{"id":31419,"date":"2019-10-31T21:41:09","date_gmt":"2019-10-31T18:41:09","guid":{"rendered":"https:\/\/prohoster.info\/blog\/termodinamika-chernyh-dyr\/"},"modified":"2019-10-31T21:41:09","modified_gmt":"2019-10-31T18:41:09","slug":"termodinamika-chernyh-dyr","status":"publish","type":"post","link":"https:\/\/prohoster.info\/lv\/blog\/news\/termodinamika-chernyh-dyr","title":{"rendered":"Melnraksturu termodinamika","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"Melnraksturu<\/a><\/noindex>
\nPriec\u012bgu kosmonautikas dienu! M\u0113s iesniedz\u0101m druk\u0101\u0161anai \u201eMaz\u0101 gr\u0101mata par melnajiem caurumiem\u201d<\/a><\/noindex>. Tie\u0161i \u0161aj\u0101s dien\u0101s astronomi par\u0101d\u012bja visai pasaulei, k\u0101 izskat\u0101s melnie caurumi. Sakrit\u012bba? Negribam to dom\u0101t \ud83d\ude09 T\u0101tad gaidiet, dr\u012bz par\u0101d\u012bsies apbr\u012bnojama gr\u0101mata, kuru sarakst\u012bju\u0161i St\u012bvens Gabsers un Franss Pretoriuss, tulkoja lieliskais Pulkova astronoms aka Astrodeb Kirils Mas\u013cennikovs, veica zin\u0101tnisko redakciju le\u0123end\u0101rais Vladimirs Surdins un atbalst\u012bjusi t\u0101s izdo\u0161anu fonds Trajektorija.<\/p>\n

Fragments \u201eMelnraksturu termodinamika\u201d zem griezuma.
\n<\/a><\/noindex>
\nL\u012bdz \u0161im meln\u0101s caurums apskat\u012bj\u0101m k\u0101 astrofizik\u0101lus objektus, kas radu\u0161ies supernovu spr\u0101dzienos vai atrodas galaktiku centros. M\u0113s tos nov\u0113rojam netie\u0161i, m\u0113rot tuvu eso\u0161o zvaig\u017e\u0146u pa\u0101trin\u0101jumu. Slaven\u0101 gravit\u0101cijas vi\u013c\u0146u re\u0123istr\u0101cija ar LIGO detektoru 2015. gada 14. septembr\u012b k\u013cuva par piem\u0113ru tie\u0161\u0101kiem nov\u0113rojumiem melno caurumu sadursm\u0113. Matem\u0101tiskie r\u012bki, ko izmantojam, lai lab\u0101k izprastu melno caurumu dabu, ir \u0161\u0101di: diferenci\u0101l\u0101 \u0123eometrija, Ein\u0161teina vien\u0101dojumi un jaud\u012bgas anal\u012btisk\u0101s un skaitlisk\u0101s metodes, kas tiek pielietotas, risinot Ein\u0161teina vien\u0101dojumus un aprakstot to \u0123eometriju, ko rada melnie caurumi. Un tikl\u012bdz m\u0113s sp\u0113sim sniegt piln\u012bgu kvantitat\u012bvu aprakstu meln\u0101 cauruma rad\u012btajai laika un telpas strukt\u016brai, no astrofizikas viedok\u013ca melno caurumu t\u0113ma var\u0113s tikt uzskat\u012bta par sl\u0113gtu. Pla\u0161\u0101k\u0101 teor\u0113tisk\u0101 perspekt\u012bv\u0101 joproj\u0101m ir \u013coti daudz iesp\u0113ju izp\u0113tei. \u0160\u012bs noda\u013cas m\u0113r\u0137is ir past\u0101st\u012bt par daudziem teor\u0113tiskajiem sasniegumiem m\u016bsdienu melno caurumu fizik\u0101, kur idejas no termodinamika un kvantu teorijas apvienojas ar visp\u0101r\u0113jo relativit\u0101tes teoriju, radot negaid\u012btas jaunas koncepcijas. Galven\u0101 ideja ir t\u0101da, ka melnie caurumi nav tikai \u0123eometriski objekti. Tie ir ar temperat\u016bru, tiem ir milz\u012bga entropija un tie var r\u0101d\u012bt kvantu savi\u013c\u0146ojuma izpausmes. M\u016bsu p\u0101rdomas par termodinamikas un kvantu aspektiem melno caurumu fizik\u0101 b\u016bs vair\u0101k fragment\u0101ras un virspus\u0113jas nek\u0101 iepriek\u0161\u0113j\u0101 noda\u013c\u0101 sniegtais anal\u012bzes apraksts par t\u012bri \u0123eometriskaj\u0101m iez\u012bm\u0113m laika un telpas strukt\u016br\u0101 melnajos caurumos. Bet gan \u0161ie, gan it \u012bpa\u0161i kvantu aspekti ir b\u016btiska un dz\u012bvotsp\u0113j\u012bga da\u013ca no uzs\u0101ktajiem teor\u0113tiskajiem p\u0113t\u012bjumiem par melnajiem caurumiem, un m\u0113s daudz cent\u012bsimies nodot vismaz darba garu, ja ne sare\u017e\u0123\u012bt\u0101s deta\u013cas.<\/p>\n

