आपेक्षिकता सिद्धांत  हिन्दी देवनागरी में पढ़ें।

apekshikata siddhant (riletiviti thyori) snkshep men yah hai ki 'nirapeksh' gati tatha 'nirapeksh' tvaran ka astitv asnbhav hai, arthath‌ 'nirapeksh gati' evn 'nirapeksh tvaran' shabd vastut: nirarthak hain. yadi 'nirapeksh gati' ka arth hota to vah any pindo ki charcha kie bina hi nishchit ho sakati. parntu sab prakar se cheshta karane par bhi kisi pind ki 'nirapeksh' gati ka pata nishchit roop se prayog dvara pramanit nahin ho saka hai aur ab to apekshikata siddhant batata hai ki aisa nishchit karana asnbhav hai. apekshikata siddhant se bhautiki men ek ne drishtikon ka prarnbh hua. bhautiki ke katipay purane siddhanton ka dridh sthan apekshikata siddhant se dig gaya aur anek maulik kalpanaon ke vishay men sookshm vichar karane ki avashyakata dikhaee dene lagi. vigyan men siddhant ka kary pray: gyat phalon ko vyavasthit roop se sootrit karana hota hai aur tatpashchath‌ us siddhant se ne phalon ka anuman karake prayog dvara un phalon ki pariksha ki jati hai. apekshikata siddhant in donon kayan men saphal raha hai.

19 vin shatabdi ke ant tak bhautiki ka vikas nyootan pranit siddhanton ke anusar ho raha tha. pratyek ne avishkar athava prayogik phal ko in siddhanton ke drishtikon se dekha jata tha aur avashyak nee parikalpanaen banaee jati thin. inamen sarvavyapi eethar ka ek vishisht sthan tha. eethar ke astitv ki kalpana karane ke do pramukh karan the. pratham to vidyuchchunbakiy tarngon ke knpan ka ek sthan se doosare sthan tak prasaran hone ke lie eethar jaise madhyam ki avashyakata thi. dvitiy, yantriki men nyootan ke gati tatha tvaran vishayak samikaranon ke lie, aur jis parshvabhoomi par ye samikaran adharit the usake lie bhi, ek pramanik nirdeshak (staindard aauv refarens) ki avashyakata thi. prayogon ke phalon ka yatharth akalan hone ke lie eethar par vishisht gunadharmo ka aropan kiya jata tha. eethar sarvavyapi samajha jata tha aur snpoorn dishaon men tatha pindon men bhi usaka astitv mana jata tha. is sthir eethar men pind bina pratirodh ke bhraman kar sakate hain, aisi kalpana thi. in gunon ke karan eethar ko nirapeksh manak samajhane men koee badha nahin thi. prakash ki gati 3´1010 sen. mi. prati sekend hai, yah gyat hua tha aur prakash ki tarngen 'sthir' eethar ke sapeksh is gati se vikirit hoti hain, aisi kalpana thi. yantriki men gati, tvaran, bal ityadi ke lie bhi eethar nirapeksh manak samajha jata tha.

19vin shatabdi ke uttarardh men eethar ka astitv tatha usake gunadharm sthapit karane ke anek prayatn prayog dvara kie ge. inamen maikelasanamaaurle ka prayog vishesh mahatvapoorn tatha ullekhaniy hai. (dr. maikelasanamaaurle 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. kintu 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 nahin hai. yadi eethar hi nahin hai to nirapeksh manak ka bhi astitv nahin ho sakata. at: gati keval sapeksh hi ho sakati hai. bhautiki men samanyat: gati ka mapan karane ke lie athava phal vyakt karane ke lie kisi bhi ek paddhati ka nirdesh (refarens) dekar kary kiya jata hai. kintu in nirdeshak paddhatiyon men koee bhi paddhati 'vishishtatapoorn' nahin ho sakati, kyonki yadi aisa hota to us 'vishishtatapoorn' nirdeshak paddhati ko ham vishranti ka manak samajh sakate. anek prayogon se aisa hi phal prapt hua.

