili jedan elektron. Druga .mogucnost jeste par u ciji sastav ulaze jedan .kvark i jedan antikvark (crveno + anticrveno, 2zeleno + antizeleno ili plavo + antiplavo = belo).)Ovakve kombinacije tvore cestice koje se /nazivaju mezoni i koje su nestabilne, zato to,se kvark i antikvark mogu medusobno potrti, ,pri cemu nastaju elektroni i druge cestice. +Slicno tome, ogranicenje onemogucava da se 0izdvojeno dobije pojedinacni gluon, zato to i ,gluoni imaju boju. Umesto toga, potrebno je 0imati skup gluona cije se boje sabiraju u belu. ,Ovakav skup obrazuje nestabilnu cesticu koja"se naziva 'vezano stanje gluona'. *Okolnost da ogranicenje onemogucava da se -dobiju izdvojeni kvark ili gluon kao da celu $zamisao o kvarkovima i gluonima kao 'cesticama cini unekoliko metafizickom. +Postoji, medutim, jo jedno svojstvo jake +nuklearne sile koje se naziva asimptoticka (sloboda i koje predstavu o kvarkovima i .gluonima cini sasvim odredenom. Pri normalnim /energijama, jaka nuklearna sila uistinu je jaka/i ona cvrsto povezuje kvarkove. Ogledi vreni ,na velikim akceleratorima cestica pokazuju, -medutim, da pri velikim energijama jaka sila .postaje znatno slabija, tako da se tu kvarkovi/i gluoni ponaaju gotovo kao slobodne cestice./Ilustracija 5.2 prikazuje snimak sudara izmedu -visokoenergetskih protona i antiprotona. Pri )tom je nastao veci broj gotovo slobodnih 0kvarkova, koji su svoj trag ostavili u vidu niza 'mlazeva'. .Uspeno objedinjenje elektromagnetne i slabe 0nuklearne sile nadahnulo je veci broj pokuaja $da se ove dve sile poveu sa jakom 0nuklearnom silom u velikoj objedinjenoj teoriji +(VOT). Ovaj naziv je, medutim, prekomeran: 1postavljene teorije nisu ni narocito velike, niti$su sasvim objedinjene, buduci da ne /obuhvataju gravitaciju. Uz to, posredi nisu ni ,uistinu celovite teorije, zato to sadre .izvestan broj parametara cije se vrednosti ne .mogu predvideti iz teorije, vec ih valja tako +odabrati da budu u saglasnosti sa nalazima .opita. No, one ipak predstavljaju korak napred/ka celovitoj, potpuno objedinjenoj teoriji. Evo+osnovne zamisli na kojoj se temelje VOT-i: *kao to je prethodno bilo pomenuto, jaka +nuklearna sila postaje slabija pri visokim -energijama. Sa druge strane, elektromagnetna /i slaba sila, koje nisu asimptoticki slobodne, .postaju snanije pri visokim energijama. Pri -nekoj veoma visokoj energiji, koja se naziva 1velika energija objedinjenja, ove tri sile imale *bi istu snagu, te bi tako mogle biti samo /razliciti vidovi jedne jedinstvene sile. VOT-i *takode predvidaju da ce pri ovoj energiji )razlicite cestice materije sa spinom 1/2 1takode biti u osnovi iste, cime se postie jo jedno objedinjenje. 0Vrednost velike energije objedinjenja nije jo *tacno poznata, ali ce ona po svoj prilici *morati da iznosi najmanje hiljadu miliona /miliona GeV. Sadanja generacija akceleratora .cestica moe da izazove njihovo sudaranje pri(energijama od oko 100 GeV, a planira se /izgradnja maina koje bi ovu vrednost podigle .na nekoliko hiljada GeV. Medutim, maina koja+bi bila dovoljno mocna da ubrza cestice do /velike energije objedinjenja morala bi da bude +velika poput Suncevog sistema - tako da je /malo verovatno da bi se za nju nala sredstva +u trenutnoj ekonomskoj klimi. Nemoguce je, -dakle, staviti na proveru velike objedinjene 0teorije neposredno u laboratoriji. Medutim, ba)kao i u slucaju teorije koja objedinjuje /elektomagnetnu i slabu nuklearnu silu, postoje -niskoenergetske posledice teorije koju treba proveriti. -Najzanimljivije medu njima jeste predvidanje ,da se protoni, koji sacinjavaju najveci deo $mase obicne materije, mogu spontano (raspadati na lake cestice kao to su ,antielektroni. Ovo je moguce stoga to pri +velikoj energiji objedinjenja nema nikakve *sutinske razlike izmedu jednog kvarka i *jednog antielektrona. Tri kvarka u jednom -protonu normalno nemaju dovoljno energije da -se promene u antielektrone, ali sasvim retko /jedan od njih moe steci dovoljno energije za .ovaj prelaz, buduci da iz nacela neodredenosti,proishodi da energija kvarkova u protonu ne ,moe tacno biti fiksirana. To bi dovelo do *raspadanja protona. No, verovatnoca da ce ,jedan kvark steci dovoljno energije tako je ,mala da bi se na ovako neto moralo cekati 0najmanje milion miliona miliona miliona miliona +godina (jedinica iza koje se prua niz od .trideset nula). To je znatno due od vremena -proteklog od Velikog Praska, koje priblino .iznosi tek pukih deset hiljada miliona godina 1(jedinica iza koje se prua niz od deset nula). ,Na osnovu ovoga moglo bi se pomisliti da se *mogucnost spontanog raspadanja protona ne *moe eksperimentalno proveriti. Medutim, -izgledi za otkrice ovakvog raspadanja mogu se)povecati ako se posmatra velika kolicina ,materije koja sadri ogroman broj protona. -(Ako se, na primer, posmatra tokom razdoblja *od godinu dana broj protona koji je ravan ,jedinici iza koje se prua niz od trideset )jedne nule, moglo bi se ocekivati, prema -najjednostavnijem VOT-u, da se uoci vie od jednog raspadanja protona.) -Izveden je izvestan broj ovakvih ogleda, ali %nijedan nije pruio konacan dokaz o *raspadanju protona ili neutrona. U jednom /opitu koriceno je osam hiljada tona vode i on.je preduzet u rudniku soli Morton u Ohaju (da 'bi se izbegli drugi dogadaji, izazvani /kosmickim zracima, koji bi mogli biti pobrkani (sa raspadanjem protona). Buduci da nije (zabeleeno spontano raspadanje protona +tokom eksperimenta, moe se izracunati da +verovatni ivot protona mora biti veci od .deset miliona miliona miliona miliona miliona +godina (jedinica iza koje se prua niz od .trideset jedne nule). Ovo je due od vremena +koje predvida najjednostavnija objedinjena 1teorija, ali postoje sloenije teorije u kojima .je predvideni vek protona dui. Da bi se one 3proverile, bice potrebni jo osetljiviji opiti sa vecim kolicinama materije. +Iako je veoma teko registrovati spontano (raspadanje protona, sasvim je moguce da ,samo nae postojanje predstavlja posledicu ,obrnutog procesa, obrazovanja protona, ili, .jednostavnije, kvarkova, iz pocetne situacije &u kojoj nije bilo vie kvarkova nego -antikvarkova, to predstavlja najprirodniji 'nacin da se zamisli pocetak Vaseljene. +Materija na Zemlji poglavito je sazdana od .protona i neutrona, koji su, pak, sastavljeni &od kvarkova. Ne postoje antiprotoni i -antineutroni sacinjeni od antikvarkova, osim 0onih nekoliko koje fizicari proizvode u velikim -akceleratorima cestica. Posredstvom kosmickih*zraka znamo da isto vai i za svu ostalu 1materiju u naoj Galaksiji: nema antiprotona ili.antineutrona, osim onog malog broja koji biva ,obrazovan u vidu parova cestica-anticestica *pri visokoenergetskim sudarima. Kada bi u +naoj Galaksiji postojala velika podrucja +antimaterije, ocekivali bismo da beleimo +obimne kolicine zracenja sa granica izmedu +oblasti materije i antimaterije, gde bi se !mnoge cestice sudarale sa svojim 1anticesticama, potiruci se pri tom i odailjuci visokoenergetsko zracenje. ,Ne raspolaemo neposrednim nalazima o tome .da li je materija u drugim galaksijama sazdana+od protona i neutrona ili od antiprotona i -antineutrona, ali mora biti jedna od ove dve +mogucnosti: ne moe postojati meavina u /jednoj galaksiji, buduci da bismo u tom slucaju.takode registrovali zamano zracenje nastalo (pri potiranju. Stoga smatramo da se sve 'galaksije sastoje od kvarkova, a ne od -antikvarkova; izgleda, naime, neverovatno da +su neke galaksije sacinjene od materije, a druge od antimaterije. *Zbog cega, medutim, ima nesravnjivo vie ,kvarkova od antikvarkova? Zato ne postoji *jednak broj jednih i drugih? Po nas je to ,svakako srecna okolnost to su ovi brojevi (nejednaki, jer da nije tako, gotovo svi /kvarkovi i antikvarkovi medusobno bi se potrli -jo u ranoj Vaseljeni, koja bi potom ostala .ispunjena jedino zracenjem, a ne i materijom. )Tada ne bi postojale galaksije, zvezde i .planete na kojima bi se mogao razviti ljudski 0ivot. Srecom, velike objedinjene teorije mogle'bi da prue odgovor na pitanje zato +Vaseljena sada sadri vie kvarkova nego +antikvarkova, cak i ako je u pocetku imala *podjednak broj ovih cestica. Kao to smo )videli, VOT-i doputaju mogucnost da se (kvarkovi pretvaraju u antielektrone pri 'visokim energijama. Ove teorije takode (doputaju obrnute procese, pretvaranje "antikvarkova u elektrone, odnosno (pretvaranje elektrona i antielektrona u ,antikvarkove i kvarkove. Postojalo je jedno +vreme u veoma ranoj Vaseljeni kada je bilo (tako toplo da su energije cestica imale )dovoljno visoku vrednost da dode do ovih )pretvaranja. Ali zato je ovo dovelo do -nastajanja vie kvarkova nego antikvarkova? 1Razlog je to to zakoni fizike nisu sasvim isti za cestice i anticestice. *Sve do 1956. smatralo se da zakoni fizike -ostaju ravnopravno na snazi u sve tri zasebne0simetrije koje se nazivaju C, P i T. Simetrija C*znaci da su zakoni isti kod cestica i kod 0anticestica. Simetrija P znaci da su zakoni isti*kod bilo koje situacije i njenog odraza u -ogledalu (odraz u ogledalu neke cestice koja +ima desni spin jeste cestica koja ima levi /spin). Simetrija T znaci da ako se okrene smer /kretanja cestica i anticestica, onda bi sistem 0trebalo da se vrati u predanja stanja; drugim -recima, zakoni su isti kod kretanja napred i nazad kroz vreme. )Godine 1956. dvojica americkih fizicara, *Cung-Dao Li i Cen Ning Jang, izloila su /zamisao da se slaba sila ne pokorava simetriji *P. Drugim recima, slaba sila dovela bi do -razvoja Vaseljene na drugaciji nacin od onoga)na koji bi se razvijala slika u ogledalu +Vaseljene. Jo iste godine, jedna njihova /koleginica, Cijen iung Vu, dokazala je da je /pretpostavka Lija i Janga tacna. To je ucinila &na taj nacin to je postavila jezgra ,radioaktivnih atoma u magnetno polje tako da-su se sva okretala u istom smeru, pokazavi +pri tom da do oslobadanja elektrona dolazi ,vie u jednom smeru nego u drugom. Naredne /godine Li i Jang dobili su Nobelovu nagradu za ,svoju zamisao. Takode je ustanovljeno da se 0slaba sila ne pokorava ni simetriji C. To znaci *da bi se Vaseljena sazdana od anticestica 0ponaala razlicito od nae Vaseljene. No, kako-izgleda, slaba sila se pokorava kombinovanoj -simetriji CP. Drugim recima, Vaseljena bi se ,razvijala na isti nacin kao i njena slika u *ogledalu ako bi se svaka cestica zamenila ,anticesticom! Medutim, 1964. godine dvojica .drugih Amerikanaca, D. V. Kronin i Vol Fic, /ustanovila su da cak ni CP simetrija ne ostaje ,na snazi u slucaju izvesnih cestica koje se +nazivaju K-mezoni. Kronin i Fic su konacno *dobili Nobelovu nagradu za svoj rad 1980. /(Mnotvo ovih nagrada je dodeljeno fizicarima (koji su pokazali da Vaseljena nije tako +jednostavna kako se to nama moglo ciniti!) ,Postoji jedna matematicka teorema koja kae*da svaka teorija koja je u saglasnosti sa ,kvantnom mehanikom i relativnocu mora uvek/da se pokorava udruenoj simetriji CPT. Drugim/recima, Vaseljena bi morala da se ponaa isto ,ako se cestice zamene anticesticama, ako je 0posredi njena slika u ogledalu i ako je okrenut .smer vremena. Ali Kronin i Fic su pokazali da +ako se cestice zamene anticesticama i uzme (slika u ogledalu, ali se ne okrene smer .vremena, onda se Vaseljena ne ponaa na isti 'nacin. Zakoni fizike se, dakle, moraju +promeniti - ako se okrene smer vremena oni se ne pokoravaju simetriji T. &Rana Vaseljena svakako se ne pokorava .simetriji T: kako vreme tece napred, Vaseljena0se iri - kada bi teklo unazad, Vaseljena bi se0saimala. Kako, dakle, postoje sile koje se ne (pokoravaju simetriji T, odavde sledi da )prilikom irenja Vaseljene te sile mogu .izazvati da se vie antielektrona pretvara u (kvarkove nego elektrona u antikvarkove. *Potom, kako se Vaseljena bude rairila i 'ohladila, antikvarkovi bi se potrli sa 1kvarkovima, ali kako bi ovih potonjih bilo vie &nego prvih, javio bi se izvestan mali (preostatak kvarkova. Upravo ovaj pretek -obrazovao bi materiju koju mi vidimo danas i .od koje smo i sami sazdani. Prema tome, nae )samo postojanje moglo bi se smatrati kao -potvrda velikih objedinjenih teorija, premda -samo kvalitativna; neodredenosti su takve da -se ne moe predvideti broj kvarkova koji bi 0preostao posle potiranja, pa cak ni to da li bi ,preostali kvarkovi ili antikvarkovi. (Da je *posredi bio pretek antikvarkova, medutim, )onda bismo naprosto antikvarkove nazvali (kvarkovima, a kvarkove antikvarkovima.) .Velike objedinjene teorije ne obuhvataju silu &gravitacije. Ovo, medutim, nije odvec *znacajno, buduci da je gravitacija sasvim ,slaba sila, tako da se njena dejstva obicno ,mogu zanemariti kada su posredi elementarne .cestice i atomi. Medutim, cinjenica da je ona ,dalekodometna i uvek privlacna znaci da joj .se dejstva sabiraju. Prema tome, kod dovoljno ,velikog broja cestica materije gravitaciona 0sila odnosi prevagu u odnosu na sve ostale sile.0To je i razlog to gravitacija odreduje razvoj (Vaseljene. Cak i kada su u pitanju tela /velicine zvezda, privlacno dejstvo gravitacije -moe da nadjaca sve ostale sile i da dovede *do kolabiranja zvezde. Tokom sedamdesetih *godina, ja sam se bavio izucavanjem crnih 'rupa koje mogu da proishode iz ovakvog #kolabiranja zvezda, kao i snanog .gravitacionog polja oko njih. Upravo ovaj rad +naveo me je na pomisao o tome kako se mogu )dovesti u vezu kvantna mehanika i opta /relativnost: bio je to prvi nagovetaj buduce kvantne teorije gravitacije. 6. CRNE RUPE )Termin crne rupe sasvim je novog datuma. +Godine 1969. skovao ga je americki naucnik 0Don Viler kao graficki opis jedne zamisli koja*je stara najmanje dve stotine godina. Ova ,zamisao potice iz vremena kada su postojale /dve teorije o svetlosti. Prema prvoj, kojoj je -Njutn davao preimucstvo, svetlost je sazdana ,od cestica; prema drugoj, ona se sastoji od ,talasa. Mi danas znamo da su, u stvari, obe /teorije ispravne. Prema dvojnosti talas-cestica+iz kvantne mehanike, svetlost moe biti i *talas i cestica. U teoriji prema kojoj je /svetlost sazdana od talasa nije bilo jasno kako,ce ona reagovati na gravitaciju. Ali ako se +svetlost sastoji od cestica, onda se moe 0ocekivati da na njih deluje gravitacija na isti .nacin na koji utice na topovsku dulad, rakete /i planete. Naucnici su u pocetku mislili da se -cestice svetlosti krecu beskonacno brzo, tako)da gravitacija ne bi bila u stanju da ih .usporava, ali Remerovo otkrice da se svetlost (krece konacnom brzinom znacilo je da bi +gravitacija mogla da vri na nju znacajan uticaj. +Poavi od ove pretpostavke, profesor sa *Kembrida Don Micel objavio je 1783. u /Philosophical Transaction of the Royal Society -of London rad u kome je istakao da bi zvezda .koja je dovoljno masivna i zbijena imala tako /snano gravitaciono polje da mu ni svetlost ne/bi mogla pobeci: svetlost zracenu sa povrine /zvezde gravitaciono polje vratilo bi natrag pre*no to bi ona znatnije odmakla. Micel je .smatrao da moda postoji veliki broj ovakvih -zvezda. Iako mi ne bismo bili u stanju da ih 0vidimo, zato to do nas ne bi stizala svetlost $sa njih, ipak bismo osecali njihovo )gravitaciono privlacenje. Ove objekte mi +danas nazivamo crne rupe, zato to su oni .upravo to: crne praznine u kosmosu. Na slicnu *zamisao doao je nekoliko godina kasnije 'francuski naucnik Laplas, kako izgleda /nezavisno od Micela. Zanimljivo je da je Laplas.ukljucio ovu ideju samo u prvo i drugo izdanje*svoje knjige Sistem sveta, da bi je potom *izostavio u narednim izdanjima; moda je /doao do zakljucka da je posredi luda zamisao..(I teorija prema kojoj se svetlost sastoji od &cestica pala je u nemilost naucnika u -devetnaestom stolecu; izgledalo je da se sve /moe objasniti iz perspektive talasne prirode .svetlosti, a prema njoj nije bilo jasno da li )gravitacija uopte deluje na svetlost.) +Nije, medutim, sasvim na mestu izjednaciti )svetlost sa topovskom duladi u Njutnovoj 2teoriji gravitacije, zato to je brzina svetlosti(nepromenljiva. (Topovsko dule koje biva /ispaljeno uvis sa Zemlje gravitacija ce najpre ,usporavati, a potom i zaustaviti, da bi ono *zatim pocelo da pada natrag na povrinu; ,jedan foton, medutim, mora da nastavi nagore$stalnom brzinom. Kako u tom slucaju *njutnovska gravitacija moe da deluje na -svetlost?) Koherentna teorija o tome na koji 0nacin gravitacija utice na svetlost pojavila se *tek 1915, kada Ajntajn objavljuje svoju .optu relativnost. Pa cak i tada, proteci ce -jo dugo pre no to bude shvaceno ta sve ,proishodi iz ove teorije u slucaju masivnih zvezda. +Da bismo razumeli kako moe nastati jedna 'crna rupa, potrebno je prethodno da se -upoznamo sa ivotnim ciklusom jedne zvezde. (Zvezda biva obrazovana onda kada velika .kolicina gasa (poglavito vodonika) pocinje da .kolabira pod dejstvom vlastitog gravitacionog /privlacenja. Kako se gas saima, njegovi atomi,se sve cece i sve vecom brzinom medusobno )sudaraju to dovodi do zagrevanja gasa. (Konacno, gas postaje toliko topao da se -vodonikovi atomi prilikom sudaranja vie ne )odbijaju jedan od drugoga, vec srastaju, /obrazujuci helijum. Toplota oslobodena pri ovoj(reakciji, koja nalikuje na kontrolisanu -eksploziju vodonicne bombe, dovodi do sijanja+zvezde. Ova dodatna toplota takode povecava.pritisak gasa, sve dok on ne postane dovoljno /visok da se javi kao protivtea gravitacionom +privlacenju, to zaustavlja njegovo dalje .saimanje. Situacija pomalo podseca na onu sa-balonom - postoji ravnotea izmedu pritiska .unutranjeg vazduha, koji pokuava da dalje /proiri balon, i napetosti gume, koja nastoji ,da smanji balon. Zvezda zadrava postojano -stanje veoma dugo, sa toplotom iz nuklearnih 'reakcija u ravnotei sa gravitacionim *privlacenjem. Konacno, medutim, zvezda ce 0istroiti zalihe vodonika i ostalog nuklearnog +goriva. Paradoksalno, to jedna zvezda na -pocetku svog veka ima vie goriva, to ce ga 1ona bre istroiti. Uzrok ovome je okolnost da +to je zvezda masivnija, to ona mora biti (toplija da bi uspostavila ravnoteu sa 1gravitacionim privlacenjem. A to je toplija, to0ce bre koristiti svoje gorivo. Nae Sunce po 0svoj prilici ima dovoljno goriva za narednih pet-hiljada miliona godina, ali masivnije zvezde *mogu da potroe svoje zalihe za samo sto -miliona godina, to je znatno krace od veka -Vaseljene. Kada zvezdi ponestane goriva, ona .pocinje da se hladi, pa tako i da se saima. -Ono to se tada moe dogoditi sa njom prvi ,put je shvaceno tek krajem dvadesetih godina ovog veka. &Godine 1928, mladi diplomac iz Indije ,Subramanijan Candrasekar krenuo je na put u %Englesku da bi u Kembridu preduzeo (izucavanja sa britanskim astronomom ser *Arturom Edingtonom, strucnjakom za optu 'relativnost. (Prica se da je, pocetkom (dvadesetih godina, jedan novinar upitao ,Edingtona da li je tacno da samo tri coveka ,na celom svetu shvataju optu relativnost. 'Edington je malo zastao, pa odgovorio: ,'Pokuavam da se setim ko bi mogao da bude 'treci.') Za vreme putovanja iz Indije, -Cendrasekar je preduzeo da izracuna koliko bi-jedna zvezda mogla da bude velika, a da se i 2dalje suprotstavi vlastitoj gravitaciji poto je 1utroila sve svoje gorivo. Zamisao se sastojala &u sledecem: kada zvezda postane mala, ,cestice materije se veoma zblie, tako da, ,prema Paulijevom nacelu iskljucenja, moraju .da imaju veoma razlicite brzine. Ovo ih nagoni(da se udaljuju jedne od drugih, to za ,posledicu ima tenju zvezde da se rairi. *Jedna zvezda moe stoga zadrati stalan ,precnik time to ce uspostaviti ravnoteu -izmedu gravitacionog privlacenja i odbijanja /koje proishodi iz nacela iskljucenja, ba kao /to je u prethodnom razdoblju toplota stajala kao protivtea gravitaciji. ,Candrasekar je, medutim, shvatio da postoji 'granica odbijanja to sledi iz nacela 0iskljucenja. Teorija relativnosti nalae da je ,najveca razlika u brzinama cestica materije .neke zvezde brzina svetlosti. Ovo znaci da bi,$kada zvezda postane dovoljno gusta, .odbijanje uzrokovano nacelom iskljucenja bilo &slabije od gravitacionog privlacenja. ,Candrasekar je izracunao da hladna zvezda sa-masom vecom od jedne i po Sunceve ne bi vie'bila kadra da se suprotstavi vlastitoj ,gravitaciji. (Ova masa je danas poznata kao ,Candrasekarova granica.) Do slicnog otkrica 0doao je priblino u isto vreme ruski naucnik Lav Davidovic Landau. .Odavde su sledile vane posledice po krajnju *sudbinu masivnih zvezda. Ako je masa neke )zvezde ispod Candrasekarove granice, ona 0moe da prestane da se saima i da se ustali u0zavrnom stanju koje se naziva 'beli patuljak',)sa precnikom od nekoliko hiljada milja i .gustinom od vie stotina tona po kubnom incu.(Osnov postojanosti belog patuljka jeste -odbijanje izmedu elektrona njegove materije, 2proisteklo iz nacela iskljucenja. Zabeleili smo ,veliki broj ovakvih zvezda-belih patuljaka. )Jedna od prvih koja je otkrivena bila je .zvezda koja krui oko Sirijusa, najsjajnijeg sunca na nocnom nebu. .Landau je istakao da postoji jo jedno moguce,zavrno stanje neke zvezde, takode sa masom+ogranicenom na vrednost izmedu jedne i dve +Sunceve, ali koje je znatno manje cak i od (belog patuljka. Kod ovakvih zvezda, kao ,protivtea gravitaciji takode bi se javilo 0odbijanje proisteklo iz nacela iskljucenja, ali &ne vie izmedu elektrona, vec izmedu )neutrona i protona. Ove zvezde dobile su (stoga naziv neutronske zvezde. One bi u ,precniku imale tek desetak milja, dok bi im ,gustina iznosila na stotine miliona tona po ,kubnom incu. U vreme kada je prvobitno bila .izloena pretpostavka o njihovom postojanju, %nije bilo nacina na koji su se mogle +registrovati. Do njihovog stvarnog otkrica dolo je tek znatno kasnije. &Zvezde sa masama iznad Candrasekarove *granice, sa druge strane, suocavaju se sa ,jednim velikim problemom kada utroe svoje (gorivo. U nekim slucajevima one mogu da )eksplodiraju, te tako uspevaju da odbace ,dovoljno materije, cime smanjuju masu ispod )recene granice i na taj nacin izbegavaju 0katastrofalan gravitacioni kolaps; no, teko je,poverovati da se ovo uvek dogada, bez obzira-na velicinu zvezde. Kako bi ona mogla da zna ,da treba da izgubi teinu? Pa cak i ako bi ,svaka zvezda uspela da izgubi dovoljno mase 0da izbegne kolaps, ta bi se dogodilo ako biste,dodavali novu masu nekom belom patuljku ili .neutronskoj zvezdi, tako da oni na kraju ipak .prekorace Candrasekarovu granicu? Da li bi oni-kolabirali do beskrajne gustine? Edington je ,bio zapanjen ovom mogucnocu i odbio je da -poveruje u Candrasekarov nalaz. Smatrao je da$je naprosto nemoguce da neka zvezda 2kolabira do razmera tacke. Isto miljenje delila /je vecina naucnika: i sam Ajntajn je objavio (rad u kome je tvrdio da se zvezde ne bi -smanjile do nultih razmera. Odbojno dranje &drugih naucnika, a posebno Edingtona, 'Candrasekarovog predanjeg ucitelja i 'vodeceg autoriteta na polju ustrojstva +zvezda, nagnalo je Candrasekara da napusti +rad na ovom podrucju i da se usredsredi na (druge astronomske probleme, kao to je %kretanje zvezdanih jata. Kada mu je, -medutim, pripala Nobelova nagrada 1983, bilo &je to, bar delimicno, za njegova rana *izucavanja granicnih masa hladnih zvezda. -On je pokazao da nacelo iskljucenja ne moe .spreciti kolabiranje jedne zvezde cija se masa)nalazi iznad Candrasekarove granice, ali -problem razumevanja onoga to ce se dogoditi$sa takvom zvezdom, saglasno optoj 3relativnosti, prvi je reio mladi americki fizicar,Robert Openhajmer 1939. Iz njegovih nalaza, .medutim, proishodilo je da nece biti nikakvih (posmatrackih posledica koje bi se mogle -registrovati teleskopima iz tog vremena. No, .ubrzo je izbio drugi svetski rat i Openhajmer ,se potpuno posvetio radu na projektu atomske)bombe. Posle rata, problem gravitacionog ,kolapsa bio je uglavnom zaboravljen, buduci -da je vecina naucnika postala usredsredena na&ono to se zbiva u razmerama atoma i +njegovog jezgra. Tokom ezdesetih godina, +medutim, zamano povecanje obima i dometa "astronomskih posmatranja, nastalo *zahvaljujuci primeni moderne tehnologije, &dovelo je do oivljenja zanimanja za %makrokosmicke probleme astronomije i .kosmologije. Vie naucnika ponovo je otkrilo *Openhajmerov rad i krenulo dalje njegovim tragom. ,Openhajmerovo pregalatvo omogucilo nam je &da dodemo do sledece predstave o ovom *problemu. Gravitaciono polje zvezde menja ,putanje svetlosnih zraka u prostorvremenu u -odnosu na one kojima bi se ovi zraci kretali +kada tu ne bi bilo zvezde. Svetlosne kupe, ,koje oznacavaju putanje kojima se u prostoru.i vremenu krecu blesci svetlosti emitovani sa .njihovih temena, bivaju blago povijeni unutra 0u blizini povrine zvezde. Ovo se moe videti *kod povijanja svetlosti sa dalekih zvezda (uocenog tokom pomracenja Sunca. Kako se -zvezda saima, gravitaciono polje na njenoj 0povrini postaje jace i svetlosne kupe se jo +vie povijaju unutra. To dodatno oteava .svetlosti da se otisne sa zvezde, tako da ona -izgleda zatamnjenija i crvenija posmatracu na+vecoj udaljenosti. Konacno, kada se zvezda (smanji do odredenog kriticnog precnika, (gravitaciono polje na povrini postaje *izuzetno snano, a svetlosne kupe toliko 0povijene unutra da se svetlost uopte vie ne *moe otisnuti (Ilus. 6.1). Prema teoriji .relativnosti, nita nije bre od svetlosti. /Stoga, kad svetlost nije u stanju da se otisne,*onda ni bilo ta drugo nije za to kadro; *gravitaciono polje privlaci sve natrag ka 0povrini. Postoji, dakle, jedan skup dogadaja, +jedno podrucje prostorvremena odakle se ne 2moe otisnuti nita to bi stiglo do udaljenog +posmatraca. Ovo podrucje mi danas nazivamo +crna rupa. Njegova granica dobila je naziv ,horizont dogadaja i podudara se sa putanjama0svetlosnih zraka koji zamalo to nisu uspeli dase otisnu iz crne rupe. /Da biste shvatili ta biste videli kada biste 'posmatrali kako neka zvezda kolabira i +obrazuje crnu rupu, morate imati na umu da 0prema teoriji relativnosti ne postoji apsolutno )vreme. Svaki posmatrac ima vlastitu meru +vremena. Usled gravitacionog polja zvezde, -vreme za nekoga na njoj bilo bi razlicito od (vremena za nekoga ko je udaljen od nje. -Zamislite jednog neustraivog astronauta na +povrini kolabirajuce zvezde; on kolabira ,zajedno sa njom, upucujuci pri tom po jedan &signal svake sekunde, mereno njegovim (casovnikom, ka maticnom kosmickom brodu )koji krui oko zvezde. U nekom trenutku +prema njegovom hronometru, recimo u 11:00, .zvezda ce se smanjiti ispod kriticnog precnika-na kome gravitaciono privlacenje postaje tako.snano da mu vie nita ne moe umaci, te 1tako njegovi signali vie nece stizati do broda.