आपेक्षिकता सिद्धांत

apekshikata siddhaant (riletiviti thyori) sankshep mean yah hai ki 'nirapeksh' gati tatha 'nirapeksh' tvaran ka astitv asanbhav hai, arthath‌ 'nirapeksh gati' evan 'nirapeksh tvaran' shabd vastut: nirarthak haian. yadi 'nirapeksh gati' ka arth hota to vah any piando ki charcha kie bina hi nishchit ho sakati. parantu sab prakar se cheshta karane par bhi kisi piand ki 'nirapeksh' gati ka pata nishchit roop se prayog dvara pramanit nahian ho saka hai aur ab to apekshikata siddhaant batata hai ki aisa nishchit karana asanbhav hai. apekshikata siddhaant se bhautiki mean ek ne drishtikon ka praranbh hua. bhautiki ke katipay purane siddhaantoan ka dridh sthan apekshikata siddhaant se dig gaya aur anek maulik kalpanaoan ke vishay mean sookshm vichar karane ki avashyakata dikhaee dene lagi. vijnan mean siddhaant ka kary pray: jnat phaloan ko vyavasthit roop se sootrit karana hota hai aur tatpashchath‌ us siddhaant se ne phaloan ka anuman karake prayog dvara un phaloan ki pariksha ki jati hai. apekshikata siddhaant in donoan kayaan mean saphal raha hai.

19 vian shatabdi ke aant tak bhautiki ka vikas nyootan pranit siddhaantoan ke anusar ho raha tha. pratyek ne avishkar athava prayogik phal ko in siddhaantoan ke drishtikon se dekha jata tha aur avashyak nee parikalpanaean banaee jati thian. inamean sarvavyapi eethar ka ek vishisht sthan tha. eethar ke astitv ki kalpana karane ke do pramukh karan the. pratham to vidyuchchuanbakiy tarangoan ke kanpan ka ek sthan se doosare sthan tak prasaran hone ke lie eethar jaise madhyam ki avashyakata thi. dvitiy, yaantriki mean nyootan ke gati tatha tvaran vishayak samikaranoan ke lie, aur jis parshvabhoomi par ye samikaran adharit the usake lie bhi, ek pramanik nirdeshak (staiandard aauv refareans) ki avashyakata thi. prayogoan ke phaloan ka yatharth akalan hone ke lie eethar par vishisht gunadharmo ka aropan kiya jata tha. eethar sarvavyapi samajha jata tha aur sanpoorn dishaoan mean tatha piandoan mean bhi usaka astitv mana jata tha. is sthir eethar mean piand bina pratirodh ke bhraman kar sakate haian, aisi kalpana thi. in gunoan ke karan eethar ko nirapeksh manak samajhane mean koee badha nahian thi. prakash ki gati 3´1010 sean. mi. prati sekeand hai, yah jnat hua tha aur prakash ki tarangean 'sthir' eethar ke sapeksh is gati se vikirit hoti haian, aisi kalpana thi. yaantriki mean gati, tvaran, bal ityadi ke lie bhi eethar nirapeksh manak samajha jata tha.

19vian shatabdi ke uttarardh mean eethar ka astitv tatha usake gunadharm sthapit karane ke anek prayatn prayog dvara kie ge. inamean maikelasanam aaurle ka prayog vishesh mahatvapoorn tatha ullekhaniy hai. (dr. maikelasanam aaurle ka prayog). prithvi soory ki parikrama eethar ke sapeksh jis gati se karati hai us gati ka yatharth mapan karana is prayog ka uddeshy tha. kiantu yah prayatn asaphal raha aur prayog ke phal se yah anuman nikala gaya ki eethar ke sapeksh prithvi ki gati shoony hai. isaka yah bhi arth hua ki eethar ki kalpana asaty hai, arthath‌ eethar ka astitv hi nahian hai. yadi eethar hi nahian hai to nirapeksh manak ka bhi astitv nahian ho sakata. at: gati keval sapeksh hi ho sakati hai. bhautiki mean samanyat: gati ka mapan karane ke lie athava phal vyakt karane ke lie kisi bhi ek paddhati ka nirdesh (refareans) dekar kary kiya jata hai. kiantu in nirdeshak paddhatiyoan mean koee bhi paddhati 'vishishtatapoorn' nahian ho sakati, kyoanki yadi aisa hota to us 'vishishtatapoorn' nirdeshak paddhati ko ham vishraanti ka manak samajh sakate. anek prayogoan se aisa hi phal prapt hua.

in prayogoan ke phaloan se keval bhautiki mean hi nahian, pratyut vijnan tatha darshan mean bhi ganbhir ashaanti utpann huee. 20vian shatabdi ke praranbh mean (1904 mean) prasiddh fech ganitajn ech. p aauinkare ne apekshikata ka praniyam prastut kiya . inake anusar bhautiki ke niyam aise svaroop mean vyakt hone chahie ki ve kisi bhi prekshak (dekhanevale) ke lie vastavik hoan. isaka arth yah hai ki bhautiki ke niyam prekshak ki gati ke oopar avalanbit n rahean. is praniyam se dikh‌ tatha kal ki prachalit dharanaoan par naya prakash p da. is vishay mean aianstain ki vicharadhara, yadyapi vah kaantikarak thi, prayogoan ke phaloan ko samajhane mean adhik saphal rahi. aianstain ne gati, tvaran, dikh‌, kal ityadi maulik shabdoan ka aur unase sanyukt prachalit dharanaoan ka vishesh vishleshan kiya. is vishleshan se yah spasht hua ki nyootan ke siddhaantoan par adharit tatha pratishthit bhautiki mean trutiyaan haian. aianstin pranit apekshikata siddhaant ke do vibhag haian : (1) vishisht apekshikata siddhaant aur (2) vyapak apekshikata siddhaant. vishisht apekshikata siddhaant mean bhautiki ke niyam is svaroop mean vyakt hote haian ki ve kisi bhi atvarit prekshak ke lie saman hoange. vyapak apekshikata siddhaant mean bhautiki ke niyam is prakar vyakt hote haian ki ve prekshak ki gati se svatantr ya abadhit hoange. vishisht apekshikata siddhaant ka vikas 1905 mean hua aur vyapak apekshikata siddhaant ka vikas 1915 mean hua.