in prayogon ke phalon se keval bhautiki men hi nahin, pratyut vigyan tatha darshan men bhi gnbhir ashanti utpann huee. 20vin shatabdi ke prarnbh men (1904 men) prasiddh fech ganitgy ech. paauinkare ne apekshikata ka praniyam prastut kiya . inake anusar bhautiki ke niyam aise svaroop men vyakt hone chahie ki ve kisi bhi prekshak (dekhanevale) ke lie vastavik hon. isaka arth yah hai ki bhautiki ke niyam prekshak ki gati ke oopar avalnbit n rahen. is praniyam se dikh‌ tatha kal ki prachalit dharanaon par naya prakash pada. is vishay men ainstain ki vicharadhara, yadyapi vah kantikarak thi, prayogon ke phalon ko samajhane men adhik saphal rahi. ainstain ne gati, tvaran, dikh‌, kal ityadi maulik shabdon ka aur unase snyukt prachalit dharanaon ka vishesh vishleshan kiya. is vishleshan se yah spasht hua ki nyootan ke siddhanton par adharit tatha pratishthit bhautiki men trutiyan hain. ainstin pranit apekshikata siddhant ke do vibhag hain : (1) vishisht apekshikata siddhant aur (2) vyapak apekshikata siddhant. vishisht apekshikata siddhant men bhautiki ke niyam is svaroop men vyakt hote hain ki ve kisi bhi atvarit prekshak ke lie saman honge. vyapak apekshikata siddhant men bhautiki ke niyam is prakar vyakt hote hain ki ve prekshak ki gati se svatntr ya abadhit honge. vishisht apekshikata siddhant ka vikas 1905 men hua aur vyapak apekshikata siddhant ka vikas 1915 men hua.

vishisht apekshikata siddhant-vishisht apekshikata siddhant samajhana saral hone ke karan usapar vichar pahale kiya jayaga. nity vyavahar men kisi ne padarth ka sthan nishchit karane ke lie ham gyat padarthon ka nirdesh karate hain aur unake sapeksh ne padarth ka sthan soochit karate hain. isi prakar gati ka nishchay hota hai, kintu gati ke nishchay ke lie usaki disha tatha veg gyat karane ki avashyakata hoti hai. relagadi ya viman ka veg prithvi ko sthir samajhakar nishchit kiy jata hai. kintu prithvi sthir nahin hai, vah apane aksh par ghoomati rahati hai aur sath hi soory ka paribhraman karati rahati hai. soory bhi sthir nahin hai, any taron ke sapeksh vah apani grahasnstha ke sath vishisht veg se bhraman kar raha hain. viman, prithvi, soory ityadi padarthon ki gati spasht karane ke lie hamane jis padarth ki svechchha se 'sthir' samajha hai vah ho sakata hai, any nirdeshakon ke sapeksh 'sthir' ho ya n ho. kshan matr ke lie yadi ham kalpana karen ki akash men keval ek hi pind hai aur kahin bhi koee any padarth nahin hai, to aise padarth ke lie 'vishranti' tatha 'gati' ki dharana nirarthak hai. at: gati athava vishranti ki dharanaen keval sapeksh hi ho sakati hain. isi prakar viman ya relagadi ki 'nirapeksh gati' nikalana asnbhav hai. vishisht apekshikata siddhant ek any roop men bhi vyakt kiya gaya hai: prakash ki gati sab prekshakon ke lie (vastut: keval aise prekshakon ke lie jinake oopar koee bhi bal kary n kar raha ho) achar hai, arthath‌ utani hi rahati hai, badalati nahin.

vishisht apekshikata siddhant is prakar saral hi dikhaee deta hai, paratu bhautiki ke bhinn-bhinn kshetron men isaka upayog karane ke pashchath‌ jo phal prapt hote hain, ve nity vyavahar ke phalon ki tulana men atynt ashcharyajanak hain. nity vyavahar men jo varg hamare samane ate hain, ve prakash ke veg ki tulana men upekshaniy hote hain aur aise vegon ke lie nyootan ke (arthat pratishthit bhautiki ke) siddhant tatha niyam upayukt hain. jab prakash ke veg ke samip ke vegon ka prashn ata hai, tabhi nyootan ke niyam lagoo nahin hote aur unake sthan par apekshikata siddhant ke anusar prapt hue niyamon tatha phalon ki avashyakata hoti hai. apekshikata siddhant se bhautiki men jo kranti huee usaka yatharth gyan hone ke lie keval samany ganit hi nahin, kintu uchch ganit ki avashyakata hoti hai, jisamen dikh‌ tatha kal ki bhi mith: kriya hoti hai. bina poora ganit die vishisht apekshikata siddhant se prapt hue thode se phal yahan die jate hain:

