pramanit quantum gurutvakarshan

bhautikshastrat, pramanit quantum gurutvakarshan haah samanya sapekshatechya (kinwa vihit gurutvakarshan) pramanit rachaneche praman mojanyacha prayatna aahe. heey einsteinchya sapekshatechya samanya siddhantache hamiltonian sootra aahe. moolbhut siddhant 1967 chya eka moolbhut peparmadhye brice devitne spasht keela hota aanee pieter jee. chya aadhichya karyavar aadharit hota. paul derackne shodhalelya maryadit hamiltonian pranalinsathi tathakathit pramanit parimanatmak tantracha vapar karoon bergman. diarakcha drushtikon nishchit gej nivadimadhye hamiltonian tantrancha vapar karoon gej samamiti samavisht asalelya pranalinche parimanikaran karnyas anumati deto. devit aanee directchya karyavar aadharit naveen drushtikonanmadhye hartle-hocking sthitee, rege calculus, wheeler-devit samikaran aanee loop quantum gurutvakarshan yancha samavesh hoto.
vihit parimanan.
samanya shastriy yantrikichya hamiltonian rachnet poison brackett hii eka mahattvachi sankalpana aahe. vihit samanvay pranali" madhye vihit sthitee aanee gatee chull asatat jeey vihit poison-brackett sambandh purn karatat.
sootra _ 1
jethe poison brackett dile jaate
sootra _ 2
aniyantrit fages space functions formula _ 3 aanee formula _ 4 sathee. poison bracketchya vaparasah, hamiltonchi samikarane ashee punha lihili jaau shakatatah
sootra _ 5
sootra _ 6
hii samikarane hamiltonian sootra _ 7 dware tayar jhalelya fages spacemadhil "flow" kinwa kakshache varnan karatat. konatehi fages space function sootra _ 8 dile tarr, aamchyakade aahe
sootra _ 9
canonical quantisationmadhe fages space variablesna hilbert spacever quantum operatormadhye padonnati dilee jaate aanee fages space variablesmadhil poison bracketchi jaaga canonical commutation sambandhane ghetali jaateh
sootra _ 10
tathakathit sthitichya pratinidhitvamadhye haah parivartanacha sambandh nivadidvare lakshat yetoh
sootra _ 11 aanee sootra _ 12
scroadinger samikaranadvare gatishilateche varnan kele aaheh
sootra _ 13
jethe formula _ 14 haah hamiltonian formula _ 15 pasoon tayar jhalela operator aahe jyache replacement formula _ 16 aanee formula _ 17 aahe.
nirbandhansah pramanit pariman.
shastriy samanya sapekshata heey purnapane maryadit siddhantache eka udaharan aahe. maryadit siddhantanmadhye vividh prakarchi fages space aaheth aniyantrit (jyala kinematic dekhil mhanatat) fages space jyavar nirbandh karye paribhashit kelee jaatat aanee qamee jhaleli fages space jyavar nirbandh aadhich sodavale gele aahet. sarvasadharanpane pramanit parimanikaranasathi, fages spacechi jaaga yogya hilbert spacene ghetali jaate aanee fages space variablesla quantum operatorsmadhye badhati dilee jaate.
diarakchya parimanikaranachya drushtikonat aniyantrit tappyatil jaagechi jaaga tathakathit kinematic hilbert spacene ghetali aahe aanee kinematic hilbert spacemadhye lagoo kelelya nirbandh operatordware nirbandh karye badalali aahet; tyanantar upay shodhale jaatat. hii quantum nirbandh samikarane hii kiman diarac drushtikonatun, jee samanyatah ghetali jaate, pramanit quantum samanya sapekshatechi madhyavarti samikarane aahet.
nirbandh asalelya siddhantanmadhye qamee jhalelya tappyatil jaageche parimanikaran dekhil aahe jithe nirbandh shastriy staravar sodavale jaatat aanee qamee jhalelya tappyatil jagechya tappyatil chalanna nantar quantum operatormadhye badhati dilee jaate, tathapi haah drushtikon samanya sapekshatemadhye ashakya asalyache manale jaat hote kaaran too shastriy kshetra samikarananche samanya uttar shodhanyaitakach asalyache disate. tathapi, carlo roveline sadar kelelya kalpananvar aadharit, bianca detreachdware samanya sapekshatechya nirikshaniy vastunchi ganana karnyasathi (prathamach) paddhatshir andaj yojanechya agadi alikadchya vikasasah, gurutvakarshanachya qamee tappyatil antaral parimananasathi eka vyavharya yojana thomas thimen yanni vikasit kelee aahe. tathapi, heey diarac parimananachya purnapane samatulya nahee kaaran diarac parimananachya babatit 'ghadyal-variables' heey qamee jhalelya tappyatil jaaga parimanamadhye shastriy manale jaane aavashyak aahe.