vishisht apekshikata siddhaant-vishisht apekshikata siddhaant samajhana saral hone ke karan usapar vichar pahale kiya jayaga. nity vyavahar mean kisi ne padarth ka sthan nishchit karane ke lie ham jnat padarthoan ka nirdesh karate haian aur unake sapeksh ne padarth ka sthan soochit karate haian. isi prakar gati ka nishchay hota hai, kiantu gati ke nishchay ke lie usaki disha tatha veg jnat karane ki avashyakata hoti hai. relaga di ya viman ka veg prithvi ko sthir samajhakar nishchit kiy jata hai. kiantu prithvi sthir nahian hai, vah apane aksh par ghoomati rahati hai aur sath hi soory ka paribhraman karati rahati hai. soory bhi sthir nahian hai, any taroan ke sapeksh vah apani grahasanstha ke sath vishisht veg se bhraman kar raha haian. viman, prithvi, soory ityadi padarthoan ki gati spasht karane ke lie hamane jis padarth ki svechchha se 'sthir' samajha hai vah ho sakata hai, any nirdeshakoan ke sapeksh 'sthir' ho ya n ho. kshan matr ke lie yadi ham kalpana karean ki akash mean keval ek hi piand hai aur kahian bhi koee any padarth nahian hai, to aise padarth ke lie 'vishraanti' tatha 'gati' ki dharana nirarthak hai. at: gati athava vishraanti ki dharanaean keval sapeksh hi ho sakati haian. isi prakar viman ya relaga di ki 'nirapeksh gati' nikalana asanbhav hai. vishisht apekshikata siddhaant ek any roop mean bhi vyakt kiya gaya hai: prakash ki gati sab prekshakoan ke lie (vastut: keval aise prekshakoan ke lie jinake oopar koee bhi bal kary n kar raha ho) achar hai, arthath‌ utani hi rahati hai, badalati nahian.

vishisht apekshikata siddhaant is prakar saral hi dikhaee deta hai, paratu bhautiki ke bhinn-bhinn kshetroan mean isaka upayog karane ke pashchath‌ jo phal prapt hote haian, ve nity vyavahar ke phaloan ki tulana mean atyant ashcharyajanak haian. nity vyavahar mean jo varg hamare samane ate haian, ve prakash ke veg ki tulana mean upekshaniy hote haian aur aise vegoan ke lie nyootan ke (arthat pratishthit bhautiki ke) siddhaant tatha niyam upayukt haian. jab prakash ke veg ke samip ke vegoan ka prashn ata hai, tabhi nyootan ke niyam lagoo nahian hote aur unake sthan par apekshikata siddhaant ke anusar prapt hue niyamoan tatha phaloan ki avashyakata hoti hai. apekshikata siddhaant se bhautiki mean jo kraanti huee usaka yatharth jnan hone ke lie keval samany ganit hi nahian, kiantu uchch ganit ki avashyakata hoti hai, jisamean dikh‌ tatha kal ki bhi mith: kriya hoti hai. bina poora ganit die vishisht apekshikata siddhaant se prapt hue tho de se phal yahaan die jate haian:

apekshikata aur samakshanikata-nirvat pradeshoan mean prakash ka veg 3´1010 seantimitar prati sekeand hota hai. prakash ke sab varnoan ke lie yah veg saman hota hai. jis sthan ya udgam se prakash nikalata hai usake veg par prakash ka veg avalanbit nahian hota. is prakar prakash ka (tatha sab vidyuchchuanbakiy tarangoan ka) veg nirvat mean utana hi rahata hai. prakash ke is gun ke parinam mahatvapoorn hote haian. udaharanat:, ham kalpana kareange ki ek prekshak prithvi par kh da hai aur usake oopar se ek viman pashchim se akar poorv disha ki or veg v se ja raha hai. jis samay viman prekshak ke mastak ke oopar ata hai thik usi samay prekshak ke saman aantar par do vidyuth‌ ki battiyaan jala di gee, jinamean ek batti poorv disha mean doori d par hai aur doosari pashchim disha mean doori d par hi hai. prithvi par sthit prekshak ke lie donoan battiyoan ka jalana samakshanik (ek hi kshan par honevala) dikhaee p dega, kiantu viman mean bhi yadi koee prekshak ho, to usake lie donoan battiyoan ka jalana samakshanik nahian dikhaee p dega. kyoanki viman poorv disha ki or veg v se ja raha hai, isilie poorv dishavali batti ka prakash pahale dikhaee p dega aur pashchim disha ki batti ka prakash kuchh kshan bad dikhaee p dega. isaka arth yah hai ki ek ghatana kisi prekshak ke lie samakshanik ho to usake sapeksh gatiyukt any prekshak ke lie vahi ghatana samakshanik nahian rahegi. at: samakshanikata nirapeksh nahian, kiantu apekshik hai. is parinam ko vyapak roop se dekhane par ham yah nishkarsh nikal sakate haian ki samay bhi nirapeksh nahian hai, pratyut pratyek nirdeshapiand ke lie apani apani svatantr samayaganana hoti hai, aur do nirdeshapiando par, jo ek doosare ke sapeksh ek saman (yoonif aaurm) veg se gatiman hoan, samayagananaean bhinn hoangi. in donoan samayagananaoan ke paraspar sanbandh se apekshik veg v ka bhi sanbandh hoga. at: samay ke vishay mean hamari jo vyavaharik dharana hai usamean sapekshikata siddhaant ke anusar parivartan karana p dega.