*Kako se 11:00 pribliava, njegove kolege (astronauti, koji posmatraju sa maticnog &broda, ustanovili bi da razmak izmedu /naizmenicnih signala to ih on alje postaje 0sve dui i dui, ali ovaj efekat bio bi veoma ,mali pre 10:59:59. Morali bi da cekaju samo *neto malo due od jedne sekunde izmedu .astronautovog signala u 10:59:58 i onoga to ,ga je on uputio kada mu je casovnik pokazao 110:59:59, ali bi zato na signal u 11:00 mogli da /cekaju celu vecnost. Svetlosni talasi emitovani-sa povrine zvezde izmedu 10:59:59 i 11:00, -mereno astronautovim casovnikom, rasprostrli -bi se na beskrajno dugo razdoblje, videno iz +perspektive kosmickog broda. Razmak izmedu *prispeca naizmenicnih talasa do kosmickog 0broda postajao bi sve dui, te bi tako svetlost,sa zvezde izgledala sve crvenija i slabija. +Konacno, zvezda bi postala tako zatamnjena *da se vie uopte ne bi mogla videti sa .kosmickog broda: sve to bi preostalo od nje )bila bi crna rupa u prostoru. Zvezda bi, .medutim, nastavila da vri isti gravitacioni 1uticaj na kosmicki brod, koji bi i dalje kruio oko crne rupe. $Ovaj scenario nije, medutim, sasvim /realistican zbog sledeceg problema. Gravitacija/postaje slabija to ste udaljeniji od zvezde, 0tako da bi sila tee koja dejstvuje na stopala -naeg astronauta uvek bila jaca od one koja *dejstvuje na njegovu glavu. Ova razlika u 2gravitacionoj sili izduila bi naeg astronauta .kao kakav rezanac ili bi ga raskomadala pre no0to bi se zvezda saela do kriticnog precnika 'na kome nastaje horizont dogadaja! Mi, )medutim, smatramo da postoje znatno veci ,objekti u Vaseljeni, kao to su sredinja -podrucja galaksija, koja takode mogu podleci +gravitacionom kolapsu i postati crne rupe; +jedan astronaut na nekom od njih ne bi bio .raskomadan pre nastanka crne rupe. tavie, )on ne bi osetio nita posebno dok bi se +pribliavao kriticnom precniku, pa bi cak *proao i tacku posle koje nema povratka, 0uopte je ne primetivi. No, za samo nekoliko &sati, kako podrucje bude nastavilo da .kolabira, razlika u gravitacionom privlacenju .na nivou njegove glave i nogu postala bi tako %velika da bi on ipak bio raskomadan. )Izucavanja koja smo Roder Penrouz i ja -obavili izmedu 1965. i 1970. pokazala su da, 1saglasno optoj relativnosti, u crnoj rupi mora +postojati singularnost beskrajne gustine i )beskrajne zakrivljenosti prostorvremena. .Situacija prilicno podseca na Veliki Prasak u *pocetku vremena, osim to bi to bio kraj -vremena za kolabirajuce telo i astronauta. U -toj singularnosti otkazali bi zakoni nauke i *naa sposobnost da predvidamo buducnost. -Svaki posmatrac, medutim, koji bi ostao izvan#crne rupe ne bi bio obuhvacen ovim *otkazivanjem mogucnosti predvidanja, zato 3to ni svetlost niti bilo koji drugi signal ne bi +do njega mogli stici iz singularnosti. Ova .izuzetna okolnost navela je Rodera Penrouza -da postavi hipotezu o kosmickoj cenzuri, koja/se moe parafrazirati kao 'Bog se gnua gole 2singularnosti'. Drugim recima, singularnosti to /ih stvara gravitacioni kolaps nastaju jedino na.onim mestima, kao to su crne rupe, gde ih od,spoljnjih pogleda savreno skriva horizont -dogadaja. Ova hipoteza poznata je i kao slaba-kosmicka cenzura: ona titi posmatrace koji $ostaju izvan crne rupe od posledica ,otkazivanja mogucnosti predvidanja, do cega .dolazi u singularnosti, ali nita ne cini za +ubogog i nesrecnog astronauta koji upada u rupu. *Postoje izvesna reenja jednacina opte .relativnosti u okviru kojih je moguce da na /astronaut vidi golu singularnost: on bi moda .mogao da izbegne sudar sa singularnocu i da (propadne kroz 'crvotocinu' u neko drugo +podrucje Vaseljene. Ovo bi pruilo velike 'mogucnosti za putovanja kroz prostor i -vreme, ali, na alost, izgleda da su sva ta &reenja veoma nestabilna; i najmanji 'poremecaj, kao to je prisustvo nekog +astronauta, mogao bi ih promeniti, tako da -astronaut ne vidi singularnost sve do sudara )sa njom i okoncanja svog vremena. Drugim 0recima, singularnost bi uvek leala u njegovoj ,buducnosti, a nikada u njegovoj prolosti. )Prema jakoj verziji hipoteze o kosmickoj (cenzuri, u jednom realisticnom reenju ,singularnosti ce uvek leati ili potpuno u ,buducnosti (kao singularnosti gravitacionog .kolapsa) ili potpuno u prolosti (kao Veliki +Prasak). Postoje, medutim, i takve verzije +hipoteze cenzure prema kojima je u blizini -golih singularnosti moda moguce putovati u 0prolost. I dok je ova okolnost zgodna za pisce.naucne fantastike, iz nje proishodi da niciji 1ivot vie ne bi bio bezbedan: neko bi, naime, -mogao da ode u prolost i da vam tamo ubije .oca ili majku pre no to ste vi uopte bili zaceti. $Horizont dogadaja, granica podrucja +prostorvremena iz koga nije moguce pobeci, *deluje u prilicnoj meri kao membrana to )optace crnu rupu, propusna samo sa jedne 0strane: tela, kao to su neoprezni astronauti, (mogu da upadnu kroz horizont dogadaja u 2crnu rupu, ali nita iz nje ne moe izici natrag-kroz horizont dogadaja. (Imajte na umu da je +horizont dogadaja putanja u prostorvremenu .svetlosti koja pokuava da se otisne iz crne /rupe, a nita nije u stanju da se krece bre +od svetlosti.) Za horizont dogadaja sasvim +vae reci koje je Dante stavio na ulazu u 0pakao: 'Vi koji ulazite, napustite svaku nadu.' (Sve to prode i svi koji produ granicu )horizonta dogadaja uskoro ce se obreti u ,podrucju beskrajne gustine i kraja vremena. .Opta relativnost predvida da ce teka tela -koja se krecu izazvati emisije gravitacionih 0talasa, talasanja u zakrivljenosti prostora koja/ce se kretati brzinom svetlosti. Oni su slicni (svetlosnim talasima, koji predstavljaju ,talasanje elektromagnetnog polja, ali ih je 2znatno tee otkriti. Poput svetlosti, ovi talasi ,odnose energiju iz tela koja ih emituju. Na +osnovu ovoga, ocekivalo bi se da se sistem ,masivnih tela konacno ustali u stacionarnom +stanju, zato to ce emisije gravitacionih -talasa odnositi energiju pri svakoj kretnji. .(Stvar prilicno nalikuje na bacanje plutace u .vodu: u pocetku ona znatno oscilira gore-dole,/ali kako joj talasi odnose energiju, konacno se.smiruje u stacionarnom stanju.) Primera radi, )kretanje Zemlje njenom orbitom oko Sunca .proizvodi gravitacione talase. Posledica ovog ,gubitka energije trebalo bi da bude promena (orbite Zemlje, tako da se ona sve vie 0pribliava Suncu, da bi se konacno sudarila sa *njim i tako prela u stacionarno stanje. *Medutim, stopa gubitka energije u slucaju (Zemlje i Sunca veoma je mala - dovoljna 1otprilike za rad jedne male elektricne grejalice.0To znaci da bi bilo potrebno priblino hiljadu 0miliona miliona miliona miliona godina da Zemlja(zbog ovoga padne na Sunce, tako da nema ,neposrednog razloga za zabrinutost! Promena -Zemljine orbite odvec je mala da bi se mogla 0registrovati, ali ovaj efekat ipak je zabeleen,tokom poslednjih godina u sistemu koji nosi +oznaku PSR 1913+16 (PSR oznacava 'pulsar', )jedan poseban tip neutronske zvezde koji *emituje pravilne impulse radio-talasa). U ,sistemu se nalaze dve neutronske zvezde koje,orbitiraju jedna oko druge, a energija koju -gube emitovanjem gravitacionih talasa nagoni #ih da se medusobno stalno spiralno pribliavaju. ,Za vreme gravitacionog kolapsa jedne zvezde ,koja postaje crna rupa sva kretanja bila bi -znatno bra, tako da bi i daleko via bila ,stopa kojom se odliva energija. Stoga ne bi ,proteklo dugo pre no to se ona upostoji u *stacionarnom stanju. Kako bi izgledalo to .zavrno stanje? Moe se pretpostaviti da bi /ono zavisilo od niza sloenih svojstava zvezde*obrazovanih pri njenom nastanku - ne samo 0od mase i brzine okretanja, vec i od razlicitih +gustina u raznim delovima zvezde, kao i od .sloenih kretanja gasa u njoj. A ako su crne &rupe arolike kao i objekti cijim su -kolabiranjem one nastale, onda bi bilo veoma +teko doci do nekih optih predvidanja o crnim rupama. -Godine 1967, medutim, Verner Izrael, kanadski-naucnik (koji je roden u Berlinu, odrastao u 1Junoj Africi, a doktorirao u Irskoj), doveo je -do prave revolucije u izucavanju crnih rupa. $On je pokazao da, saobrazno optoj 0relativnosti, nerotirajuce crne rupe moraju biti/veoma jednostavne; bile bi savreno loptaste, /a velicina bi im zavisila jedino od mase, to -znaci da bi bilo koje dve crne rupe sa istom *masom bile istovetne. One bi se, zapravo, (mogle opisati jednim posebnim reenjem 0Ajntajnovih jednacina, do koga je doao Karl )varcild neposredno po otkricu opte +relativnosti. U pocetku su mnogi fizicari, /racunajuci tu i samog Izraela, smatrali da crne/rupe, buduci da moraju biti savreno loptaste,'mogu nastati kolabiranjem jedino nekog 0savreno loptastog tela. Shodno tome, prilikom .kolabiranja stvarnih zvezda - koje nikada nisu.savreno loptaste - mogla bi da nastane samo gola singularnost. -Javilo se, medutim, jedno drugacije tumacenje/rezultata do kojih je Izrael doao, a njegovi 0glavni zagovornici postali su Roder Penrouz i 1Don Viler. Oni su smatrali da bi brza kretanja /proistekla iz kolabiranja zvezde znacila da bi 0je emitovanje gravitacionih talasa ucinilo jo (loptastijom, tako da bi, u casu kada bi /dospela u stacionarno stanje, postala savreno.loptasta. Prema ovom gleditu, medutim, svaka.nerotirajuca zvezde, bez obzira na sloenost )njenog oblika i unutranjeg ustrojstva, )okoncala bi gravitaciono kolabiranje kao /savreno loptasta crna rupa, cija bi velicina 'zavisila jedino od njene mase. Potonja 1izracunavanja ila su u prilog ovom stanovitu +i ono je uskoro postalo opte prihvaceno. 0Ishodi Izraelovih izucavanja odnosili su se samo/na slucaj crnih rupa nastalih iz nerotirajucih -tela. Godine 1963, novozelandski fizicar Roj 0Ker doao je do niza reenja jednacina opte /relativnosti koja su opisivala rotirajuce crne .rupe. Ove 'Kerove' crne rupe okrecu se stalnom-brzinom, pri cemu im velicina i oblik zavise .jedino od mase i brzine rotiranja. Ukoliko je ,rotacija ravna nuli, crna rupa je savreno 1okrugla i reenje se poklapa sa varcildovim /reenjem. Ako se, pak, okretanje razlikuje od 1nule, crna rupa se izbocuje blizu polutara (ba ,kao to je to slucaj sa Zemljom ili Suncem 1takode usled rotiranja); to je okretanje bre,/to je i ova izbocenost naglaenija. Stoga, da *bi se Izraelovim rezultatima obuhvatila i /rotirajuca tela, bilo je pretpostavljeno da bi +svako rotirajuce telo koje se kolabiranjem )pretvorilo u crnu rupu konacno dospelo u &stacionarno stanje, opisano u Kerovom reenju. Godine 1970. jedan moj kolega i +student-istraivac sa Kembrida, Brendon 'Karter, nacinio je prvi korak u pravcu ,dokazivanja ove pretpostavke. On je pokazao *da, pod uslovom da stacionarna rotirajuca .crna rupa ima osu simetrije, poput cigre koja 3se vrti, njena velicina i oblik zavisili bi jedino *od mase i brzine rotiranja. Potom sam ja, #1971, dokazao da svaka stacionarna 0rotirajuca crna rupa uistinu ima ovu simetrije. ,Konacno, 1973, Dejvid Robinson sa londonskog(koleda Kings pokazao je, koristeci se &Karterovim i mojim rezultatima, da je ,pretpostavka tacna: ovakva crna rupa odista .se poklapala sa Kerovim reenjem. Prema tome,,posle gravitacionog kolapsa jedna crna rupa -mora dospeti u stanje u kome bi se okretala, 6ali ne i pulsirala. tavie, njena velicina i oblik 0zavisili bi jedino od mase i brzine okretanja, a)ne od prirode tela cijim je kolabiranjem *nastala. Ovaj rezultat postao je poznat u (obliku maksime: 'Crna rupa nema dlaka.' -Teorema 'bez dlaka' od velikog je prakticnog ,znacaja, zato to sasvim ogranicava moguce +tipove crnih rupa. Postalo je stoga moguce -naciniti veoma podrobne modele objekata koji 'bi mogli da sadre crne rupe, a potom )uporediti predvidanja modela sa nalazima -posmatranja. Odavde je takode proishodilo da .veoma velika kolicina informacija o telu koje .je kolabiralo mora biti izgubljena u trenutku ,nastanka crne rupe, zato to potom sve ono .to moemo da izmerimo kod tela jesu njegova&masa i brzina rotiranja. Znacaj ovoga "pokazace se u narednom poglavlju. -Crne rupe predstavljaju jedan od sasvim malog-broja slucajeva u povesti nauke kada je neka *teorija bila veoma podrobno razvijena kao 0matematicki model pre no to se dolo do bilo .kakvih posmatrackih nalaza da je ona valjana. 1tavie, ovo je koriceno kao glavni argument +protivnika zamisli o crnim rupama: kako se .moe verovati u objekte za cije su postojanje*jedini dokaz proracuni koji se temelje na .sumnjivoj teoriji opte relativnosti? Godine )1963, medutim, Marten mit, astronom iz 0kalifornijske opservatorije Palomar, izmerio je +crveni pomak jednog slabanog zvezdolikog (objekta koji se nalazio u pravcu izvora *radio-talasa sa oznakom 3C273 (posredi je ,izvor pod brojem 273 u trecem kembridskom /katalogu radio-izvora). Ustanovio je da je ovaj,pomak preveliki da bi njegov uzrocnik moglo +biti gravitaciono polje: da je posredi bio -gravitacioni crveni pomak, objekt bi morao da,bude toliko masivan i tako blizu nama da bi &nesumnjivo izazivao poremecaje orbita +planeta u Suncevom sistemu. Ovo je ukazalo )na mogucnost da bi uzrok recenog crvenog /pomaka moglo biti irenje Vaseljene, to je, .opet, znacilo da se doticni objekat nalazi na -ogromnoj udaljenosti. A da bi bio vidljiv na )tako ogromnoj udaljenosti, morao je biti *veoma sjajan, odnosno morao je da emituje ,ogromnu kolicinu energije. Jedini zamislivi -mehanizam za stvaranje ovako velikih kolicina-energije bilo je gravitaciono kolabiranje ne )samo jedne zvezde, vec celog sredinjeg +podrucja neke galaksije. Potom je otkriven ,veliki broj drugih, slicnih 'kvazistelarnih 1objekata', ili kvazara, koji su svi imali velike .crvene pomake. Ali svi su oni veoma udaljeni, ,tako da je veoma teko posmatranjem doci do,cvrstog dokaza o tome da su tu posredi crne rupe. 2Do novih nalaza koji su ili u prilog postojanju )crnih rupa dolo se 1967, kada je jedna 1studentkinja-istraivac sa Kembrida, Doselin*Bel, otkrila na nebu objekte koji emituju +pravilne impulse radio-talasa. U prvi mah, 2Belova i njen mentor, Entoni Hjui, pomislili su #da su uspostavili kontakt sa nekom +vanzemaljskom civilizacijom u Galaksiji! I +odista, secam se da su na seminaru na kome .su obznanili svoje otkrice prva cetiri ovakva *izvora oznacili skracenicama LGM 1-4, pri *cemu je LGM akronim od 'Little Green Man' /('mali zeleni covek'). Konacno, medutim, oni i *svi ostali doli su do manje romanticnog ,zakljucka da su svi objekti, koji su dobili /naziv pulsari, u stvari, rotirajuce neutronske .zvezde koje emituju impulse radio-talasa usled&sloenog medudejstva izmedu njihovih .magnetnih polja i okolne materije. Bila je to ,loa vest za pisce kosmickih vesterna, ali .veoma prijatna za nekolicinu nas koji smo u to+vreme verovali u crne rupe: bio je to prvi )pozitivan nalaz o postojanju neutronskih ,zvezda. Jedna neutronska zvezda ima precnik /od desetak milja, to je samo za nekoliko puta)vece od kriticnog precnika na kome jedna +zvezda postaje crna rupa. Ako jedna zvezda .moe da kolabira do tako malih razmera, nije *neosnovano ocekivati da druge zvezde mogu 0da kolabiraju do jo manjih velicina i da tako postanu crne rupe. )Kako moemo ocekivati da otkrijemo crnu )rupu kada ona, po definiciji, ne emituje /svetlost? Situacija pomalo nalikuje na traganje*za crnom mackom u tamnom podrumu. Srecom, ,postoji nacin. Kao to je to pokazao Don +Micel u svom pionirskom radu iz 1783, crna 3rupa i dalje vri gravitacioni uticaj na oblinje)objekte. Astronomi su registrovali mnogo -sistema kod kojih dve zvezde krue jedna oko*druge, medusobno privlacene gravitacijom. +Takode su uocili sisteme kod kojih postoji +samo jedna vidljiva zvezda to krui oko )nekog nevidljivog pratioca. Ne moe se, 'razume se, odmah zakljuciti da je ovaj /pratilac crna rupa: moda je posredi naprosto ,zvezda koja je odvec slaba da bi se videla. +Medutim, neki od ovih sistema, kao to je 0onaj koji je dobio naziv Labud X-1 (Ilus. 6.2), +takode su veoma snani izvori rendgenskog +zracenja. Najverovatnije objanjenje ovog 'fenomena jeste da materija nekako biva /skidana sa povrine vidljive zvezde. Kako pada/na nevidljivog pratioca, ona se krece spiralno *(poput vode koja otice iz kade) i postaje +veoma topla, emitujuci rendgensko zracenje .(Ilus. 6.3). Da bi ovaj mehanizam dejstvovao, /nevidljivi objekat mora biti veoma mali, poput +belog patuljka, neutronske zvezde ili crne .rupe. Na osnovu uocene orbite vidljive zvezde 'moe se odrediti najmanja moguca masa .nevidljivog objekta. U slucaju Labuda X-1, ova-masa estostruko nadmaa Suncevu, to je, 'prema Candrasekarovom rezultatu, odvec 1velika vrednost da bi nevidljivi objekat bio beli)patuljak. Posredi je prevelika masa i za +neutronsku zvezdu. Kako izgleda, u pitanju mora biti crna rupa. +Postoje, dodue, i drugi modeli kojima se +objanjava Labud X-1, a koji ne ukljucuju 1crnu rupu, ali svi su oni prilicno nategnuti. Po +svemu sudeci, crna rupa predstavlja jedino +uistinu prirodno objanjenje posmatrackih )nalaza. No, uprkos svemu tome, ja sam se +opkladio sa Kipom Tornom iz Kalifornijskog .instituta za tehnologiju da Labud X-1 ipak ne ,sadri crnu rupu! To je za mene svojevrsno 0osiguranje. Uloio sam silan trud u crne rupe, *koji bi sav postao uzaludan ukoliko bi se 0ispostavilo da one, u stvari, ne postoje. Ali u ,tom slucaju naao bih utehu u okolnosti da %sam dobio opkladu, koja bi mi donela .cetvorogodinju pretplatu na casopis Private 'Eye. Ako se, pak, pokae da crne rupe 0postoje, Kip ce dobiti jednogodinju pretplatu -na Penthouse. Kada smo sklopili ovu opkladu, -1975, bili smo osamdeset odsto sigurni da je -Labud X-1 crna rupa. Rekao bih da danas naa/sigurnost dostie oko 95 odsto, ali tek treba videti ko je dobio opkladu. -Danas takode raspolaemo nalazima o nekoliko-drugih crnih rupa u sistemima slicnim Labudu ,X-1 u naoj Galaksiji, kao i u dve susedne .galaksije koje se nazivaju Magelanovi oblaci. ,Broj crnih rupa, medutim, gotovo je sigurno ,znatno veci; u dugoj povesti Vaseljene mnoge%zvezde mora da su izgorele sve svoje /nuklearno gorivo, da bi potom kolabirale. Nije -cak iskljuceno da je broj crnih rupa veci od +broja vidljivih zvezda, koji samo u naoj *Galaksiji iznosi oko sto hiljada miliona. 'Dodatno gravitaciono privlacenje ovako *velikog broja crnih rupa moglo bi da bude -objanjenje cinjenice da se naa Galaksija *okrece sadanjom brzinom: masa vidljivih ,zvezda nedovoljna je za tako veliku brzinu. )Takode raspolaemo izvesnim nalazima da (postoji jedna znatno veca crna rupa, sa &masom koja iznosi oko stotinu hiljada 0Suncevih, u sreditu nae Galaksije. Zvezde u 1Galaksiji koje se odvec priblie ovoj crnoj rupi*raskomadace razlika u snazi gravitacionog -privlacenja na blioj i udaljenijoj strani. -Njihovi ostaci, kao i gas koji je odbacen sa )drugih zvezda, pocece da padaju ka crnoj /rupi. Kao i u slucaju Labuda X-1, gas ce stati *da se spiralno sunovraca i da se zagreva, (premda ne u istoj meri. On nece postati %dovoljno topao da emituje rendgensko ,zracenje, ali bi mogao da bude objanjenje %veoma zbijenog izvora radio-talasa i -infracrvenog zracenja koji su registrovani u sreditu Galaksije. +Smatra se da slicne, premda jo vece crne *rupe, sa masama koje oko sto miliona puta *premauju Suncevu, postoje u sreditima #kvazara. Materija koja pada u tako ,supermasivne crne rupe obrazovala bi jedini ,dovoljno snaan izvor energije kojim bi se /mogla objasniti ogromna kolicina zracenja to -je emituju ovi objekti. Kako se ova materija 0spiralno sputa u crnu rupu, ona bi je nagnala .da pocne da se okrece u istom pravcu, to bi -za posledicu imalo nastajanje magnetnog polja*slicnog onome na Zemlji. Materija koja se 0sunovraca tvorila bi u blizini crne rupe cestice+sa veoma visokom energijom. Magnetno polje *bilo bi tako snano da bi fokusiralo ove /cestice u mlazove koji bi bili izbacivani du )ose rotacije crne rupe, odnosno u pravcu /njenog severnog i junog pola. Ovakvi mlazevi /uistinu su uoceni kod izvesnog broja galaksija i kvazara. %Moe se takode razmotriti mogucnost 'postojanja crnih rupa sa masama znatno *manjim od Sunceve. Ovakve crne rupe ne bi ,mogle da nastanu pod dejstvom gravitacionog +kolapsa, zato to im se mase nalaze ispod *Candrasekarove granice: zvezde ovako male -mase mogu da se suprotstave sili tee cak i /onda kada su utroile svoje nuklearno gorivo. )Crne rupe sa malom masom mogu da nastanu (jedino onda ako je materija sabijena do (ogromnih gustina veoma velikim spoljnim ,pritiscima. Ovakvi uslovi mogu da nastanu u +izuzetno velikoj vodonicnoj bombi: fizicar /Don Viler izracunao je jednom da ako bi se iz-svih okeana na Zemlji uzela sva teka voda, -mogla bi se napraviti vodonicna bomba koja bi0u toj meri sabila materiju u sreditu da bi tu *nastala crna rupa. (Razume se, niko ne bi -preostao kao ocevidac!) Prakticnija mogucnost+jeste da su takve crne rupe sa malom masom /nastale pri visokim temperaturama i pritiscima )veoma rane Vaseljene. Crne rupe mogle su ,nastati jedino ako rana Vaseljena nije bila .savreno ravnomerna i jednoobrazna, zato to)se jedino neko malo podrucje sa gustinom -vecom od prosecne moglo sabiti na ovaj nacin -da se tu obrazuje crna rupa. A mi znamo da su.morale postojati ovakve nepravilnosti, jer bi 1inace materija u Vaseljeni i dalje bila savreno,jednoobrazno razmetena, umesto da postane okupljena u zvezde i galaksije. ,Pitanje da li bi nepravilnosti neophodne za (nastanak zvezda i galaksija dovele i do -obrazovanja znacajnijeg broja 'praiskonskih' -crnih rupa ocigledno zavisi od tacnih uslova /koji su vladali u ranoj Vaseljeni. Stoga, kada .bismo mogli da ustanovimo koliko praiskonskih .crnih rupa ima sada, izuzetno bismo obogatili 'nae znanje o veoma ranim razdobljima +Vaseljene. Praiskonske crne rupe sa masama -iznad hiljadu miliona tona (masa neke velike /planine) mogle bi se otkriti jedino posredstvom)njihovog gravitacionog uticaja na drugu, 2vidljivu materiju ili na irenje Vaseljene. Kako ,cemo, medutim, videti u narednom poglavlju, .crne rupe nisu, zapravo, stvarno crne: one se /sjaje poput usijanog tela, a to su manje, to 2im je sjaj snaniji. I tako, paradoksalno, moe ,se pokazati da je lake otkriti manje crne rupe od onih velikih. 