Klasiskaj\u0101 visp\u0101r\u0113j\u0101 relativit\u0101tes teorij\u0101 \u2014 run\u0101jot par Ein\u0161teina vien\u0101dojumu risin\u0101jumu diferenci\u0101lo \u0123eometriju \u2014 melnie caurumi ir patiesi melni, jo no tiem nekas nevar izb\u0113gt. St\u012bvens Hokinga par\u0101d\u012bja, ka \u0161\u012b situ\u0101cija piln\u012bb\u0101 main\u0101s, ja \u0146emam v\u0113r\u0101 kvantu efektus: izr\u0101d\u0101s, melnie caurumi izstaro noteikta temperat\u016bra, ko sauc par Hokinga temperat\u016bru. Astrofizisko izm\u0113ru melnajiem caurumiem (t.i., no zvaig\u017e\u0146u masas melnajiem caurumiem l\u012bdz supermasveida) Hokinga temperat\u016bra ir niec\u012bga sal\u012bdzin\u0101jum\u0101 ar kosmisk\u0101 mikrovi\u013c\u0146u fona temperat\u016bru \u2014 radi\u0101ciju, kas piepilda visu Visumu un kas, starp citu, var tikt uzskat\u012bta par Hokinga radi\u0101cijas variantu. Hokinga veiktie apr\u0113\u0137ini, lai noteiktu melno caurumu temperat\u016bru, ir da\u013ca no pla\u0161\u0101kas p\u0113tniec\u012bbas programmas jom\u0101, ko sauc par melno caurumu termodinamiku. Liela da\u013ca \u0161\u012bs programmas ir saist\u012bta ar melno caurumu entropijas izp\u0113ti, kas raksturo inform\u0101cijas daudzumu, kas paz\u016bd meln\u0101 caurum\u0101. Parastiem objektiem (piem\u0113ram, \u016bdens kr\u016bzei, t\u012bra magnija stienim vai zvaigznei) ar\u012b ir entropija, un viens no centr\u0101lajiem apgalvojumiem par meln\u0101 cauruma termodinamikas teoriju ir tas, ka melns caurums noteikta izm\u0113ra ir liel\u0101ka entropija nek\u0101 jebkura cita mat\u0113rijas forma, ko var\u0113tu ietvert t\u0101da pa\u0161a izm\u0113ra apgabal\u0101, bet bez meln\u0101 cauruma veido\u0161an\u0101s.<\/p>\n

Pirms m\u0113s detaliz\u0113ti apl\u016bkosim Hokinga radi\u0101cijas un melno caurumu entropijas probl\u0113mas, veiksim \u0101tru ekskursiju kvantu meh\u0101nik\u0101, termodinamik\u0101 un savstarp\u0113j\u0101 saist\u012bb\u0101. Kvantu meh\u0101nika tika izstr\u0101d\u0101ta galvenok\u0101rt 1920. gados, un t\u0101s galvenais m\u0113r\u0137is bija \u013coti mazu da\u013ci\u0146u, piem\u0113ram, atomu, apraksts. Kvantu meh\u0101nikas izstr\u0101de noveda pie t\u0101du b\u016btisku fizikas j\u0113dzienu, k\u0101 prec\u012bza individu\u0101las da\u013ci\u0146as atra\u0161an\u0101s vieta, izpl\u016b\u0161anas. Piem\u0113ram, izr\u0101d\u012bj\u0101s, ka elektrona atra\u0161an\u0101s vietu t\u0101 kust\u012bb\u0101 ap atomu kodolu nevar noteikt prec\u012bzi. T\u0101 viet\u0101 elektroniem tika pie\u0161\u0137irtas t\u0101 saucam\u0101s orb\u012btas, kur\u0101s to faktisk\u0101s atra\u0161an\u0101s vietas var noteikt tikai varb\u016bt\u012bbas izteiksm\u0113. Tom\u0113r m\u016bsu m\u0113r\u0137iem ir svar\u012bgi nep\u0101riet uz \u0161o \u2014 varb\u016bt\u012bbas \u2014 pusi p\u0101r\u0101k \u0101tri. Apskat\u012bsim vienk\u0101r\u0161\u0101ko piem\u0113ru: \u016bde\u0146ra\u017ea atoma. Tas var atrasties noteikt\u0101 kvantu st\u0101vokl\u012b. Vienk\u0101r\u0161\u0101kais \u016bde\u0146ra\u017ea atoma st\u0101voklis, ko sauc par pamata st\u0101vokli, ir st\u0101voklis ar viszem\u0101ko ener\u0123iju, un \u0161\u012b ener\u0123ija ir prec\u012bzi zin\u0101ma. Visp\u0101r\u012bg\u0101k\u0101 noz\u012bm\u0113 kvantu meh\u0101nika \u013cauj mums (princip\u0101) noteikt jebkuras kvantu sist\u0113mas st\u0101vokli piln\u012bgi prec\u012bzi.<\/p>\n

Iesp\u0113jam\u012bbas k\u013c\u016bst aktu\u0101las, kad uzdodam noteikta veida jaut\u0101jumus par kvantu meh\u0101nisku sist\u0113mu. Piem\u0113ram, ja ir noteikti zin\u0101ms, ka \u016bde\u0146ra\u017ea atoms ir pamata st\u0101vokl\u012b, m\u0113s varam uzdot jaut\u0101jumu: \u201cKur atrodas elektrons?\u201d un saska\u0146\u0101 ar kvantu
\nmeh\u0101nikas m\u0113s sa\u0146emsim uz \u0161o jaut\u0101jumu tikai k\u0101du varb\u016bt\u012bbas nov\u0113rt\u0113jumu, aptuveni kaut ko l\u012bdz\u012bgu: \u201cvisticam\u0101k, elektrons atrodas l\u012bdz pusam angstr\u0113m no \u016bde\u0146ra\u017ea atoma kodola\u201d (viens angstr\u0113ms ir vien\u0101ds ar \"Melnraksturu metru). Ta\u010du mums ir iesp\u0113ja, izmantojot noteiktu fizisku procesu, atrast elektrona st\u0101vokli daudz prec\u012bz\u0101k, nek\u0101 l\u012bdz vienam angstr\u0113mam. \u0160is diezgan ierastais fizikas process sast\u0101v no t\u0101, ka elektronam uzsist fotonu ar \u013coti \u012bsu vi\u013c\u0146a garumu (vai, k\u0101 saka fizi\u0137i, izklied\u0113t fotonu uz elektrona) \u2014 p\u0113c tam m\u0113s var\u0113sim rekonstru\u0113t elektrona atra\u0161an\u0101s vietu izklied\u0113\u0161an\u0101s br\u012bd\u012b ar precizit\u0101ti, kas aptuveni atbilst fotona vi\u013c\u0146a garumam. Bet \u0161is process main\u012bs elektrona st\u0101vokli, t\u0101d\u0113\u013c p\u0113c tam tas vairs neb\u016bs galvenaj\u0101 st\u0101vokl\u012b \u016bde\u0146ra\u017ea atom\u0101 un neb\u016bs tie\u0161i noteiktas ener\u0123ijas. Ta\u010du noteikt\u0101 laik\u0101 t\u0101 pozicija b\u016bs gandr\u012bz prec\u012bzi noteikta (ar precizit\u0101ti l\u012bdz vi\u013c\u0146a garumam, ko izmantoja \u0161im fotonam). Iepriek\u0161\u0113ju elektrona poz\u012bcijas nov\u0113rt\u0113jumu var veikt tikai varb\u016bt\u012bbas zi\u0146\u0101 ar precizit\u0101ti ap vienu angstr\u0113mu, ta\u010du, tikl\u012bdz m\u0113s to izm\u0113r\u0101m, m\u0113s prec\u012bzi zin\u0101m, kas tas bija. \u012asi sakot, ja m\u0113s k\u0101d\u0101 veid\u0101 m\u0113ram kvantu meh\u0101nisku sist\u0113mu, tad, vismaz izplat\u012btaj\u0101 noz\u012bm\u0113, m\u0113s \"piesprie\u017eam\" tai st\u0101vokli ar noteiktu izm\u0113ram\u0101 lieluma v\u0113rt\u012bbu.<\/p>\n