apekshikata aur lanbaee tatha samay-(1) apekshikata siddhaant ke anusar 'nirapeksh' gati ka yadi astitv nahian hai, to 'nirapeksh' vishraanti ka bhi astitv nahian hai. bhautiki mean mapan karane ke lie pahale kisi ek manak ki avashyakata hoti hai aur us manak ka nirdesh karake mapan kie jate haian. svechchha se ham kisi ek paristhiti ko pramanik samajh sakate haian. svechchha se ham kisi ek paristhiti ko pramanik samajh sakate haian. ab ham yah kalpana kareange ki ek viman prithvi se ek vishesh ooanchaee par ruka hai aur usamean lanbaee l ka ek dand hai, arthath‌ is dand ki lanbaee ka yatharth mapan ek mapani ki sahayata se ho sakata hai. ab yadi vah viman veg v se jane lage to apekshikata siddhaant ke anusar us dand ki map mean kitana parivartan hoga? is phal ko prapt karane ke lie ham do prekshakoan ki kalpana kareange. ek prekshak k viman mean baitha hai; at: usaka veg prithvi ke sapeksh v hai, kiantu viman ke sapeksh shoony hai. doosara prekshak kh prithvi par (viman ke poorv sthan par) kh da hai, arthath‌ prithvi ke sapeksh usaka veg shoony hai. viman ka veg v hone ke karan usamean baithe hue prekshak k ka tatha dand ka veg prekshak kh ke sapeksh v hoga. yadi jis samay viman nishchal tha us samay dand ki lanbaee l rahi ho, to prekshak k ke lie vah lanbaee sada l hi rahegi, karan, usake sapeksh dand sada vishraanti mean hi rahega. kiantu prekshak kh ke lie dand veg v se gatiyukt hai. isalie apekshikata siddhaant ke anusar usaki lanbaee mean parivartan hoga aur navin lanbaee l Ö(1-v2/pr2) hogi, jahaan pr2= prakash ki nirvat mean gati hai, arthat k aur kh prekshakoan ke lie ek hi dand ki lanbaee bhinn-bhinn hogi.

lanbaee ke vishay mean apekshikata siddhaant ka yah phal ham vyapak roop mean nimnalikhit prakar se vyakt kar sakate hai : kisi dand ya padarth ki lanbaee mapane par prayog ka jo phal ata hai usako ham lanbaee l kahate haian. bhautiki ki drishti se vastut: yah lanbaee l yatharth nahian hai, varanh‌ l Ö(1-v2/pr2) hai, jahaan v dand ki lanbaee ki disha mean prekshak ka dand ke sapeksh veg hai. isaka arth yah nahian hai ki us dand mean akuanchan ho raha hai. lanbaee us dand ka maulik gun nahian hai, varanh‌ us dand ke sanbandh mean hamari ek dharana hai aur is dharana ko ham l tatha v ke ek phalan (fanqshan) ke roop mean vyakt karate haian. jaise jaise v mean vriddhi hoti hai vaise vaise yah phalan ghatata hai. lanbaee ki sarvasadharan paribhasha yadi is svaroop mean di jae to bhautiki mean prayogoan ke phal samajhane mean kathinaee nahian rahati aur maeekelasan-m aaurle ke prayog ka athava kennedi-th aaurnadaik ke prayog ka saralata se arth bataya ja sakata hai.

bhautiki mean ganit ki tarah hi sthan athava veg nishchit karane ke lie kartisiy (kartisiyan) nirdeshaank paddhati ka upayog kiya jata hai. is paddhati mean ek mool biandu m se tin paraspar lanb rekhaean khianchi jati haian, jo aksh kahalati haian. pratyek do akshoan se ek samatal milata hai aur biandu k ki in samataloan se dooriyaan k ke nirdeshaank hoti haian. yadi ye dooriyaan y, r, l hoan to kaha jata hai ki biandu k ki sthiti (y, r, l,) haichitr:Relativity-Theory.gif

ab ham kalpana kareange ki ek doosari aisi hi aksh paddhati hai, jisake aksh purane akshoan ke samaantar haian or usake sapeksh ,y aksh ke samaantar, ek saman veg v se gatiyukt haian (chitr 2). yadi in paddhatiyoan mean se pratyek mean prekshak ho, to prekshak p' prekshak p ke sapeksh veg v se y aksh ki disha mean ja raha hai. man lean kisi biandu k ke nirdeshaank prekshak p ki paddhati mean (y, r, l) haian aur prekshak p ki paddhati mean (y', r', l'). yah bhi man lean ki jis kshan biandu moo' biandu moo par tha us kshan se samay ki ganana ka praranbh hua. samay s ke pashchath‌ moo se moo' ki doori vas hogi. isilie samay s parchitr:Relativity-Theory-2.gif
kiantu apekshikata siddhaant ke anusar is sanbandh mean parivartan karana p data hai. nirdeshaank mapan mean jis ek ka ham paddhati p mean upayog kareange usaki lanbaee keval y ki disha mean paddhati p' mean Ö(1-v2/pr2) hogi. isalie poorvakt samikaranoan ke badale nimnalikhit samikaran thik hoange :chitr:Relativity-Theory-3.gif

samikaran (2) ko 'roopaantaran samikaran' kahate haian.