7. CRNE RUPE NISU TAKO CRNE .Pre 1970. moja izucavanja opte relativnosti 0bila su usredsredena poglavito na pitanje da li *je postojala singularnost Velikog Praska. ,Medutim, jedne veceri u novembru te godine, ,nedugo po rodenju moje kceri Lusi, poceo sam)da razmiljam o crnim rupama dok sam se ,spremao za pocinak. Zbog moje invalidnosti, -odlaenje s veceri u postelju prilicno dugo -traje, tako da sam imao vremena na pretek. U +to vreme nije postojala tacna definicija o ,tome koje tacke prostorvremena lee unutar %crne rupe, a koje izvan nje. Vec sam +razmotrio sa Roderom Penrouzom zamisao o ,definisanju crnih rupa kao niza dogadaja iz .kojih nije moguce pobeci na veliku udaljenost,(to sada predstavlja opte prihvacenu ,definiciju. Ovo znaci da granicu crne rupe, ,horizont dogadaja, obrazuju u prostorvremenu/putanje svetlosnih zraka koji zamalo to nisu +uspeli da se otisnu iz crne rupe, ostavi .zauvek na njenom rubu (Ilus. 7.1). Ovo pomalo *podseca na beanje od policije: uspevate .nekako da budete na korak ispred nje, ali ne ida je se otarasite! (Najednom sam shvatio da se putanje ovih ,svetlosnih zraka nikada ne mogu pribliiti /jedna drugoj. Ako bi do toga dolo, one bi na /kraju morale da se sretnu. A to bi bilo kao da ,naletite na nekog drugog ko takode bei od /policije, ali u suprotnom smeru, tako da biste 3obojica bili uhvaceni! (Ili, u ovom slucaju, pali u+crnu rupu.) Ukoliko bi, medutim, crna rupa .progutala ove svetlosne zrake, onda oni ne bi *mogli biti na njenoj granici. Prema tome, &putanje svetlosnih zraka na horizontu *dogadaja uvek moraju ici uporedo jedna sa +drugom ili se medusobno udaljavati. Ovo se /moe predociti na jo jedan nacin: zamislite ,da je horizont dogadaja, granica crne rupe, *ivica neke senke - senke neumitnog usuda. -Ako osmotrite senku koju stvara neki izvor na%velikoj udaljenosti, kakav je Sunce, .zapazicete da se zraci svetlosti na ivicama nepribliuju jedni drugima. +Ako zraci svetlosti koji obrazuju horizont ,dogadaja, granicu crne rupe, nikada ne mogu (da se priblie jedni drugima, podrucje /horizonta dogadaja moe da ostane isto ili da *se povecava sa vremenom, ali nikada se ne 1moe smanjiti, zato to bi to znacilo da bi bar-neki zraci svetlosti na granici morali da se 0priblie jedni drugima. U stvari, ovo podrucje )bi se povecavalo kad god bi materija ili /zracenje dospeli u crnu rupu (Ilus. 7.2). Isto )tako, ako bi se dve crne rupe sudarile i +spojile, obrazujuci jedinstvenu crnu rupu, )podrucje horizonta dogadaja te nove crne -rupe bilo bi vece od zbira ili jednako zbiru -podrucja horizonta dogadaja prvobitnih crnih -rupa (Ilus. 7.3). Ovo svojstvo nesmanjivanja &podrucja horizonta dogadaja postavlja (znacajno ogranicenje mogucem ponaanju .crnih rupa. Otkrice do koga sam doao toliko -me je uzbudilo da nisam mnogo spavao te noci.,Narednog dana pozvao sam Rodera Penrouza. .On se saglasio sa mnom. Mislim, zapravo, da je(on vec podozrevao ovo svojstvo podrucja -horizonta dogadaja. On je, medutim, koristio .jednu malo drugaciju definiciju crne rupe. Ono-to nije shvatio bilo je da ce granice crne -rupe prema obema teorijama biti iste, pa tako+i njihova podrucja, pod uslovom da je crna -rupa dospela u stanje u kome se nece menjati sa vremenom. -Ovakvo ponaanje crne rupe, cije se podrucje+nije moglo smanjiti, veoma je podsecalo na ,ponaanje jedne velicine iz fizike koja se (naziva entropija i kojom se meri stepen )nereda nekog sistema. Cinjenica da ce se +nered samo povecati ako se stvari prepuste +samima sebi predstavlja stvar svakodnevnog (iskustva. (Potrebno je samo prestati sa $opravkama oko kuce, pa da ovo odmah *postane jasno!) Moguce je stvoriti red iz 0nereda (moe se, na primer, obojiti kuca), ali 1to nalae ulaganje napora ili energije, te tako 0smanjuje kolicinu raspoloive uredene energije.,Tacan iskaz ove zamisli poznat je kao drugi (zakon termodinamike. Prema ovom zakonu, +entropija nekog izdvojenog sistema uvek se ,povecava, a kada se dva takva sistema spoje,)entropija novog sistema veca je od zbira .entropija pojedinacnih sistema. Primera radi, *razmotrimo slucaj sistema molekula gasa u 0nekoj kutiji. Ovi molekuli mogu se zamisliti kao)male bilijarske kugle koje se neprekidno (medusobno sudaraju i odbijaju od zidova .kutije. to je via temperatura gasa, to se ,molekuli bre krecu, te se tako i cece i 0silovitije sudaraju sa zidovima kutije, pa je i -veci pritisak sa usmerenjem ka spolja na ove +zidove. Zamislimo da su u pocetku molekuli (nekom pregradom ograniceni samo na levu /stranu kutije. Ukoliko se ova pregrada ukloni, .molekuli ce ispoljiti tenju da se raire i +rasprostru na obe polovine kutije. U nekom -poznijem vremenu oni mogu, igrom slucaja, svi0da se nadu u desnoj polovini ili natrag u levoj,.ali je nesravnjivo verovatnije da ce se u obe 2polovine naci priblino isti broj. Ovo stanje je -manje sredeno, ili nesredenije od prvobitnog -stanja u kome su se svi molekuli nalazili na 0jednoj polovini. Stoga se kae da se entropija +gasa povecala. Slicno tome, zamislimo da u )pocetku imamo dve kutije, od kojih jedna -sadri molekule kiseonika, a druga molekule 0azota. Ako se dve kutije spoje i ukloni zid koji.ih razdvaja, molekuli kiseonika i azota pocece$da se meaju. U neko poznije vreme 'najverovatnije stanje bila bi prilicno ,jednoobrazna meavina molekula kiseonika i -azota u obe kutije. Ovo stanje bilo bi manje /sredeno, te bi stoga imalo i vecu entropiju, od$pocetnog stanja dve zasebne kutije. /Drugi zakon termodinamike ima prilicno razlicit-status od ostalih zakona nauke, kao to je, +na primer, Njutnov zakon gravitacije, zato 0to on ne vai uvek, vec samo u velikoj vecini-slucajeva. Verovatnoca da ce se svi molekuli 0gasa u naoj prvoj kutiji naci u jednoj njenoj +polovini u neko poznije vreme iznosi jedan ,prema mnogo miliona miliona, ali se to ipak .moe dogoditi. Kada je, medutim, posredi crna.rupa, postoji jedan znatno laki nacin da se -narui drugi zakon: samo ubacite u nju malo .materije sa puno entropije, kakva je kutija sa-gasom. Ukupna entropija izvan crne rupe ce se/smanjiti. Moe se, razume se, i dalje reci da /se ukupna entropija, racunajuci tu i entropiju ,u crnoj rupi, nije smanjila - ali kako nema .nacina da se zaviri u crnu rupu, ne moemo ni+da ustanovimo kojom se entropijom odlikuje .materija u njoj. Bilo bi stoga zgodno kada bi -postojalo neko svojstvo crne rupe po kome bi .posmatraci izvan nje mogli da ustanove kolika /joj je entropija i koje bi se povecalo kad god 1bi materija to nosi entropiju pala u crnu rupu./Poavi od prethodno opisanog otkrica, prema $kome se podrucje horizonta dogadaja +povecava kad god nova materija dospe u crnu.rupu, jedan student-istraivac sa Prinstona, *po imenu Dejkob Bekenstajn, izloio je 'zamisao da podrucje horizonta dogadaja *predstavlja meru entropije crne rupe. Kad *materija koja nosi entropiju padne u crnu ,rupu, povecava se podrucje njenog horizonta -dogadaja, tako da se nikada ne smanjuje zbir -entropije materije izvan crnih rupa i unutar podrucja horizonta dogadaja. -Ova zamisao kao da je sprecavala da u vecini +situacija dode do naruenja drugog zakona ,termodinamike. Postojala je, medutim, jedna +kobna pogreka. Ako, naime, crna rupa ima .entropiju, onda ona mora imati i temperaturu. (Ali telo sa nekom posebnom temperaturom (mora emitovati zracenje nekom odredenom -stopom. Iz uobicajenog iskustva se zna da ako0se arac zagreje u vatri, on ce poceti da sjaji1crvenim usijanjem i da odailje zracenje, ali i *tela na nioj temperaturi takode emituju )zracenje; no, ono se normalno ne uocava, /zato to je posredi sasvim mala kolicina. Ovo (zracenje je neophodno da bi se sprecilo .naruavanje drugog zakona. Crne rupe, dakle, .moraju da odailju zracenje. Ali prema samoj /njihovoj definiciji, crne rupe su objekti koji .ne mogu nita da emituju. Izgledalo je stoga )da podrucje horizonta dogadaja neke crne +rupe ne moe da bude smatrano merom njene .entropije. Godine 1972. objavio sam jedan rad *sa Brendonom Karterom i americkim kolegom ,Dimom Bardinom u kome smo istakli da iako 'ima mnogo slicnosti izmedu entropije i +podrucja horizonta dogadaja, postoji, kako ,izgleda, ova nepremostiva potekoca. Moram 'priznati da me je na pisanje ovog rada +delimicno podstakla ljutnja na Bekenstajna (koji je, smatrao sam, zloupotrebio moje 'otkrice o povecanju podrucja horizonta .dogadaja. Ispostavilo se, medutim, na kraju da,je on u osnovi bio u pravu, premda na nacin "koji zacelo ni sam nije ocekivao. (Septembra 1973, prilikom posete Moskvi, *razgovarao sam o crnim rupama sa dvojicom 'vodecih sovjetskih strucnjaka, Jakovom .Zeldovicem i Aleksandrom Starobinskim. Oni su *me uverili da, prema nacelu neodredenosti -kvantne mehanike, rotirajuce crne rupe treba )da stvaraju i odailju cestice. Njihovi )argumenti izgledali su mi prihvatljivi u )fizikalnom pogledu, ali mi se nije dopao ,matematicki nacin na koji su izracunali ovo -emitovanje. Latio sam se stoga posla da dodem*do boljeg matematickog postupka, koji sam (opisao na jednom neformalnom seminaru u *Oksfordu krajem novembra 1973. U to vreme )jo nisam obavio proracune tacnog obima ,emitovanja. Ocekivao sam jedino da otkrijem +zracenje iz rotirajucih crnih rupa koje su ,predvideli Zeldovic i Starobinski. Medutim, ,kada sam najzad obavio proracune, ustanovio )sam, na moje iznenadenje i ljutnju, da i .nerotirajuce crne rupe treba, kako izgleda, da/stvaraju i odailju cestice postojanom stopom.*U prvi mah sam pomislio da ovo emitovanje -ukazuje na to da jedna od aproksimacija koje /sam koristio nije bila valjana. Pobojao sam se (da bi Bekenstajn, ukoliko bi to otkrio, ,iskoristio ovu okolnost kao novi argument u 0prilog svojim zamislima o entropiji crnih rupa, /koje mi se i dalje nisu dopadale. No, to sam 1vie razmiljao o celoj stvari, to mi je vie -izgledalo da su aproksimacije ipak na mestu. )Ali ono to me je konacno uverilo da su +emitovanja stvarna bila je cinjenica da je ,spektar odaslanih cestica bio upravo onakav &kakav bi emitovalo neko telo u stanju /usijanja, kao i da crne rupe odailju cestice +upravo onom stopom koja je neophodna da bi ,se sprecilo naruenje drugog zakona. Posle /toga, drugi fizicari ponovili su ove proracune -u citavom nizu razlicitih oblika. Svi su oni (potvrdili da crna rupa treba da emituje ,cestice i zracenje kao da je posredi telo u ,stanju usijanja sa temperaturom koja zavisi -jedino od mase crne rupe: to je masa veca, to je temperatura nia. 'Kako je moguce da izgleda da crna rupa .odailje cestice kada nam je dobro poznato da1se ne moe otisnuti nita to se nalazi ispod -horizonta dogadaja? Odgovor glasi, govori nam.kvantna teorija, da cestice ne poticu iz crne +rupe, vec iz 'praznog' prostora neposredno -iznad njenog horizonta dogadaja! Ovo se moe'razumeti na sledeci nacin: ono to mi )podrazumevamo pod 'praznim' prostorom ne +moe biti potpuno prazno, zato to bi to /znacilo da bi vrednost svih polja, kao to su ,gravitaciono ili elektromagnetno, morala da *bude ravna nuli. Medutim, vrednost jednog )polja i stopa njegove promene s vremenom /odgovaraju poloaju i brzini neke cestice: iz *nacela neodredenosti proishodi da to se +tacnije zna jedno od ovih svojstava, to se &nepouzdanije zna drugo. Prema tome, u ,praznom prostoru polje nikada ne moe biti ,ravno nuli, zato to bi u tom slucaju bile ,sasvim odredene i njegova vrednost (nula) i -stopa promene (nula). Mora postojati izvesna /minimalna kolicina neodredenosti, ili kvantnih 0fluktuacija, u vrednosti polja. Ove fluktuacije .mogu se predociti kao parovi cestica svetlosti(ili gravitacije, koje u jednom trenutku .izgledaju zajedno, da bi se potom razdvojile, +a zatim ponovo spojile i medusobno potrle. .Posredi su virtuelne cestice slicne cesticama .koje nose gravitacionu silu Sunca: za razliku $od stvarnih cestica, one se ne mogu ,neposredno registrovati detektorom cestica. -Moguce je, medutim, izmeriti njihova posredna-dejstva, kao to su male promene u energiji /elektrona to orbitiraju u atomu, pri cemu ce (se pokazati da ce se ona izuzetno tacno /podudariti sa teorijskim predvidanjima. Nacelo $neodredenosti takode predvida da ce *postojati slicni virtuelni parovi cestica /materije kao to su elektroni ili kvarkovi. U ,ovom slucaju, medutim, jedan clan para bice *cestica, a drugi anticestica (anticestice 0svetlosti i gravitacije iste su kao i cestice). .Buduci da se energija ne moe stvoriti ni iz cega, jedan od clanova para .cestica-anticestica imace pozitivnu energiju, ,dok ce drugi clan imati negativnu energiju. +Onome sa negativnom energijom sudeno je da .bude kratkovecna virtuelna cestica, zato to -stvarne cestice uvek imaju pozitivnu enegiju +pod normalnim okolnostima. On, dakle, mora .potraiti svog partnera i potrti se sa njim. .Medutim, jedna stvarna cestica u blizini nekog.masivnog tela ima manje energije nego to bi ,imala kada bi se nalazila podalje od njega, .zato to troi energiju na suprotstavljanje .gravitacionom privlacenju tog tela. Normalno, (energija cestice jo je pozitivna, ali 0gravitaciono polje u crnoj rupi tako je snano (da tu cak i stvarna cestica moe imati 'negativnu energiju. Stoga je moguce da +virtuelna cestica sa negativnom energijom, )koja upadne u crnu rupu, postane stvarna 1cestica ili anticestica. U ovom slucaju ona vie-ne mora da se potre sa svojim partnerom. Njen.naputen partner moe i sam da dospe u crnu -rupu. Ili, buduci da ima pozitivnu energiju, -takode moe da pobegne iz blizine crne rupe 1kao stvarna cestica ili anticestica (Ilus. 7.4). ,Udaljenom posmatracu izgledalo bi da je ovu /cesticu emitovala crna rupa. to je crna rupa .manja, to je kraca razdaljina koju cestica sa *negativnom energijom mora da prede pre no /to postane stvarna cestica, te je tako veci i,obim emitovanja, kao i prividna temperatura crne rupe. /Kao protivtea pozitivnoj energiji emitovanog 'zracenja javio bi se priliv cestica sa (negativnom energijom u crnu rupu. Prema +Ajntajnovoj jednacini, E = mc2 (gde je E )energija, m masa, a c brzina svetlosti), +energija je upravno srazmerna masi. Priliv ,negativne energije u crnu rupu dovodi stoga ,do smanjenja njene mase. Kako crna rupa gubi)masu, podrucje njenog horizonta dogadaja +postaje manje, ali ovo smanjenje entropije -crne rupe dobija vie nego punu nadoknadu u -entropiji emitovanog zracenja, tako da nikada)ne dolazi do naruavanja drugog zakona. /tavie, to je manja masa crne rupe, to je *via njena temperatura. Prema tome, kako )crna rupa gubi masu, dolazi do povecanja +njene temperature i stope emitovanja, tako /da ona bre gubi masu. Nije sasvim jasno ta &se dogada kada masa crne rupe postane /izuzetno mala, ali najrazlonija pretpostavka +jeste da ce potpuno nestati u fantasticnom .zavrnom odlivu emitovanja, ravnom eksploziji mnogo miliona vodonicnih bombi. ,Jedna crna rupa s masom koja svega nekoliko -puta premaa Suncevu imala bi temperaturu od*samo jednog desetomilionitog dela stepena -iznad apsolutne nule. Ovo je znatno manje od (temperature mikrotalasnog zracenja koje +ispunjava Vaseljenu (oko 2,7 stepeni iznad -apsolutne nule), tako da ce ovakve crne rupe *emitovati jo manje nego to apsorbuju. 0Ukoliko je Vaseljeni sudeno da se zauvek iri, +temperatura mikrotalasnog zracenja konacno ,ce pasti ispod one to je ima jedna ovakva ,crna rupa koja ce tada poceti da gubi masu. ,Ali cak i onda temperatura ce joj biti tako -niska da ce biti potrebno oko milion miliona 0miliona miliona miliona miliona miliona miliona -miliona miliona miliona godina (jedinica iza 2koje se prua niz od ezdeset est nula) da bi )potpuno isparila. Ovo je znatno due od .starosti Vaseljene, koja dostie svega deset 2ili dvadeset hiljada miliona godina (jedinica ili /dvojka iza kojih se prua niz od deset nula). (Sa druge strane, kao to je pomenuto u .estom poglavlju, moda postoje praiskonske )crne rupe sa znatno manjom masom koje su ,nastale kolabiranjem nepravilnosti u sasvim ,ranom razdoblju Vaseljene. Ovakve crne rupe 2imale bi znatno viu temperaturu i odailjale bi*zracenje daleko vecom stopom. Praiskonska 'crna rupa sa pocetnom masom od hiljadu ,miliona tona imala bi vek priblino jednak -starosti Vaseljene. Praiskonske crne rupe sa +pocetnim masama ispod ove vrednosti vec bi *bile potpuno isparile, dok bi one sa malo +vecom masom i dalje emitovale rendgensko i gama-zracenje. Ovo rendgensko i -gama-zracenje slicno je svetlosnim talasima, -ali ima znatno kracu talasnu duinu. Ovakve /rupe teko da zasluuju pridev crne: one su, -zapravo, u stanju belog usijanja i odailju %energiju obimom od oko deset hiljada megavata. *Ovakva crna rupa mogla bi da napaja deset +velikih elektrana kada bismo samo mogli da .ukrotimo njenu energiju. Ovo bi, medutim, bilo1prilicno teko: crna rupa imala bi masu planine ,sabijenu u zapreminu manju od jednog milion -milionitog dela inca, to odgovara velicini ,jezgra atoma! Ako biste na povrini Zemlje /imali jednu takvu crnu rupu, ne bi bilo nacina +da se spreci njeno propadanje do sredita -nae planete. Ona bi jedno vreme oscilirala +kroz Zemlju, da bi se konacno zaustavila u +sreditu. Prema tome, jedino mesto gde se -moe postaviti ovakva crna rupa, cija bi se -emitovana energija mogla korisno upotrebiti, 1bila bi orbita oko nae planete - a jedini nacin.na koji se ona moe dopremiti tamo bio bi da /se privuce tako to bi ispred nje bila vucena /neka velika masa, ba kao to magarac ide za .argarepom koja je postavljena ispred njega. -Ali cak i ako ne budemo u stanju da ukrotimo *energetska emitovanja iz tih praiskonskih 0crnih rupa, kakvi su izgledi da ih registrujemo?!Mogli bismo se dati u potragu za *gama-zracenjem koje praiskonske crne rupe ,emituju tokom najveceg dela svog veka. Iako ,bi zracenje sa vecine njih bilo veoma slabo -zbog velike udaljenosti, ukupan zbir sa svih ,njih moda bi se mogao otkriti. Mi uistinu /beleimo takav fon gama-zracenja: ilustracija (7.5 pokazuje kako se registrovana snaga -menja sa promenom ucestalosti (brojem talasa .u sekundi). Ovaj fon je, medutim, mogao biti, -a verovatno i jeste stvoren drugim procesima,/a ne praiskonskim crnim rupama. Iscrtana linija*na ilustraciji 7.5 pokazuje kako bi snaga (trebalo da se menja sa ucestalocu kod ,gama-zracenja to ga odailju praiskonske ,crne rupe, ukoliko bi ih u proseku bilo tri .stotine po kubnoj svetlosnoj godini. Moe se -stoga reci da zabeleen fon gama-zracenja ne,prua nikakav pozitivan dokaz o postojanju /praiskonskih crnih rupa, ali nam zato govori da0ih u proseku ne moe biti vie od tri stotine )po kubnoj svetlosnoj godini u Vaseljeni. *Odavde proishodi da praiskonske crne rupe -mogu da sacinjavaju najvie jedan milioniti !deo ukupne materije u Vaseljeni. (Buduci da su praiskonske crne rupe tako ,retke, moe izgledati neverovatno da ce se +jedna od njih naci dovoljno blizu nas kako 0bismo je mogli zabeleiti kao pojedinacni izvor)gama-zracenja. Ali s obzirom na to da bi -gravitacija privlacila praiskonske crne rupe .prema bilo kojoj materiji, njih bi trebalo da .bude prilicno u galaksijama i oko njih. Prema +tome, iako nam fon gama-zracenja govori da 0ne moe biti vie od tri stotine praiskonskih )crnih rupa po kubnoj svetlosnoj godini u .proseku, on nam nita ne kae o tome koliko 1ih moe biti u naoj Galaksiji. Ako su one tu, .recimo, milion puta zastupljenije, onda bi se /crna rupa najblia nama verovatno nalazila na /udaljenosti od oko hiljadu miliona kilometara, 0to priblino odgovara razdaljini do Plutona, &najudaljenije poznate planete. Na toj 0razdaljini i dalje bi bilo veoma teko otkriti .postojanu emisiju neke crne rupe, cak i ako bi-njena snaga iznosila deset hiljada megavata. -Da bi se registrovala jedna praiskonska crna &rupe potrebno je otkriti vie kvanta *gama-zracenja koji dolaze iz istog pravca *tokom nekog dueg razdoblja, kao to je -jedna sedmica. U protivnom, posredi bi mogao .biti naprosto deo fona zracenja. Ali Plankovo )kvantno nacelo govori nam da svaki kvant )gama-zracenja ima veoma visoku energiju, ,zato to se ovo zracenje odlikuje izuzetno )visokom ucestalocu, tako da ne bi bilo ,potrebno mnogo kvanta da bi se odaslalo cak .deset hiljada megavata. A da bi se registrovao/taj mali broj kvanta koji dolazi sa razdaljine &ravne Plutonovoj bio bi potreban veci *detektor gama-zracenja od svih koji su do 1sada sazdani. tavie, taj detektor trebalo bi "da se nalazi u kosmosu, zato to &gama-zracenje ne moe da prodre kroz atmosferu. .Razume se, ukoliko bi jedna crna rupa koja se 0nalazi na Plutonovoj udaljenosti dola do kraja2svog veka i eksplodirala, bilo bi lako zabeleiti1ovaj zavrni emisioni prasak. Ali ako crna rupa .emituje poslednjih deset ili dvadeset hiljada /miliona godina, izgledi da ona stigne do kraja *svog veka tokom narednih nekoliko godina, *umesto negde tokom vie miliona godina u 2prolosti ili buducnosti uistinu su sasvim mali! 0Prema tome, da biste doli u izvesnu priliku da-vidite neku eksploziju crne rupe pre no to .vam isteknu sredstva za istraivanje, morali )biste da pronadete nacin da registrujete -ovakve eksplozije na razdaljini od oko jedne 0svetlosne godine. I dalje biste bili suoceni sa )problemima obezbedenja velikog detektora &gama-zracenja kojim biste zabeleili ,gama-kvante odaslate prilikom eksplozije. U ,ovom slucaju, medutim, ne bi bilo neophodno /utvrditi da svi kvanti dolaze iz istog pravca: .bilo bi dovoljno uociti da svi stiu u veoma &kratkom razmaku, pa na osnovu toga sa -prilicno pouzdanosti znati da poticu iz iste eksplozije. +Jedan detektor gama-zracenja koji bi mogao -da bude kadar da registruje praiskonske crne ,rupe jeste svekolika Zemljina atmosfera. (U ,svakom slucaju, malo je verovatno da smo mi ,u stanju da sazdamo veci detektor!) Kada se +jedan visokoenergetski kvant gama-zracenja )sudari sa atomima u naoj atmosferi, on $stvara parove elektrona i pozitrona -(antielektrona). Kada se ovi, pak, sudare sa )drugim atomima, oni stvaraju nove parove ,elektrona i pozitrona, tako da tada nastaje 0ono to se naziva elektronski pljusak. Krajnji -ishod jeste jedan oblik svetlosti poznat kao ,Cerenkovljevo zracenje. Eksplozivne emisije -gama-zracenja mogle bi se, dakle, otkriti po ,bleskovima svetlosti na nocnom nebu. Razume 'se, postoje i druge pojave koje takode .izazivaju bleskove na nebu, kao to su munje ,i odrazi Sunceve svetlosti sa satelita koji /padaju i raznih otpadaka na orbiti. Eksplozivne.emisije gama-zracenja mogle bi se razlikovati -od ovakvih dejstava tako to bi se bleskovi -uocili istovremeno sa dve ili vie prilicno *udaljenih tacaka. Istraivanja ove vrste .preduzela su dvojica naucnika iz Dablina, Nil *Porter i Trevor Viks, koji su za tu svrhu 2koristili teleskope u Arizoni. Oni su zabeleili 0izvestan broj bleskova, ali nijedan od njih nije,se bez ostatka mogao pripisati eksplozivnim &emisijama iz praiskonskih crnih rupa. )Cak i ako traganje za praiskonskim crnim -rupama ne urodi plodom, kao to bi to moglo )da se dogodi, ipak bismo doli do veoma %znacajnih informacija o sasvim ranim -razdobljima Vaseljene. Ako je rana Vaseljena 2bila haoticna ili nepravilna, ili ako je pritisak *materije bio nizak, ocekivalo bi se da ce -nastati znatno vie praiskonskih crnih rupa *nego to na to ukazuju naa dosadanja +posmatranja fona gama-zracenja. Jedino ako *je rana Vaseljena bila veoma ravnomerna i -jednoobrazna, sa visokim pritiskom, moglo bi .se objasniti odsustvo praiskonskih crnih rupa koje bi se mogle registrovati. -Zamisao o zracenju iz crnih rupa bio je prvi /primer predvidanja koje je na sutinski nacin -zavisilo od obe velike teorije ovog stoleca, *opte relativnosti i kvantne mehanike. U ,pocetku je ono izazvalo mnoga protivljenja, 0zato to je ugroavalo vladajuce stanovite: -'Kako crna rupa moe bilo ta da emituje?' +Kada sam prvi put obznanio rezultate mojih #proracuna na jednoj konferenciji u (Raderford-Epltonovoj laboratoriji blizu -Oksforda, suocio sam se sa optom nevericom..Pri kraju mog izlaganja predsedavajuci skupa, .Don G. Tejlor iz koleda Kings, u Londonu, -izjavio je da su sve to besmislice. Cak je o -tome objavio i jedan rad. Medutim, na kraju, 0vecina fizicara, racunajuci tu i Dona Tejlora,+dola je do zakljucka da crne rupe moraju 0zraciti poput tela u stanju usijanja, ukoliko se.nae ostale zamisli o optoj relativnosti i )kvantnoj mehanici isparavne. Prema tome, )iako jo nismo uspeli da pronademo neku .praiskonsku crnu rupu, postoji prilicno visok *stepen saglasnosti oko toga da ce, ako do 'ovog otkrica jednom dode, ta crna rupa (zacelo emitovati obimno gama-zracenje i rendgensko zracenje. -Postojanje zracenja iz crnih rupa ukazuje na )to da gravitacioni kolaps nije konacan i 0ireverzibilan kao to smo jednom smatrali. Ako -bi neki astronaut pao u crnu rupu, njena masa+bi se povecala, ali bi na kraju energetska .protivvrednost te mase bila vracena Vaseljeni *u obliku zracenja. Prema tome, u izvesnom 3smislu, astronaut bi bio 'recikliran'. Bila bi to, $medutim, ne ba najidealnija vrsta &besmrtnosti, buduci da bi svaka licna (predstava o vremenu kod astronauta bila +okoncana okolnocu da bi on munjevito bio .raskomadan u unutranjosti crne rupe! Cak bi /se i tipovi cestica koje bi crna rupa na kraju /emitovala u osnovi razlikovali od onih koji su (sacinjavali astronauta: jedino svojstvo .astronauta koje bi preivelo bila bi njegova masa ili energija. *Aproksimacije koje sam ja koristio da bih .doao do zakljucka o emisijama iz crnih rupa *sasvim su valjane u svim slucajevima kada )crna rupa ima masu vecu od delica jednog +grama. Medutim, one zakazuju na kraju veka ,crne rupe kada joj masa postaje veoma mala. /Kako izgleda, najverovatniji ishod jeste da ce -crna rupa naprosto iceznuti, bar iz naeg &podrucja Vaseljene, ponevi sa sobom .astronauta i sve singularnosti koje se u njoj /mogu nalaziti, ako uopte ima neke. Bio je ovo-prvi nagovetaj da bi kvantna mehanika mogla0da ukloni singuarnosti koje je predvidela opta+relativnost. Medutim, metodi koje smo ja i 3ostali fizicari koristili 1974. nisu bili kadri da &prue odgovor na pitanja da li ce se 0singularnosti javiti u kvantnoj gravitaciji. Od *1975. poceo sam da radim na jednom novom, /celovitijem pristupu kvantnoj gravitaciji koji *se temeljio na zamisli Ricarda Fajnmena o *zbiru po istorijama. O odgovorima na koje *ukazuje ovaj pristup u pogledu nastanka i 0sudbine Vaseljene i onoga to se nalazi u njoj,(racunajuci tu i astronaute, bice reci u )naredna dva poglavlja. Videcemo da, iako (nacelo neodredenosti ogranicava tacnost .naih predvidanja, ono bi u isto vreme moglo 0da otkloni temeljnu nepredvidljivost koja vai "za prostorvremensku singularnost. 8. NASTANAK I SUDBINA VASELJENE -Uzeta izdvojeno, Ajntajnova opta teorija )relativnosti predvida da je prostorvreme /pocelo singularnocu Velikog Praska i da ce se/okoncati ili singularnocu Velikog Saimanja *(ako cela Vaseljena bude kolabirala), ili /singularnocu u unutranjosti neke crne rupe ((ako dode do kolabiranja nekog lokalnog .podrucja, kao to je jedna zvezda). Materija .koja bi upala u crnu rupu bila bi unitena u 0singularnosti, a spolja bi nastavio da dejstvuje*jedino gravitacioni uticaj njene mase. Sa +druge strane, kada se uzmu u obzir kvantna /dejstva, masa ili energija konacno bi se, kako -izgleda, vratile u ostatak Vaseljene, a crna .rupa, zajedno sa eventualnom singularnocu u /njoj, isparila bi i konacno icezla. Moe li #kvantna mehanika da ima podjednako +dramatican uticaj na singularnosti Velikog -Praska i Velikog Saimanja? ta se uistinu (dogada tokom najranijih ili najpoznijih *razdoblja Vaseljene, kada su gravitaciona /polja tako snana da se kvantna dejstva vie -ne mogu zanemariti? Ima li Vaseljena uopte .pocetak ili kraj? A ako ih ima, kakvi su oni? %Tokom sedamdesetih godina, ja sam se ,poglavito bavio izucavanjem crnih rupa, ali +1981. moje zanimanje za pitanje nastanka i ,sudbine Vaseljene ponovo je oivelo poto 'sam prisustvovao jednoj konferenciji o 1kosmologiji koju su u Vatikanu priredili jezuiti./Katolicka crkva napravila je veliku greku sa ,Galilejem kada je pokuala da ospori jedan *naucni zakon, tvrdeci da Sunce krui oko .Zemlje. Sada, mnogo stoleca kasnije, odlucila .je da pozove izvestan broj strucnjaka koji bi ,joj pruili savete o kosmologiji. Na kraju .konferencije ucesnici su pozani na audijenciju*kod pape. On nam je kazao da je sasvim na 'mestu izucavati razvoj Vaseljene posle /Velikog Praska, ali ne bi trebalo da pokuamo ,da dokucimo sam Veliki Prasak, buduci da je .to bio trenutak Postanja, pa samim tim i delo ,Boga. Bilo mi je tada milo to on nije bio &upoznat sa predmetom mog izlaganja na -upravo okoncanoj konferenciji: ja sam, naime,(govorio o mogucnosti da je prostorvreme ,konacno, ali da nema granica, to znaci da ,nema ni pocetka, odnosno trenutka Postanja. )Nisam eleo da me snade isti usud kao i +Galileja, sa kojim osecam veliku srodnost, ,delimicno i zbog toga to sam roden istoga ,dana kada se napunilo tri stotine godina od njegove smrti! -Da bi se rastumacile zamisli kojima smo ja i /drugi fizicari pokuali da objasnimo nacin na +koji bi kvantna mehanika mogla da utice na +nastanak i sudbinu Vaseljene, neophodno je -najpre steci uvid u opte prihvacenu povest -Vaseljene saglasno modelu koji je poznat pod .nazivom 'topli Veliki Prasak'. Ovo podrazumeva+da se Vaseljena opisuje jednim Fridmanovim )modelom sve do samog Velikog Praska. Kod ,ovakvih modela osobeno je to da se prilikom .irenja Vaseljene materija i zracenje u njoj /hlade. (Kada se velicina Vaseljene udvostruci, ,temperatura joj se prepolovi.) Buduci da je ,temperatura naprosto mera prosecne energije +ili brzine cestica, ovo hladenje Vaseljene .trebalo bi da bude od izuzetno vanog uticaja&na materiju u njoj. Pri veoma visokim *temperaturama, cestice bi se kretale tako &brzo da ne bi moglo doci ni do kakvog $privlacenja medu njima pod dejstvom +nuklearne ili elektromagnetne sile, ali sa .hladenjem one bi stale da privlace jedne druge+i da se spajaju. tavie, od temperature +zavise cak i tipovi cestica koji postoje u .Vaseljeni. Pri dovoljno visokim temperaturama /cestice imaju toliko energije da bi pri svakom ,njihovom sudaru nastalo mnotvo razlicitih .parova cestica-anticestica. Iako bi se neke od'ovih cestica potrle prilikom sudara sa +anticesticama, one bi ipak nastajale bre #nego to bi nestajale. Pri niim *temperaturama, medutim, kada cestice koje .se sudaraju imaju manje energije, dolazilo bi do sporijeg nastajanja parova *cestica-anticestica, tako da bi potiranje $postalo bre od stvaranja cestica. )Smatra se da su pri samom Velikom Prasku ,razmere Vaseljene bile ravne nuli, te da je .njena toplota tu bila beskonacna. Ali kako se +Vaseljena irila, temperatura zracenja je ,opadala. Jednu sekundu posle Velikog Praska )ona je pala za oko deset hiljada miliona +stepeni. Ova temperatura je za oko hiljadu .puta veca od one koja vlada u sreditu Sunca,0ali ovako visoke vrednosti dostiu se prilikom ,eksplozija vodonicnih bombi. U tom trenutku ,Vaseljena se sastojala poglavito od fotona, /elektrona i neutrona (izuzetno lakih cestica na0koje dejstvuje jedino slaba sila gravitacije) i 0njihovih anticestica, kao i od neto protona i ,neutrona. Kako je Vaseljena nastavila da se .iri, a temperatura da opada, stopa kojom su $prilikom sudaranja nastajali parovi .elektron-antielektron spustila se ispod stope 0kojom su oni bili unitavani potiranjem. Ovo je&dovelo do medusobnog potiranja vecine 'elektrona i antielektrona, pri cemu je ,preostalo sasvim malo elektrona. Neutrini i *antineutrini ne bi se, medutim, medusobno +potrli, zato to ove cestice sasvim slabo +dejstvuju medusobno i sa drugim cesticama. +One bi, dakle, trebalo da postoje i danas. 