eka samanya gairsamaj assa aahe qee samanvay parivartan heey samanya sapekshateche gej samamiti aahet, jevha pratyakshat vastavik gej samamiti hii ganitshastradnyane paribhashit kelyapramane bhinnarupata asatat (chhidra yuktivad pahaa)-jeey barech adhik moolgami asatat. samanya sapekshatechya pratham shrenichya maryada mhanje avkashiy bhinnarupata maryada aanee hamiltonian maryada (jyala wheeler-dii viit samikaran asehi mhanatat) aanee anukrame yaa siddhantachya avkashiy aanee asthayi bhinnarupata aparivartaniyatechi chhap padatat. shastriyadrushtya yaa maryada ladane hii mulat prarambhik mahitivaril swikararhatechya atty aahet, tasech tyaa poison bracketdware 'utkranti' samikarane (kharokhar moj badal) tayar karatat. mahattvache mhanje nirbandhanmadhil poison brackett bijganit shastriy siddhant purnapane nirdharit karate-heey asey kahitari aahe jeey quantum gurutvakarshanacha vyavharya siddhant honyasathi kahee pramanat pramanit quantum gurutvakarshanachya ardh-shastriy maryadet punarutpadit kele jaane aavashyak aahe.
diarakchya drushtikonatun asey disun yete qee wavefunctionver ladalelya pratham shrenichya quantum nirbandhanmule gej parivartan dekhil hote. asha prakare nirbandh sootra 18 sodavanyachya shastriy siddhantatil done charananchi prakriya (prarambhik mahitisathi swikararhatechya atty sodavnyaitaki) aanee gej kaksha shodhanyachya ('utkranti' samikarane sodavane) quantum siddhantatil eka charan prakriyedvare badalali jaate, mhanje quantum samikaran sootra 20 chey sootra 19 sodavane. yache kaaran asey aahe qee teey spashtapane quantum patalivaril nirbandh sodavate aanee teey ekach velee gej aparivartaniy asalelya avasthancha shodh ghete kaaran sootra 21 heey gej parivartananche quantum generator aahe. shastriy staravar, swikararhatechya paristhitiche nirakaran karane aanee utkrantichi samikarane hii einsteinchya serve kshetra samikarane sodavinyaitakich aahet, heey diarakchya pramanit quantum gurutvakarshanachya drushtikonatil quantum nirbandh samikarananchi madhyavarti bhoomika adhorekhit karate.
vihit pariman, bhinnarupata aparivartaniyata aanee prakat maryada.
bhinnarupavadacha vichar keela jaau shakato qee, ekach samanvay pranalimadhye rahoon metrik (gurutvakarshan kshetra) aanee dravya kshetranna ekach velee ughadya anek patinvar 'odhane' aanee tyamule keval samanvay parivartanakhali teey aparivartanapeksha adhik moolgami asatat. hii samamiti yaa sookshm garajevarun udbhavate qee samanya sapekshateche niyam dilelya avkash-velechya bhoomitivar konatyahi aii-prayorivar avalambun rahoo shakat naheet.
yaa bhinnarupachya aparivartanacha eka mahattvacha parinam aaheh pramanit quantum gurutvakarshan spashtapane maryadit asel kaaran metrik karya ughadya anek patanvar 'odhanyachi' kshamata mhanje amurtapane paribhashit kelelya nirdeshank bindunmadhil lahan aanee mothe 'antar' gej-samatulya aahet! lii smollinne adhik kathor yuktivad deela aaheh
parshvabhoomi swatantra operator nehmich maryadit asane aavashyak aahe. yache kaaran asey qee niyaman prakriyet niyamak praman aanee parshvabhoomi metrik nehmi ekatra aanale jaatat. heey aavashyak aahe, kaaran niyamitkaran mapdand jyaa pramanala sandarbhit karato tyache varnan, niyantrit prachalakachya bandhkamat sadar kelelya parshvabhoomi metrik kinwa samanvay taktachya sandarbhat kele jaane aavashyak aahe. yamule, niyantrit pradatyache cutoff kinwa niyamak mapdandavaril avalambitva, parshvabhoomi metrikavareel avalambitvashi sambandhit aahe. jevha konee niyamak parameterchi maryada shunyavar jaate tevha eka adrushya naan naan ateenna vegale karate. jarr heey niyamak mapdandavar avalambun asateel (jarr sandnya udat asel tarr asey hoil) tarr teey parshvabhoomi metrikavar dekhil avalambun asane aavashyak aahe. yaulat, niyamkane kadhoon takalelya maryadet naan naan atinche parshvabhoomi metrikavar avalambun nasane, tarr teey maryadit asane aavashyak aahe."