(2) samay ko ganana karane ke jo upakaran hote haian unamean yaantriki ke sadhanoan ka upayog kiya jata hai aur pratyaksh athava apratyaksh riti se hamari samayaganana dikh‌ athava lanbaee ki ganana par avalanbit rahati hai. at: apekshikata siddhaant ke anusar yadi lanbaee ke mapan mean veg ke karan parivartan hota hai to veg ke karan samay ke mapan mean bhi parivartan hona avashyak hai.

oopar nirdisht rootaantaran samikaran (2) keval kshanik bianduoan ke lie yatharth hote haian, kiantu kisi bhi sthan ke lie samay se svatantr nahian hote. isaka arth yah hua ki in samikaranoan mean jo samay ka kshan s ata hai usaka vastavik svaroop ek nirdeshaank jaisa hai. kisi sthan ko nishchit karane ke lie jis prakar (y,r,l) in tin nirdeshaanko ki avashyakata hoti hai; usi prakar kisi ghatana ko nishchit karane ke lie samay ki avashyakata hoti hai. at: in tin nirdeshaankoan ke sath samay s bhi yukt karana p dega. yadi paddhati p me kisi ghatana ke nirdeshaank (y,r,l,s) hoan to paddhati p' mean unake sangat nirdeshaank (y',r',r',s') hoangean jinamean kramanusar y',r',l', ke y, r, l se sanbandh samikaran (2) dvara prapt hote haian. s tatha s' ka paraspar sanbandh nikalane ke lie pun: apekshikata siddhaant ki sahayata leni hogi. maikelasan-m aaurle ke prayog ka phal moolabhoot samajhakar chalana adhik saral hoga. maikelasan-m aaurle ke prayog ke anusar prakash ki gati sarvanirdeshaank paddhatiyoan mean (udaharanarth poovokt paddhatiyoan p, p' mean) saman hoti hai.

ham kalpana kareange ki samay s= 0 par moo tatha moo' (chitr1) abhinn the aur thik usi samay par prakash ki ek kiran y-aksh ki disha mean nikalati hai. paddhati p' paddhati p ke sapeksh y-aksh ki disha mean saman veg v se ja rahi hai, at: kuchh samay pashchath‌ yah kiran jis sthan par pahuanchegi usake nirdeshaank is prakar ke hoange:

paddhati p' mean :(y',r',l') samay s' ke pashchath‌.

paddhati p mean : (y, r, l) samay s ke pashchath‌.

maikelasan-morle ke prayoganusar in donoan paddhatiyoan mean prakash ka veg saman hoga. at:chitr:Relativity-Theory-4.gif

is samikaran mean s tatha s' ka jo paraspar sanbandh nishchit hota hai usamean v bhi ata hai. ab samikaran (2) tatha (3) ko ekatrit karane se, dikh‌ ke tin nirdeshaank aur samay, in charoan, in charoan, kean sanbandh ke lie nimnalikhit char samikaran milate haian :chitr:Relativity-Theory-5.gif

samikaran (4) ko loreantz ka roopaantaran samikaran athava sootr kahate haian loreants ke samikaran apekshikata siddhaant ke pahale hi prapt kie ge the, kiantu unaka poora mahatv us samay logoan ne nahian samajha tha.

(3) loreantz ke roopaantaran samikaranoan se dalaplar parinam (d aauplar efekt), prakashavipathan ityadi any phal pramanit kie ja sakate haian. phir fijoan ne pravahit pani mean prakash ka jo veg prayog se napa tha, usake man ka samarthan apekshikata siddhaant se saralata se hota hai. veg tatha tvaran ke lie bhi roopaantaran sootroan ki avashyakata hoti hai. lareantz ke roopaantaran samikaranoan se ye sootr saralata se prapt ho sakate haian.

apekshikata siddhaant mean dravyaman tatha oorja-yaantriki mean apekshikata siddhaant ka upayog karane se ek aur mahatvapoorn phal milata hai. dikh‌ tatha samay ke sath-sath bhautiki mean dravyaman ka bhi mahatvapoorn sthan hai. veg tatha samay apekshik haian aur unake sanbandh samikaran (4) se prapt hote haian. apekshikata siddhaant ke mool tatvoan ka yaantriki mean upayog karane se (visheshat: aise prayogoan mean jahaan dravyaman ka sanbandh ata hai-udaharanarth, do adarsh pratyasth goloan ke sanghat mean) yah phal prapt hota hai ki jaise lanbaee veg par nirbhar hai vaise hi dravyaman bhi veg par nirbhar hai. kisi ek nirdeshapaddhati ke sapeksh vishraanpi sthiti mean ek piand ka dravyaman yadi m. ho, to jab piand veg v se chalata rahata hai jab usake dravyaman mean nimnalikhit samikaran ke anusar vriddhi hoti hai chitr:Relativity-Theory-6.gif samikaran (5) se yah spasht hai ki dravyaman piand ka achar gun nahian hai, kyoanki usamean veg ke anusar parivartan hota hai. apekshikata siddhaant ke pahale dravyaman ke vishay mean jo dharana thi usamean ganbhirata se vichar karane ki avashyakata samikaran (5) se utpann huee.