2Ukoliko bismo ih registrovali, bila bi to valjana +potvrda ispravnosti ove slike veoma toplog /ranog razdoblja Vaseljene. Na alost, njihove +energije sada bi bile odvec niske da bismo .neposredno mogli da ih registrujemo. Ako, pak,'neutrini nisu bez mase, vec imaju malu +vlastitu masu, kako to proishodi iz jednog &nepotvrdenog opita izvrenog 1981. u .Sovjetskom Savezu, moda bismo bili u stanju -da ih posredno registrujemo: oni bi mogli da .predstavljaju jedan oblik 'tamne materije', o 'kojoj je ranije bilo reci, sa dovoljno )gravitacionog privlacenja da se zaustavi &irenje Vaseljene i dovede do njenog kolabiranja. )Oko stotinu sekundi posle Velikog Praska +temperatura je pala na oko hiljadu miliona -stepeni, to odgovara onoj u unutranjosti *najtoplijih zvezda. Pri ovoj temperaturi, )protoni i neutroni vie nemaju dovoljno .energije da se otrgnu privlacnom dejstvu jake )nuklearne sile, tako da tu pocinju da se -spajaju, proizvodeci jezgra atoma deuterijuma1(teki vodonik), koja sadre po jedan proton i ,jedan neutron. Deuterijumova jezgra potom se*spajaju sa novim protonima i neutronima - ,obrazujuci jezgra helijuma, koja sadre po (dva protona i dva neutrona - kao i male (kolicine dva tea elementa, litijuma i /berilijuma. Moe se izracunati da se u modelu .toplog Velikog Praska oko cetvrtina protona i *neutrona pretvara u helijumova jezgra, uz (malu kolicinu tekog vodonika i drugih /elemenata. Preostali neutroni raspali bi se na )protone, koji predstavljaju jezgra atoma obicnog vodonika. /Sliku toplog ranog razdoblja Vaseljene prvi je -izloio naucnik Dord Gamov u znamenitom ,radu koji je 1948. objavio u koautorstvu sa *svojim studentom Ralfom Alferom. Gamov je ,imao smisla za humor - ubedio je nuklearnog +fizicara Hansa Betea da se takode potpie 1pod ovaj rad, kako bi njegovi autori bili Alfer, (Bete i Gamov, kao prva tri slova grckog (alfabeta, alfa, beta i gama: vie nego ,prikladno za rad o pocetku Vaseljene! U tom 0tekstu oni su izloili znamenito predvidanje da+bi zracenje iz veoma toplih ranih razdobja -Vaseljene trebalo da postoji jo i danas sa 'temperaturom od samo tri stepena iznad )apsolutne nule (-273 stepena Celzijusa). (Penzijas i Vilson otkrili su upravo ovo -zracenje 1965. U vreme kada su Alfer, Bete i )Gamov objavili svoj rad, nije mnogo bilo *poznato o nuklearnim reakcijama protona i (neutrona. Predvidanja vezana za razmere +raznih elemenata u ranoj Vaseljeni bila su /stoga netacna, ali ovi proracuni ponovljeni su ,u svetlosti novih saznanja i sada se sasvim 0slau sa nalazima posmatranja. tavie, veoma/je teko objasniti na neki drugi nacin zato -ima toliko mnogo helijuma u Vaseljeni. Stoga /smo prilicno sigurni da smo doli do ispravne .slike, bar sve do jedne sekunde posle Velikog Praska. *Samo nekoliko casova posle Velikog Praska +okoncalo se obrazovanje helijuma i ostalih /elemenata. Nakon toga, tokom priblino milion -godina, Vaseljena se samo irila, bez nekih .znacajnijih dogadaja u njoj. Konacno, kada je *temperatura pala na samo nekoliko hiljada /stepeni, a elektroni i jezgra nisu vie imali $dovoljno energije da se suprotstave %elektromagnetnom privlacenju koje je +dejstvovalo medu njima, oni su stali da se *povezuju, obrazujuci atome. Vaseljena kao /celina nastavila je da se iri i hladi, ali u .podrucjima koja su bila malo guca od proseka&to irenje bilo je usporeno dodatnim )gravitacionim privlacenjem. Konacno, ovo /privlacenje obustavilo bi irenje u pojedinim /oblastima i nagnalo ih da pocnu da kolabiraju. /Prilikom kolabiranja, gravitaciono privlacenje )materije izvan ovih podrucja moglo ih je -navesti da pocnu lagano da se okrecu. Kako se-kolabirajuca oblast smanjivala, ona se bre 0okretala iz istog razloga iz koga se klizaci na ,ledu bre okrecu ako privuku ruke uz telo. -Konacno, kada se podrucje dovoljno smanjilo, .njegovo okretanje postalo je prikladno brzo da&se javi kao protivtea gravitacionom /privlacenju i na taj nacin su rodene diskolike .rotirajuce galaksije. Druga podrucja, koja se 1nisu zavrtela, postala su objekti koji su dobili /naziv elipticne galaksije. U njima bi podrucje .prestalo da kolabira zato to bi pojedinacni /delovi galaksije postojano orbitirali oko svog 2sredita, ali sama galaksija ne bi imala vlastitu rotaciju. ,Sa prolaskom vremena, vodonikov i helijumov *gas u galaksijama razbijao bi se na manje 0oblake koji bi kolabirali pod dejstvom vlastite 1gravitacije. Kako bi se oni saimali, a atomi u -njima medusobno sudarali, temperatura gasa bi'rasla, sve dok on konacno ne bi postao -dovoljno topao da otpocnu nuklearne reakcije +fuzije. Pri ovim reakcijama vodonik bi bio *pretvaran u helijum, a toplota koja bi se .oslobadala dovodila bi do povecanja pritiska, 0koji bi sprecio dalje saimanje oblaka. Oni bi *se postojano zadrali u tom stanju veoma %dugo kao zvezde slicne naem Suncu, )sagorevajuci vodonik u helijum i zraceci -energiju oslobodenu pri tom u vidu toplote i +svetlosti. Masivnije zvezde morale su biti ,toplije kako bi mogle da prue protivteu .snanijem gravitacionom privlacenju, tako da (su se njihove reakcije nuklearne fuzije +odigravale znatno bre, pa su im i zalihe )vodonika bile utroene za samo stotinak /miliona godina. One bi se onda malo saele, a )kako bi se zbog ovoga dodatno zagrejale, (pocele bi da pretvaraju helijum u tee .elemente kao to su ugljenik i kiseonik. Tom .prilikom, medutim, ne bi bilo oslobodeno mnogo2energije, te bi tako dolo do krize, kao to je -bilo opisano u poglavlju o crnim rupama. Ono .to se potom zbiva nije sasvim jasno, ali po (svoj prilici sredinja podrucja zvezde ,kolabiraju do nekog veoma gustog stanja kao 0to je neutronska zvezda ili crna rupa. Spoljna+podrucja zvezde mogu ponekad da se rasprsnu+u zastraujucoj eksploziji koja se naziva )supernova i koja po sjaju nadmauje sve .zvezde u datoj galaksiji. Neki tei elementi -koji su nastali pred kraj veka zvezde odlaze ,tada u galakticki gas, gde postaju sirovina .narednog pokolenja zvezda. Nae Sunce sadri/oko dva odsto ovih teih elemenata, zato to +je ono zvezda drugog ili treceg pokolenja, 1nastala pre otprilike pet hiljada miliona godina ,iz oblaka rotirajuceg gasa koji je sadrao .ostatke ranijih supernova. Najveci deo gasa u /tom oblaku otiao je na obrazovanje Sunca ili .bio razvejan, ali jedna manja kolicina teih ,elemenata predstavljala je gradu iz koje su ,nastala tela to sada krue oko Sunca kao (planete, medu kojima je i naa Zemlja. +Zemlja je u pocetku bila veoma topla i bez )atmosfere. Tokom potonjeg vremena ona se 0ohladila i stekla atmosferu od gasova to su ih'isputale stene. Mi ne bismo mogli da (opstanemo u toj ranoj atmosferi. Umesto -kiseonika u njoj je bilo mnogo drugih gasova $koji su za nas otrovni, kao to su .vodoniksulfid (gas koji pokvarenim jajima daje,osoben neprijatan miris). Postoje, medutim, .drugi, primitivni oblici ivota koji mogu da .opstanu i napreduju u tim uslovima. Smatra se +da su oni nastali u okeanima verovatno kao )ishod slucajnog povezivanja atoma u veca ,ustrojstva koja se nazivaju makromolekuli i +koja su u stanju da povezuju druge atome u /okeanima u slicne sklopove. Na taj nacin oni bi,se reprodukovali i umnoavali. U pojedinim 2slucajevima javile bi se greke pri reprodukciji.&Vecina greaka bila je takva da novi %makromolekuli nisu vie mogli da se )reprodukuju i konacno su bili uniteni. (Medutim, mali broj greaka doveo je do -nastanka novih makromolekula koji su se jo )bolje reprodukovali. Oni su stoga bili u .preimucstvu i stali su da zamenjuju prvobitne &makromolekule. Tako je zapoceo proces 'evolucije koji je doveo do razvoja sve !sloenijih organizama kadrih za 1samoreprodukciju. Prvi primitivni oblici ivota .troili su razni materijal, ukljucujuci tu i 0vodoniksulfid, a oslobadali su kiseonik. Ovo je $postepeno dovelo do promene sastava (atmosfere ka njenom sadanjem obliku i 1omogucilo nastanak viih oblika ivota kao to/su ribe, gmizavci, sisari i, na kraju, ljudska rasa. +Ova slika Vaseljene koja je u pocetku bila 0veoma topla, da bi se prilikom potonjeg irenja/hladila, u saglasnosti je sa svim posmatrackim ,nalazima kojima danas raspolaemo. No, ona )ipak ostavlja bez odgovora izvestan broj znacajnih pitanja: -1. Zato je rana Vaseljena bila tako topla? (2. Zato je Vaseljena u makrokosmickim ,razmerama tako jednoobrazna? Zato izgleda &ista u svim tackama prostora i u svim *pravcima? A posebno zato je temperatura +mikrotalasnog pozadinskog zracenja bezmalo *ista ma u kom pravcu pogledali? Situacija &pomalo nalikuje onoj kada vecem broju /studenata na ispitu postavite isto pitanje. Ako+svi oni daju potpuno isti odgovor, moete /prilicno biti sigurni da su bili u vezi. No, u ,prethodno opisanom modelu od Velikog Praska +nije proteklo dovoljno vremena da svetlost 'prevali rastojanje od jednog udaljenog -podrucja do drugog, cak i ako su ta podrucja .bila medusobno blizu u ranoj Vaseljeni. Prema /teoriji relativnosti, ako svetlost ne moe da ,stigne od jednog podrucja do drugog, onda za.to nije kadra ni bilo koja druga informacija. (Prema tome, nije bilo nacina na koji su .razlicita podrucja rane Vaseljene mogla steci *istu temperaturu, osim ako iz nekog zasad -neobjanjenog razloga to nije bio slucaj od samog pocetka. .3. Zato je Vaseljena od pocetka imala gotovo0kriticnu stopu i- renja, to razdvaja modele +u kojima dolazi do kolabiranja od onih kod ,kojih se irenje nastavlja u beskonacnost, /tako da se i sada, deset hiljada miliona godina0kasnije, ona jo iri tom istom stopom? Da je +stopa irenja jednu sekundu posle Velikog /Praska bila manja makar i za jedan sto hiljada 1milioniti milioniti deo, Vaseljena bi kolabirala 1pre no to bi uopte dosegla sadanje razmere.)4. Uprkos cinjenici da je Vaseljena tako )jednoobrazna i homogena u makrokosmickim .razmerama, ona sadri lokalne nepravilnosti, +kao to su zvezde i galaksije. Za njih se 0smatra da su nastale iz malih razlika u gustini *pojedinih podrucja rane Vaseljene. Odakle $vuku koren ove fluktuacije gustine? .Uzeta zasebno, opta teorija relativnosti ne /moe da objasni ove osobenosti niti da prui )odgovor na ova pitanja, zato to iz nje %proishodi da je Vaseljena pocela kao /beskrajno gusta u singularnosti Velikog Praska./A u toj singularnosti vie ne vae ni opta /relativnost, ni ostali zakoni fizike: ne moe *se, dakle, predvideti ta ce proizici iz /singularnosti. Kao to je ranije objanjeno, 'ovo znaci da se iz teorije sasvim mogu *iskljuciti Veliki Prasak i sve to mu je -prethodilo, zato to oni ne mogu ni na koji -nacin uticati na ono to mi registrujemo. U -tom slucaju, prostorvreme bi imalo granicu - #pocetak u trenutku Velikog Praska. /Nauka je, kako izgleda, otkrila niz zakona koji/nam, u okviru granica to ih postavlja nacelo (neodredenosti, govore o tome kako ce se )Vaseljena razvijati sa vremenom, ukoliko ,znamo njeno stanje u nekom trenutku. Moda -je te zakone u pocetku propisao Bog, ali je, 'po svemu sudeci, on potom pustio da se /Vaseljena razvija po njima, odnosno vie nije +uticao na nju. Ali kako je odabrao pocetno 1stanje ili konfiguraciju Vaseljene? Kakvi su bili&'granicni uslovi' na pocetku vremena? ,Jedan moguci odgovor jeste tvrdnja da je Bog+odabrao pocetnu konfiguraciju Vaseljene iz ,razloga koje mi nikako ne moemo razumeti. &Ovako neto svakako bi bilo u okviru -mogucnosti jednog svemocnog bica, ali ako je #ono pocelo Vaseljenu na jedan tako .nepojaman nacin, zato je onda pustilo da se )ona razvija saglasno zakonima koje smo u (stanju da shvatimo? Cela istorija nauke .predstavljala je postepeno uvidanje cinjenice *da se zbivanja ne dogadaju na proizvoljan ,nacin, vec da odraavaju izvestan red koji *pociva u njihovoj osnovi, iza koga moda 2stoji, a moda i ne stoji boanski upliv. Sasvim-je, onda, prirodno pretpostaviti da ovaj red -vai ne samo za zakone, nego i za uslove na -granici prostorvremena koji odreduje pocetno -stanje Vaseljene. Moguce je zamisliti veliki -broj modela Vaseljene sa razlicitim pocetnim *stanjima, koji se svi pokoravaju zakonima .nauke, ali mora postojati neko nacelo koje ce *odrediti pravo pocetno stanje, pa stoga i -model koji ce predstavljati nau Vaseljenu. )Jedna takva mogucnost jeste ono to smo *nazvali haoticni granicni uslovi. Iz njih (proishodi ili da je Vaseljena prostorno %beskrajna ili da ima beskrajno mnogo /Vaseljena. U okviru haoticnih granicnih uslova 'verovatnoca da se pronade neko posebno .podrucje prostora u nekoj datoj konfiguraciji -neposredno po Velikom Prasku istovetna je, u 'izvesnom smislu, verovatnoci da se ono +pronade u bilo kojoj drugoj konfiguraciji: ,pocetno stanje Vaseljene odabrano je sasvim %nasumicno. Ovo bi znacilo da je rana 0Vaseljena po svoj prilici bila veoma haoticna i +nepravilna, zato to postoji znatno vie .haoticnih i nesredenih konfiguracija Vaseljene1nego to ima onih pravilnih i sredenih. (Ako je *svaka konfiguracija podjednako verovatna, -onda je sva prilika da je Vaseljena pocela u $nekom haoticnom i nesredenom stanju )jednostavno zato to ovakvih stanja ima .izuzetno mnogo.) Teko je, medutim, razabrati+kako je iz ovako haoticnih pocetnih uslova (mogla nastati jedna Vaseljena koja je u *makrokosmickim razmerama tako ravnomerna i/pravilna kao to je to naa danas. Takode bi +se ocekivalo da fluktuacije gustine u ovom *modelu dovode do obrazovanja znatno vie (praiskonskih crnih rupa nego to ih mi +registrujemo na osnovu fona gama-zracenja. 'Ukoliko je Vaseljena uistinu prostorno )beskonacna, ili ako ima beskonacno mnogo )Vaseljena, onda bi po svoj prilici negde ,postojala velika podrucja koja su u pocetku +bila ravnomerna i jednoobrazna. Ovo pomalo ,podseca na onu poznatu situaciju sa coporom 'majmuna koji udaraju po dirkama pisace ,maine - daleko najveci deo onoga to oni /napiu bilo bi smece, ali pukom igrom slucaja 'neko bi od njih mogao otkucati i jedan )ekspirov sonet. Slicno tome, u slucaju -Vaseljene, da li je moguce da mi obitavamo u (jednom podrucju koje je sasvim slucajno +ravnomerno i jednoobrazno? Na prvi pogled, -ovo deluje krajnje neverovatno, zato to bi -broj haoticnih i nepravilnih podrucja znatno %nadmaio ovakve ravnomerne oblasti. $Pretpostavimo, medutim, da jedino u ,ravnomernim podrucjima dolazi do nastajanja *galaksija i zvezda, kao i da se jedino tu /javljaju pravi uslovi za razvoj tako sloenih .samoreplicirajucih organizama kao to smo to ,mi koji smo kadri da sebi postavimo sledece /pitanje: 'Zato je Vaseljena tako ravnomerna?',Ovo je primer primene onoga to je poznato %kao antropicko nacelo, koje se moe ,parafrazirati kao: 'Vaseljenu vidimo onakvu "kakva jeste zato to postojimo.' .Postoje dve verzije antropickog nacela, slaba +i jaka. Prema slabom antropickom nacelu, u ,Vaseljeni koja je prostorno i/ili vremenski *ogromna ili beskonacna stvorice se uslovi *neophodni za razvoj inteligentnog ivota &jedino u odredenim podrucjima koja su /prostorno i vremenski ogranicena. Inteligentna .bica iz tih podrucja ne bi, dakle, trebalo da $budu iznenadena kada uoce da oblast (Vaseljene u kojoj se nalaze zadovoljava .uslove nune za njihovo postojanje. To pomalo1nalikuje na situaciju kada neki bogata ivi u (imucnom susedstvu, te tako nema nikakvu predstavu o siromatvu. ,Jedan od primera primene slabog antropickog /nacela jeste pokuaj 'objanjenja' zato se *Veliki Prasak odigrao pre otprilike deset /hiljada miliona godina - priblino je, naime, 0toliko bilo potrebno da se razviju inteligentna )bica. Kao to je prethodno rastumaceno, ,najpre je trebalo da nastane rano pokolenje %zvezda. Kod ovih zvezda dolo je do -pretvaranja jednog dela prvobitnog vodonika i+helijuma u elemente kao to su ugljenik i -kiseonik, iz kojih smo mi sazdani. Te zvezde *su potom eksplodirale kao supernove, a iz ,njihovih ostataka nastale su druge zvezde i 0planete, medu njima i one to sacinjavaju na 0Suncev sistem, koji je star pet hiljada miliona .godina. Prvih hiljadu ili dve hiljade miliona 0godina postojanja Zemlje, naa planeta bila je -odvec topla da bi na njoj moglo nastati bilo /ta sloeno. Tokom preostalih priblino tri .hiljade miliona godina trajao je spori proces 'biloloke evolucije, koji je vodio od ,najjednostavnijih organizama do bica kadrih ,da mere vreme unazad sve do Velikog Praska. -Nema mnogo onih koji ce osporavati valjanost .ili korisnost slabog antropickog nacela. Ima, )medutim, autora koji idu i znatno dalje, ,predlauci jaku verziju ovog nacela. Prema .ovoj teoriji, postoji ili mnotvo razlicitih 0Vaseljena ili mnotvo razlicitih podrucja jedne'Vaseljene, od kojih svako ima vlastitu /pocetnu konfiguraciju, a moda i vlastiti skup.zakona nauke. U velikoj vecini ovih Vaseljena 1ne bi postojali pravi uslovi za razvoj sloenih +organizama; tek u retkima medu njima, koje 2su slicne naoj, razvila bi se inteligentna bica 0koja bi postavila pitanje: 'Zato je Vaseljena ,onakva kakvu je mi vidimo?' Odgovor je tada +jednostavan: 'Da je drugacija, mi ne bismo postojali!' *Zakoni nauke, onakvi kakve ih mi trenutno ,poznajemo, sadre mnogo osnovnih konstanti,(kao to su vrednost elektricnog naboja /elektrona i odnos masa protona i elektrona. Mi +ne moemo, bar u ovom casu, da iz teorije ,predvidimo vrednost tih brojeva, vec moramo $da ih utvrdujemo posmatranjem. Nije (iskljuceno da cemo jednoga dana doci do )celovite objedinjene teorije koja ih sve .predvida, ali takode je moguce da neki od njih2ili svi oni variraju od Vaseljene do Vaseljene ili-unutar jedne Vaseljene. Izuzetna je okolnost +da je, kako izgleda, vrednost ovih brojeva (upravo tako fino podeena da omogucuje /razvoj ivota. Primera radi, da je elektricni ,naboj elektrona bio samo malcice drugaciji, /zvezde ili ne bi mogle da sagorevaju vodonik i 1helijum ili ne bi eksplodirale. Razume se, mogli 0bi postojati drugaciji oblici ivota, o kojima 0nita ne slute cak ni pisci naucne fantastike i.kojima ne bi bila potrebna svetlost zvezda kao0to je nae Sunce ili tei hemijski elementi *koji nastaju u zvezdama, da bi potom bili (odbaceni natrag u kosmos kada te zvezde /eksplodiraju. No, izgleda jasno da postoji samo,srazmerno mali raspon mogucih vrednosti tih ,brojeva koji bi dopustio razvoj bilo kakvog 1oblika inteligentnog ivota. Ubedljivo pretean-broj skupova ovih vrednosti dao bi Vaseljene *koje, iako mogu biti izuzetno lepe, ne bi 0sadrale nikoga ko bi se divio toj lepoti. Ovo *se moe uzeti ili kao dokaz o boanskoj 0promisli pri Postanju i izboru zakona nauke ili 'kao potkrepa jakog antropickog nacela. /Postoji vie primedbi koje se mogu uputiti na -racun jakog antropickog nacela. Pre svega, u .kom smislu se moe reci da sve ove razlicite *Vaseljene postoje? Ukoliko su one uistinu *medusobno razdvojene, ono to se zbiva u *nekoj drugoj Vaseljeni ne bi moglo da ima +posmatracke posledice u naoj. Trebalo bi -stoga da primenimo nacelo ekonomicnosti i da -ih iskljucimo iz teorije. Ako su posredi, sa ,druge strane, samo razlicita podrucja jedne +Vaseljene, zakoni nauke trebalo bi da budu /isti u svakom od njih, zato to se u protivnom+ne bi moglo kontinuirano kretati iz jednog /podrucja u drugo. U tom slucaju, jedina razlika(izmedu podrucja bile bi njihove pocetne -konfiguracije, te bi se tako jako antropicko nacelo svelo na slabo. *Druga primedba na racun jakog antropickog .nacela jeste da ono ide protiv toka svekolike (istorije nauke. Mi smo prevalili put od .geocentricnih kosmologija Ptolemeja i njegovih)sledbenika, preko heliocentricne teorije /Kopernika i Galileja, do moderne slike u kojoj .je Zemlja jedna planeta srednje velicine koja 'krui oko prosecne zvezde na spoljnim /rubovima jedne obicne spiralne galaksije, koja ,je i sama samo jedna medu priblino milion (miliona galaksija u Vaseljeni dostupnoj +posmatranjima. No, prema jakom antropickom -nacelu, ovo svekoliko ogromno zdanje postoji +jednostavno nas radi. U to je veoma teko 'poverovati. Na Suncev sistem svakako .predstavlja preduslov za nae postojanje, pa /bi se ovo cak moglo proiriti i na celu nau ,Galaksiju, kako bi bila obuhvacena i ranija 'pokolenja zvezda koja su sazdala tee *elemente. Ali, kako izgleda, nema nikakve &potrebe za svim onim mnotvom drugih 0galaksija, niti za Vaseljenom koja bi bila tako (jednoobrazna i slicna u svim pravcima u makrokosmickim razmerama. 0Lake bi se moglo prihvatiti antropicko nacelo,/ili bar njegova slaba verzija, ukoliko bi bilo %moguce pokazati da izvesan veci broj ,razlicitih pocetnih konfiguracija dovodi do 'nastanka Vaseljene koju mi danas imamo )prilike da posmatramo. Ako je to slucaj, )Vaseljena koja se razvila iz svojevrsnih )nasumicnih pocetnih uslova trebalo bi da 'sadri izvestan broj podrucja koja su *ravnomerna i jedoobrazna, odnosno pogodna *za razvoj inteligentnog ivota. Sa druge )strane, ukoliko pocetno stanje Vaseljene -treba odabrati krajnje paljivo da bismo na -kraju dobili neto slicno ovome to vidimo (sada oko nas, onda je neverovatno da ce .Vaseljena sadrati ijedno podrucje u kome bi .se pojavio ivot. U prethodno opisanom modelu*toplog Velikog Praska, nije bilo dovoljno .vremena u ranoj Vaseljeni da toplota stigne iz(jednog podrucja u drugo. To znaci da je &pocetno stanje Vaseljene moralo imati -potpuno istu temperaturu svuda, jer se jedino%time moe objasniti cinjenica da je ,temperatura mikrotalasnog fona istovetna bez-obzira na to u kom pravcu pogledali. Pocetna (stopa irenja takode je morala da bude ,odabrana sasvim precizno kako bi se i dalje &nalazila na istoj kriticnoj vrednosti )neophodnoj da bi se izbeglo kolabiranje. &Odavde proishodi da je pocetno stanje 'Vaseljene moralo biti odabrano krajnje ,briljivo, ukoliko je model Velikog Praska ,ispravan sve do samog pocetka vremena. Bilo .bi veoma teko objasniti zato je Vaseljena *pocela upravo na taj nacin, osim da je tu .posredi cin Boga koji je imao nameru da stvoribica poput nas. *U nastojanju da pronade model Vaseljene u -kome je iz mnogih razlicitih pocetnih uslova *moglo da nastane neto slicno sadanjoj .Vaseljeni, fizicar iz Masacusetskog instituta /za tehnologiju Alen Gat izloio je zamisao da -je rana Vaseljena mogla proci kroz razdoblje ,veoma brzog irenja. Za ovakvo irenje se )kae da je 'inflatorno', u smislu da se -Vaseljena u pocetku irila ubrzanom stopom, .za razliku od sadanje usporene stope. Prema *Gatu, precnik Vaseljene povecao se milion /miliona miliona miliona miliona puta (jedinica +iza koje se prua niz od trideset nula) u jednom majunom delu sekunde. *Gat smatra da je Vaseljena pocela Velikim 'Praskom u veoma toplom, ali i prilicno )haoticnom stanju. Ove visoke temperature 0znacile bi da su se cestice u Vaseljeni kretale *veoma brzo i da im je energija bila veoma /visoka. Kao to je prethodno receno, ocekivalo.bi se da pri tako visokim temperaturama jaka i0slaba nuklearna sila, kao i elektromagnetna sila(budu objedinjene u jedinstvenu silu. Sa /potonjim irenjem, Vaseljena bi se hladila, a .energija cestica bi opadala. Konacno, usledio -bi takozvani fazni prelaz i simetrija izmedu -sila bila bi naruena: jaka sila postala bi ,razlicita od slabe i elektromagnetne. Jedan $poznati primer faznog prelaza jeste *smrzavanje vode prilikom njenog hladenja. .Tecna voda je simetricna, ista u svakoj tacki *i u svim pravcima. Kada, medutim, dode do .nastanka kristala leda, oni ce imati odredene /poloaje i bice upravljeni u nekom pravcu. Ovo$naruava prethodnu simetriju vode. -U slucaju vode, ukoliko paljivo postupate, +moguce je izvesti 'superhladenje', odnosno -smanjenje temperature ispod tacke mrnjenja ,(0 stepeni Celzijusa) bez obrazovanja leda. -Prema Gatovom miljenju, Vaseljena je mogla 0da se ponaa na isti nacin: temperatura joj je 0mogla pasti ispod kriticne granice, ali pri tom .ne bi dolo do naruavanja simetrije izmedu +sila. Ako se ovo dogodilo, Vaseljena bi se 0nalazila u nestabilnom stanju sa vie energije /nego to bi imala onda kada bi simetrija bila -naruena. Moe se pokazati da ovaj poseban .viak energije ima antigravitaciono dejstvo: )on bi se ponaao upravo kao kosmoloka *konstanta koju je Ajntajn uveo u optu (relativnost kada je pokuavao da sazda *staticni model Vaseljene. Buduci da bi se /Vaseljena vec nalazila u stanju irenja, ba .kao i u modelu toplog Velikog Praska, odbojno ,dejstvo ove kosmoloke konstante dovelo bi )do toga da se Vaseljena iri sve brom .stopom. Cak i u podrucjima u kojima bi cestica*materije bilo iznad proseka, gravitaciono 'privlacenje materije bilo bi nadjacano *odbojnim dejstvom gravitacione konstante. .Prema tome, ova podrucja takode bi se irila -na ubrzani, inflatorni nacin. Kako bi se ovo ,irenje nastavljalo, a cestice materije se (razmicale, na kraju bi preostala jedino 0Vaseljena koja se iri i koja je gotovo sasvim )liena cestica, premda se jo nalazi u .superohladenom stanju. Sve nepravilnosti u toj1Vaseljeni bile bi otklonjene irenjem, ba kao ,to se nabori na balonu otklanjaju kada ga -naduvate. Sadanje ravnomerno i jednoobrazno-stanje Vaseljene moglo je, dakle, nastati iz -mnotva razlicitih nejednoobraznih pocetnih stanja. (U takvoj Vaseljeni, u kojoj kosmoloka )konstanta ubrzava irenje, umesto da ga ,usporava gravitaciono privlacenje materije, -bilo bi dovoljno vremena da svetlost prevali )put od jednog do drugog podrucja u ranoj 0Vaseljeni. Ovo bi moglo da predstavlja reenje 'ranije pomenutog problema istovetnosti ,osobina razlicitih podrucja rane Vaseljene. 