kharey tarr, khalee namood kelyapramane, thomas thimen yanni spashtapane dakhavun dile aahe qee loop quantum gurutvakarshan (pramanit quantum gurutvakarshanachi eka vikasit aavrutti) serve prakarchya padarthanchya upasthitit dekhil spashtapane maryadit aahe! tyamule punaraadhunikikaran aanee anantata door karanyachi garaj nahee. tathapi, itar karyanmadhye, thomas thimenne parimanatmak sandigdhata door karnyacha eka marg mhanoon punarpramanan karanyachi garaj manya kelee. 
konatyahi vikshobhkari yojnepramane, vikshobhkari quantum gurutvakarshanamadhye (jyatoon gair-punarrachana yuktivad udbhavtat), ekhadi vyakti vajvi dharana karate qee mothya pramanavaril jaagecha vel sapat jagedware changlya prakare andajit keela pahije; eka vyakti yaa andaje sapat parshvabhumivar gurutvakarshanache vikhurate aanee ekhadyala asey aadhalate qee tyanchya vikhuralelya amplitudemadhye vichalan aahe jeey neuton sthirankachya punarnirdharanat shoshale jaau shakat nahee. pramanit quantum gurutvakarshan siddhantkaryanna haah yuktivad manya nahee; tathapi tyanni adyap gurutvakarshanachya vikhuralelya amplitudechi paryayi ganana pradan keleli nahee jee ashant upcharanmadhye gair-asamanya gair-asamanya sandnyanche kaay hote heey samajoon ghenyasathi vaparali jaau shakate. dirghkalapasun ashee apeksha aahe qee, pramanit quantum gurutvakarshanasarkhya quantum bhoomitichya siddhantat kshetra aanee ghanfal yasarkhya bhaumitik pramananmadhye quantum nirikshanyogya banate aanee shoonya nasaleli swatantra moolye ghetat, jyamule naisargik niyamak upalabdh hoto, jeey padarthachya yogdanasah siddhantatun siddhantatun anantata door karato. bhaumitik nirikshaniy vastunche heey 'pariman' pratyakshat loop quantum gurutvakarshanamadhye (ell. kyu. jee.) prapt hote.
metrik chalanmadhye pramanit pariman.
parimanikaran heey khalilpramane metrik tensorchya vighatit honyavar aadharit aahe,
sootra _ 22
jethe punaravrutti kelelya nirdeshankanvar berries soochit kelee jaate, tethe nirdeshank 0 heey veleche sootra _ 23 darshavito, greek nirdeshank serve mulyanvar chalatat 0,. . . , 3 aanee lattin nirdeshank sthanik mulyanpeksha jaast aahet. . .3. function sootra _ 24 laa laps function mhanatat aanee function sootra _ 25 laa shift functions mhanatat. avkashiy nirdeshank avkashiy metrik sootra _ 26 aanee tyache ulat sootra _ 27: sootra _ 28 aanee sootra _ 29, sootra _ 30 vaparoon vadhavale aanee qamee kele jaatat, jethe sootra _ 31 haah kronekar delta aahe. yaa vighatananusar, einstein-hilbert lagrangian ekoon vyutpannanparyant,
sootra _ 32
jethe sootra _ 33 heey remanian metrik sootra _ 26 chya sandarbhat mojale jaanare avkashiy scalar vakrata aahe aanee sootra _ 35 heey bahya vakrata aahe,
sootra _ 36
jethe sootra _ 37 heey khote-farak darshavate, sootra _ 38 heey sthir sootra _ 39 chya prushthbhagasathi samanya ekak aahe aanee sootra _ 40 heey metrik sootra _ 26 chya sandarbhat sahparivartan farak darshavate. lakshat ghya qee sootra _ 42. devit lihitat qee lagrangianche 'gatij urja vaja sambhavya urja' heey abhijat swaroop aahe, jyamadhye bahya vakrata gatij urjechi bhoomika bajavate aanee aantarik vakrata sambhavya urjechi nakaratmak bhoomika bajavate."sthanik nirdeshankanchya punarnirdharnantargat lagrangianche heey swaroop spashtapane aparivartaniy asale taree, teey samanya sahparivartan apardarshak banavate.