is vicharadhara ko age badhane se dravyaman tatha oorja ke sanbandh mean bhi vilakshan parinam milata hai. yaantriki ke anusar yadi m dravyaman ka piand v veg se gatiyukt ho to usaki gatij oorja 1/2 mav2 hoti hai. apekshikata siddhaant ke anusar veg ke karan dravyaman mean vaddhi hoti hai aur sath-sath samanupati gatij oorja bhi prapt hoti hai. is dharana ko ganit ki sahayata se vistrit karane par yah phal prapt hota hai ki jis piand ka dravyaman m hai usaki sanpoorn oorja m´pr2 hoti hai, arthat

oo= m.pr2

[E=mc2]

dravyaman tatha oorja ka paraspar sanbandh samikaran (6) se spasht hota hai. at: dravyaman tatha oorja ye ek hi vastu ke keval do vibhinn svaroop haian aur dravyaman ka oorja mean athava oorja ka dravyaman mean parivartan ho sakata hai. kisi padarth se oorja ka vikiran hota ho to samikaran (6) ke anuroop usaka dravyaman ghatata jayaga (udaharanarth soory ka). kisi bhautik ghatana mean keval dravyaman ki avinashita athava keval oorja ki avinashita manana apoorn hoga, kiantu samikaran (6) ka upayog karake ghatana ke poorv aur ghatana ke pashchat usaki sanpoorn oorja athava sanpoorn dravyaman avinashita ke niyam ke anusar saman rahega.

dravyaman mean veg ke karan jo parivartan hota hai vah samany vegoan ke lie atyant upekshaniy hota hai; at: nity vyavahar mean yah parivartan anubhav mean nahian ata hai. oorja tatha dravyaman ki samanata bhi nity vyavahar ke lie nirupayogi hai. jahaan vishal vegoan ka sanbandh ata hai, keval vahian samikaran (5) aur (6) ka upayog ho sakata hai. jab dravyaman hai mean nyoonata hoti hai tab samikaran (6) ke anusar is nasht dravyaman se itani prachand oorja prapt hoti hai ki avashisht dravyaman ko vishal gati milati hai (dr.paramanviy oorja).

apekshikata siddhaant ke parinam ke prayogik tatha any praman-maikelasan'm aaurle ke prayog ke phal ka akalan tatha spashtikaran karane ke lie apekshikata siddhaant prastut kiya gaya tha. kiantu is vad ko vistrit karane ke pashchath‌ samikaran (4)(5)evan(6) ke anusar jo atirikt phal milate haian unako pramanit karane ke lie vishesh prayogoan ki avashyakata thi. upakaranoan ke nirman mean jaise-jaise pragati huee vaise-vaise yatharth mapan ke lie uchit upakaran upalabdh hone lage. aise upakaranoan dvara kie ge prayogoan se samikaran (4),(5) aur (6) yatharthata se pramanit hue aur apekshikata siddhaant ko adhik pushti mili. bhautiki mean, visheshat: nabhikiy bhautiki mean, katipay prayogoan ke phal apekshikata siddhaant ke drishtikon se hi santusht hote haian. apekshikata siddhaant ke apavad ka ek bhi udaharan vartaman kal tak bhautiki mean nahian mila hai. keval di.si. milar ke prayogoan mean eethar ke sapeksh prithvi ki gati ka abhas milata hai. ye prayog maikelasan-morle ke prayog ke saman the. parantu milar ke prayog ke phal vaijnanikoan mean sarvamany nahian hai.