1tavie, stopa irenja Vaseljene automatski bi/postala veoma bliska kriticnoj stopi odredenoj .gustinom energije Vaseljene. A ovo bi, dalje, +moglo da bude objanjenje zato je stopa 0irenja i dalje tako blizu kriticne vrednosti, ,bez obaveze da se pretpostavi da je pocetna *stopa irenja Vaseljene bila veoma pomno odabrana. ,Zamisao o inflaciji takode moe da objasni *zato u Vaseljeni ima toliko materije. U +podrucju Vaseljene koje je dostupno naim /posmatranjima postoji priblino deset miliona 0miliona miliona miliona miliona miliona miliona 0miliona miliona miliona miliona miliona miliona ,miliona (jedinica iza koje se prua niz od ,osamdeset pet nula) cestica. Odakle sve one )poticu? Odgovor glasi da, prema kvantnoj 0teoriji, cestice mogu biti stvorene iz energije .u obliku parova cestica-anticestica. Ali time *se otvara pitanje odakle potice energija. &Odgovor glasi da je ukupna energija u +Vaseljeni ravna nuli. Materija u Vaseljeni +sazdana je od pozitivne energije. Medutim, -materija samu sebe privlaci silom tee. Dva +komada materije koja se nalaze blizu jedan +drugome imaju manje energije nego onda kada,su udaljeniji, zato to treba da utroite -energiju da biste ih razdvojili, dejstvujuci 0protiv gravitacione sile koja ih privlaci jedan (drugome. Prema tome, u izvesnom smislu, -gravitaciono polje ima negativnu energiju. U %slucaju Vaseljene koja je priblino -jednoobrazna u prostoru moe se pokazati da -se ova negativna gravitaciona energija tacno $potire sa pozitivnom energijom koju (predstavlja materija. Ukupna energija u !Vaseljeni ravna je, dakle, nuli. ,A dva puta nula takode je nula. Prema tome, 'Vaseljena moe da udvostruci kolicinu ,pozitivne energije materije i da udvostruci $negativnu gravitacionu energiju bez -naruavanja zakona o ocuvanju energije. Ovo .se ne dogada kod normalnog irenja Vaseljene,*gde se gustina energije materije smanjuje &kako se Vaseljena povecava. Zbiva se, -medutim, kod inflatornog irenja, zato to -gustina energije superohladenog stanja ostaje0stalna dok se Vaseljena iri: kada se velicina )Vaseljene udvostruci, pozitivna energija +materije i negativna gravitaciona energija 'takode se udvostrucuju, tako da ukupna -energija ostaje ravna nuli. Tokom inflatorne ,faze, velicina Vaseljene veoma se povecava. )Prema tome, ukupna kolicina raspoloive &energije za stvaranje cestica postaje +izuzetno velika. Tim povodom Gat je jednom /prilikom primetio: 'Kau da nema takve stvari 0kao to je besplatan rucak. Ali Vaseljena jestenajveci besplatan rucak.' 0Vaseljena se danas vie ne iri na inflatoran 'nacin. Prema tome, mora postojati neki (mehanizam koji odstranjuje veoma veliku )efektivnu kosmoloku konstantu, te tako .menja stopu irenja, cija se brzina vie ne (povecava, nego se smanjuje pod dejstvom 0gravitacije, upravo kao to je to sada slucaj. /Kod inflatornog irenja moe se ocekivati da &ce simetrija izmedu sila konacno biti /naruena, ba kao to se superohladena voda .na kraju ipak uvek smrzne. Viak energije iz /stanja nenaruene simetrije tada se oslobada i+zagreva Vaseljenu do temperature tik ispod -kriticne vrednosti za simetriju izmedu sila. 2Vaseljena bi potom nastavila da se iri i hladi, -ba kao u modelu toplog Velikog Praska, ali 1sada postoji objanjenje zato se iri upravo *kriticnom stopom i zato njena razlicita !podrucja imaju istu temperaturu. .Prema Gatovoj prvobitnoj zamisli, fazni prelaz0se zbio naglo, ba kao to se ledeni kristali *pojavljuju najednom u veoma hladnoj vodi. /Ideja se ogledala u tome da se 'mehurovi' nove +faze naruene simetrije obrazuju u staroj (fazi, slicno mehurovima pare okruenim *kljucalom vodom. Mehurovi bi se irili i +povezivali sve dok se cela Vaseljena ne bi -nala u novoj fazi. Potekoca se, medutim, *ogledala u tome - kako smo primetili ja i -nekoliko drugih fizicara - to se Vaseljena 1irila tako brzo da bi se mehurovi, cak i da su /rasli brzinom svetlosti, medusobno udaljavali, .te tako ne bi moglo doci do njihovog spajanja.Vaseljena bi se nala u veoma *nejednoobraznom stanju, u kome bi u nekim -oblastima i dalje postojala simetrija izmedu -razlicitih sila. Takav model Vaseljene ne bi .odgovarao onome to imamo prilike da vidimo. &Oktobra 1981. boravio sam u Moskvi na /konferenciji o kvantnoj gravitaciji. Posle ovog+skupa odrao sam predavanje o inflatornom )modelu i potekocama vezanim za njega u )ternbergovom astronomskom institutu. U .publici se nalazio mladi ruski naucnik Andrej +Linde iz Instituta Lebedev u Moskvi. On je &primetio da se nevolja sa nespajanjem +mehurova moe izbeci ako su mehurovi bili -toliko veliki da se nae podrucje Vaseljene *celo nalazilo u jednom od njih. Da bi ovo -dejstvovalo, prelaz iz simetrije u naruenu (simetriju morao se odigrati veoma sporo -unutar jednog mehura, ali to je sasvim moguce.prema velikim objedinjenim teorijama. Lindeova/zamisao o sporom naruavanju simetrije bila je+veoma dobra, ali kasnije sam shvatio da bi (njegovi mehurovi morali da budu veci od -nekadanje Vaseljene! Pokazao sam, naprotiv,/da bi do naruavanja simetrije dolo svuda u +isto vreme, a ne samo unutar mehurova. Ovo -bi dovelo do jednoobrazne Vaseljene, kakvu i )uocavamo danas. Veoma me je uzbudila ova ,zamisao i stao sam da raspravljam o njoj sa )jednim mojim studentom, Janom Mosom. Kao ,Lindeov prijatelj, naao sam se u prilicno )nezgodnoj situaciji, medutim, kada mi je +jedan naucni casopis kasnije posalo njegov 0rad i zatraio moje miljenje o tome da li ga .treba objaviti. Odgovorio sam im da postoji ta&greka sa mehurovima koji su veci od ,Vaseljene, ali da je osnovna ideja o sporom .naruavanju simetrije veoma dobra. Preporucio,sam rad za objavljivanje u njegovom izvornom*obliku, zato to bi Lindeu bilo potrebno ,nekoliko meseci da ga ispravi, buduci da je *sve to je slao na Zapad moralo da prode .sovjetsku cenzuru, koja nije bila ni narocito -umena ni posebno brza kada su posredi bili *naucni radovi. Stoga sam u istom casopisu /objavio i svoj kratak rad napisan u saradnji sa,Janom Mosom, u kome smo skrenuli panju na .problem sa mehurovima i ukazali na to kako bi on mogao biti reen. -Narednog dana poto sam se vratio iz Moskve,.krenuo sam na putovanje za Filadelfiju, gde je)trebalo da primim medalju u Frenklinovom 0institututu. Moja sekretarica Dudi Fela uspela1je, koristeci svoj zavidan arm, da kod Briti -Ervejza dobije za sebe i mene besplatne karte#na Konkordu iz reklamnog fonda ove -kompanije. Medutim, provala oblaka zadrala (nas je na putu za aerodrom, tako da smo *zakasnili na avion. No, na kraju sam ipak 0stigao u Filadelfiju i primio medalju. Tu su me -zamolili da odrim predavanje o inflatornoj ,Vaseljeni na univerzitetu Dreksel. Glavninu ,izlaganja posvetio sam razmatranju problema .vezanih za inflatornu Vaseljenu, ba kao i u Moskvi. ,Na zamisao veoma slicnu Lindeovoj nezavisno 1su doli, nekoliko meseci kasnije, Pol Stajnhart%i Andreas Albreht sa Pensilvanijskog -univerziteta. Njima dvojici i Lindeu sada se *ravnopravno pripisuje u zaslugu takozvani +'novi inflatorni model' koji se zasniva na 0zamisli o sporom naruavanju simetrije. (Stari .inflatorni model predstavlja Gatovu prvobitnu .ideju o brzom naruavanju simetrije prilikom obrazovanja mehurova.) -Novi inflatorni model bio je valjan pokuaj .objanjenja zato je Vaseljena upravo takva 0kakva je. Ja i nekoliko drugih fizicara pokazali(smo, medutim, da ovaj model, bar u svom &izvornom obliku, predvida znatno vece /varijacije mikrotalasnog fona nego to su one *koje uocavamo. Potonja proucavanja takode (su dovela u sumnju mogucnost postojanja %odgovarajuceg faznog prelaza u ranoj 0Vaseljeni. Prema mom miljenju, novi inflatorni(model sada je mrtav kao naucna teorija, (premda mnogi naucnici jo nisu culi za -njegovo obesnaenje, te ga u svojim radovima0i dalje pominju kao da je na snazi. Jedan bolji ,model, takozvani haoticni inflatorni model, ,izloio je Linde 1983. U njemu nema faznog .prelaza ili superhladenja. Umesto toga, tu je *polje sa spinom 0 koje bi, usled kvantnih 0fluktuacija, imalo velike vrednosti u pojedinim .podrucjima rane Vaseljene. Energija ovog polja%u tim podrucjima ponaala bi se kao .kosmoloka konstanta. Ona bi vrila odbojno 'gravitaciono dejstvo, te bi se tako ta /podrucja irila na inflatorni nacin. Prilikom 0ovog irenja, energija polja u njima lagano bi .opadala, sve dok se inflatorno irenje ne bi ,pretvorilo u irenje slicno onom iz modela -toplog Velikog Praska. Jedno od tih podrucja .postalo bi ono to danas vidimo kao Vaseljenu+dostupnu posmatranjima. Ovaj model ima sva *preimucstva u odnosu na ranije inflatorne *modele, ali ne zavisi od sumnjivog faznog 0prelaza, i iz njega, tavie, proishodi takva !vrednost fluktuacija temperature ,mikrotalasnog fona koja je u saglasnosti sa nalazima posmatranja. ,Ovaj rad na inflatornim modelima pokazao je )da je sadanje stanje Vaseljne moglo da -nastane iz prilicno velikog broja razlicitih (pocetnih konfiguracija. Ova okolnost je (znacajna, buduci da pokazuje da pocetno (stanje onog dela Vaseljene u kome se mi (nalazimo nije moralo biti krajnje pomno .odabrano. Moemo, dakle, ukoliko to elimo, $da pomocu slabog antropickog nacela *objasnimo zato Vaseljena izgleda upravo ,ovako danas. Iskljuceno je, medutim, da bi, &svaka pocetna konfiguracija dovela do -Vaseljene slicne onoj koju mi danas uocavamo.)Ovo se moe pokazati razmatranjem nekog )veoma razlicitog stanja Vaseljene u ovom )trenutku, koje bi, na primer, bilo veoma )neravnomerno i nepravilno. Pomocu zakona ,nauke ta Vaseljena mogla bi se projektovati *unazad kroz vreme da bi se odredila njena +konfiguracija u ranijim razdobljima. Prema +teoremama singularnosti iz klasicne opte 0relativnosti, i dalje bi postojala singularnost +Velikog Praska. Ukoliko projektujete takvu ,Vaseljenu napred u vreme, saglasno zakonima +nauke, na kraju cete dobiti neravnomerno i ,nepravilno stanje od koga ste poceli. Prema "tome, morale su postojati pocetne 0konfiguracije koje ne bi dale Vaseljenu to je *mi vidimo danas. Ni inflatorni model nam, .dakle, ne govori zato pocetna konfiguracija 0nije bila takva da da neto veoma razlicito od ,onoga to posmatramo sada. Moramo li da se .obratimo antropickom nacelu radi objanjenja?'Da li je posredi bio samo srecni splet /okolnosti? Ovako neto predstavljalo bi izraz (ocajanja, poricanje svih naih nada da %dokucimo temeljni poredak Vaseljene. .Da bi se predvidelo kako je Vaseljena pocela, /potrebno je znati zakone koji su bili na snazi ,na pocetku vremena. Ako je klasicna teorija 0opte relativnosti tacna, teoreme singularnosti'koje smo Roder Penrouz i ja dokazali ,pokazuju da je pocetak vremena predstavljao $tacku beskrajne gustine i beskrajne +zakrivljenosti prostorvremena. Svi poznati /zakoni nauke prestali bi da vae u toj tacki. .Moglo bi se pretpostaviti da neki novi zakoni 1vae u singularnostima, ali bilo bi veoma teko-cak i formulisati ove zakone kod tacaka koje .se tako rdavo ponaaju, a nalazi posmatranja .ne bi nam nita govorili o tome kakvi bi oni 2mogli biti. No, ono na ta singularnosti uistinu .ukazuju jeste to da gravitaciono polje postaje*tako snano da na znacaju veoma dobijaju /kvantna gravitaciona dejstva: klasicna teorija ,vie ne predstavlja valjan opis Vaseljene. .Potrebno je, dakle, primeniti kvantnu teoriju (gravitacije pri razmatranju veoma ranih -razdoblja Vaseljene. Kao to cemo videti, u ,kvantnoj teoriji je moguce da obicni zakoni ,nauke budu na snazi svuda, ukljucujuci tu i (pocetak vremena: nije, naime, neophodno /postulisati nove zakone za singularnosti, zato /to u kvantnoj teoriji uopte nema potrebe zasingularnostima. $Mi jo ne raspolaemo celovitom i +koherentnom teorijom koja bi dovela u vezu .kvantnu mehaniku i gravitaciju. Prilicno smo, )medutim, uvereni u neka svojstva koja bi *takva objedinjena teorija trebalo da ima. .Jedno od njih jeste da bi trebalo da obuhvati *Fajnmenovu zamisao o formulisanju kvantne ,teorije iz perspektive zbira po istorijama. +Prema ovoj zamisli, data cestica nema samo ,jednu istoriju, kao to bi to bio slucaj u .klasicnoj teoriji. Umesto toga, pretpostavlja +se da se ona krece svim mogucim putanjama u,prostorvremenu, a sa svakom od tih istorija *stoje u vezi po dva broja, od kojih jedan ,predstavlja velicinu talasa, a drugi njegov /poloaj u ciklusu (njegovu fazu). Verovatnoca 'da cestica, na primer, prode kroz neku +posebnu tacku ustanovljava se na taj nacin .to se zbrajaju talasi svih mogucih istorija -koje prolaze kroz tu tacku. Kada se, medutim,,konkretno pokua da se dobiju ovi zbirovi, +nailazi se na nekoliko tehnickih problema. -Jedini nacin da se oni otklone jeste sledeca -neobicna preporuka: moraju se sabrati talasi -istorija cestica koje ne spadaju u 'stvarno' )vreme, to predstavlja deo mog i vaeg )iskustva, vec se odigravaju u takozvanom ,imaginarnom vremenu. Imaginarno vreme moe ,nalikovati na naucnu fantastiku, ali to je, +zapravo, sasvim odreden matematicki pojam. 2Ako uzmemo bilo koji obican (ili 'stvarni') broj i-pomnoimo ga samim sobom, dobijeni rezultat 1je pozitivan broj. (Na primer, 2 puta 2 je 4, ali/i -2 puta -2 takode je 4). Postoje, medutim, i /posebni brojevi (nazvani imaginarni) koji, kada$bivaju pomnoeni samim sobom, daju +negativne brojeve. (Broj i pomnoen samim )sobom daje -1, 2i pomnoeno samim sobom 0daje -4 i tako dalje.) Da bi se izbegle tehnicke$potekoce sa Fajnmenovim zbirom po /istorijama, mora se koristiti imaginarno vreme.(Drugim recima, za potrebe izracunavanja 'vreme se mora meriti imaginarnim, a ne -stvarnim brojevima. Ovo ima jednu zanimljivu *posledicu po prostorvreme: razlika izmedu $prostora i vremena potpuno nestaje. #Prostorvreme u kome dogadaji imaju *imaginarne vrednosti vremenske koordinate &naziva se euklidovsko, po starogrckom (matematicaru Euklidu, koji je utemeljio %izucavanje geometrije dvodimenzionih &povrina. Ono to mi danas nazivamo ,euklidovskim prostorvremenom veoma je slicno&tome, osim to umesto dve ima cetiri )dimenzije. U euklidovskom prostorvremenu (nema razlike izmedu vremenskog pravca i -pravca u prostoru. Nasuprot tome, u stvarnom #prostorvremenu, u kome se dogadaji )oznacavaju obicnim, stvarnim vrednostima *vremenske koordinate, ovu razliku je lako ,razabrati - vremenski pravac u svim tackama .lei unutar svetlosne kupe, dok su prostorni 0pravci izvan nje. U svakom slucaju, to se tice$svakodnevne kvantne mehanike, nae .koricenje imaginarnog vremena i euklidovskog%prostorvremena predstavlja samo puko &matematicko sredstvo (ili trik) kojim !izracunavamo odgovore o stvarnom prostorvremenu. 'Druga osobina za koju smatramo da mora .predstavljati deo svake konacne teorije jeste $Ajntajnova zamisao prema kojoj se /gravitaciono polje predstavlja zakrivljenocu ,prostorvremena: cestice nastoje da se krecu 0pravolinijski u zakrivljenom prostoru, ali kako (prostorvreme nije ravno njihove putanje !izgledaju krive kao pod dejstvom $gravitacionog polja. Kada primenimo -Fajnmenov zbir po istorijama na Ajntajnovo 0videnje gravitacije, ono to odgovara istoriji +neke cestice sada je celokupno zakrivljeno 'prostorvreme koje predstavlja istoriju /svekolike Vaseljene. Da bi se izbegle tehnicke +potekoce u konkretnom dobijanju zbira po ,istorijama, mora se pretpostaviti da su ova .zakrivljena prostorvremena euklidovska. Drugim-recima, vreme je tu imaginarno i ne moe se )razlikovati od pravca prostora. Da bi se (izracunala verovatnoca nalaenja nekog %stvarnog prostorvremena sa odredenim *svojstvima, kao to je, na primer, to da /izgleda isto u svakoj tacki i u svim pravcima, 1valja zbrojiti talase svih istorija koje imaju to svojstvo. 0U klasicnoj teoriji opte relativnosti postoji )mnotvo razlicitih mogucih zakrivljenih (prostorvremena, od kojih svako odgovara ,nekom razlicitom pocetnom stanju Vaseljene. &Kada bismo znali pocetno stanje nae )Vaseljene, znali bismo i njenu celokupnu *istoriju. Slicno tome, u kvantnoj teoriji 0gravitacije postoji mnotvo razlicitih mogucih (kvantnih stanja Vaseljene. Ponovo, kada ,bismo znali kako se euklidovsko zakrivljeno /prostorvreme u zbiru po istorijama ponaalo u +rana vremena, znali bismo i kvantno stanje Vaseljene. 1U klasicnoj teoriji gravitacije, koja se temelji )na stvarnom prostorvremenu, postoje samo ,dva moguca nacina na koja se Vaseljena moe'ponaati: ona je ili mogla da postoji (neodredeno dugo, ili je imala pocetak u )singularnosti u nekom konacnom vremenu u /prolosti. U kvantnoj teoriji gravitacije, sa +druge strane, javlja se i treca mogucnost. &Zahvaljujuci koricenju euklidovskog +prostorvremena, u kome je vremenski pravac +izjednacen sa pravcima u prostoru, mogucno -je da prostorvreme bude konacno u dosegu, ali+i da nema singularnosti koje bi obrazovale 0neku granicu ili ivicu. Prostorvreme bilo bi tu 1slicno povrini Zemlje, s tom razlikom to ima -jo dve dodatne dimenzije. Povrina Zemlje 0konacna je u dosegu, ali nema granicu ili ivicu:+ukoliko otplovite ka zalasku Sunca, necete .pasti preko ivice ili uleteti u singularnost. +(Znam to iz licnog iskustva, zato to sam obiao svet!) )Ako se euklidovsko prostorvreme protee +unatrag do beskrajnog imaginarnog vremena, )ili pocinje singularnocu u imaginarnom $vremenu, onda se suocavamo sa istim ,problemom kao u klasicnoj teoriji odredenja *pocetnog stanja Vaseljene: Bog moda zna .kako je Vaseljena pocela, ali mi ne moemo da,navedemo nijedan praktican razlog zbog koga .bismo smatrali da je ona pocela na jedan, a ne)na drugi nacin. Sa druge strane, kvantna +teorija gravitacije otvorila je jednu novu +mogucnost u okviru koje ne bi bilo granica +prostorvremena, te tako ne bi postojala ni )potreba da se ustanovljava ponaanje na .granici. Ne bi bilo singularnosti kod koje bi +zakoni nauke prestali da vae, niti ivice 0prostorvremena gde bi valjalo prizivati Boga ili,neki nov zakon da vaspostave granicne uslove,prostorvremena. Moglo bi se reci: 'Granicni ,uslov Vaseljene jeste da ona nema granicu.' .Vaseljena bi bila potpuno samosvojna i na nju 2ne bi uticalo nita izvan nje. Ona ne bi bila ni -stvorena ni unitena, vec bi naprosto BILA. .Na konferenciji u Vatikanu, o kojoj je ranije 0bilo reci, prvi put sam izloio zamisao o tome %da su moda prostor i vreme zajedno 2obrazovali jednu povrinu, cija je velicina bila 2konacna, ali i koja nije imala granicu ili ivicu. %Moj rad je bio prilicno matematickog +karaktera, medutim, tako da ono to je iz +njega proishodilo o ulozi Boga u stvaranju *Vaseljene nije svima odmah bilo jasno (na ,moju srecu). U vreme vatikanskog skupa jo (nisam znao kako da iskoristim zamisao o -odsustvu granica za predvidanja o Vaseljeni. -No, naredno leto proveo sam na Kalifornijskom)univerzitetu u Santa Barbari. Tamo sam u *saradnji sa prijateljem i kolegom Dimom -Hartlom ustanovio koje uslove Vaseljena mora )da zadovoljava ukoliko prostorvreme nema )granica. Kada sam se vratio u Kembrid, )nastavio sam ovaj rad sa dvojicom svojih /istraivaca-studenata, Dulijanom Latrelom i Donatanom Halivelom. +eleo bih da naglasim da je ova zamisao o ,tome da su prostor i vreme konacni, ali bez -granica, samo pretpostavka: ona se, naime, ne,moe izvesti iz nekog drugog nacela. Kao i *svaka druga naucna teorija, ona prvobitno 2moe biti izloena iz estetskih ili metafizickih/razloga, ali njena stvarna provera jeste to da )li daje predvidanja koja se poklapaju sa -nalazima posmatranja. Ovo je, medutim, teko/ustanoviti u slucaju kvantne gravitacije, i to 'iz dva razloga. Prvo, kao to ce biti /objanjeno u narednom poglavlju, mi jo nismo/sasvim sigurni u to koja tacno teorija uspeno)objedinjuje optu relativnost i kvantnu +mehaniku, premda smo prilicno upuceni u to +kakav oblik ta teorija mora da ima. Drugo, 'svaki model koji podrobno opisuje celu (Vaseljenu bio bi u matematickom pogledu +odvec sloen da bismo mogli da izracunamo -tacna predvidanja. Potrebno je stoga pribeci #pojednostavljenim pretpostavkama i (priblinostima - pa cak i tada problem *dolaenja do predvidanja ostaje izuzetno teak. /Svaka istorija u zbiru po istorijama opisace ne'samo prostorvreme, nego i sve u njemu, /racunajuci tu i sloene organizme kao to su *ljudska bica, koja su kadra da razmatraju /istoriju Vaseljene. Ovo ne moe da predstavlja,novu potvrdu antropickog nacela, jer ako su %sve istorije moguce, onda sve dok mi &postojimo u jednoj od njih moemo da %koristimo antropicko nacelo da njime *objasnimo zato nalazimo da je Vaseljena -upravo ovakva kakva je. Nije, medutim, jasno -kakav se tacno smisao moe pripisati drugim )istorijama u kojima mi ne postojimo. Ovo -videnje kvantne teorije gravitacije bilo bi, .medutim, znatno vie zadovoljavajuce ukoliko &bi se moglo pokazati, pomocu zbira po /istorijama, da naa Vaseljena nije samo jedna "od mogucih istorija, vec jedna od -najverovatnijih. Da bismo to ucinili, moramo *doci do zbira po istorijama za sva moguca 'euklidovska prostorvremena koja nemaju granice. +Pod idejom o bezgranicnosti podrazumeva se -to da su zanemarljivi izgledi da se ustanovi 'kako Vaseljena prolazi kroz sve moguce -istorije; umesto toga, postoji jedan poseban ,skup istorija koje su znatno verovatnije od .drugih. Ove istorije mogu se predstaviti tako ,kao da su slicne povrini Zemlje, pri cemu %udaljenost od severnog pola odgovara &imaginarnom vremenu, a velicina kruga ,nepromenljivih udaljenosti od severnog pola (odgovara prostornoj velicini Vaseljene. ,Vaseljena pocinje na severnom polu kao jedna$tacka. Kako se krecemo na jug, krug %geografskih irina na nepromenjivoj 'udaljenosti od severnog pola stalno se .povecava, to odgovara irenju Vaseljene sa /imaginarnim vremenom (Ilus. 8.1). Vaseljena ce ,dostici najvecu velicinu na polutaru, da bi ,potom pocela da se suava sa daljim rastom ,imaginarnog vremena, sve dok se ne same u /jednu tacku na junom polu. Iako bi Vaseljena 0imala nultu velicinu na severnom i junom polu,0ove tacke ne bi bile singularnosti nimalo vie 0nego to su singularni severni i juni pol na 1Zemlji. Zakoni nauke tu bi i dalje vaili, ba 1kao to vae i na severnom i junom polu nae planete. 'Istorija Vaseljene u stvarnom vremenu, ,medutim, izgledala bi sasvim drugacije. Pre -otprilike deset ili dvadeset hiljada miliona /godina ona je imala najmanju velicinu, koja je (odgovarala najvecem precniku istorije u 'imaginarnom vremenu. U potonje stvarno /vreme Vaseljena bi se irila slicno haoticnom /inflatornom modelu koji je izloio Linde (ali /sada se vie ne bi moralo pretpostaviti da je -Vaseljena na neki nacin stvorena u prikladnom,stanju). Vaseljena bi se rairila do veoma 0velike velicine, da bi potom pocela da kolabira )ka onome to izgleda kao singularnost u )stvarnom vremenu. Prema tome, u izvesnom -smislu, nas i dalje sve ceka zao usud, cak i -ako se drimo podalje od crnih rupa. Jedino *ako bismo mogli da zamislimo Vaseljenu iz ,perspektive imaginarnog vremena, onda ne bi bilo nikakvih singularnosti. +Ako je Vaseljena stvarno u takvom kvantnom $stanju, onda u istoriji Vaseljene u .imaginarnom vremenu ne bi bilo singularnosti. +Moglo bi stoga izgledati da su moji noviji (radovi opovrgli rezultate mojih ranijih +izucavanja singularnosti. Ali, kao to je ,prethodno istaknuto, stvarni znacaj teorema (singularnosti ogledao se u tome to su ,pokazale da gravitaciono polje mora postati (tako snano da se kvantna gravitaciona )dejstva ne mogu zanemariti. A ovo je, sa -svoje strane, dovelo do zamisli da Vaseljena .moe biti konacna u imaginarnom vremenu, ali 0bez granica ili singularnosti. Kada se vratimo u*stvarno vreme u kome mi ivimo, medutim, 2izgledalo bi da singularosti jo postoje. Siroti -astronaut koji upadne u crnu rupu i dalje bi .doiveo sumoran kraj; jedino ako bi iveo u -imaginarnom vremenu ne bi naiao ni na kakvesingularnosti. ,Odavde bi moglo da proishodi da je takozvano*imaginarno vreme, zapravo, stvarno vreme, ,dok je ono to nazivamo stvarno vreme samo .proizvod nae uobrazilje. U stvarnom vremenu .Vaseljena ima pocetak i kraj u singularnostima)koje obrazuju granicu prostorvremena i u -kojima prestaju da vae zakoni nauke. Ali u -imaginarnom vremenu nema ni singularnosti ni 'granice. Prema tome, ono to nazivamo ,imaginarnim vremenom zapravo je temeljnije, +dok je ono to nazivamo stvarnim vremenom (samo zamisao koju koristimo kao pomocno ,sredstvo da bismo opisali ta mislimo kako .izgleda Vaseljena. Ali saglasno pristupu koji +sam opisao u prvom poglavlju, jedna naucna +teorija samo je matematicki model kojim se 0sluimo da bismo opisali naa posmatranja: ona-postoji jedino u naim umovima. Prema tome, *besmisleno je postaviti pitanje: 'Koje je 2stvarno: 'stvarno' ili 'imaginarno' vreme?' Stvar -je naprosto u tome koje je od njih korisnije pri pomenutom opisivanju. .Takode se moe primeniti zbir po istorijama, -zajedno sa idejom o bezgranicnosti, da bi se )ustanovilo za koja je svojstva Vaseljene +verovatno da ce se javiti zajedno. Primera /radi, moe se izracunati verovatnoca irenja )Vaseljene priblino istom stopom u svim +razlicitim pravcima u razdoblju kada njena "gustina ima sadanju vrednost. U +pojednostavljenim modelima koji su do sada +ispitani pokazalo se da je ova verovatnoca )visoka; drugim recima, predloeni uslov +bezgranicnosti dovodi do predvidanja da je )izuzetno verovatno da je sadanja stopa /irenja Vaseljene gotovo ista u svim pravcima.