Kvantu meh\u0101nika ir piem\u0113rojama ne tikai maziem, bet ar\u012b (k\u0101 m\u0113s uzskat\u0101m) vis\u0101m sist\u0113m\u0101m; tom\u0113r liel\u0101m sist\u0113m\u0101m kvantu meh\u0101nisk\u0101s normas \u0101tri k\u013c\u016bst \u013coti sare\u017e\u0123\u012btas. Atsl\u0113gas koncepcija ir kvantu sap\u012b\u0161an\u0101s, kuras vienk\u0101r\u0161s piem\u0113rs var\u0113tu b\u016bt grie\u0161an\u0101s (spin). Individu\u0101li elektroni ir ar grie\u0161anos, t\u0101d\u0113\u013c praks\u0113 atsevi\u0161\u0137s elektrons var b\u016bt ar grie\u0161anos, kas virz\u012bta uz aug\u0161u vai uz leju attiec\u012bb\u0101 pret izv\u0113l\u0113to telpisko asi. Elektrona spin ir nov\u0113rojama v\u0113rt\u012bba, jo elektrons rada v\u0101ju magn\u0113tisko lauku, l\u012bdz\u012bgu magn\u0113tisk\u0101 stie\u0146a laukam. T\u0101d\u0113\u013c grie\u0161an\u0101s uz aug\u0161u noz\u012bm\u0113, ka elektrona zieme\u013cp\u016bles nor\u0101da uz leju, bet grie\u0161an\u0101s uz leju noz\u012bm\u0113, ka zieme\u013cp\u016ble \u201eskat\u0101s\u201d uz aug\u0161u. Divi elektroni var tikt novietoti sap\u012b\u0161an\u0101 kvanta st\u0101vokl\u012b, kur vienam no tiem spin ir v\u0113rsta uz aug\u0161u, bet otram uz leju, tom\u0113r nav iesp\u0113jams pateikt, kuram no elektroniem k\u0101ds spin ir. Princip\u0101 h\u0113lija atoma pamatst\u0101vokl\u012b divi elektroni atrodas \u0161\u0101d\u0101 st\u0101vokl\u012b, kas tiek saukts par spin-singletu, jo abu elektronus kop\u0113j\u0101 spina summa ir nulle. Ja m\u0113s sadal\u012bsim \u0161os divus elektronus, nemainot to spinus, m\u0113s joproj\u0101m var\u0113sim apgalvot, ka tie kop\u0101 ir spin-singlets, bet joproj\u0101m nevar\u0113sim pateikt, k\u0101ds b\u016bs jebkura no tiem spins atsevi\u0161\u0137i. Ja m\u0113s izm\u0113r\u012bsim viena no to spiniem un konstat\u0113sim, ka tas ir virz\u012bts uz aug\u0161u, tad m\u0113s b\u016bsim piln\u012bgi p\u0101rliecin\u0101ti, ka otrs ir virz\u012bts uz leju. \u0160aj\u0101 situ\u0101cij\u0101 m\u0113s sak\u0101m, ka spin ir sap\u012bti \u2014 neviens no tiem pats par sevi nav ar noteiktu v\u0113rt\u012bbu, kam\u0113r kop\u0101 tie atrodas noteikt\u0101 kvanta st\u0101vokl\u012b.<\/p>\n

Ein\u0161teins \u013coti uztrauca sap\u012b\u0161an\u0101s fenomens: tas, \u0161\u0137iet, apdraud pamatprincipus attiec\u012bbu teorij\u0101. Apskat\u012bsim divu elektronus spin-sindz\u0113t\u0101 st\u0101vokl\u012b, kad tie ir t\u0101lu viens no otra telp\u0101. Lai preciz\u0113tu, pie\u0146emsim, ka vienu no tiem sauc Alise, bet otru \u2014 Bobs. Pie\u0146emsim, ka Alise izm\u0113ra sava elektrona spinu un atkl\u0101j, ka tas ir v\u0113rsts uz aug\u0161u, bet Bobs neko nem\u0113ra. Kam\u0113r Alise nav veikusi savu m\u0113r\u012bjumu, nebija iesp\u0113jams pateikt, k\u0101ds ir vi\u0146a elektrona spins. Bet tikl\u012bdz vi\u0146a ir pabeigusi savu m\u0113r\u012bjumu, vi\u0146a absol\u016bti prec\u012bzi uzzin\u0101ja, ka Bobam piedero\u0161\u0101 elektrona spins ir v\u0113rsts uz leju (virzien\u0101, kas ir pret\u0113js vi\u0146as pa\u0161u elektrona spinam). Vai tas noz\u012bm\u0113, ka vi\u0146as m\u0113r\u012bjums nekav\u0113joties p\u0101rv\u0113rta Bobu elektronu st\u0101vokl\u012b, kad vi\u0146a spins ir v\u0113rsts uz leju? K\u0101 tas var\u0113ja notikt, ja elektroni ir telpiski atdal\u012bti? Ein\u0161teins un vi\u0146a kol\u0113\u0123i Natans Rozen un Boriss Podolskis uzskat\u012bja, ka st\u0101sts par m\u0113r\u012b\u0161anu sap\u012b\u0161an\u0101 sist\u0113m\u0101s ir tik nopietns, ka apdraud kvantu meh\u0101nikas pa\u0161u eksistenci. Vi\u0146u izstr\u0101d\u0101tais Ein\u0161teina\u2014Podolskija\u2014Rozena (EPR) paradokss izmanto dom\u0101\u0161anas eksperimentu, l\u012bdz\u012bgu tam, ko m\u0113s \u0161obr\u012bd aprakst\u0101m, lai secin\u0101tu: kvantu meh\u0101nika nevar b\u016bt piln\u012bga re\u0101l\u0101s pasaules apraksts. Pa\u0161laik, pamatojoties uz turpm\u0101kajiem teor\u0113tiskajiem izp\u0113tes un daudziem m\u0113r\u012bjumiem, ir izveidojusies visp\u0101r\u0113ja p\u0101rliec\u012bba, ka EPR paradoks\u0101 ir k\u013c\u016bda, un kvantu teorija ir pareiza. Kvantu meh\u0101nisk\u0101 sap\u012b\u0161ana ir re\u0101la: m\u0113r\u012bjumi sap\u012b\u0161an\u0101 sist\u0113m\u0101s korel\u0113, pat ja \u0161\u012bs sist\u0113mas ir t\u0101lu atdal\u012btas telpas-laika dimensij\u0101s.<\/p>\n