laps function aanee shift functions gej transformationdware kadhoon takale jaau shakatat, tyamule teey physical degree auph friedamche pratinidhitva karat naheet. hamiltonian aupchariktekade valatana heey soochit kele jaate qee tyanche sanyugmit moment, anukrame sootra _ 43 aanee sootra _ 44, samanpane (kavchavar aanee kavchabaher) nahise hotat. hyanna dayarakdware "prathamik nirbandh" mhanatat. sootra 45 aanee sootra 46 hii samkramit gej navachi gejchi eka lokpriy nivad aahe, jaree tattvatah, teey nirdeshankanche konatehi karya mhanoon nivadle jaau shakatat. yaa prakaranat, hamiltonian form gheto
sootra _ 47
kuthe?
sootra _ 48
aanee sootra _ 49 heey sootra _ 26 chey sanyugma sanyugma aahe. hamiltonians poison cons gheuun einsteinchi samikarane punarprapt kelee jaau shakatat. dayarakdware 'duyyam nirbandh' mhanoon olakhalya olakhalya atirikt kholyavaril nirbandh, poison brackett bijganitachya susangatatemule udbhavtat. heey sootra _ 51 aanee sootra _ 52 aahet. haah siddhant aahe jyache praman praman pramanatmak quantum gurutvakarshanachya drushtikonatun kele jaat aahe.
heey darshavile jaau shakate qee velechya utkrantiche varnan karnari sahaa einstein samikarane (kharokhar eka gej parivartan) teen-metrikchya poison bracketschee ganana karoon aanee sthanik bhinnarupata aanee hamiltonian nirbandhanchya resheey sanyojanasah tyachya sanyugmit gatichi ganana karoon prapt kelee jaau shakatat. nirbandhanche nahise hone, bhautik tappyala jaaga dene, hii einsteinchi itar chaar samikarane aahet. mhanje, aamchyakade aaheh
avkashiy bhinnarupata nirbandh
sootra _ 53
jyapaiki eka anant sankhya aahe-eka sootra 54 chya mulyasathi, tathakathit shift functions sootra 55 dware lape keela jaau shakato, jyamule lape kelelya avkashiy bhinnarupata nirbandhancha samatulya sanch midato,
sootra _ 56
heey shift function sootra _ 57 dware paribhashit kelelya kakshanmadhye avkashiy bhinnarupata nirman karatat.
hamiltonian nirbandh
sootra _ 58
jyapaiki eka anant sankhya aahe, jyala tathakathit laps functions sutradvare lape keela jaau shakato _ 59 lape kelelya hamiltonian nirbandhancha samatulya sanch denyasathi,
sootra _ 60
varr namood kelyapramane, (lape kelelya) nirbandhanmadhil poison brackett rachana mahattvachi aahe kaaran tee shastriy siddhant purnapane nirdharit karatat aanee quantum gurutvakarshanachya konatyahi siddhantachya ardh-shastriy maryadet punarutpadit karane aavashyak aahe.
wheeler-devit samikaran.
wheeler-devit samikaran (kadhikadhi hamiltonian nirbandh, kadhikadhi einstein-schroedinger samikaran mhanatat) heey quantum patalivaril gatishilatela sanketikrut karate mhanoon teey madhyavarti asate. heey shrodingerchya samikaranashi samaan aahe, vel nirdeshank, sootra _ 39, unfigical aahe, bhautik wavefunction sootra _ 39 varr avalambun rahoo shakat nahee aanee mhanoon shrodingerche samikaran eka nirbandhat qamee hoteh
metrik chalancha vapar kelyane shastriy abhivyaktila changlya prakare paribhashit kelelya quantum operatormadhye protsahan denyacha prayatna kartana ganiteey adachani udbhavtat aanee asha prakare dashake yaa drushtikonatun pragati naan karata gelee. hii samasya talhanyat aalee aanee ashtekar-barbero chull aanee loop pratinidhitva, thomas thimen yanni tayar kelelya yaa changlya paribhashit operatorchya parichayasah changlya prakare paribhashit wheeler-dii-viit samikaranache sootra pratham purn karnyat aale.
yaa vikasapurvi wheeler-dii-viit samikaran keval samamiti-qamee kelelya modelmadhye tayar kele gele hote, jase qee quantum cosmology.