samikaran (4) ke anusar lanbaee tatha samay donoan vegasanbaddh haian. in samikaranoan ka pratyaksh phal napane ke lie veg v prakash ke veg pr se tulaniy hona chahie. jaisa pahale bataya gaya hai, vyavahar ke samany vegoan ke lie lanbaee tatha samay mean jo parivartan hota hai vah upekshaniy hai. paramanu bhautiki mean adhunik kal mean jo pragati huee aur prachand oorja prapt karane ka avishkar hua, unaki sahayata se pr se tulaniy veg prayogashala mean ab mil sakata hai. isi prakar prithvi par aantariksh kiranoan (k aausmik rez) ki jo varsha hoti hai, usamean prachand veg tatha oorja ke kan hote haian. inamean ek vishesh prakar ke kan, mesan, hote haian. jo akash mean prithvi se 10 kilomitar ki ooanchaee par nirmit hote haian. inaka jivanakal lagabhag 3´10-6 sekeand hota hai. samany ganana ke anusar prithvi par pahuanchane ke lie inaka veg pr se bahut adhik hoga, kiantu vishisht apekshikata siddhaant ke anusar yah asanbhav hai. yadi vishisht apekshikata siddhaant ka yahaan upayog kiya jay to yah jivanakal pratyek mesan ke sath usake hi veg se chalanevali gh di ka samay hai. prithvi par ke prekshak ke lie yah gh di vilambit (mand gati) chalegi. at: samay ke sootr mean uchit sanshodhan karane par in mesanoan ka veg 0.99 pr ata hai aur jivanakal bhi thik ata hai. dravyaman ka veg ke oopar avalanban (samikaran 5) to anek prayogoan mean pramanit hua hai. ilektran ko prachand vibhav (poteanshiyal) se tvarit karane par usaki gati pr se tulaniy ho sakati hai aur usaka pratyaksh path nikalane ke lie usake dravyaman ki ganana samikaran (5) ke anusar karani p dati hai. dvitiy vishvayuddh ko jisane shighr samapt kiya aur vartaman kal mean oorja ka ek navayug prasthapit kiya, vah paramanu bam oorja samikaran (6) ka hi phal hai. yadi m gram dravyaman nasht ho to mapr arg oorja milati hai. yooreniyam-235 ka keval 0.1 pratishat dravyaman nasht hone se paramanu bam jaisa mahastr taiyar hota hai (dr.paramanviy oorja) isase adhik dravyaman nasht ho to adhik oorja prapt hogi aur adhik shaktishali mahassr prapt hoga, udaharanat: haidrojan bam. jis samay ati prachand tap mean haidrojan ke paramanu ekatrit hote haian aur hiliyam ke ne paramanu banate haian, us samay adhik dravyaman nasht hone ke karan paramanu bam se sahasraguni adhik oorja utpann hoti hai. soory anek koti shatabdiyoan se satat prachand ushma (oorja ka hi ek svaroop) deta a raha hai. soory ki is shakti ka rahasy bhi samikaran (6) se spasht hota hai. at: bhautiki ki vartaman pragati se ham yah nishchit roop se kah sakate haian ki vishisht apekshikata siddhaant ke sab phal pratyaksh athava apratyaksh riti se pramanit ho chuke haian aur unaki yatharthata mean koee sandeh nahian raha hai.

vyapak apekshikata siddhaant (janaral riletiviti thyori)-vyapak apekshikata siddhaant (1)apekshikata niyam aur (2)gurutvakarshaniy tatha j data (inarshiya) par ashrit dravyamanoan ki samanata, in do parikalpanaoan par adharit hai. lanbaee, dikh‌,kal, sanhati, oorja ityadi ke vishay mean bhotiki mean jo dharanaean thian unamean vishisht apekshikata siddhaant ne sudhar kiya. inake atirikt bhautiki ke kshetr mean any vishay haian jo utane hi mahatvapoorn haian, kiantu unaka samavesh vishisht apekshikata siddhaant mean nahian hai. bal tatha vidyuchchuanbakiy kshetroan mean vishisht apekshikata siddhaant ka jaisa upayog ho sakata hai jaisa gurootvakarshaniy kshetr mean nahian ho sakata. gurootvakarshan bhautiki ka ek atyant mahatvapoorn vibhag hai, at: vishisht apekshikata siddhaant ko vyapak banane ki avashyakata spasht hai.

dravyaman ka sanbandh bhautiki mean do prakar se ata hai. kisi piand par jab bal kary karata hai tab piand ka sthan badalata hai aur usaka veg badalata hai. jab tak bal kary karata hai tab tak piand ko tvaran milata hai. yaantriki ke niyamoan ke anusar bal (p), piand ka dravyaman (m) aur tvaran (ph) mean nimnalikhit sanbandh hai :

p=m´ph . . . (7)

samikaran (7) mean jo dravyaman m hai usako j data ya ashrit (athava avasthititviy) dravyaman kahate haian. dravyaman ka doosara sanbandh nyootan ke gurutvakarshaniy kshetr mean ata hai. nyootan pranit gurutvakarshan ke siddhaant ke anusar yadi do dravyaman, m' tatha m, doori d par hoan, to unake bich mean nimnalikhit gurutvakarshaniy bal p' kam karega :

samikaran (8) mean g gurutvakarshan sthiraank hai. yadi ham m' ko prithvi ka dravyaman samajhean aur m ko samikaran (7) mean ke kisi piand ka dravyaman samajhean to samikaran (8) dravyaman m ka bhar vyakt karega. nyootan ki yaantriki mean gativijnan tatha gurutvakarshan svatantr aur bhinn haian, kiantu donoan mean hi dravyaman ka sanbandh ata hai. dravyaman ke in do svatantr tatha bhinn vibhagoan mean prayukt kalpanaoan ka ekikaran aianstain ne apane vyapak apekshikata siddhaant mean kiya. yah jnat tha ki j data par ashrit dravyaman (samikaran 7) aur gurutvakarshaniy dravyaman (samikaran 8) saman hote haian. aianstain ne dravyaman ki is samanata ka upayog karake gativijnan aur gurutvakarshan ko ekaroop kiya aur sanh‌ 1915 ee. mean vyapak apekshikata siddhaant prastut kiya.