Atgriez\u012bsimies pie situ\u0101cijas, kad m\u0113s ievietoj\u0101m divus elektronus spin-singlet st\u0101vokl\u012b un nodev\u0101m tos Alisei un Bobam. Ko m\u0113s varam teikt par elektroniem pirms m\u0113r\u012bjumiem? Ka abi kop\u0101 atrodas noteikt\u0101 kvantu st\u0101vokl\u012b (spin-singlet). Alises elektrona spins ar vien\u0101du varb\u016bt\u012bbu ir v\u0113rsts uz aug\u0161u vai uz leju. Prec\u012bz\u0101k, Alises elektrona kvantu st\u0101voklis ar vien\u0101du varb\u016bt\u012bbu var b\u016bt viens (spins uz aug\u0161u) vai otrs (spins uz leju). Tagad varb\u016bt\u012bbas j\u0113dziens mums ieg\u016bst dzi\u013c\u0101ku noz\u012bmi nek\u0101 iepriek\u0161. Iepriek\u0161 m\u0113s apl\u016bkoj\u0101m noteiktu kvantu st\u0101vokli (\u016bde\u0146ra\u017ea atoma pamata st\u0101vokli) un redz\u0113j\u0101m, ka ir da\u017ei \"ne\u0113rti\" jaut\u0101jumi, piem\u0113ram, \"Kur atrodas elektrons?\", \u2014 jaut\u0101jumi, uz kuriem atbildes past\u0101v tikai varb\u016bt\u012bbas izpratn\u0113. Ja m\u0113s uzdotu \"labus\" jaut\u0101jumus, piem\u0113ram: \"K\u0101da ir \u0161\u012b elektrona ener\u0123ija?\", m\u0113s sa\u0146emtu uz tiem noteiktas atbildes. Tagad vairs nav \"labu\" jaut\u0101jumu, kurus m\u0113s var\u0113tu uzdot par Alises elektronu, kura atbildes nen\u0101ktu atkar\u012bb\u0101 no Boba elektrona. (M\u0113s nerun\u0101jam par mu\u013c\u0137\u012bgiem jaut\u0101jumiem, piem\u0113ram: \"Vai Alises elektronam visp\u0101r ir spins?\" \u2014 jaut\u0101jumiem, uz kuriem past\u0101v tikai viens atbilde.) T\u0101d\u0113j\u0101di, lai noteiktu viena no saputotaj\u0101m sist\u0113mas pus\u0113m parametrus, mums b\u016bs j\u0101izmanto varb\u016bt\u012bbu valoda. Noteikt\u012bba rodas tikai tad, kad m\u0113s apl\u016bkojam saist\u012bbu starp jaut\u0101jumiem, kurus par saviem elektroniem var uzdot Alise un Bobs.<\/p>\n

M\u0113s apzin\u0101ti s\u0101k\u0101m ar vienu no vienk\u0101r\u0161\u0101kaj\u0101m kvantu meh\u0101nikas sist\u0113m\u0101m, kuras m\u0113s zin\u0101m: individu\u0101lo elektronspinu sist\u0113mu. Past\u0101v cer\u012bba, ka uz \u0161\u0101du vienk\u0101r\u0161u sist\u0113mu pamata tiks veidoti kvantu datori. Individu\u0101lo elektronspinu sist\u0113ma vai citas ekvivalentes kvantu sist\u0113mas tagad tiek d\u0113v\u0113tas par kubitiem (sa\u012bsin\u0101jums no \"kvantu biti\"), kas uzsver to lomu kvantu datoros, l\u012bdz\u012bgi k\u0101 parastie biti digit\u0101lajos datoros.<\/p>\n