ashtekar-barbero chull aanee ell. kyu. jee. madhye pramanit pariman.
pramanit quantum gurutvakarshanatil anek tantrik samasya nirbandhambhovati firatat. vihit samanya sapekshata hii moolatah metrik chalanchya sandarbhat tayar kelee gelee hotee, parantu vihit chalanvar tyanche atyant gair-rekheey avalambitva asalyamule quantum operatorna nirbandhanna protsahan denyat ganiteey adachani door karnyayogya asalyache disate. ashtakaranchya naveen chalanchya parichayasah samikarane khoop sopee karnyat aalee. ashtekar chull heey gej siddhantanchya jawal asalelya naveen jodichya pramanit chalanchya sandarbhat pramanit samanya sapekshateche varnan karatat. asey kartana tyane sthanik bhinnarupata aanee hamiltonian nirbandh, goss gej nirbandh yanchya varr eka atirikt nirbandh aanala.
loopche pratinidhitva heey loopchya drushtine gej siddhantanche quantum hamiltonian pratinidhitva aahe. yang-mills siddhantanchya sandarbhat loopchya pratinidhitvacha uddesh goss gej samamitidvare sadar keleli anavashyakta talhane haah aahe, jyamule goss gej aparivartaniy avasthanchya jaaget thet kaam karata yete. yaa pratinidhitvacha vapar naisargikaritya ashtekar-barbero pratinidhitvatun udbhavala kaaran teey achook gair-ashant varnan pradan karate aanee yaa pratinidhitvamadhye avkashiy bhinnarupata adthala sahajpane hatalala jaato.
loopchya pratinidhitvamadhye thimenne serve prakarchya padarthanchya upasthitit eka suspasht siddhant pradan keela aahe aanee too spashtapane maryadit asalyache dakhavun dile aahe! tyamule punaraadhunikikaranachi garaj nahee. tathapi, plank scalever bhautikshastrache varnan karnyasathi ell. kyu. jee. drushtikon yogya asalyane, parichit qamee urja bhautikshastrashi sampark sadhanyat adachani yetat aanee tyachi yogya ardh-shastriy maryada aahe heey sthapit karnyat adachani yetat.
velechi samasya.
samanya sapekshatechya serve pramanit siddhantanna velechya samasyela samore jaave lagate. quantum gurutvakarshanamadhye, velechi samasya hii samanya sapekshata aanee quantum yantriki yanchyatil sankalpanatmak sangharsh aahe. samanya sapekshatemadhye, samanya sahprasangacha parinam mhanoon vel haah fakt aanakhi eka nirdeshank aahe. quantum kshetra siddhantanmadhye, visheshtah hamiltonian sutramadhye, sutrasthan heey jaageche teen pariman aanee veleche eka pariman asha done prakaranmadhye vibhagale jaate. sadharanpane sangayache tarr, kalachi samasya ashee aahe qee samanya sapekshatet kahihi nahee. yache kaaran asey qee samanya sapekshatemadhye hamiltonian hii eka maryada aahe jee nahishi jhalich pahije. tathapi, konatyahi adhikrut siddhantat, hamiltonian veleche bhashantar tayar karato. mhanoon, aapan yaa nishkarshavar pohochato qee samanya sapekshatemadhye 'kahihi halat nahee' ('vel nahee'). vel nahee" mhanoon, dilelya velechya kshananmadhye quantum yantriki mojamapancha nehmicha arth lavala jaato. kalachi hii samasya hii aupchariktachya serve vyakhyatmak samasyansathi vyapak aadharstambh aahe.
james yorkchya bhoomiti-gatishilatechya anuroop vighatan, jyamule samanya sapekshatechya 'york vel' laa chalana milate, yachee adhikrut aupcharikta charles wang yanni vikasit kelee aahe. heey kaam nantar tyanni aanee tyanchya sahkaryanni scale-invarient dialeton gurutvakarshan-vishayanchya siddhantanchya mothya vargala anukool vel olakhanyacha aanee tyache praman tharvanyacha drushtikon vikasit keela aahe. 
quantum vishvashastrachi samasya.
quantum brahmandshastrachi samasya ashee aahe qee pramanit quantum gurutvakarshanachya maryada maryada bhautik avastha sampoorn vishvachya quantum avasthanche pratinidhitva karatat aanee tyamule bahya nirikshak vagalala jaato, tathapi quantum yantrikichya bahutek vyakhyanmadhye bahya nirikshak haah eka mahattvapoorn ghatak aahe.