vyapak apekshikata siddhaant ko ganit mean sootrit karane ki jo paddhati hai vah any paddhatiyoan se bhinn hai. isamean vishesh jyamiti ka upabhog kiya jata hai, jo yooklid ki tri-ayamiy jyamiti se bhinn hai. miankovski ne yah bataya ki yadi vishisht apekshikata siddhaant mean dikh‌ ke tin ayam tatha samay ka chaturth ayam, in charoan ayamoan ko lekar ek 'chaturayam satati' (for daimeanshanal k aauntinuam), ki kalpana ki jae to apekshikata siddhaant adhik saral ho jata hai. samakshanikata nirapeksh nahian hai, yah pramanit kiya ja chuka hai. isase nyootan pranit dikh‌ tatha samay ki nirapekshata aur svatantrata samapt ho jati hai. at: bhautik ghatana vyakt karane ke lie dikh‌ tatha samay ki chaturayam satati adhik svabhavik hai. riman ne 'chaturayam dikh‌' ki kalpana karake usaki jyamiti ka jo vikas kiya tha usaka aianstain ne adhik upayog kiya. dikh‌ tatha samay ki is chaturayam satati mean bhaumiki ke siddhaant jyamitiy roop se vyapak apekshikata siddhaant mean rakhe ge. is chaturayam satati ka (athava 'vishv' ka) yuklid ke tin ayam ke dikh‌ se samy hai. tin ayam ki satati mean (y, r, l) in tin nirdeshaankoan se (athava ayamoan se) jis prakar biandu athava ek sthan nishchit hota hai, vaise hi do biandu (y1, r1, l1) aur (y2, r2, l2) ke bich ki lanbaee bhi nishchit hoti hai. chaturayam satati mean dikh‌ ke (y, r, l) in tin ayamoan ke sath jab samay bhi jo da jata hai tab samay ka ayam roop Ö(-1) s pr ata hai, jahaan s=samay aur pr=prakash ka veg hai. ek prekshak ke lie ek vishvaghatana ke nirdeanshaank (y, r, l, s) hoan to us prekshak ke sapeksh gatiman doosare prekshak ke lie usi ghatana ke nirdeshank (y', r', l', s') hoange. loreantz ke roopaantarana niyam yadi yatharth hoan to siddh kiya ja sakata hai ki (9). samikaran (9) mean chaturth nirdeshaank Ö(-1) pras, ata hai jisamean Ö(-1) kalpanik sankhya hai.

samikaran (9) ka vikas karake kisi bhi prakar ki gati ke lie isi prakaraki kiantu atyadhik sanmishr padasanhatiyaan milati haian. isake lie nishchaloan (invairieants) aur atanakoan (tensars) ke siddhaantoan ki avashyakata hoti hai. maulik kalpanaoan ka is riti se vistar karane par vyapak apekshikata siddhaant mean gurutvakarshan svabhavat: ata hai. usake lie vishisht parikalpanaoan ki avashyakata nahian hati hai.

vyapak apekshikata siddhaant ke phaloan ka praman-anek ghatanaoan ke phal aianstain pranit vyapak apekshikata siddhaant ke anusar tatha nyootan pranit pratishthit yaantriki ke anusar saman hi hote hean. kiantu khagoliki mean jab vyapak apekshikata siddhaant ka upayog kiya gaya tab tin ghatanaoan ke phal pratishthit yaantriki ke anusar nikale phaloan se kuchh bhinn rahe. in phaloan se vyapak apekshikata siddhaant ki kasauti ka kam le sakate haian. ye tin phal is prakar haian:

(1) anek varshoan se yah jnat tha ki budh grah ki pratyaksh kaksha nyootan ke siddhaantoan ke anusar nahian rahati. ganana ke pashchath‌ yah pramanit hua ki vyapak apekshikata siddhaant ke kshetr samikaranoan ke anusar budh grah ki jo kaksha ati hai vah prekshit kaksha ke anuroop hai. usi prakar prithvi ki pratyaksh kaksha bhi nyootan ke siddhaantoan ke anusar nahian haian, kiantu prithvi ki kaksha mean truti budh grah ki kaksha ki truti se bahut kam hai. to bhi kaha ja sakata hai ki prithvi ki kaksha ki ganana mean vyapak apekshikata siddhaant saphal raha. at: is vishal mapakramoan ki ghatanaoan mean jahaan pratishthit yaantriki asaphal thi vahaan vyapak apekshikata siddhaant saphal raha.

(2) vyapak apekshikata siddhaant ki doosari kasauti prakash ki vakriyata hai. prakash ki kiranean jab tivr gurutvakarshan kshetr mean se hokar jati haian, tab vyapak apekshikata siddhaant ke anusar unaka path alp matra mean vakr ho jata hai. prakash oorja ka hi ek svaroop hai. at: oorja evan dravyaman ke sanbandh ke anusar (samikaran 6) prakash mean bhi dravyaman hota hai aur dravyaman ko akarshit karana gurutvakarshan kshetr ka gun hone ke karan prakashakiran ka path aisi sthiti mean svalp matra mean tedha ho jata hai. is phal ki pariksha keval sarvasooryagrahan ke samay ho sakati hai. kisi tare ka prakash soory ke nikat se hokar nikale to prakash ke marg ko alp matra mean vakr ho jana chahie aur isalie tare ki abhasi sthiti badal jani chahie. vyapak apekshikata ke is phal ko napane ka prayatn 1919, 1922, 1927, 1947 ityadi varshoan mean sarv sooryagrahan ke samay kiya gaya. pata chala ki prakashakiran ke path ki mapit vakrata aur vyapak apekshikata siddhaant ke anusar nikali vakrata mean itana sookshm aantar hai ki ham yah kah sakate haian ki ye prekshan vyapak apekshikata siddhaant ka samarthan karate haian.