Iedom\u0101simies, ka m\u0113s katru elektronu aizvietojam ar daudz sare\u017e\u0123\u012bt\u0101ku kvantu sist\u0113mu, kurai ir daudzas, nevis tikai divas kvantu st\u0101vok\u013ci. Piem\u0113ram, iedodam Alisei un Bobam t\u012bra magnija stien\u012b\u0161us. Pirms Alise un Bobs izkl\u012bst katrs sav\u0101 virzien\u0101, vi\u0146u stien\u012b\u0161i var mijiedarboties, un m\u0113s vienojamies, ka \u0161aj\u0101 br\u012bd\u012b tie ieg\u016bst noteiktu kop\u012bgu kvantu st\u0101vokli. Tikl\u012bdz Alise un Bobs iz\u0161\u0137iras, vi\u0146u magnija stien\u012b\u0161i vairs nemijiedarbojas. T\u0101pat k\u0101 elektronos, katrs stien\u012btis ir nenoteikt\u0101 kvantu st\u0101vokl\u012b, kaut ar\u012b kop\u0101, k\u0101 m\u0113s uzskat\u0101m, tie veido pavisam noteiktu st\u0101vokli. (\u0160aj\u0101 apspried\u0113 m\u0113s pie\u0146emam, ka Alise un Bobs sp\u0113j p\u0101rvietot savus magnija stien\u012b\u0161us, netrauc\u0113jot to iek\u0161\u0113jo st\u0101vokli, tie\u0161i t\u0101pat k\u0101 iepriek\u0161 pie\u0146\u0113m\u0101m, ka Alise un Bobs var\u0113ja dal\u012bties ar saviem sap\u012btu\u0161ajiem elektroniem, nemainot to spinus.) Bet at\u0161\u0137ir\u012bba starp \u0161o dom\u0101\u0161anas eksperimentu un eksperimentu ar elektroniem ir t\u0101da, ka katra stien\u012b\u0161a kvantu st\u0101vok\u013ca nenoteikt\u012bba ir milz\u012bga. Stien\u012btis var ieg\u016bt vair\u0101k kvantu st\u0101vok\u013cu, nek\u0101 ir atomu Visum\u0101. Tie\u0161i \u0161aj\u0101 br\u012bd\u012b uz skatuves n\u0101k termodinamika. \u013boti neprec\u012bzi defin\u0113tas sist\u0113mas tom\u0113r var b\u016bt ar da\u017e\u0101m labi noteikt\u0101m makroskopisk\u0101m \u012bpa\u0161\u012bb\u0101m. \u0160\u0101da \u012bpa\u0161\u012bba ir, piem\u0113ram, temperat\u016bra. Temperat\u016bra ir m\u0113rs tam, cik liela ir varb\u016bt\u012bba, ka jebkura sist\u0113mas da\u013ca ir ar noteiktu vid\u0113jo ener\u0123iju, turkl\u0101t augst\u0101ka temperat\u016bra atbilst liel\u0101kai varb\u016bt\u012bbai, ka ir liela ener\u0123ija. V\u0113l viena termodinamiskais parametrs ir entropija, b\u016bt\u012bb\u0101 vien\u0101da ar st\u0101vok\u013cu skaita logarithmu, kuriem sist\u0113ma var b\u016bt. V\u0113l viena termodinamisk\u0101 \u012bpa\u0161\u012bba, kas b\u016btu b\u016btiska magnija stien\u012btim, ir t\u0101 kop\u0113j\u0101 magn\u0113tisma pak\u0101pe, tas ir, b\u016bt\u012bb\u0101 parametrs, kas par\u0101da, cik daudz vair\u0101k stien\u012bt\u012b var b\u016bt elektronu ar aug\u0161u virz\u012btu spinu nek\u0101 ar leju virz\u012btu spinu.<\/p>\n

M\u0113s piev\u0113rs\u0101mies termodinamikai k\u0101 veidam, k\u0101 aprakst\u012bt sist\u0113mas, kuru kvantumst\u0101vok\u013ci ir prec\u012bzi nezin\u0101mi to sapinu\u0161os attiec\u012bbu d\u0113\u013c ar cit\u0101m sist\u0113m\u0101m. Termodinamika ir sp\u0113c\u012bgs anal\u012bzes r\u012bks \u0161\u0101d\u0101m sist\u0113m\u0101m, ta\u010du t\u0101s rad\u012bt\u0101ji noteikti neparedz\u0113ja \u0161\u0101du t\u0101s pielietojumu. Sadi Karn\u014d, D\u017eeimss D\u017eouls un R\u016bdolf Kl\u0101uzijs bija 19. gadsimta industri\u0101l\u0101s revol\u016bcijas darbinieki, un vi\u0146us interes\u0113ja vispraktisk\u0101kais jaut\u0101jums: k\u0101 darbojas dzin\u0113ji? Spiediens, tilpums, temperat\u016bra un siltums \u2014 dzin\u0113ju pamats. Karn\u014d konstat\u0113ja, ka ener\u0123ija siltuma veid\u0101 nekad nevar tikt piln\u012bb\u0101 p\u0101rv\u0113rsta der\u012bg\u0101 darb\u0101, piem\u0113ram, kravu pacel\u0161an\u0101. Da\u013ca ener\u0123ijas vienm\u0113r tiks izniekota. Kl\u0101uzijs deva lielu ieguld\u012bjumu entropijas izpratnes veido\u0161an\u0101 k\u0101 univers\u0101la r\u012bka, lai noteiktu ener\u0123\u0113tiskos zudumus, kas saist\u012bti ar jebkuru siltuma procesu. Vi\u0146a galvenais sasniegums bija apzin\u0101\u0161an\u0101s, ka entropija nekad nemazin\u0101s \u2014 gandr\u012bz visos procesos t\u0101 pieaug. Procesus, kuros entropija palielin\u0101s, sauc par neatgriezeniskiem \u2014 jo tie nevar iet atpaka\u013c bez entropijas samazin\u0101\u0161anas. N\u0101kamais solis statistisk\u0101s meh\u0101nikas att\u012bst\u012bb\u0101 tika sperts Kl\u0101uzija, Maksvela un Ludviga Boltzma\u0146a (un daudzu citu) apg\u0101d\u012bb\u0101 \u2014 vi\u0146i par\u0101d\u012bja, ka entropija ir haosa m\u0113rs. Parasti, jo vair\u0101k j\u016bs iedarbojaties uz kaut ko, jo vair\u0101k haosa taj\u0101 ievies\u012bsiet. Un pat ja j\u016bs esat izstr\u0101d\u0101jis procesu, kura m\u0113r\u0137is ir sak\u0101rtot lietas, t\u0101 gait\u0101 neizb\u0113gami veidosies vair\u0101k entropijas, nek\u0101 tiks izn\u012bcin\u0101ts, \u2014 piem\u0113ram, siltuma izdal\u012b\u0161an\u0101s proces\u0101. Kr\u0101ns, kas sak\u0101rto t\u0113rauda sijas ide\u0101l\u0101 k\u0101rt\u012bb\u0101, rada sak\u0101rtot\u012bbu attiec\u012bb\u0101 uz sij\u0101m, ta\u010du t\u0101 darb\u012bbas laik\u0101 tik un t\u0101 tiek izdal\u012bts tik daudz siltuma, ka kop\u0113j\u0101 entropija joproj\u0101m pieaug.<\/p>\n