-Ovo je u saglasnosti sa nalazima posmatranja -fona mikrotalasnog zracenja, koji pokazuju da,je njegova snaga gotovo potpuno ista u svim .pravcima. Da se Vaseljena iri bre u nekim -pravcima nego u drugim, snaga zracenja iz tih)pravaca bila bi smanjena usled povecanog crvenog pomaka. .Na ostalim predvidanjima koja slede iz uslova 'bezgranicnosti trenutno se radi. Jedan .posebno zanimljiv problem jeste velicina malog+odstupanja od jednoobrazne gustine u ranoj ,Vaseljeni, koje je dovelo do nastanka prvih )galaksija, a potom zvezda i konacno nas. )Nacelo neodredenosti podrazumeva da rana "Vaseljena nije mogla biti potpuno +jednoobrazna zato to su morale postojati /izvesne neodredenosti ili fluktuacije u pogledu*poloaja i brzina cestica. Pomocu uslova .bezgranicnosti ustanovili smo da je Vaseljena ,morala, u stvari, poceti uz najmanju mogucu &nejednoobraznost koju doputa nacelo )neodredenosti. Ona je potom prola kroz ,razdoblje brzog irenja, kao u inflatornim &modelima. Tokom tog razdoblja pocetne -nejednoobraznosti bile bi pojacane sve dok ne-bi postale dovoljno velike da se njima moe *objasniti nastanak ustrojstava koja danas 0uocavamo oko nas. U Vaseljeni koja se iri i u -kojoj gustina materije blago varira od mesta 'do mesta gravitacija bi nagnala guca &podrucja da uspore irenje i otpocnu )saimanje. Ovo bi dovelo do obrazovanja %galaksija, zvezda i, konacno, cak do -beznacajnih stvorenja kao to smo mi. Prema ,tome, sva sloena ustrojstva koja vidimo u (Vaseljeni mogla bi se objasniti uslovom %bezgranicnosti udruenim sa nacelom neodredenosti kvantne mehanike. 'Zamisao o tome da prostor i vreme mogu +obrazovati zatvorenu povrinu bez granica -takode ima duboke implikacije po ulogu Boga u'stvarima Vaseljene. Sa uspehom naucnih -teorija u opisivanju dogadaja mnogi ljudi su &poverovali u to da Bog doputa da se 'Vaseljena razvija saglasno nekom skupu -zakona i da ne utice na nju kako bi osujetio -ove zakone. Medutim, ti zakoni nam nita ne +govore o tome kako je Vaseljena trebalo da ,izgleda u pocetku; prema tome, od Boga bi i -dalje zavisilo navijanje casovnika i njegovo /putanje u rad. Sve dok Vaseljena, dakle, ima ,pocetak, mogli bismo pretpostaviti da ima i -nekog tvorca. Ali ako je ona uistinu potpuno .samosvojna, bez granica ili rubova, onda ne bi0imala ni pocetak ni kraj, vec bi naprosto bila. A zar tu ima mesta za Tvorca? 9. STRELA VREMENA .U prethodnim poglavljima videli smo kako su se)naa videnja prirode vremena menjala sa ,godinama. Sve do pocetka ovog stoleca ljudi .su verovali u apsolutno vreme. Drugim recima, *bilo koji dogadaj mogao se oznaciti nekim -brojem nazvanim 'vreme' na jedinstven nacin, 1a svi valjani casovnici sloili bi se u pogledu )intervala proteklog izmedu dva dogadaja. .Otkrice, medutim, da je brzina svetlosti ista ,za sve posmatrace, bez obzira na to kako se /oni krecu, dovelo je do teorije relativnosti u -kojoj je trebalo napustiti zamisao o tome da ,postoji jedinstveno apsolutno vreme. Umesto +toga, svaki posmatrac imao bi vlastiti tok .vremena koje bi merio casovnik to se nalazi (kod njega: casovnici koji se nalaze kod /razlicitih posmatraca ne bi, nuno, morali da +pokazuju isto vreme. Vreme je tako postalo +jedan licniji pojam, relativan u odnosu na posmatraca koji ga meri. .Prilikom pokuaja objedinjenja gravitacije i %kvantne mehanike neophodno je uvesti *zamisao o imaginarnom vremenu. Imaginarno -vreme se ne razlikuje od pravaca u prostoru. +Ako neko ide na sever, onda se jednostavno 0moe okrenuti i uputiti ka jugu; isto tako, ako'neko moe da ide napred u imaginarnom (vremenu, trebalo bi da bude kadar da se /okrene i vrati natrag. Ovo znaci da ne bi bilo -neke bitnije razlike izmedu smera 'napred' i -smera 'nazad' u imaginarnom vremenu. Sa druge-strane, ukoliko se razmotri 'stvarno' vreme, .postoji ogromna razlika izmedu smera 'napred' .i smera 'nazad', kao to to svi dobro znamo. -Odakle potice ta razlika izmedu prolosti i 1buducnosti? Zato se secamo prolosti, ali ne i buducnosti. 'Zakoni prirode ne prave razliku izmedu /prolosti i buducnosti. Tacnije govoreci, kao 1to je ranije objanjeno, zakoni prirode ostaju,nepromenjeni kod kombinacija operacija (ili 1simetrija) koje se oznacavaju sa 'C', 'P' i 'T'. *('C' je zamena cestica anticesticama. 'P' &podrazumeva sliku u ogledalu, odnosno 'promenu mesta leve i desne strane. 'T' *pretpostavlja promenu smera kretanja svih +cestica: drugim recima, kretanje unatrag.) +Zakoni prirode koji upravljaju ponaanjem (materije pod svim normalnim okolnostima +ostaju nepromenjeni u slucaju kombinovanja 1prve dve operacije, 'C' i 'P', odnosno ivot bi 1bio potpuno isti za itelje neke planete koji bi4predstavljali nae slike u ogledalu i koji bi bili +sazdani od antimaterije, a ne od materije. ,Ako se zakoni prirode ne menjaju u uslovima (kombinovanja operacija 'C' i 'P', kao i -operacija 'C', 'P' i 'T', onda moraju ostati -nepromenjeni i u slucaju samo operacije 'T'. .Postoji, medutim, velika razlika izmedu smera ,'napred' i smera 'nazad' stvarnog vremena u /obicnom ivotu. Zamislite cau punu vode koja-pada sa stola i razbija se u komade na podu. .Ukoliko biste to snimili, lako biste mogli da 2kaete da li se film puta napred ili nazad. Ako1biste ga pustili nazad, videli biste delice kako .se iznenada sakupljaju sa poda i obrazuju celu(cau, koja potom skace na plohu stola. .Ustanovili biste da je film puten unazad po +tome to se ovakvo ustrojavanje nikada ne -dogada u obicnom ivotu. Ukoliko bi se ipak 0dogadalo, proizvodaci staklarije ubrzo bi ostali bez posla. -Razlog kojim se obicno objanjava zato ne ,vidimo razbijene cae kako se skupljaju sa -poda i skacu natrag na sto jeste taj to se !takvom necem protivi drugi zakon ,termodinamike. Prema ovom zakonu, u bilo kom,zatvorenom sistemu uvek dolazi do povecanja 0nereda ili entropije. Drugim recima, posredi je -vid poznatog Marfijevog zakona: 'Stvari uvek -tee da se pogoraju!' Cela caa na stolu (predstavlja stanje visokog reda, dok je .razbijena caa na podu stanje nereda. Lako se2moe ici od cele cae na stolu u prolosti, do /razbijene cae na podu u buducnosti, ali ne i obrnuto. +Povecanje nereda ili entropije sa vremenom /jedan je od primera onoga to se naziva strela'vremena i cime se pravi razlika izmedu /prolosti i buducnosti, odnosno odreduje smer /vremena. Postoje najmanje tri razlicite strele .vremena. Tu je, najpre, termodinamicka strela *vremena, smer vremena u kome se nered ili .entropija povecavaju. Zatim je tu psiholoka ,strela vremena. To je smer u kome mi osecamo,da vreme protice, smer u okviru koga pamtimo1prolost, ali ne i buducnost. Konacno, postoji i,kosmoloka strela vremena. Posredi je smer /vremena u sklopu koga se Vaseljena iri, a ne saima. -U ovom poglavlju ja cu pokazati da se uslovom'bezgranicnosti Vaseljene, kao i slabim /antropickim nacelom moe objasniti zato sve /tri strele pokazuju u istom smeru - tavie, 'zato uopte mora da postoji potpuno (odredena strela vremena. Pokazacu da je ,psiholoka strela odredena termodinamickom (strelom, kao i da ove dve stele nunim ,nacinom pokazuju uvek u istom smeru. Ukoliko.se pretpostavi uslov bezgranicnosti Vaseljene,%videce se da moraju postojati sasvim *odredena termodinamicka i sasvim odredena )kosmoloka strela vremena, ali one nece ,pokazivati u istom smeru tokom cele povesti *Vaseljene. Ja cu, medutim, pokazati da se ,jedino onda kada one pokazuju u istom smeru /sticu pogodni uslovi za nastanak inteligentnih 0bica, kadrih da postave sledece pitanje: 'Zato,se nered povecava u istom smeru u kome se i Vaseljena iri?' +Najpre cu razmotriti termodinamicku strelu -vremena. Drugi zakon termodinamike proishodi *iz cinjenice da uvek postoji znatno vie /nesredenih, nego sredenih stanja. Primera radi,.uzmimo slucaj delova neke slagalice u kutiji. -Postoji jedan i samo jedan razmetaj u kome /delovi obrazuju potpunu sliku. Sa druge strane /postoji veoma veliki broj razmetaja u kojima /su delovi nepravilno rasporedeni i ne obrazuju sliku. ,Zamislimo da neki sistem zapocne u jednom od(malog broja sredenih stanja. Kako vreme 0protice, sistem ce se razvijati u saglasnosti sa&zakonima nauke i njegovo stanje ce se -menjati. U neko docnije vreme verovatnije je )da ce se sistem naci u nesredenom nego u ,sredenom stanju, zato to ima znatno vie /nesredenih stanja. Ukoliko se protrese kutija, 0sasvim je izgledno da ce se slagalica raspasti i.da ce se njeni delovi naci u potpunom rasulu u-kome ne obrazuju nikakvu sliku. Nered delova 'verovatno ce se povecavati sa vremenom /ukoliko delovi zadovolje pocetni uslov da se na&pocetku nalaze u stanju visokog reda. ,Zamislimo da se delovi slagalice na pocetku *nalaze pravilno rasporedeni u kutiji i da ,obrazuju neku sliku. Ako protresete kutiju, -delovi ce se naci u drugom rasporedu. To ce, /po svoj prilici, biti nesreden raspored u kome .delovi ne obrazuju pravu sliku, naprosto stoga,to postoji premnogo nesredenih rasporeda. +Neke grupe delova i dalje mogu da obrazuju /sliku, ali to vie protresate kutiju tim je +verovatnije da ce se i ove grupe raspasti, 'odnosno da ce se delovi naci u potpuno (haoticnom stanju u kome nece obrazovati *nikakvu sliku. Nered delova ce se, dakle, !verovatno povecavati s vremenom. ,Pretpostavimo, medutim, da Bog odluci da se &Vaseljena ima okoncati jednim stanjem ,visokog reda, pri cemu je svejedno kakvo je 0bilo njeno pocetno stanje. Sva je prilika da bi +se onda Vaseljena u svom osvitu nalazila u +nesredenom stanju. Ovo bi znacilo da bi se -nered smanjivao s vremenom. Tada biste imali *prilike da vidite kako se razbijene cae +sastavljaju i skacu na sto. Medutim, svako *ljudsko bice koje bi posmatralo ove cae .takode bi bilo deo Vaseljene u kojoj se nered )smanjuje s vremenom. Kod takvih stvorova )psiholoka strela vremena pokazivala bi -unazad. Oni bi se, naime, secali zbivanja iz 2buducnosti, a nita ne bi pamtili iz prolosti. 1Kada bi se caa razbila, oni bi se secali da se .nalazila na stolu, ali kada bi se nalazila na 1stolu oni se ne bi secali da je bila razbijena napodu. 0Prilicno je teko govoriti o ljudskom pamcenju,-zato to nismo dovoljno upoznati sa nacinom 'na koji mozak dejstvuje. Dobro nam je, )medutim, poznato kako dejstvuje memorija +racunara. Stoga cu u razmatranjima uzeti u /obzir psiholoku strelu vremena kod racunara. ,Smatram da je razlono pretpostaviti da je +strela vremena kod racunara ista kao i kod 0ljudi. Da to nije slucaj, svako bi se lako mogao+obogatiti na berzi pomocu racunara koji bi pamtio sutranje cene! (U osnovi, memorija nekog racunara jeste )sredstvo koje sadri elemente to mogu "postojati u jednom od dva stanja. -Jednostavan primer je racunalo zvano abakus. -U svom najprostijem obliku ono se sastoji od +izvesnog broja ica. Na kraju svake ice 0nalazi se kuglica koja se moe staviti u jedan 0od dva poloaja. Pre no to neki podatak biva -zapamcen u memoriji racunara, ona se nalazi u"nesredenom stanju, u kome postoje )podjednaki izgledi za dva moguca stanja. ,(Kuglice abakusa razmetene su bez reda na 0icama ovog racunala.) Poto memorija stupi u -medudejstvo sa sistemom koji treba upamtiti, -njeni elementi ce se zacelo naci u jednom od .dva stanja, vec prema optem stanju sistema. /(Svaka kuglica abakusa naci ce se bilo na levoj-ili desnoj ici racunala.) Memorija je tako 0prela iz stanja nereda u stanje reda. Kako bi +se, medutim, dolo do toga da se memorija %nalazi u pravom stanju, neophodno je /upotrebiti izvesnu kolicinu energije (da bi se .pomerile kuglice, ili da bi kompjuter uopte .radio, na primer). Ova energija se oslobada u .vidu toplote, to povecava kolicinu nereda u *Vaseljeni. Moglo bi se pokazati da je ovo (povecanje nereda uvek vece od povecanja +reda u samoj memoriji. Prema tome, toplota +koju otklanja ventilator racunara znaci da -kada ovaj zabelei jedan podatak u memoriju,+ukupna kolicina nereda u Vaseljeni ipak se (povecava. Drugim recima, smer vremena u 0kome racunar pamti prolost isti je kao i smer "vremena u kome se nered povecava. *Nae subjektivno osecanje smera vremena, /psiholoka strela vremena, odredena je, tako, +u naim mozgovima termodinamickom strelom -vremena. Ba kao i racunar, mi takode moramo-da pamtimo stvari poretkom kojim se entropija,povecava. Ovo cini gotovo beznacajnim drugi *zakon termodinamike. Nered se povecava sa *vremenom zato to merimo vreme u smeru u +kome se nered povecava. Nita u Vaseljeni nije izvesnije od toga! 0Ali zato uopte postoji termodinamicka strela*vremena? Ili, drugim recima, zato bi se ,Vaseljena nalazila u stanju visokog reda na ,jednom kraju vremena, kraju koji mi nazivamo,prolost? Zbog cega nije u stanju potpunog *nereda u svim vremenima? Takvo stanje bi, 1uostalom, izgledalo verovatnije. I zato je smer,vremena u kome se nered povecava isti kao i (smer vremena u kome se Vaseljena iri? 1U klasicnoj teoriji opte relativnosti ne moe -se predvideti kako je Vaseljena pocela, zato /to svi poznati zakoni nauke prestaju da vae-u singularnosti Velikog Praska. Vaseljena je +mogla da pocne na veoma ravnomeran i sreden'nacin. To bi dovelo do sasvim odredene -termodinamicke i sasvim odredene kosmoloke *strele vremena, kao to i uocavamo da je /slucaj. Ali ona je isto tako mogla poceti veoma-haoticnim i nesredenim stanjem. U tom slucaju.Vaseljena bi se vec nalazila u stanju potpunog(nereda, tako da se on vie ne bi mogao 'povecavati s vremenom. On bi ili ostao -nepromenjen, u kom slucaju ne bi bilo sasvim .odredene termodinamicke strele vremena, ili bi.se smanjivao, a tada bi termodinamicka strela (vremena pokazivala u suprotnom smeru od /kosmoloke strele. Nijedna od ovih mogucnosti &nije u saglasnosti sa nalazima naih +posmatranja. Medutim, kao to smo videli, .klasicna opta relativnost predvida vlastiti (krah. Kada zakrivljenost prostorvremena -postane velika, do izraaja ce doci kvantna .gravitaciona dejstva i klasicna teorija vie 'nece moci da valjano opie Vaseljenu. .Potrebno je, dakle, primeniti kvantnu teoriju +gravitacije da bi se proniklo u to kako je Vaseljena pocela. -U kvantnoj teoriji gravitacije, kao to smo 0videli u prethodnom poglavlju, da bi se odredilo/stanje Vaseljene i dalje je potrebno ustanoviti/kako bi se moguce istorije Vaseljene ponaale ,na granici prostorvremena u prolosti. Ova +nelagodna obaveza opisivanja onoga to ne *znamo i to ne moemo znati mogla bi se .izbeci jedino ako bi ove istorije zadovoljile 'uslov bezgranicnosti: da im je, naime, *pruanje konacno, ali da nemaju granica, 0rubova ili singularnosti. U tom slucaju pocetak -vremena predstavljao bi pravilnu, ravnomernu ,tacku prostorvremena, a Vaseljena bi pocela %svoje irenje u veoma ravnomernom i -sredenom stanju. Ono ne bi moglo biti potpuno-jednoobrazno, zato to bi se time naruilo .nacelo neodedenosti kvantne teorije. Morale bi-da postoje male fluktuacije gustina i brzina /cestica. Uslov bezgranicnosti, medutim, nalae*da ove fluktuacije ne budu nimalo vece od &onoga to minimalno propisuje nacelo neodredenosti. Vaseljena bi pocela razdobljem 2eksponencijalnog ili 'inflatornog' irenja kojim .bi se njena velicina povecavala veoma velikim *ciniocem. Tokom ovog irenja fluktuacije 0gustine ostale bi male u pocetku, ali bi kasnije)stale da rastu. Kod podrucja u kojima je *gustina neto iznad proseka dolo bi do .usporenja irenja pod dejstvom gravitacionog )privlacenja dodatne mase. Konacno, takva 2podrucja prestala bi da se ire i kolabirala bi, /obrazujuci galaksije, zvezde i bica poput nas. ,Vaseljena bi, dakle, pocela u ravnomernom i +sredenom stanju, a postajala bi haoticna i )nesredena s protokom vremena. Ovim bi se +objasnilo postojanje termodinamicke strele vremena. -Ali ta bi se dogodilo ako i kada Vaseljena 2prestane da se iri i pocne da se saima? Da li .ce se termodinamicka strela okrenuti, a nered )poceti da se smanjuje s vremenom? Ovo bi 0ljude koji preive prelazak iz faze irenja u &fazu saimanja suocilo sa svom silom 1naucnofantasticnih posledica. Da li bi oni videli-kako se razbijene cae sakupljaju sa poda i /skacu natrag na sto? Da li bi mogli da se sete 0sutranjih cena i obogate se na berzi? Izgleda +prilicno akademski brinuti se o onome to -moe da se dogodi kada Vaseljena bude stala .da se saima, buduci da to ionako nece poceti-da se dogada bar jo narednih deset hiljada 0miliona godina. No, postoji jedan bri nacin da.se ustanovi ta ce se dogoditi: jednostavno, -skocite u crnu rupu. Kolabiranje zvezde koje -se okoncava crnom rupom prilicno nalikuje na /zavrne faze kolabiranja svekolike Vaseljene. 'Ako, dakle, nered treba da se smanji u /saimajucoj fazi Vaseljene, moe se ocekivati+da ce se on smanjivati i unutar crne rupe. -Jedan astronaut koji bi pao u crnu rupu mogao0bi da silno zaradi na ruletu setivi se gde je /kuglica pala pre no to stavi etone na sto. +(Na alost, medutim, on se ne bi naigrao, ,buduci da bi uskoro bio petvoren u rezance. 0Isto tako, ne bi bio u prilici da nas izvesti o -okretanju termodinamicke strele, pa cak ni da-uloi svoj dobitak u banku, zato to bi se -naao u stupici iza horizonta dogadaja crne rupe.) &U pocetku, verovao sam da ce se nered -smanjivati kada Vaseljena pocne da kolabira. (Bilo je to stoga to sam smatrao da se -Vaseljena mora vratiti u ravnomerno i sredeno(stanje kada ponovo postane mala. Ovo bi ,znacilo da bi faza saimanja predstavljala .vremenski obrnutu fazu irenja. Ljudi u fazi 3saimanja iveli bi svoje ivote unazad: oni bi /umrli pre no to se rode, postajuci sve mladi kako se Vaseljena saima. #Ova zamisao je privlacna zato to )pretpostavlja zgodnu simetricnost izmedu )faze irenja i faze saimanja. Ona se, +medutim, ne moe prihvatiti sama po sebi, 0nezavisno od ostalih ideja o Vaseljeni. Kljucno 1pitanje ovde glasi: da li ona proishodi iz uslova(bezgranicnosti ili je nesaglasna sa tim -uslovom? Kao to sam rekao, u prvo vreme sam,smatrao da iz uslova bezgranicnosti uistinu 'sledi da ce se nered smanjivati u fazi (saimanja. Ovde me je delimicno zavela 'analogija sa povrinom Zemlje. Ako se *pretpostavi da pocetak Vaseljene odgovara *severnom polu, onda bi kraj Vaseljene bio /slican njenom pocetku, ba kao to je juni /pol slican severnom. Medutim, severni i juni +pol odgovaraju pocetku i kraju Vaseljene u &imaginarnom vremenu. Pocetak i kraj u )stvarnom vremenu mogu se medusobno veoma +razlikovati. Takode me je zaveo moj rad na 'jednom jednostavnom modelu Vaseljene u )okviru koga je faza saimanja licila na *vremenski obrnutu fazu irenja. Medutim, .jedan moj kolega, Don Pejd, sa univerziteta !Pen Stejt, ustanovio je da uslov -bezgranicnosti ne nalae da faza saimanja +nuno mora biti vremenski obrnuta od faze )irenja. Pored toga, jedan moj student, +Rejmond Laflam, naao je da se u neznatno .sloenijem modelu saimanje Vaseljene veoma ,razlikuje od irenja. Shvatio sam da mi se +potkrala greka: iz uslova bezgranicnosti /proishodilo je da ce nered, zapravo, nastaviti &da se povecava i za vreme saimanja. .Termodinamicka i psiholoka strela Vremena ne-bi se okrenule ni kada Vaseljena pocne da se +saima, niti u unutranjosti crnih rupa. ,ta vam valja ciniti kad ustanovite da ste .napravili takvu greku? Neki ljudi nikada ne *priznaju da nisu u pravu i nastavljaju da +pronalaze nove, cesto medusobno nesaglasne ,argumente u prilog svoje pretpostavke - kao -to je to bio slucaj sa Edingtonom, koji se -suprotstavljao teoriji o crnim rupama. Drugi ,tvrde da nikada, u stvari, nisu stajali iza 0netacnog stanovita, ili, cak i ako jesu, bilo (je to samo stoga da pokau kako je ono /neodrivo. Meni se cini da je znatno bolje, a (svakako manje zbunjujuce, ako napismeno /priznate da niste bili u pravu. Dobar primer u 0ovom smislu pruio je Ajntajn koji je nazvao -najvecom grekom u svom ivotu kosmoloku -konstantu to ju je sam uveo, pokuavajuci #da sazda staticni model Vaseljene. -Ako se vratimo streli vremena, preostaje nam $sledece pitanje: zato uocavamo da ,termodinamicka i kosmoloka strela vremena -pokazuju u istom smeru? Drugim recima, zato+se nered povecava u istom smeru vremena kao1to je i onaj u kome se Vaseljena iri? Ukoliko/neko smatra da ce se Vaseljena iriti, a potom,ponovo saeti, kako to proishodi iz uslova 0bezgranicnosti, onda ovo pitanje glasi: 'Zato 1smo mi u fazi irenja, a ne u fazi saimanja?' ,Na ovo se moe odgovoriti na osnovu slabog /antropickog nacela. Uslovi u fazi saimanja ne0bi bili pogodni za postojanje inteligentnih bica,kadrih da postave pitanje: 'Zato se nered )povecava u istom smeru vremena u kome se 2odigrava i irenje Vaseljene?' Inflacija u ranim +razdobljima Vaseljene, koju predvida uslov -bezgranicnosti, znaci da se ona mora iriti )stopom veoma bliskom kriticnoj, na kojoj ,jedva da izbegava prelazak u saimanje, te )tako do ovoga veoma dugo ne dolazi. Kada )ipak dode, sve zvezde ce vec sagoreti, a +protoni i neutroni u njima verovatno ce se *raspasti na svetlosne cestice i zracenje. .Vaseljena ce se tada nalaziti u stanju gotovo (potpunog nereda. Nece postojati snana -termodinamicka strela vremena. Nered se dalje-nece moci znacajnije povecavati, zato to ce*se Vaseljena vec nalaziti u stanju gotovo "potpunog nereda. Medutim, snana +termodinamicka strela neophodna je kako bi .inteligentni ivot mogao da dejstvuje. Da bi .opstala, ljudska bica moraju da troe hranu, 0koja predstavlja sredeni oblik energije, i da je'pretvaraju u toplotu, koja predstavlja 'nesredeni oblik energije. Shodno tome, /inteligentni ivot ne moe da postoji u fazi .saimanja Vaseljene. To je ujedno odgovor na ,pitanje zato uocavamo da termodinamicka i ,kosmoloka strela vremena pokazuju u istom (smeru. Stvar je ne u tome to irenje ,Vaseljene dovodi do povecanja nereda, vec u &tome to uslov bezgranicnosti ima za $posledicu ovo povecanje, uzrokujuci .istovremeno da uslovi pogodni za inteligentan 'ivot postoje jedino u fazi irenja. -Da rezimiramo: zakoni nauke ne prave razliku (izmedu smera 'napred' i smera 'nazad' u .vremenu. Postoje, medutim, najmanje tri strele/vremena koje razlikuju prolost od buducnosti.-To su: termodinamicka strela (smer vremena u .kome dolazi do povecanja nereda), psiholoka )strela (smer vremena u okviru koga se mi *secamo prolosti, ali ne i buducnosti) i +kosmoloka strela (smer vremena u kome se /Vaseljena iri, a ne saima). Pokazao sam da *je psiholoka strela u osnovi ista kao i )termodinamicka, tako da ce njih dve uvek .pokazivati u istom smeru. Uslov bezgranicnosti%Vaseljene predvida postojanje sasvim ,odredene termodinamicke strele vremena, zato)to Vaseljena mora poceti ravnomernim i ,sredenim stanjem. A razlog to uocavamo da /se termodinamicka strela slae sa kosmolokom.strelom jeste taj to inteligentna bica mogu 1postojati jedino u fazi irenja. Faza saimanja)bila bi nepogodna zato to nema snanu termodinamicku strelu vremena. (Napredovanje ljudske rase u razumevanju +Vaseljene vaspostavilo je mali ugao reda u )rastucem neredu Vaseljene. Ukoliko biste ,zapamtili svaku rec iz ove knjige, u vaem *pamcenju nalo bi se zabeleeno oko dva /miliona delica informacija: red u vaem mozgu +povecao bi se za oko dva miliona jedinica. .Medutim, dok ste citali ovu knjigu pretvorili /ste najmanje hiljadu kalorija sredene energije,-u obliku hrane, u nesredenu energiju toplote &koju ste isputali u vazduh oko sebe ,kretanjem i znojenjem. Ovo ce povecati nered*Vaseljene za oko dvadeset miliona miliona 1miliona miliona jedinica - ili oko deset miliona 0miliona miliona puta vie nego to se povecao -red u vaem mozgu - i to pod uslovom da ste ,upamtili ba sve u ovoj knjizi. U narednom /poglavlju pokuacu da jo malo povecam red u +naoj okolini time to cu objasniti kako *fizicari pokuavaju da poveu delimicne (teorije koje sam do sada opisao u jednu /celovitu objedinjenu teoriju koja bi obuhvatilasve u Vaseljeni. 