(3) vyapak apekshikata siddhaant ki tisari pariksha gurutvakarshaniy kshetr ke karan varn-kram-rekhaoan (spektr aauskopik laians) ka sthanaantaran hai. is vad ke anusar jo tare tivr gurutvakarshaniy kshetr mean haian unake kisi vishesh tatv ke paramanuoan se nikale prakash ka tarangadairdhy prithvi ke usi tatv ke paramanuoan ke prakash-tarang-dairdhy se adhik hoga. at: tare ke kisi ek tatv ke prakash ke varnakram aur prayogashala mean prapt usi tatv ke varnakram ki tulana se tarangadairdhy ke parivartan ka mapan ho sakata hai. anek nirikshanoan ke phal vyapak apekshikata siddhaant ke anuroop haian, yadyapi kuchh prakshakoan (phhऱaeandalikh adi) ke anusar sab phal vyapak apekshikata siddhaant ke anuroop nahian haian.

apekshikata siddhaant aur gurutvakarshan-apekshikata ke siddhaant ke anusar yah vichar ki bhautik vastuean ek doosar ko akarshit karati haian, ek bhram hai, jo prakriti sanbandhi galat yaantrik dharanaoan ke karan paida hua hai. vastut: gurutvakarshan j data ka ek bhag matr hai, tare aur grahoan ki gatividhiyaan, unaki svabhavagat j data (inarshiya) se utpann hoti hai aur unaka marg dikh‌-kal-satati (spes-taim-k aauntinuam) ke vrittiy tatvoan par nirbhar karata hai. jis prakar chuanbak ke charoan or chuanbakiy kshetr hota hai usi prakar khagoliy vastu apane charoan or ke akash mean ek kshetr bikherati hai. jis tarah chuanbakiy kshetr mean ek lohe ke tuk de ki gatividhi kshetr ki banavat se nirdeshit hoti hai usi tarah gurutviy kshetr mean kisi vastu ka marg us kshetr ki jyamitik avastha se nirdharit hota hai.

aianstain ka gurutvakarshan sanbandhi niyam dikkal satati ke kshetriy tatvoan ki janakari deta hai. mukhyat: is niyam ka ek bhag gurutvakarshanajany vastu ke charoan or ke kshetr ke dhaanche se sanbandh vyakt karata hai.

apekshikata ke siddhaant mean pragati-apekshikata ke siddhaant ke pratipadan ke bad bhi isamean kuchh pragatiyaan huee haian. inamean se ek tathakathit 'brahmaand-rachana-samasya' ke sanbandh mean hai. apekshikata ke siddhaant se pahale aisa samajha jata tha ki dikroopi agadh sagar mean brahmaand tairate hue ek dvip ke saman hai. lekin achal taroan ke prekshan se yah spasht ho gaya hai ki brahmaand anant riktakash (dikroopi agadh sagar) mean tairate hue dvip ke sadrish nahian hai aur jitana dravy brahmaand mean vidyaman hai us sab ke lie gurutvakeandr (seantar aauv graiviti) jaise kisi biandu ka astitv nahian hai. apekshikata ke siddhaant ke dvara brahmaand ka jo roop samane aya usaki tulana sabun ke ek aise bulabule se ki gee hai jisaki satah par silavatean hoan. aantar itana hai ki sabun ke bulabule mean keval do vistar hote haian jabaki brahmaandiy bulabule ke char vistar haian-tin dikh‌ (spes) ke aur ek kal ka. shoony dikh‌ (jo ki shoony kal se sanyukt hai) se is bulabule ka janm hota hai.

apekshikata ke siddhaant ke anusar brahmaand anant hai aur vah anant par yuklidiy hai. brahmaand ko simit man lene par bhi usaka ek ayam asimit hi rahata hai.

apekshikata ke siddhaant ki pragati ka ek bhag yah bhi hai ki prakash ke udgam ke (rrinatmak) gurutviy vibhav ke karan honevale spektramiy rekhaoan ke rakt visthapan (red shift) ka astitv prekshan dvara asandigdh roop se pramanit ho gaya hai. isaka praman tathakathit vaman taroan ke avishkar se sanbhav hua hai jinaka ghanatv jal ke ghanatv se lagabhag 10,000 guna adhik hai. prekshit visthapan ka man bhi apekshit simaoan ke bhitar paya gaya.

apekshikata ke siddhaant ke praranbhik nirman ke gurutvakarshit kan ki gati ka niyam gurutviy kshetr ke niyam ke atirikt ek svatatr maulik sankalpanaoan ke roop mean mana gaya tha jisake anusar gurutvakarshit kan alpaantari (jiyodesik) rekha par gaman karata hai. lekin bad mean yah pramanit hua ki gati ke is niyam ka vishal dravyapuanjoan ke lie vyapakikrit roop bhi keval riktakash ke kshetr samikaranoan mean se hi kiya ja sakata hai jisaki vyutpatti ke anusar gati ka yah niyam is pratibandh se garbhit hai ki jin dravyabianduoan se is kshetr ki utpatti hoti hai unase bahar kahian bhi kshetriy vichitrataoan (siangyulairitiz) ka astitv nahian hona chahie.

aianstain ke vishisht apekshikata siddhaant se prapt kee parinamoan ko anek prayogoan dvara parakha ja chuka hai aur usaki satyata siddh ki ja chuki hai. prakash se adhik tivr gativale kanoan (taikyan) ka astitv aianstain ke siddhaant ko asaty siddh nahian karata apitu aise kanoan ke astitv ka sanket deta hai. is bat se kee bhautikajnoan ne sahamati jataee hai.

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