Tom\u0113r at\u0161\u0137ir\u012bba starp XIX gadsimta fiziku viedokli par termo dinamikas jaut\u0101jumiem un viedokli, kas saist\u012bts ar kvantu sap\u012b\u0161anos, nav tik liela, k\u0101 var\u0113tu likties. Katru reizi, kad sist\u0113ma mijiedarbojas ar \u0101r\u0113ju a\u0123entu, t\u0101s kvantu st\u0101voklis sapin\u0101s ar a\u0123enta kvantu st\u0101vokli. Parasti \u0161\u012b sap\u012b\u0161an\u0101s noved pie kvantu st\u0101vok\u013ca neskaidr\u012bbas pieauguma sist\u0113m\u0101, citiem v\u0101rdiem sakot, pie palielin\u0101\u0161anas kvantu st\u0101vok\u013cu skait\u0101, kuros sist\u0113ma var atrasties. Sist\u0113mu mijiedarb\u012bbas rezult\u0101t\u0101 entropija, kas defin\u0113ta k\u0101 pieejamo kvantu st\u0101vok\u013cu skaits, parasti pieaug.<\/p>\n

Kopum\u0101 kvantu meh\u0101nika sniedz jaunu veidu, k\u0101 raksturot fizisk\u0101s sist\u0113mas, kur\u0101s da\u017ei parametri (piem\u0113ram, poz\u012bcija telp\u0101) k\u013c\u016bst neskaidri, bet citi (piem\u0113ram, ener\u0123ija) bie\u017ei ir prec\u012bzi zin\u0101mi. Kvantu sap\u012b\u0161an\u0101s gad\u012bjum\u0101 divas princip\u0101 atsevi\u0161\u0137as sist\u0113mas da\u013cas ir zin\u0101m\u0101 kop\u012bg\u0101 kvantu st\u0101vokl\u012b, kam\u0113r katra da\u013ca atsevi\u0161\u0137i ir neskaidra st\u0101vokl\u012b. Standarta piem\u0113rs sap\u012b\u0161anai ir spin p\u0101ris singlet\u0101 st\u0101vokl\u012b, kur\u0101 nav iesp\u0113jams noteikt, kur\u0161 spins ir v\u0113rsts uz aug\u0161u, bet kur\u0161 uz leju. Lielas sist\u0113mas kvantu st\u0101vok\u013ca neskaidr\u012bba prasa termodinamikas pieeju, kur\u0101 makroskopiskie parametri, piem\u0113ram, temperat\u016bra un entropija, ir prec\u012bzi zin\u0101mi, neskatoties uz to, ka sist\u0113mai ir daudz iesp\u0113jam\u0101s mikroskopisk\u0101s kvantu st\u0101vok\u013cu.<\/p>\n

Pabeidzot m\u016bsu \u012bso ekskursiju kvantu meh\u0101nik\u0101, sap\u012b\u0161an\u0101s un termodinamik\u0101, m\u0113\u0123in\u0101sim tagad saprast, k\u0101 viss \u0161is noved pie izpratnes par faktu, ka melnaj\u0101m caurumiem ir temperat\u016bra. Pirmais solis \u0161aj\u0101 virzien\u0101 bija Bila Unru paveiktais \u2014 vi\u0146\u0161 par\u0101d\u012bja, ka pa\u0101trin\u0101ts nov\u0113rot\u0101js plakn\u0113 b\u016btu ar temperat\u016bru, kas vien\u0101da ar vi\u0146a pa\u0101trin\u0101jumu, dal\u012btu ar 2\u03c0. Atsl\u0113ga Unru apr\u0113\u0137iniem ir taj\u0101, ka nov\u0113rot\u0101js, kur\u0161 kustas ar nemain\u012bgu pa\u0101trin\u0101jumu noteikt\u0101 virzien\u0101, var redz\u0113t tikai pusi plaknes laika telpas. Otr\u0101 puse, b\u016bt\u012bb\u0101, atrodas aiz horizonta, l\u012bdz\u012bga meln\u0101 cauruma horizontam. Pirmaj\u0101 mirkl\u012b tas \u0161\u0137iet neiesp\u0113jami: k\u0101 var plakne laika telpa iztur\u0113ties k\u0101 meln\u0101 cauruma horizonta? Lai saprastu, k\u0101 tas notiek, piesaist\u012bsim m\u016bsu uzticamos nov\u0113rot\u0101jus Alisi, Bobu un Bilu. M\u016bsu l\u016bgum\u0101 vi\u0146i izk\u0101rtojas rind\u0101, kur Alisa atrodas starp Bobu un Bilu, un starp nov\u0113rot\u0101jiem katr\u0101 p\u0101r\u012b att\u0101lums ir tie\u0161i 6 kilometri. M\u0113s vienojamies, ka nulles mirkl\u012b Alisa s\u0101ks l\u0113kt iek\u0161\u0101 ra\u0137et\u0113 un dosies uz Bilu (t\u0101tad prom no Boba) ar nemain\u012bgu pa\u0101trin\u0101jumu. Ra\u0137ete vi\u0146ai ir \u013coti laba, sp\u0113j\u012bga att\u012bst\u012bt pa\u0101trin\u0101jumu, kas ir 1,5 triljoni reizes liel\u0101ks par gravit\u0101cijas pa\u0101trin\u0101jumu, ar kuru p\u0101rvietojas objekti tuvu Zemes virsmai. Protams, Alisai nav viegli iztur\u0113t \u0161\u0101du pa\u0101trin\u0101jumu, bet, k\u0101 m\u0113s redz\u0113sim, \u0161ie skait\u013ci izv\u0113l\u0113ti ar noteiktu nodomu; galu gal\u0101, m\u0113s vienk\u0101r\u0161i apsprie\u017eam potenci\u0101l\u0101s iesp\u0113jas, tas ar\u012b viss. Tie\u0161i taj\u0101 br\u012bd\u012b, kad Alisa izl\u0113k no savas ra\u0137etes, Bobs un Bils m\u0101j vi\u0146ai. (M\u0113s dr\u012bkstam lietot izteicienu \u201etie\u0161i taj\u0101 mirkl\u012b, kad\u2026\u201d, jo kam\u0113r Alisa v\u0113l nav s\u0101kusi lidojumu, vi\u0146a atrodas taj\u0101 pa\u0161\u0101 atsauces sist\u0113m\u0101, k\u0101 Bobs un Bils, t\u0101p\u0113c visi vi\u0146i pavisam noteikti var sinhroniz\u0113t savas pulkste\u0146us.) M\u0101jo\u0161ais Bils, protams, ir redzams Alisai: paties\u012bb\u0101, b\u016bdama ra\u0137et\u0113, vi\u0146a vi\u0146u redz\u0113s \u0101tr\u0101k, nek\u0101 tas notiktu, ja vi\u0146a paliktu tur, kur bija, jo vi\u0146as ra\u0137ete kop\u0101 ar vi\u0146u lido tie\u0161i uz vi\u0146u. No Boba vi\u0146a, glu\u017ei pret\u0113ji, att\u0101lin\u0101s, t\u0101p\u0113c m\u0113s varam sapr\u0101t\u012bgi pie\u0146emt, ka vi\u0146a redz\u0113s, k\u0101 vi\u0146\u0161 vi\u0146ai m\u0101j, nedaudz v\u0113l\u0101k, nek\u0101 vi\u0146a to redz\u0113tu, ja paliktu iepriek\u0161\u0113j\u0101 viet\u0101. Bet paties\u012bba ir v\u0113l p\u0101rsteidzo\u0161\u0101ka: Boba vi\u0146a visp\u0101r neredz\u0113s! Citiem v\u0101rdiem sakot, fotoni, kas lido no m\u0101jojo\u0161\u0101 Boba uz Alisu, nekad vi\u0146u nesasniegs, pat \u0146emot v\u0113r\u0101, ka vi\u0146a nekad nevar\u0113s sasniegt gaismas \u0101trumu. Ja Bobs b\u016btu s\u0101cis m\u0101jot, b\u016bdams nedaudz tuv\u0101k Alisai, tad fotoni, kas no vi\u0146a aizlidoja vi\u0146as nos\u016bt\u012b\u0161anas mirkl\u012b, vi\u0146u sasniegtu, bet, ja vi\u0146\u0161 atrastos nedaudz t\u0101l\u0101k, tad visticam\u0101k, ne sasniegtu. T\u0101d\u0101 zi\u0146\u0101 m\u0113s sak\u0101m, ka Alisai ir redzama tikai puse laika telpas. Mirkl\u012b, kad Alisa s\u0101k kust\u012bbu, Bobs atrodas nedaudz t\u0101l\u0101k par horizontu, kuru Alisa nov\u0113ro.<\/p>\n