10. OBJEDINJENJE FIZIKE 0Kao to je objanjeno u prvom poglavlju, bilo 'bi veoma teko sazdati jednu celovitu -objedinjenu teoriju koja bi obuhvatala sve u +Vaseljeni. Umesto toga, napredovali smo na 1taj nacin to smo postavljali delimicne teorije .koje su opisivale ograniceni raspon pojava, a .zanemarivale ostala dejstva ili im odredivale 0pribline vrednosti izvesnim brojevima. (Hemija*nam, na primer, omogucuje da izracunavamo #medudejstva atoma bez upucenosti u +unutranje ustrojstvo atomskog jezgra.) U 0krajnjoj liniji, medutim, ocekivalo bi se da se #ipak dode do celovite, koherentne, +objedinjene teorije koja bi obuhvatila sve .delimicne teorije kao pribline i koja ne bi -trebalo da bude podeavana izborom vrednosti-izvesnih proizvoljnih brojeva kako bi bila u (saglasnosti sa cinjenicama. Traganje za 'jednom ovakvom teorijom poznato je kao 0'objedinjenje fizike'. Ajntajn je svoje pozne -godine ivota proveo u neuspenom traganju +za objedinjenom teorijom, ali vreme za nju 2tada jo nije bilo zrelo: postojale su, dodue, /delimicne teorije gravitacije i elektromagnetne'sile, ali je veoma malo bilo poznato o +nuklearnim silama. Osim toga, Ajntajn je &odbijao da prihvati valjanost kvantne -mehanike, iako je sam odigrao znacajnu ulogu )u njenom razvoju. Kako izgleda, medutim, *nacelo neodredenosti predstavlja temeljno )svojstvo Vaseljene u kojoj mi obitavamo. *Uspena objedinjena teorija mora, dakle, *nunim nacinom da obuhvati i ovo nacelo. ,Kao to cu pokazati, izgledi da se postavi *jedna ovakva teorija sada su mnogo bolji, -zato to su naa znanja o Vaseljeni znatno &veca. No, moramo se cuvati prekomerne .samouverenosti koja nas je u prolosti cesto 'upucivala u corsokake! Na pocetku ovog /stoleca, na primer, smatralo se da se sve moe.objasniti iz perspektive svojstava neprekidne 1materije, kao to su elasticnost i provodljivost&toplote. Otkrica grade atoma i nacela /neodredenosti namah su rasprila ovu zabludu. ,A onda, ponovo, fizicar i dobitnik Nobelove +nagrade Maks Born izjavio je, 1928, jednoj .skupini posetilaca Getingenskog univerziteta: -'Sa fizikom koju mi poznajemo bice gotovo za .est meseci.' Njegova samouverenost zasnivala-se na skoranjem Dirakovom otkricu jednacine-koje upravlja elektronom. Mislilo se da neka /slicna jednacina upravlja protonom, koji je bio-druga od dve poznate cestice u to vreme, to/ce ujedno predstavljati kraj teorijske fizike. 0No, otkrice neutrona i nuklearnih sila ubrzo je -obesnailo ovu tvrdnju. Uprkos svemu ovome, +medutim, ja ipak verujem da ima razloga za +oprezni optimizam i da se sada nalazimo na ,samom pragu otkrica konacnih zakona prirode.+U prethodnim poglavljima opisao sam optu 1relativnost, delimicnu teoriju gravitacije, kao i-delimicne teorije koje opisuju slabu, jaku i ,elektromagnetnu silu. Poslednje tri mogu se +obuhvatiti takozvanim velikim objedinjenim )teorijama, ili VOT-ima, koje nisu sasvim (zadovoljavajuce zato to ne obuhvataju .gravitaciju i zato to sadre izvestan broj -svojstava, kao to su relativne mase raznih .cestica, koje se ne mogu predvideti teorijom, &vec se moraju tako odabrati da budu u .saglasnosti sa rezultatima posmatranja. Glavna/potekoca u pokuajima da se postavi teorija ,koja povezuje gravitaciju sa ostalim silama ,ogleda se u tome to je opta relativnost *'klasicna' teorija; drugim recima, ona ne &obuhvata nacelo neodredenosti kvantne ,mehanike. Sa druge strane, ostale delimicne .teorije na sutinski nacin zavise od kvantne -mehanike. Neophodan prvi korak jeste, dakle, /da se dovedu u vezu opta relativnost i nacelo.neodredenosti. Kao to smo videli, ovo moe ,da ima neke izuzetne posledice, kao to je -ona da crne rupe ne budu crne i da Vaseljena 'nema nikakvih singularnosti, vec da je .potpuno samosvojna i bez granica. Nevolja je, )medutim, u tome, kao to sam objasnio u .sedmom poglavlju, to iz nacela neodredenosti0proishodi da je cak i 'prazan' prostor ispunjen /parovima virtuelnih cestica i anticestica. Ovi 0parovi imali bi beskrajnu kolicinu energije, pa &stoga, prema Ajntajnovoj znamenitoj /jednacini, E = mc2, imali bi i beskrajnu masu. .Njihovo gravitaciono privlacenje zakrivilo bi ,stoga Vaseljenu do beskrajno male velicine. .Slicno tome, prividno besmislene beskonacnosti1javljaju se i u drugim delimicnim teorijma, ali u,svim tim slucajevima ove beskonacnosti mogu )se potrti jednim procesom koji se naziva +renormalizacija. On pretpostavlja ukidanje beskonacnosti uvodenjem novih %beskonacnosti. Iako je ovaj postupak 'matematicki prilicno sumnjiv, on, kako /izgleda, dejstvuje u praksi i koricen je kod 0ovih teorija da bi se dolo do predvidanja koja,se izuzetno slau sa nalazima posmatranja. -Renormalizacija, medutim, ima jedan izuzetan *nedostatak iz perspektive pokuaja da se .postavi celovita teorija, buduci da proishodi -da se stvarne vrednosti masa i snaga sila ne /mogu predvideti teorijom, vec ih valja izabrati,tako da se poklope sa nalazima posmatranja. +U nastojanjima da se optom relativnocu -obuhvati i nacelo neodredenosti postoje samo -dva svojstva koja se mogu podeavati: snaga -gavitacije i vrednost kosmoloke konstante. .No, podeavanje ovih svojstava nije dovoljno -da bi se uklonile sve beskonacnosti. I tako, .dobijamo teoriju koja, kako izgleda, predvida %da su odredena svojstva, kao to je *zakrivljenost prostorvremena, beskonacna, !dok mi posmatranjima i merenjima ,ustanovljavamo da su ona savreno konacna! )Vec se due podozrevalo da postoji ovaj .problem pri povezivanju opte relativnosti i (nacela neodredenosti, ali on je konacno )potvrden podrobnim izracunavanjima 1972. +Cetiri godine kasnije predloeno je jedno /moguce reenje - takozvana 'supergravitacija'.)Zamisao se ogledala u tome da se povee ,cestica sa spinom 2, nazvana graviton, koja +nosi gravitacionu silu, sa izvesnim drugim -novim cesticama sa spinom 3/2, 1, 1/2 i 0. U -izvesnom smislu, sve ove cestice mogle bi se 'tada smatrati za razlicite vidove iste &'supercestice', cime bi se objedinile *materijalne cestice sa spinom 1/2 i 3/2 i +cestice koje nose silu sa spinom 0, 1 i 2. .Virtuelni parovi cestica-anticestica sa spinom31/2 i 3/2 imali bi negativnu energiju i teili bi /stoga da potru pozitivnu energiju spina 2, 1 i /0 virtuelnih parova. Ovo bi dovelo do potiranja*mnogih mogucih beskonacnosti, ali se ipak )pretpostavljalo da bi se neke zadrale. ,Proracunavanja neophodna da bi se ustanovilo,da li bi neke beskonacnosti ostale nepotrte -bila bi, medutim, tako duga i teka da niko (nije eleo da ih se lati. Cak i pomocu -kompjutera smatralo se da bi na njih otile .pune cetiri godine, a bilo je veoma verovatno /da bi se negde potkrala bar jedna greka, a po4svoj prilici i vie njih. Znalo bi se, dakle, da se-dolo do tacnog odgovora jedino ako bi jo *neko izvrio proracunavanje i dobio isti 0rezultat, ali to nije izgledalo odvec verovatno!)Uprkos problemima, kao i cinjenici da se *cestice u teorijama o supergravitaciji ne %podudaraju sa cesticama koje stvarno -registrujemo, vecina naucnika je smatrala da *je supergravitacija po svoj prilici pravo .reenje problema objedinjenja fizike. Bio je 'to, kako izgleda, najbolji nacin da se -gravitacija dovede u vezu sa ostalim silama. (No, 1984. dolo je do znacajne promene 0stanovita u korist onoga to je dobilo naziv *teorija struna. U ovim teorijama, osnovni %objekti nisu cestice, koje zauzimaju .pojedinacne tacke prostora, vec velicine koje 0imaju duinu, ali ne i druge dimenzije, slicno +kakvoj beskrajno tankoj struni. Ove strune 'mogu imati krajeve (takozvane otvorene *strune) ili ti krajevi mogu biti spojeni, &obrazujuci svojevrsne omce (zatvorene 2strune). (Ilus. 10.1 i 10.2) Jedna cestica zauzima)jednu tacku u prostoru u svakom trenutku +vremena. Njena istorija, dakle, moe biti 'predstavljena linijom u prostorvremenu +('svetska linija'). Jedna struna, sa druge (strane, zauzima jednu du u prostoru u *svakom trenutku vremena. Njena istorija u +prostorvremenu, dakle, jeste dvodimenziona 0povrina koja se naziva 'svetska ravan'. (Svaka(tacka na takvoj svetskoj plohi moe se .opisati dvama brojevima: prvi odreduje vreme, 0a drugi poloaj tacke na struni.) Svetska ploha+jedne otvorene strune jeste pojas; njegove +ivice predstavljaju putanje krajeva strune .kroz prostorvreme (Ilus. 10.1). Svetska ploha 3zatvorene strune jeste valjak ili cev (Ilus. 10.2).)Poprecni presek ove cevi jeste krug koji -predstavlja poloaj strune u nekom odredenom vremenu. .Dve strune se mogu spojiti, pri cemu obrazuju -jedinstvenu novu strunu; u slucaju otvorenih +struna, one se naprosto spoje na krajevima .(Ilus. 10.3), dok u slucaju zatvorenih struna *imamo situaciju kao kod pantalona, gde se -dve nogavice spajaju u jedinstven deo (Ilus. *10.4). Slicno tome, jedna struna moe se 0podeliti u dve. U teorijama struna, ono to se &prethodno smatralo za cestice sada se ,predstavlja u vidu talasa koji se krecu niz /strunu, poput talasa na vibrirajucem uetu na /kome se puta zmaj od hartije. Emitovanje ili +apsorbovanje jedne cestice od strane druge /odgovara deljenju ili spajanju struna. Primera (radi, gravitaciona sila Sunca na Zemlji /prikazivana je u teoriji cestica tako kao da je)posredi emitovanje gravitacije od strane -jedne cestice u Suncu i njeno apsorbovanje od.strane jedne cestice u Zemlji (Ilus. 10.5). U ,teoriji struna, ovaj proces odgovara jednoj /cevi u obliku slova 'H' (Ilus. 10.6). (Teorija +struna na izvestan nacin prilicno nalikuje (cevovodu.) Dve okomite strane slova 'H' +odgovaraju cesticama na Suncu i na Zemlji, $dok poprecni vodoravni deo odgovara 'gravitaciji koja se krece izmedu njih. -Teorija struna ima neobicnu istoriju. Ona je +prvobitno postavljena u poznim ezdesetim *godinama prilikom pokuaja da se dode do .teorije koja bi opisala jaku silu. Zamisao se .ogledala u tome da se cestice poput protona i ,neutrona mogu smatrati za talase na struni. *Jake sile izmedu cestica tu bi odgovarale )strunama koje se poprecno pruaju preko 0ostalih struna, slicno kao niti kod paucine. Da ,bi se ova teorija poklopila sa zabeleenom )vrednocu jake sile izmedu cestica, ove -strune trebalo je da budu poput gumenih traka/kadrih da izdre silu rastezanja od oko deset tona. 2Godine 1974, oel erk iz Pariza i Don varc 2iz Kalifornijskog tehnolokog instituta objavili /su rad u kome su pokazali da bi teorija struna 0mogla da opie gravitacionu silu, ali samo ako )bi napetost struna bila znatno veca, oko 0hiljadu miliona miliona miliona miliona miliona 0miliona tona (jedinica iza koje se prua niz od*trideset devet nula). Predvidanja teorije ,struna tada bi bila istovetna sa onima koje .proishode iz opte relativnosti, u normalnim ,razmerama duine, ali bi se razlikovala na ,veoma malim udaljenostima, manjim od jednog 3hiljadu milion milion milion milion milionitog dela-centimetra (jedan centimetar podeljen brojem 'koji se oznacava jedinicom sa nizom od *trideset tri nule iza nje). Ovaj rad nije -privukao vecu panju, medutim, zato to je ,upravo u to vreme vecina fizicara napustila ,prvobitnu teoriju struna jake sile u korist ,teorije zasnovane na kvarkovima i gluonima, -koja se, kako je izgledalo, bolje slagala sa (nalazima posmatranja. erk je umro pod %tragicnim okolnostima (bolovao je od +dijabetesa i pao je u komu u casu kada oko )njega nije bilo nikog da mu da injekciju +insulina). Tako je varc ostao kao gotovo .jedini zagovornik teorije struna, ali sada sa -znatno vecom predloenom vrednocu njihove napetosti. .Godine 1984. iznenada je oivljeno zanimanje -za strune, kako je izgledalo iz dva razloga. 1Prvi je bio taj to fizicari nisu odvec odmakli !u pokuajima da pokau kako je +supergravitacija konacna, odnosno da moe /da objasni one vrste cestica koje mi beleimo..Drugi je bio objavljivanje jednog rada Dona -varca i Majka Grina iz londonskog koleda ,Kvin Meri, u kome je pokazano da bi teorija +struna mogla da objasni postojanje cestica /koje imaju levosmernu rotaciju, kao to je to -slucaj sa nekim cesticama koje registrujemo. 2Bili su to dovoljni povodi da veliki broj fizicara-uskoro pocne da radi na teoriji struna, tako +da je nedugo potom postavljena jedna njena -nova verzija, takozvana teorija heterotickih +struna, za koju se poverovalo da bi moda )mogla da objasni tipove cestica koje smo dosad registrovali. &U teorijama struna takode se javljaju .beskonacnosti, ali smatra se da ce se sve one *potrti u verziji poput ove o heterotickim (strunama (premda stvar jo nije sasvim 'pouzdana). Teorije struna se, medutim, +suocavaju sa jednom vecom potekocom: kako-izgleda, one su koherentne jedino pod uslovom1da prostorvreme ima ili deset ili dvadeset est -dimenzija, umesto uobicajenih cetiri! Razume %se, dodatne dimenzije prostorvremena %predstavljaju opte mesto u naucnoj 1fantastici; tavie, one su tu gotovo nunost,+buduci da bi, u protivnom, cinjenica da iz &relativnosti proishodi da su nemoguca +putovanja bra od svetlosti znacila da bi )prevaljivanje razdaljina izmedu zvezda i *galaksija trajalo predugo. Da bi se ovome .nekako doskocilo, u naucnoj fantastici javila &se zamisao o tome da je moda moguce 1posluiti se precicom kroz neku viu dimenziju./Stvar se ovde moe predociti na sledeci nacin.-Zamislimo da prostor u kome ivimo ima samo .dve dimenzije i da je zakrivljen poput kakvog 4kotura ili torusa (Ilus. 10.7). Ako biste se nali ,sa jedne strane unutranje ivice prstena i +eleli da stignete na neku tacku sa druge +strane, morali biste da prevalite put du 0unutranje ivice. Ukoliko biste, medutim, bili ,kadri da se krecete trecom dimenzijom mogli ,biste pravolinijski da prevalite razdaljinu izmedu dve tacke. $Zato ne zapaamo sve ove dodatne +dimenzije, ako one uistinu postoje? Zato .vidimo jedino tri prostorne i jednu vremensku 'dimenziju? Prema jednoj zamisli, druge .dimenzije zakrivljene su u prostor veoma malih/razmera, negde oko jednog milion milion milion 1milion milionitog dela inca. To je toliko malo da-mi naprosto stvar ne primecujemo, vec vidimo -jednu vremensku i tri prostorne dimenzije, u .kojima je prostorvreme prilicno ravno. Ovo je /slicno povrini neke pomorande: ako je pomno.zagledate, primeticete da je sva smeurana i .naborana, ali ako je posmatrate sa udaljenosti*ne vidite ove neravnine i ona vam izgleda -glatka. Isto je tako i sa prostorvremenom: u veoma malim razmerama, ono je ,desetodimenziono i veoma zakrivljeno, ali u -vecim razmerama ne vide se ove zakrivljenosti-dodatnih dimenzija. Ukoliko je ova predstava (ispravna, onda se loe pie nesudenim -putnicima kroz kosmos: dodatne dimenzije bile.bi daleko premale da bi kroz njih mogao proci -jedan kosmicki brod. No, ovde iskrsava jedan 0novi veliki problem. Zato su samo neke, a ne i-sve dimenzije savijene u malu loptu? Po svoj /prilici, u veoma ranoj Vaseljeni sve dimenzije ,bile su izuzetno zakrivljene. Zato su se, )medutim, jedna vremenska i tri prostorne *dimenzije izravnale, dok su ostale ostale savijene? -Jedan moguci odgovor jeste antropicko nacelo.+Dve prostorne dimenzije nisu, kako izgleda .dovoljne za nastanak sloenih bica kakva smo 0mi. Primera radi, dvodimenzione ivotinje koje 0bi ivele na jednodimenzionoj Zemlji morale bi +da se penju jedna na drugu kako bi prole ,jedna pored druge. Ako bi neko dvodimenziono)stvorenje pojelo neto to ne bi moglo *potpuno da svari ono bi ostatke moralo da /izbaci kroz isti otvor gde je progutalo hranu, -zato to bi, ukoliko bi postojao jo jedan .otvor sa suprotne strane tela, stvorenje bilo "razdvojeno na dve polovine; nae +dvodimenziono stvorenje tako bi se raspalo 3(Ilus. 10.8). Slicno tome, teko je razabrati kako%bi mogao da postoji krvotok u jednom dvodimenzionom bicu. *Potekoce bi se javile i sa vie od tri .prostorne dimenzije. Gravitaciono privlacenje $izmedu dva tela opadalo bi bre sa *udaljenocu nego to je to slucaj u tri .dimenzije. (U tri dimenzije gravitaciona sila /pada na 1/4 ukoliko se udvostruci razdaljina. U+cetiri dimenzije ona bi pala na 1/8, u pet ,dimenzija na 1/16 i tako dalje.) Znacaj ove (okolnosti ogleda se u tome da bi orbite ,planeta, kao to je Zemlja, oko Sunca bile /nestabilne: i najmanji poremecaj krune orbite)(do cega bi moglo da dovede gravitaciono (privlacenje drugih planeta) imalo bi za )posledicu da Zemlja pocne da se spiralno /udaljava od nae zvezde ili da se sunovrati ka0njoj. U tom slucaju mi bismo se ili posmrzavali 0ili bismo izgoreli. Osim toga, novi odnos izmedu2gravitacije i razdaljine u vie od tri prostorne ,dimenzije znacio bi da Sunce ne bi moglo da .postoji u stabilnom stanju u kome se pritisak 2javlja kao protivtea gravitaciji. Ono bi se ili 1raspalo ili bi kolabiralo i postalo crna rupa. U -oba slucaja ne bi bilo od velike koristi kao 1izvor toplote i svetlosti za ivot na Zemlji. U -manjim razmerama, elektricne sile koje nagone+elektrone da orbitiraju oko jezgra u atomu 1ponaale bi se na isti nacin kao i gravitacione .sile. Prema tome, elektroni bi se ili potpuno 1odvojili od atoma ili bi se zavojito sunovratili -u jezgro. U oba slucaja ne bismo imali atome kakve mi poznajemo. .Izgleda sasvim izvesno da ivot, bar onaj za .koji mi znamo, moe da postoji jedino u onim )podrucjima prostorvremena u kojima jedna )vremenska i tri prostorne dimenzije nisu +savijene u male razmere. Ovo bi znacilo da ,bismo se mogli osloniti na slabo antropicko ,nacelo, pod uslovom da se moe pokazati da *teorija struna doputa postojanje takvih -podrucja Vaseljene - to ona, kako izgleda, 1uistinu i doputa. Nije iskljuceno da postoje i .druga podrucja Vaseljene, ili druge Vaseljene 0(ma ta to znacilo), u kojima su sve dimenzije 0savijene u male razmere ili u kojima je vie od,cetiri dimenzije gotovo ravno, ali u takvim 0oblastima ne bi bilo inteligentnih bica koja bi 0posmatrala razliciti broj efektivnih dimenzija. #Pored pitanja broja dimenzija koje ,prostorvreme ima, teorija struna suocava se 0sa jo nekoliko pitanja koja se moraju reiti +pre no to ona eventualno bude prihvacena 0kao konacna objedinjena teorija fizike. Mi jo $ne znamo da li se sve beskonacnosti ,medusobno potiru, niti kako tacno dovesti u +vezu talase na struni sa posebnim tipovima +cestica koje registrujemo. Medutim, sva je ,prilika da ce se do odgovora na ova pitanja -doci u toku nekoliko narednih godina, odnosno/da cemo do kraja stoleca znati da li je teorija)struna uistinu dugo traena objedinjena teorija fizike. /Ali da li uopte moe da postoji takva jedna 0objedinjena teorija? Ili se moda mi nalazimo u%potrazi za jednom fatamorganom? Kako !izgleda, postoje tri mogucnosti: 01) Uistinu postoji celovita objedinjena teorija,*koju cemo jednoga dana otkriti ako budemo dovoljno mudri. -2) Ne postoji konacna teorija Vaseljene, vec ,samo beskrajni niz teorija koje sve tacnije opisuju Vaseljenu. /3) Ne postoji teorija Vaseljene; dogadaji se ne(mogu predvidati preko odredene granice, )buduci da tu pocinju da se odigravaju na nasumican i proizvoljan nacin. /Neki autori smatraju da je najizglednija treca -mogucnost, buduci da bi postojanje celovitog +skupa zakona ogranicilo slobodu Boga da se -predomilja i uplivie na svet. Posredi je )varijanta starog paradoksa: moe li Bog 0napraviti kamen koji bi bio toliko teak da ga ,ni on sam ne bi mogao podici? Ali zamisao o 0Bogu koji bi se predomiljao predstavlja primer/zablude zamiljanja Boga kao bica koje postoji(u vremenu, na ta je ukazao jo sveti -Augustin: vreme je svojstvo jedino Vaseljene .koju je Bog stvorio. A on je valjda znao ta hoce kada ju je stvarao! *Razvoj kvantne mehanike pomogao nam je da *uvidimo da se dogadaji ne mogu predvideti -sasvim precizno, vec da uvek postoji izvestan+stepen neodredenosti. To bi se, ukoliko se #nekome tako svida, moglo pripisati 1nasumicnosti Bojeg upliva, ali takav upliv bio .bi veoma neobican: nita ne ukazuje na to da -iza njega stoji nekakva svrha. Jer da stoji, *ona po definiciji ne bi bila nasumicna. U &modernim vremenima, mi smo delotvorno /uklonili trecu mogucnost na taj nacin to smo -predefinisali zadatak nauke: na cilj je da -formuliemo skup zakona koji bi nam omogucio+da predvidamo dogadaje do one granice koju postavlja nacelo neodredenosti. %Druga mogucnost - da, naime, postoji +beskrajni niz sve savrenijih teorija - u +saglasnosti je sa svim naim dosadanjim +iskustvima. U mnogo navrata povecavali smo 2osetljivost naih merenja ili uvodili novu klasu (posmatranja, samo da bismo otkrili nove /pojave koje nije predvidala postojeca teorija i*za cije je objanjenje valjalo postaviti -usavreniju teoriju. Ne bi stoga bilo odvec ,iznenadujuce ako bi iz sadanje generacije 'velikih objedinjenih teorija pogreno .proishodilo da se nita sutinski novo nece &dogoditi izmedu elektroslabe energije .objedinjenja od oko 100 GeV i velike energije ,objedinjenja od oko hiljadu miliona miliona /GeV. I odista, sasvim bismo mogli ocekivati da .pronademo vie novih slojeva ustrojstva koji -bi bili osnovniji od kvarkova i elektrona za %koje danas smatramo da predstavljaju 'elementarne' cestice. .Kako izgleda, medutim, gravitacija bi mogla da/postavi granicu ovom nizu 'kutija u kutijama'. +U slucaju cestice sa energijom iznad onoga 0to se naziva Plankova energija, a to iznosi 0deset miliona miliona miliona GeV (jedinica iza .koje se prua niz od devetnaest nula), njena 'masa bila bi tako zbijena da bi se ona )naprosto odvojila od ostatka Vaseljene i 'obazovala malu crnu rupu. Shodno tome, 0izgleda da niz sve savrenijih teorija mora da )se suoci sa nekom granicom kako idemo ka 0sve viim energijama, to znaci da bi trebalo +da postoji neka konacna teorija Vaseljene. -Razume se, Plankova energija nalazi se veoma -daleko od energija od oko stotinak GeV koliko-smo mi najvie u stanju da proizvedemo danas%u laboratorijama. Ovaj raspon necemo .premostiti akceleratorima cestica u doglednoj +buducnosti! Najranija razdoblja Vaseljene, -medutim, predstavljaju arenu gde su se takve /energije mogle javljati. Ja smatram da postoje .dobri izgledi za to da ce nas izucavanje rane $Vaseljene i neophodnost matematicke .koherentnosti dovesti do celovite objedinjene .teorije jo za ivota nekih od nas danas, a (sve to ponovo pod pretpostavkom da sami !sebe ne unitimo u meduvremenu. )ta bi to znacilo ako uistinu dodemo do /otkrica krajnje teorije Vaseljene? Kao to je .bilo objanjeno u prvom poglavlju, nikada ne ,bismo mogli da budemo sasvim sigurni da smo +uistinu doli do tacne teorije, buduci da *teorije ne mogu biti dokazane. Ali ako bi +teorija bila matematicki koherentna i uvek )davala predvidanja koja bi se slagala sa 'nalazima posmatranja, imali bismo puno -razloga za verovanje da je ona valjana. Time +bi bilo okoncano dugo i slavno poglavlje u 0istoriji covekovih intelektualnih nastojanja da #dokuci Vaseljenu. Ali to bi takode .revolucionisalo laicko razumevanje zakona koji-upravljaju Vaseljenom. U Njutnovo vreme bilo +je moguce da jedna obrazovana osoba stekne -predstavu o svekolikom ljudskom znanju, bar u*glavnim crtama. Ali potonji ritam razvoja (nauke sasvim je onemogucio tako neto. /Buduci da se teorije stalno preinacuju kako bi ,objasnile nova posmatranja, one nikada nisu /prikladno saete ili pojednostavljene kako bi )ih laici razumeli. Potrebno je da budete )strucnjak, pa cak se i tada moete samo *nadati da ste pronikli u jedan maleni deo .naucnih teorija. Dalje, ritam napredovanja je /tako brz da je ono to se uci u koli ili na 1univerzitetu uvek manje ili vie zastarelo. Tek *retki naucnici uspevaju da dre korak sa +hitrim pomicanjem granica znanja, morajuci -pri tom da posvete tome sve svoje vreme i da *se specijalizuju na nekom uskom podrucju. -Ostali deo populacije gotovo da nema nikakvu +predstavu o razvoju koji je u toku, niti o ,uzbudenjima koja on izaziva. Pre sedamdeset +godina, ako je verovati Edingtonu, samo su 0dva coveka shvatala optu teoriju relativnosti.$Danas je shvata na desetine hiljada .diplomiranih studenata, a mnogo miliona ljudi (bar je okvirno upoznato sa ovom idejom. &Ukoliko bi dolo do otkrica celovite +objedinjene teorije, predstavljalo bi samo 0stvar vremena pre no to bi ona bila saeta i -pojednostavljena na isti nacin i predavana u ,kolama, bar u osnovnim crtama. Tada bismo /svi bili u prilici da u izvesnoj meri shvatimo )zakone koji vladaju Vaseljenom i koji su odgovorni za nae postojanje. )Cak i ako otkrijemo celovitu objedinjenu 1teoriju, to ne bi znacilo da bismo bili u stanju -da predvidamo dogadaje uopte - i to iz dva ,razloga. Prvi se odnosi na ogranicenje koje -pred nae moci predvidanja postavlja nacelo +neodredenosti kvantne mehanike. Ne postoji -nikakav nacin na koji se ono moe izbeci. U ,praksi, medutim, ovo prvo ogranicenje manje ,je sputavajuce od drugoga koje proishodi iz %cinjenice da ne bismo mogli tacno da ,reavamo jednacine teorije, izuzev u veoma -jednostavnim situacijama. (Mi nismo u stanju -da izracunamo cak ni situaciju sa tri tela u /Njutnovoj teoriji gravitacije, a potekoce se ,samo umnoavaju sa povecanjem broja tela i ,sloenosti teorije.) Vec znamo zakone koji )upravljaju ponaanjem materije pod svim *uslovima osim onih krajnjih. Narocito smo ,dobro upuceni u osnovne zakone koji stoje u .temelju svekolike hemije i biologije. No, ovo .nipoto ne znaci da smo ove oblasti sveli na ,status reenih problema; za sada smo imali -malo uspeha u pedvidanju ljudskog ponaanja (na osnovu matematickih jednacina! Prema 'tome, cak i ako pronademo potpuni skup -osnovnih zakona, u potonjim godinama i dalje +ce postojati izazovni intelektualni zadaci ,usavrenja aproksimacionih metoda, to bi +trebalo da nam omoguci korisno predvidanje )verovatnih ishoda u sloenim i stvarnim .situacijama. Celovita, koherentna, objedinjena1teorija samo je prvi korak: na krajnji cilj je $potpuno razumevanje pojava koje nas .okruuju, kao i naeg vlastitog postojanja. 