M\u016bsu diskusij\u0101 par kvantu sap\u012b\u0161anos m\u0113s jau esam pieradu\u0161i pie idejas, ka pat ja kvantu meh\u0101nikas sist\u0113ma kopum\u0101 ir noteikt\u0101 kvantu st\u0101vokl\u012b, da\u017ei t\u0101s punkti var nepiem\u0113roties \u0161im st\u0101voklim. Paties\u012bb\u0101, kad m\u0113s apsprie\u017eam sare\u017e\u0123\u012btu kvantu sist\u0113mu, k\u0101da t\u0101s da\u013ca var vislab\u0101k tikt raksturota tie\u0161i termodinamikas ietvaros: tai var tikt pie\u0161\u0137irta diezgan noteikta temperat\u016bra, neskatoties uz to, ka visa sist\u0113ma ir augsti nenoteikt\u0101 kvantu st\u0101vokl\u012b. M\u016bsu p\u0113d\u0113j\u0101 st\u0101st\u0101 ar Alisi, Bobu un Bilu ir nedaudz l\u012bdz\u012bga situ\u0101cija, ta\u010du kvantu sist\u0113ma, par kuru m\u0113s \u0161eit run\u0101jam, ir tuk\u0161ais laika un telpas turpin\u0101jums, un Alise redz tikai t\u0101s pusi. J\u0101nor\u0101da, ka laiks un telpa kopum\u0101 ir sav\u0101 pamata st\u0101vokl\u012b, kas noz\u012bm\u0113, ka taj\u0101 nav da\u013ci\u0146u (protams, iz\u0146emot Alisi, Bobu, Bilu un ra\u0137eti). Bet t\u0101 da\u013ca laika un telpas, ko redz Alise, neb\u016bs pamata st\u0101vokl\u012b, bet dr\u012bz\u0101k b\u016bs sap\u012b\u0161ana ar to da\u013cu, ko vi\u0146a neredz. Alises uztvert\u0101 laika un telpas ir sare\u017e\u0123\u012bt\u0101 nenoteikt\u0101 kvantu st\u0101vokl\u012b, kas raksturota ar gal\u012bgu temperat\u016bru. Unru apr\u0113\u0137ini r\u0101da, ka \u0161\u012b temperat\u016bra ir aptuveni 60 nanokelvini. \u012asum\u0101, Alise, pa\u0101trinoties, it k\u0101 ienirst silt\u0101 starojuma vann\u0101 ar temperat\u016bru, kas ir (attiec\u012bg\u0101s m\u0113rvien\u012bb\u0101s) pa\u0101trin\u0101jums dal\u012bts ar \"Melnraksturu
\n
\n\"Melnraksturu<\/p>\n

Att. 7.1. Alise p\u0101rvietojas ar pa\u0101trin\u0101jumu no miera st\u0101vok\u013ca, kam\u0113r Bobs un Bils paliek nekust\u012bgi. Alises pa\u0101trin\u0101jums ir tie\u0161i t\u0101ds, lai vi\u0146a nekad neredz\u0113tu fotonus, kurus Bobs nos\u016bta vi\u0146as virzien\u0101 br\u012bd\u012b t = 0. Tom\u0113r vi\u0146a sa\u0146em fotonus, kurus vi\u0146ai nos\u016bt\u012bja Bils br\u012bd\u012b t = 0. Rezult\u0101t\u0101 Alise sp\u0113j nov\u0113rot tikai vienu laika un telpas pusi.<\/p>\n

D\u012bvain\u0101 Unru apr\u0113\u0137inu b\u016bt\u012bba ir t\u0101da, ka, neskatoties uz to, ka tie no s\u0101kuma l\u012bdz beig\u0101m attiecas uz tuk\u0161u telpu, tie pretnostat\u012btos zin\u0101miem King Lear v\u0101rdiem: \"no nek\u0101 nen\u0101k nekas\". K\u0101 var tuk\u0161a telpa b\u016bt tik sare\u017e\u0123\u012bta? No kurienes taj\u0101 var\u0113tu rasties da\u013ci\u0146as? Paties\u012bba ir t\u0101da, ka saska\u0146\u0101 ar kvantu teoriju tuk\u0161a telpa nemaz nav tuk\u0161a. Taj\u0101 \u0161eit un tur past\u0101v\u012bgi par\u0101d\u0101s un izz\u016bd \u012bslaic\u012bgi uzbudin\u0101jumi, ko sauc par virtu\u0101laj\u0101m da\u013ci\u0146\u0101m, kuru ener\u0123ija var b\u016bt gan pozit\u012bva, gan negat\u012bva. Nov\u0113rot\u0101ja no t\u0101l\u0101kas n\u0101kotnes \u2014 sauksim vi\u0146u par K\u0113rolu, \u2014 kura sp\u0113j redz\u0113t praktiski visu tuk\u0161u telpu, var apstiprin\u0101t, ka taj\u0101 nav ilgsto\u0161i eksist\u0113jo\u0161u da\u013ci\u0146u. Taj\u0101 pa\u0161\u0101 laik\u0101 da\u013ci\u0146u kl\u0101tb\u016btne ar pozit\u012bvu ener\u0123iju taj\u0101 telpas-laika da\u013c\u0101, kuru Alisa var nov\u0113rot, pateicoties kvantu sapin\u0161anai, ir saist\u012bta ar ener\u0123ijas izsistumiem, kas ir vien\u0101di un pret\u0113ji z\u012bmes zi\u0146\u0101 nenov\u0113rojamo Alisai telpas-laika da\u013c\u0101. Visa paties\u012bba par tuk\u0161u telpu-laiku kopum\u0101 ir atv\u0113rta K\u0113rolai, un \u0161\u012b paties\u012bba ir t\u0101da, ka tur nav da\u013ci\u0146u. Tom\u0113r Alisas pieredze vi\u0146ai saka, ka tur ir da\u013ci\u0146as!<\/p>\n

Tom\u0113r izr\u0101d\u0101s, ka apr\u0113\u0137in\u0101t\u0101 Unru temperat\u016bra, \u0161\u0137iet, ir vienk\u0101r\u0161i fikcija \u2014 t\u0101 ir ne tik daudz plakan\u0101s telpas \u012bpa\u0161\u012bba, cik nov\u0113rot\u0101ja \u012bpa\u0161\u012bba, kur\u0161 plakan\u0101 telp\u0101 piedz\u012bvo past\u0101v\u012bgu pa\u0101trin\u0101jumu. Ta\u010du ar\u012b pati gravit\u0101cija ir t\u0101da pati \"fikcion\u0101r\u0101\" sp\u0113ks taj\u0101 noz\u012bm\u0113, ka \"pa\u0101trin\u0101jums\", ko t\u0101 izraisa, ir nekas cits k\u0101 kust\u012bba pa \u0123eod\u0113zisko ce\u013cu izkrop\u013cotaj\u0101 metriskaj\u0101 telp\u0101. K\u0101 jau m\u0113s izskaidroj\u0101m 2. noda\u013c\u0101, Ein\u0161teina ekvivalences princips liecina, ka pa\u0101trin\u0101jums un gravit\u0101cija ir b\u016bt\u012bb\u0101 ekvivalentas. No \u0161\u012b skatpunkta nav nekas tik \u012bpa\u0161i \u0161ok\u0113jo\u0161s, ka meln\u0101 cauruma horizonam ir temperat\u016bra, kas ir vien\u0101da ar apr\u0113\u0137in\u0101to Unru temperat\u016bru pa\u0101trin\u0101tajam nov\u0113rot\u0101jam. Bet, vai m\u0113s varam jaut\u0101t, kuru pa\u0101trin\u0101juma v\u0113rt\u012bbu mums vajadz\u0113tu izmantot, lai noteiktu temperat\u016bru? Att\u0101linoties pietiekami t\u0101lu no meln\u0101 cauruma, m\u0113s varam padar\u012bt t\u0101s gravit\u0101cijas pievilk\u0161anu p\u0113c iesp\u0113jas v\u0101j\u0101ku. Vai tas noz\u012bm\u0113, ka, lai noteiktu m\u016bsu m\u0113r\u012bto efekt\u012bvo temperat\u016bru melnajam caurumam, mums b\u016btu j\u0101izmanto atbilsto\u0161a maza pa\u0101trin\u0101juma v\u0113rt\u012bba? \u0160is jaut\u0101jums izr\u0101d\u0101s diezgan vilt\u012bgs, jo, k\u0101 m\u0113s uzskat\u0101m, objekta temperat\u016bra nevar patva\u013c\u012bgi samazin\u0101ties. Tiek pie\u0146emts, ka t\u0101 ir ar k\u0101du fiks\u0113tu beigu v\u0113rt\u012bbu, ko var izm\u0113r\u012bt pat \u013coti att\u0101lins nov\u0113rot\u0101js.
\n
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\u0421 \u0414\u043d\u0435\u043c \u043a\u043e\u0441\u043c\u043e\u043d\u0430\u0432\u0442\u0438\u043a\u0438! \u041c\u044b \u0441\u0434\u0430\u043b\u0438 \u0432 \u0442\u0438\u043f\u043e\u0433\u0440\u0430\u0444\u0438\u044e \u00ab\u041c\u0430\u043b\u0435\u043d\u044c\u043a\u0443\u044e \u043a\u043d\u0438\u0433\u0443 \u043e \u0447\u0435\u0440\u043d\u044b\u0445 \u0434\u044b\u0440\u0430\u0445\u00bb. \u0418\u043c\u0435\u043d\u043d\u043e \u0432 \u044d\u0442\u0438 \u0434\u043d\u0438 \u0430\u0441\u0442\u0440\u043e\u0444\u0438\u0437\u0438\u043a\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u043b\u0438 \u0432\u0441\u0435\u043c\u0443 \u043c\u0438\u0440\u0443 \u043a\u0430\u043a \u0447\u0435\u0440\u043d\u044b\u0435 \u0434\u044b\u0440\u044b \u0432\u044b\u0433\u043b\u044f\u0434\u044f\u0442. \u0421\u043e\u0432\u043f\u0430\u0434\u0435\u043d\u0438\u0435? \u041d\u0435 \u0434\u0443\u043c\u0430\u0435\u043c \ud83d\ude09 \u0422\u0430\u043a \u0447\u0442\u043e \u0436\u0434\u0438\u0442\u0435, 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