11. ZAKLJUCAK )Obitavamo u cudesnom svetu. Nastojimo da *proniknemo u smisao onoga to vidimo oko *sebe i postavljamo sebi pitanje: kakva je *priroda Vaseljene? Kakvo je nae mesto u .njoj, odakle ona potice i odakle mi poticemo? )Zato je ona upravo onakva kakva jeste? ,Da bismo doli do odgovora na ova pitanja, 2gradimo 'slike sveta'. Ba kao to je beskrajni *niz kornjaca koje nose ravnu Zemlju takva 'jedna slika, isto vai i za teoriju o (superstrunama. U oba slucaja posredi su .teorije o Vaseljeni, premda je potonja znatno *preciznija i zasnovanija na matematici od *prve. I jednoj i drugoj teoriji, medutim, -nedostaje potpora proistekla iz posmatranja: ,niko jo nije video dinovsku kornjacu sa 0Zemljom na ledima, ali isto tako niko jo nije ,video jednu superstrunu. Medutim, teorija o +kornjacama ne moe da bude valjana naucna 1teorija zato to predvida da bi ljudi trebalo da-padnu sa ruba sveta. Ovo je potpuno protivno -iskustvu, osim ako se ne ispostavi da je taj /usud snaao ljude za koje se pretpostavlja da "su icezli u bermudskom trouglu! -Najraniji teorijski pokuaji da se opie i 0objasni Vaseljena temeljili su se na zamisli da .dogadaje i prirodne pojave kontroliu duhovi /sa ljudskim osecanjima koji se ponaaju, ba -kao i mi, na krajnje nepredvidljiv nacin. Ti .duhovi obitavali su u prirodnim objektima, kao0to su reke i planine, racunajuci tu i nebeska ,tela, poput Sunca i Meseca. Njih je valjalo ,umilostiviti i tako steci njihovu naklonost %kako bi se obezbedili plodnost tla i (smenjivanje godinjih doba. Postepeno, 'medutim, zacelo je uocavano da postoje .izvesne pravilnosti: Sunce je uvek izazilo na /istoku, a zalazilo na zapadu, bez obzira na to ,da li je prethodno prineta neka rtva bogu )Sunca. Osim toga, Sunce, Mesec i planete 'kretali su se po nebeskom svodu sasvim 'odredenim putanjama koje su se unapred /mogle prilicno tacno predvideti. Sunce i Mesec 2mogli su i dalje biti bogovi, ali ti bogovi su se *pokoravali strogim zakonima, naizgled bez .ikakvog izuzetka, ukoliko se ne racunaju price+poput one o Suncu koje je stalo zbog Isusa Navina. +U pocetku su ove pravilnosti i zakoni bili ,ocigledni jedino u astronomiji i u nekoliko +retkih drugih situacija. Kako se, medutim, 0civilizacija razvijala, a narocito u poslednjih +tri stotine godina, otkrivano je sve vie -pravilnosti i zakona. Uspenost ovih zakona +navela je Laplasa da pocetkom devetnaestog stoleca postavi temelje naucnog +determinizma, odnosno da izloi zamisao o &tome da bi, ukoliko se zna ustrojstvo )Vaseljene u jednom trenutku, bilo moguce ,odrediti njen potonji razvoj na osnovu niza pouzdanih zakona. ,Laplasov determinizam bio je nepotpun u dva /pogleda. On nije govorio nita o tome kako te 'zakone treba odabrati i nije odredivao )pocetno ustrojstvo Vaseljene. To je bilo -preputeno Bogu. Na Bogu je bilo da odabere 'kako ce Vaseljena poceti i kojim ce se /zakonima pokoravati, ali on vie ne bi vrio -nikakve uplive poto udari temelje sveta. U ,stvari, Bog je tu bio ogranicen na podrucja (koja nauka iz devetnaestog stoleca nije razumela. &Mi danas znamo da se Laplasove nade u ,determinizam nisu mogle ostvariti, bar ne u ,onom vidu koji je on imao na umu. Iz nacela ,neodredenosti kvantne mehanike proishodi da *se odredeni parovi svojstava, kao to su (poloaj i brzina neke cestice, ne mogu +istovremeno predvideti uz potpunu tacnost. -Kvantna mehanika reava ovu situaciju klasom.kvantnih teorija u okviru kojih cestice nemaju/sasvim odredene poloaje i brzine, vec bivaju )predstavljene u vidu talasa. Ove kvantne 0teorije su deterministicke u smislu da pruaju *zakone za razvoj talasa u vremenu. Shodno -tome, ako je poznat talas u jednom trenutku, ,moe se izracunati njegova vrednost u bilo &kom drugom. Nepredvidljivi, nasumicni %elemenat stupa u dejstvo jedino kada $pokuavamo da protumacimo talas iz ,perspektive poloaja i brzina cestica. Ali -moda je ovde posredi naa greka: moda /uopte ne postoje poloaji i brzine cestica, #vec samo talasi. Moda to mi samo 'pokuavamo da uklopimo talase u nae -apriorne predstave o poloajima i brzinama. .Zbrka koja odatle proishodi predstavlja uzrok prividne nepredvidljivosti. .U stvari, predefinisali smo zadatak nauke tako,da on bude ustanovljenje zakona koji ce nam (omoguciti da predvidamo zbivanja sve do #same granice koju postavlja nacelo &neodredenosti. Ostaje, medutim, jedno 3pitanje: kako su ili zato bili odabrani zakoni i pocetno stanje Vaseljene? .U ovoj knjizi ja sam posebnu panju posvetio .zakonima koji upravljaju gravitacijom, buduci 0da je gravitacija sila koja oblikuje Vaseljenu u&makrokosmickim razmerama, iako je ona -najslabija od cetiri kategorije sila. Zakoni /gravitacije bili su nesaglasni sa stanovitem ,koje je bilo na snazi sve donedavno i prema +kome je Vaseljena nepromenljiva u vremenu: .okolnost da gravitacija uvek deluje privlacno ,nalae da se Vaseljena mora nalaziti ili u /stanju irenja ili u stanju saimanja. Prema 2optoj teoriji relativnosti, jednom u prolosti .moralo je postojati stanje beskrajne gustine, .Veliki Prasak, koji je, zapravo, predstavljao +pravi pocetak vremena. Slicno tome, ako bi )svekolika Vaseljena stala da kolabira, u &buducnosti bi se ponovo javilo stanje .beskrajne gustine, Veliko Saimanje, koje bi -ujedno donelo kraj vremena. Cak i ukoliko ne )dode do kolabiranja svekolike Vaseljene, +singularnosti bi se javile u svim lokalnim .podrucjima koja su kolabirala do stanja crnih .rupa. Te singularnosti donele bi kraj vremena (svakome ko bi pao u neku crnu rupu. Kod 1Velikog Praska i ostalih singularnosti dolo bi +do ponitenja svih zakona, tako da bi Bog &ponovo imao potpuno odreene ruke da +izabere ta ce se dogoditi i kako da opet Vaseljena pocne. -Dovedemo li u vezu kvantnu mehaniku i optu -relativnost, ukazuje se, kako izgleda, jedna 0nova mogucnost koje ranije nije bilo: prostor i +vreme, naime, zajedno mogu obrazovati jedan&konacan, cetvorodimenzioni kosmos bez 3singularnosti ili granica, slican povrini Zemlje,2ali sa vie dimenzija. Iz perspektive ove zamisli,mogla bi se objasniti mnoga uocena svojstva +Vaseljene, kao to je njena makrokosmicka &jednoobraznost, odnosno mikrokosmicka 'odstupanja od homogenosti, kao to su /galaksije, zvezde, pa cak i ljudska bica. Time .bi se cak moglo pruiti objanjenje za smer ,vremena koji uocavamo. Ali ako je Vaseljena *potpuno samosvojna, bez singularnosti ili (granica, i potpuno opisana objedinjenom 'teorijom, onda odatle proishode duboke %implikacije o ulozi Boga kao Tvorca. /Ajntajn je jednom postavio pitanje: 'Kakav je.izbor Bog imao prilikom sazdavanja Vaseljene?')Ako je tacna pretpostavka o nepostojanju +granica, onda on nije imao nikakvu slobodu ,prilikom odabiranja pocetnih uslova. On bi, )razume se, i dalje imao odreene ruke u -pogledu izbora zakona kojima bi se Vaseljena /pokoravala. To, medutim, uopte ne bi bio neki+narociti izbor; nije, naime, iskljuceno da 0postoji samo jedna, ili u najboljem slucaju neki0mali broj celovitih objedinjenih teorija, kakva ,je, na primer, teorija heterotickih struna, +koje se odlikuju unutarnjom saglasnocu i %doputaju postojanje tako sloenih -ustrojstava kao to su ljudska bica koja su %kadra da ispituju zakone Vaseljene i $postavljaju pitanja o prirodi Boga. $Cak i ako postoji samo jedna moguca .objedinjena teorija, ona nije nita drugo do 2niz pravila i jednacina. ta je, medutim, to to'udahnjuje plamen u jednacine i sazdaje .Vaseljenu koju ce one opisati? Iz perspektive ,uobicajenog naucnog pristupa gradenju nekog ,matematickog modela, nije moguce odgovoriti ,na pitanje zato uopte postoji Vaseljena 0koju bi taj model opisao. Zato bi se Vaseljena,uopte uputala u to da postoji? Da li je *objedinjena teorija tako svemocna da sama /dovodi do svog postojanja? Ili joj je, moda, -potreban neki tvorac, a ako jeste, ima li on .bilo kakav drugi uticaj na Vaseljenu? I ko je njega stvorio? +Sve do sada, vecina naucnika bila je odvec -zaokupljena postavljanjem novih teorija koje -opisuju ta je Vaseljena, ne uputajuci se -uopte u pokuaj da se odgovori na pitanje 0zato. Sa druge strane, ljudi ciji je posao da /pitaju zato, filozofi, nisu bili u stanju da +dre korak sa razvojem naucnih teorija. U ,osamnaestom stolecu filozofi su smatrali da +svekoliko ljudsko znanje, ukljucujuci tu i 0nauku, predstavlja njihovo polje i raspravljali 0su o pitanjima kao to je: 'Da li je Vaseljena ,imala pocetak?' U devetnaestom i dvadesetom &veku, medutim, nauka je postala odvec ,tehnicka i matematicka za filozofe, odnosno &za bilo koga drugog osim za mali broj 1strucnjaka. Filozofi su u toj meri smanjili svoje(podrucje izucavanja da je Vitgentajn, ,najznamenitiji filozof ovog stoleca, rekao: +'Jedini preostali zadatak filozofije jeste +analiza jezika.' Kakav svretak za veliku -tradiciju filozofije od Aristotela do Kanta! +Ako mi, medutim, uspemo da dodemo do jedne +celovite teorije, onda bi nju, s vremenom, *trebalo u nacelu da shvate svi, a ne samo 'nekolicina naucnika. Tada cemo svi mi, /filozofi, naucnici, kao i obicni ljudi, biti u -stanju da uzmemo udela u raspravi o pitanjima,vezanim za razlog postojanja kako nas samih ,tako i Vaseljene. Ukoliko pronademo odgovor (na to, onda ce to biti vrhunski trijumf -ljudskog razuma - jer tada cemo pronici u sam um Boga. ALBERT AJNTAJN &Dobro je poznata Ajntajnova veza sa *politikom nuklearne bombe; on je potpisao &znamenito pismo predsedniku Frenklinu -Ruzveltu, koje je nagnalo Sjedinjene Drave )da zamisao shvate ozbiljno, a potom se u /posleratnom razdoblju pridruio naporima da se/spreci izbijanje nuklearnog rata. No, ovo nisu -bili samo izdvojeni postupci jednog naucnika 1uvucenog u svet politike. Ajntajnov ivot je, .zapravo, bio, prema njegovim vlastitim recima,('podeljen izmedu politike i jednacina'. +Ajntajnova najranija politicka aktivnost ,potice iz vremena Prvog svetskog rata, kada 0je bio profesor u Berlinu. Razgnevljen onim to.je smatrao za tracenje ljudskih ivota, uzeo 'je udela u antiratnim demonstracijama. 0Njegovo zagovaranje civilnog neposlunitva i *javno podsticanje ljudi da ne pristanu na %regrutaciju nisu mu, medutim, doneli )uvaavanje medu kolegama. A onda, posle %rata, upravio je napore ka izmirenju .sukobljenih naroda i poboljanju medunarodnih'odnosa. Ni to mu, medutim, nije donelo ,popularnost; tavie, politicka delatnost *uskoro je pocela da mu oteava pristup u (Sjedinjene Drave, cak i radi dranja predavanja. .Naredna stvar za koju se Ajntajn zalagao bio,je cionizam. Iako je poreklom bio Jevrejin, 1Ajntajn nije prihvatao biblijsku ideju o Bogu. -Rastuce antisemitsko raspoloenje, kako pre &tako i za vreme Drugog svetskog rata, -postepeno ga je navelo na to da se poistoveti+sa jevrejskom zajednicom, kao i da kasnije &postane otvoreni pristalica cionizma. )Nepopularnost koju mu je ovaj stav doneo *ponovo ga nije odvratila od toga da javno /izlae svoje poglede. Na udaru su se nale i +njegove teorije, pa je cak bila uprilicena -jedna antiajntajnovska organizacija. Jedan &covek je bio osuden zbog toga to je .podsticao druge da ubiju Ajntajna (kazna je 3iznosila pukih est dolara). Ali Ajntajn je sve /to primio flegmaticno. Kada se pojavila knjiga .pod naslovom Sto autora protiv Ajntajna, on +je uzvratio: 'Da nisam bio u pravu, bio bi dovoljan i samo jedan!' 1Godine 1933, na vlast je doao Hitler. Ajntajn1se nalazio u Americi i izjavio je da ne eli da &se vrati u Nemacku. A onda, poto je .nacisticka milicija izvrila pretres njegove (kuce i konfiskovala mu racun u banci, u .jednim berlinskim novinama pojavio se sledeci 0naslov: 'Dobre vesti od Ajntajna - odlucio je 'da se ne vrati!' Suocen sa nacistickom /pretnjom, Ajntajn je odustao od pacifistickih,uverenja i konacno, bojeci se mogucnosti da *nemacki naucnici naprave nuklearnu bombu, 0predloio je da to ucine i Sjedinjene Drave. 2Ali jo pre no to je eksplodirala prva atomska )bomba, on je poceo da javno upozorava na )opasnost od nuklearnog rata, predlauci -medunarodnu kontrolu nuklearnog naoruanja. ,Napori koje je Ajntajn ulagao tokom celog *ivota u postizanje mira nisu bili odvec 0plodotvorni niti su mu doneli mnogo prijatelja. .Njegova verbalna podrka cionistickoj stvari -bila je, medutim, nagradena 1952, kada mu je ,bilo ponudeno mesto predsednika Izraela. On .ga nije prihvatio, uzvrativi da sebe smatra 0odvec naivnim za politiku. Ali moda je stvarni0razlog bio drugaciji. Evo ponovo njegovih reci: 1'Jednacine su mi vanije, jer politika se odnosi(na sadanjost, dok jednacine pripadaju vecnosti.' GALILEO GALILEJ /Moda se Galileju, vie nego bilo kom drugom +pojednicu, ima pripisati u zaslugu rodenje )moderne nauke. Njegov znameniti sukob sa (katolickom crkvom bio je od sredinjeg .znacaja za njegovu filozofiju, jer Galilej je .bio jedan od prvih koji su ustvrdili da covek .moe da se nada da ce pronici u to kako svet -dejstvuje; tavie, to bismo mogli postici posmatranjem stvarnog sveta. ,Galilej je od pocetka verovao u Kopernikovu /teoriju (prema kojoj planete krue oko Sunca),,ali poceo je da je javno podrava tek onda *kada je otkrio dokaze koji su potvrdivali .valjanost te zamisli. Pisao je o Kopernikovoj -teoriji na italijanskom (a ne na uobicajenom *akademskom latinskom) i njegova gledita (uskoro su dobila iroku podrku izvan /univerziteta. Ovo je ozlojedilo aristotelovske -profesore koji su se ujedinili protiv njega, /nastojeci da ubede katolicku crkvu da izopti Kopernika. .Zabrinut zbog ovoga, Galilej je pohitao u Rim -na razgovor sa crkvenim vlastima. Istupio je /pred njima sa tvrdnjom da svrha Biblije nije da/nam bilo ta kae o naucnim teorijama, kao i +da je uobicajeno pretpostaviti da je Sveto %Pismo alegoricno na onim mestima gde )protivureci zdravom razumu. Ali crkva se +pobojala skandala koji je mogao da podrije -njenu borbu protiv protestantizma, te je tako-preduzela represivne mere. Kopernikove nazore.proglasila je 1616. za 'lane i pogrene' i 3naloila je Galileju da vie nikada ne brani i ne-zastupa to ucenje. Galilej se s tim pomirio. +Godine 1623, jedan dugogodinji Galilejev +prijatelj postao je papa. Galilej je odmah +pokuao da ga nagovori da povuce odredbu. /Nije u tome uspeo, ali mu je polo za rukom da,dobije dozvolu da napie knjigu u kojoj bi +raspravljao o Aristotelovoj i Kopernikovoj /teoriji, pod dva uslova: nece stati ni na ciju -stranu i doci ce do zakljucka da covek nikako-ne moe da ustanovi kako svet dejstvuje zato*to Bog moe da izazove ista dejstva na (nacine nepojamne coveku, koji ne sme da 'postavlja ogranicenja Bojoj svemoci. *Knjiga pod naslovom Rasprava o dva glavna (sistema sveta bila je privedena kraju i ,objavljena 1632, uz punu potporu cenzora, i -odmah je bila pozdravljena irom Evrope kao /knjievno i folosofsko remek-delo. Shvativi 'da ljudi u knjizi vide uverljiv prilog 0kopernikanizmu, papa je uskoro zaalio to je /dopustio njeno objavljivanje. Stoga je ustvrdio(da je Galilej, iako knjiga ima zvanicni -blagoslov cenzora, ipak prekrio odredbu iz 11616. Izveo je Galileja pred inkviziciju, koja ga3je osudila na doivotni kucni pritvor i naloila 'mu da se javno odrekne kopernikanizma. "Galilej je po drugi put ustuknuo. ,Galilej je ostao veran katolik, ali njegovo 'uverenje u nezavisnost nauke nije bilo *poljuljano. Cetiri godine pre smrti 1642, /nalazeci se i dalje u kucnom pritvoru, uspeo je.da prokrijumcari rukopis svoje druge kapitalne+knjige jednom izdavacu u Holandiji. Upravo (ovo delo, poznato pod naslovom Dve nove .nauke, postalo je, jo vie nego Galilejeva ,podrka Koperniku, zametak moderne fizike. ISAK NJUTN +Isak Njutn nije bio prijatan covek. Njegov +odnos sa ostalim akademcima bio je na zlom *glasu, a pozne godine ivota proveo je u (ucnim raspravama. Posle objavljivanja #Principiae Mathematicae, neosporno (najznacajnije knjige koja je ikada bila ,napisana u fizici, Njutnov ugled u javnosti -poceo je brzo da raste. Bio je naimenovan za -predsednika Kraljevskog drutva i postao je -prvi naucnik u istoriji koji je dobio titulu viteza. .Njutn je uskoro doao u sukob sa kraljevskim *astronomom Donom Flemstidom, koji ga je +prethodno opskrbljivao neophodnim podacima 0za Principiu, ali je sada zadravao informacije.koje su Njutnu bile potrebne. Njutn nije mogao-da se pomiri sa ovim odbijanjem; samoga sebe )je naimenovao za upravno telo Kraljevske %opservatorije, a onda je pokuao da .izdejstvuje da podaci smesta budu objavljeni. $Konacno je tako sredio stvari da se -Flemstidovog dela docepa i da ga pripremi za .objavljivanje njegov smrtni neprijatelj Edmond-Halej. Ali Flemstid je poveo parnicu i ubrzo $dobio presudu kojom se zabranjivalo (rasturanje ukradenog dela. Ovo je silno 0razjarilo Njutna koji je stao da se sveti na taj.nacin to je sistematicno brisao svaki pomen -o Flemstidu u potonjim izdanjima Principiae. ,Znatno ozbiljnija rasprava zapodenula se sa *nemackim filozofom Gotfridom Lajbnicom. I 'Lajbnic i Njutn su, nezavisno jedan od (drugoga, postavili temelje jednoj grani +matematike koja se naziva diferencijalni i )integralni racun. Ovaj racun cini temelj )najveceg dela moderne fizike. Iako danas ,znamo da je Njutn otkrio ovaj racun godinama.pre Lajbnica, on je svoje delo objavio znatno .kasnije. Dolo je do silne prepirke oko toga -kome pripada prvenstvo, pri cemu su naucnici /strastveno stajali na strani jednog ili drugog -takmaca. Zanimljivo je medutim, da je vecina *clanaka koja se pojavila u odbranu Njutna -potekla, zapravo, iz njegovog pera, pri cemu 1su ih njegovi prijatelji samo potpisali! Kada se )rasprava rasplamsala, Lajbnic je nacinio 4greku, predloivi Kraljevskom drutvu da rei*spor. Kao predsednik, Njutn je naimenovao /jedan 'napristrasan' odbor da izvri istragu; )odbor se slucajno sastojao iskljucivo od 3njegovih prijatelja! Ali to nije bilo sve: Njutn je0potom licno napisao izvetaj odbora i naloio /Kraljevskom drutvu da ga objavi, optuivi ,Lajbnica za plagijat. I dalje nezadovoljan, .potom je napisao anonimni prikaz izvetaja i 0objavio ga u periodicniku Kraljevskog drutva. .Po Lajbnicovoj smrti Njutn je navodno izjavio /da mu je bilo silno milo to je doskocio svom takmacu. &U vreme ove dve rasprave Njutn je vec /napustio Kembrid i akademiju. Bio je aktivno 0uzeo udela u antikatolickoj politici Kembrida,.a kasnije i u parlamentu, to mu je na kraju &donelo unosno mesto cuvara kraljevske /kovnice. Tu je iskoristio svoje nadarenosti za (spletkarenje i podmetanje na drutveno -prihvatljiviji nacin, uspeno vodeci veliku (kampanju protiv krivotvorenja, pa cak i %poslavi nekoliko ljudi na veala. POJMOVNIK *Akcelerator cestica: Maina koja, pomocu (elektromagneta, moe da ubrza pokretne 1naelektrisane cestice, dajuci im vie energije. /Anticestica: Svaki tip materijalne cestice ima *odgovarajucu anticesticu. Kada se cestica )sudari sa anticesticom, one se medusobno -potiru, ostavljajuci za sobom samo energiju. +Antropicko nacelo: Vaseljenu vidimo onakvu .kakva jeste, jer da je drugacija, mi ne bismo bili ovde da je posmatramo. ,Apsolutna nula: Najnia moguca temperatura ,na kojoj data supstanca ne sadri toplotnu energiju. (Atom: Osnovna jedinica obicne materije, +sazdana od sicunog jezgra (sacinjenog od /protona i neutrona) oko koga krue elektroni. .Beli patuljak: Stabilna hladna zvezda koju na ,okupu odrava odbijanje izmedu elektrona u duhu nacela iskljucenja. -Crna rupa: Podrucje prostorvremena iz koga se1nita, cak ni svetlost, ne moe otisnuti, zbog izuzetno velike sile tee. )Crveni pomak: Pomeranje ka crvenom kraju (linija u spektru svetlosti neke zvezde, )izazvano Doplerovim efektom, kada se ona udaljuje od nas. 'Candrasekarova granica: Najveca moguca -masa jedne stabilne hladne zvezde, iznad koje"ona mora da kolabira u crnu rupu. )Dogadaj: Tacka u prostorvremenu odredena svojim vremenom i mestom. 'Dvojnost talas-cestica: Prema kvantnoj 'mehanici, nema razlike izmedu talasa i +cestica; cestice se mogu ponekad ponaati "kao talasi, a talasi kao cestice. /Elektricni naboj: Svojstvo jedne cestice kojim 1ona moe da odbija (ili privlaci) druge cestice +koje imaju naboj istog (odnosno suprotnog) znaka. 0Elektromagnetna sila: Sila koja se javlja izmedu)cestica sa elektricnim nabojem, druga po &snazi od cetiri osnovne sile prirode. Elektron: Cestica sa negativnim )naelektrisanjem koja krui oko atomskog jezgra. -Elektroslaba energija objedinjenja: Energija )(oko 100 GeV) iznad koje nestaje razlika /izmedu elektromagnetne i slabe nuklearne sile. .Elementarna cestica: Cestica koja se, kako se smatra, ne moe dalje deliti. -Faza: Kod talasa, poloaj u ciklusu u nekom -odredenom vremenu - da li je, naime, posredi $breg, dolja, ili neka tacka izmedu. Foton: Kvant svetlosti. (Gama-zrak: Elektromagnetni talasi veoma *kratkih talasnih duina koji nastaju pri *radioaktivnom raspadanju ili pri sudarima elementarnih cestica. *Geodezijska linija: Najkraca ili najdua putanja izmedu dve tacke. $Gola singularnost: Prostorvremenska *singularnost koju ne okruuje crna rupa. &Horizont dogadaja: Granica crne rupe. %Imaginarno vreme: Vreme koje se meri imaginarnim brojevima. *Jaka sila: Najjaca od cetiri osnovne sile ,prirode, sa najkracim dometom. Ona dri na ,okupu kvarkove u protonima i neutronima kao (i protone i neutrone, obrazujuci atome. 0Koordinate: Brojevi koji odreduju poloaj jednetacke u prostoru i vremenu. .Kosmologija: Izucavanje Vaseljene kao celine. ,Kosmoloka konstanta: Matematicko sredstvo #koje je koristio Ajntajn kako bi ,prostorvremenu obezbedio inherentnu tenju ka irenju. .Kvant: Nedeljiva jedinica u kojoj talasi mogu biti emitovani ili apsorbovani. (Kvantna mehanika: Teorija proistekla iz +Plankovog kvantnog nacela i Hajzenbergovog nacela neodredenosti. .Kvark: Naelektrisana elementarna cestica koja 0je podlona dejstvu jake nuklearne sile. Proton'i neutron se sastoje od po tri kvarka. /Magnetno polje: Polje koje tvori magnetna sila,.sada ukljuceno, zajedno sa elektricnim poljem,u elektromagnetno polje. .Masa: Kolicina materije u jednom telu; njegovainercija ili otpor ubrzanju. +Mikrotalasno pozadinsko zracenje: Zracenje +sjaja tople rane Vaseljene, sada sa toliko ,velikim crvenim pomakom da vie ne izgleda 0kao svetlost, vec kao mikrotalasi (radio-talasi .sa talasnom duinom od nekoliko centimetara).-Nacelo iskljucenja: Dve istovetne cestice sa +spinom 1/2 ne mogu imati (u granicama koje /odreduje nacelo neodredenosti) isti poloaj i istu brzinu. )Nacelo neodredenosti: Nikada se ne moe .potpuno biti siguran istovremeno u poloaj i /brzinu neke cestice; to se tacnije zna jedan (parametar, to se manje tacno zna drugi. -Neutrino: Izuzetno laka (verovatno bez mase) ,elementarna cestica materije na koju deluju !jedino slaba sila i gravitacija. +Neutron: Cestica bez naelektrisanja, veoma *slicna protonu, na koju otpada priblino %polovina mase u jezgru vecine atoma. )Neutronska zvezda: Hladna zvezda koju na ,okupu odrava odbijanje izmedu neutrona, u duhu nacela iskljucenja. *Nuklearna fuzija: Proces u kome dolazi do .sudaranja i srastanja dva jezgra, pri cemu se obrazuje novo, tee jezgro. *Ocuvanje energije: Zakon nauke prema kome 1se energija (ili njen ekvivalent u masi) ne moeni stvoriti ni unititi. 1Opta relativnost: Ajntajnova teorija koja se 0temelji na zamisli da bi zakoni prirode trebalo -da budu isti za sve posmatrace, bez obzira na+to kako se oni krecu. Ona objanjava silu *gravitacije iz perspektive zakrivljenosti #cetvorodimenzionog prostorvremena. 'Plankovo kvantno nacelo: Zamisao da se 4svetlost (ili bilo koji dugi klasicni talasi) moe .emitovati ili apsorbovati jedino u diskretnim ,kvantima, cija je energija upravo srazmerna njihovoj ucestalosti. .Polje: Neto to postoji u celom prostoru i ,vremenu, za razliku od cestice koja postoji %samo u jednoj tacki u datom vremenu. /Posebna relativnost: Ajntajnova teorija koja .se temelji na zamisli da zakoni nauke treba da-budu isti za sve posmatrace koji se nalaze u *slobodnom kretanju, bez obzira na njihovu brzinu. .Pozitron: Pozitivno naelektrisana anticestica elektrona. +Praiskonska crna rupa: Crna rupa nastala u veoma ranoj Vaseljeni. 0Prostorna dimenzija: Bilo koja od tri dimenzije +prostorvremena koje su prostorne; odnosno, sve izuzev vremenske dimenzije. -Prostorvreme: Cetvorodimenzioni prostor cije su tacke dogadaji. .Proton: Cestica sa pozitivnim naelektrisanjem /na koju otpada priblino polovina mase jezgra kod vecine atoma. ,Radar: Sistem u kome se koriste impulsirani 0radio-talasi da se otkrije poloaj tela na taj *nacin to se meri vreme koje je potrebno ,jednom impulsu da stigne do datog objekta i bude odraen natrag. +Radioaktivnost: Spontano razlaganje jednog tipa atomskih jezgara u druga. -Singularnost: Tacka u prostorvremenu u kojoj %zakrivljenost prostorvremena postaje beskonacna. 1Slaba sila: Jedna od cetiri osnovne sile prirode,*sasvim kratkog dometa, od koje je slabija *samo gravitaciona sila. Ona deluje na sve /cestice materije, ali ne i na cestice koje nosesilu. (Spektar: Raspodela intenziteta jednog - %recimo, elektromagnetnog - talasa po "njegovim sastavnim ucestalostima. (Spin: Unutranje svojstvo elementarnih .cestica, koje ima veze, ali nije istovetno sa $uobicajenim pojmom spina (vrtenja). .Stacionarno stanje: Stanje koje se ne menja s -vremenom; kugla koja se vrti stalnom brzinom -stacionarna je zato to izgleda istovetna u 'bilo kom trenutku, iako nije staticna. +Svetlosna kupa: Povrina u prostorvremenu 'koja oznacava moguce pravce svetlosnih &zraka to prolaze kroz dati dogadaj. &Svetlosna sekunda (svetlosna godina): *Udaljenost koju svetlost prevali u jednoj sekundi (godini). /Talasna duina: Kod talasa, razdaljina izmedu )dve susedne dolje ili dva susedna brega. -Teorema singularnosti: Teorema koja pokazuje -da singularnost mora postojati pod odredenim *okolnostima, kao i da je Vaseljena morala poceti singularnocu. /Teina: Jacina sile kojom na neko telo deluje -gravitaciono polje. Ona je upravo srazmerna, ali ne i istovetna masi. +Ubrzanje: Stopa promene brzine nekog tela. -Ucestalost: Kod talasa, broj celih ciklusa u sekundi. %Upravo srazmerno: Izraz 'X je upravo ,srazmerno Y' znaci da kada Y biva pomnoeno,nekim brojem, onda to biva i X. Izraz 'X je (obrnuto srazmerno Y' znaci da kada je Y %pomnoeno nekim brojem, onda X biva podeljeno tim istim brojem. .Uslov bezgranicnosti: Zamisao da je Vaseljena ,konacna, ali da nema granica (u imaginarnom vremenu). -Velika energija objedinjenja: Energija iznad 'koje se, kako se smatra, vie ne mogu -medusobno razlikovati elektromagnetna, slaba !nuklearna i jaka nuklearna sila. /Velika objedinjena teorija (VOT): Teorija koja .objedinjuje elektromagnetnu, jaku nuklearnu i slabu nuklearnu silu. 'Veliki Prasak: Singularnost na pocetku Vaseljene. )Veliko Saimanje: Singularnost na kraju Vaseljene. (Virtuelna cestica: U kvantnoj mehanici, -cestica koja nikada ne moe neposredno biti ,otkrivena, ali cije postojanje ima merljiva dejstva. 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