apekshikata aur samakshanikata-nirvat pradeshon men prakash ka veg 3´1010 sentimitar prati sekend hota hai. prakash ke sab varnon ke lie yah veg saman hota hai. jis sthan ya udgam se prakash nikalata hai usake veg par prakash ka veg avalnbit nahin hota. is prakar prakash ka (tatha sab vidyuchchunbakiy tarngon ka) veg nirvat men utana hi rahata hai. prakash ke is gun ke parinam mahatvapoorn hote hain. udaharanat:, ham kalpana karenge ki ek prekshak prithvi par khada 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 antar par do vidyuth‌ ki battiyan jala di gee, jinamen ek batti poorv disha men doori d par hai aur doosari pashchim disha men doori d par hi hai. prithvi par sthit prekshak ke lie donon battiyon ka jalana samakshanik (ek hi kshan par honevala) dikhaee padega, kintu viman men bhi yadi koee prekshak ho, to usake lie donon battiyon ka jalana samakshanik nahin dikhaee padega. kyonki viman poorv disha ki or veg v se ja raha hai, isilie poorv dishavali batti ka prakash pahale dikhaee padega aur pashchim disha ki batti ka prakash kuchh kshan bad dikhaee padega. isaka arth yah hai ki ek ghatana kisi prekshak ke lie samakshanik ho to usake sapeksh gatiyukt any prekshak ke lie vahi ghatana samakshanik nahin rahegi. at: samakshanikata nirapeksh nahin, kintu apekshik hai. is parinam ko vyapak roop se dekhane par ham yah nishkarsh nikal sakate hain ki samay bhi nirapeksh nahin hai, pratyut pratyek nirdeshapind ke lie apani apani svatntr samayaganana hoti hai, aur do nirdeshapindo par, jo ek doosare ke sapeksh ek saman (yoonifaaurm) veg se gatiman hon, samayagananaen bhinn hongi. in donon samayagananaon ke paraspar snbndh se apekshik veg v ka bhi snbndh hoga. at: samay ke vishay men hamari jo vyavaharik dharana hai usamen sapekshikata siddhant ke anusar parivartan karana padega.

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

lnbaee ke vishay men apekshikata siddhant ka yah phal ham vyapak roop men nimnalikhit prakar se vyakt kar sakate hai : kisi dnd ya padarth ki lnbaee mapane par prayog ka jo phal ata hai usako ham lnbaee l kahate hain. bhautiki ki drishti se vastut: yah lnbaee l yatharth nahin hai, varanh‌ l Ö(1-v2/pr2) hai, jahan v dnd ki lnbaee ki disha men prekshak ka dnd ke sapeksh veg hai. isaka arth yah nahin hai ki us dnd men akunchan ho raha hai. lnbaee us dnd ka maulik gun nahin hai, varanh‌ us dnd ke snbndh men hamari ek dharana hai aur is dharana ko ham l tatha v ke ek phalan (fnqshan) ke roop men vyakt karate hain. jaise jaise v men vriddhi hoti hai vaise vaise yah phalan ghatata hai. lnbaee ki sarvasadharan paribhasha yadi is svaroop men di jae to bhautiki men prayogon ke phal samajhane men kathinaee nahin rahati aur maeekelasan-maaurle ke prayog ka athava kennedi-thaaurnadaik ke prayog ka saralata se arth bataya ja sakata hai.

bhautiki men ganit ki tarah hi sthan athava veg nishchit karane ke lie kartisiy (kartisiyan) nirdeshank paddhati ka upayog kiya jata hai. is paddhati men ek mool bindu m se tin paraspar lnb rekhaen khinchi jati hain, jo aksh kahalati hain. pratyek do akshon se ek samatal milata hai aur bindu k ki in samatalon se dooriyan k ke nirdeshank hoti hain. yadi ye dooriyan y, r, l hon to kaha jata hai ki bindu k ki sthiti (y, r, l,) haiRelativity-Theory.gif

ab ham kalpana karenge ki ek doosari aisi hi aksh paddhati hai, jisake aksh purane akshon ke samantar hain or usake sapeksh ,y aksh ke samantar, ek saman veg v se gatiyukt hain (chitr 2). yadi in paddhatiyon men se pratyek men prekshak ho, to prekshak p' prekshak p ke sapeksh veg v se y aksh ki disha men ja raha hai. man len kisi bindu k ke nirdeshank prekshak p ki paddhati men (y, r, l) hain aur prekshak p ki paddhati men (y', r', l'). yah bhi man len ki jis kshan bindu moo' bindu moo par tha us kshan se samay ki ganana ka prarnbh hua. samay s ke pashchath‌ moo se moo' ki doori vas hogi. isilie samay s parRelativity-Theory-2.gif
kintu apekshikata siddhant ke anusar is snbndh men parivartan karana padata hai. nirdeshank mapan men jis ek ka ham paddhati p men upayog karenge usaki lnbaee keval y ki disha men paddhati p' men Ö(1-v2/pr2) hogi. isalie poorvakt samikaranon ke badale nimnalikhit samikaran thik honge :Relativity-Theory-3.gif

samikaran (2) ko 'roopantaran samikaran' kahate hain.

(2) samay ko ganana karane ke jo upakaran hote hain unamen yantriki ke sadhanon ka upayog kiya jata hai aur pratyaksh athava apratyaksh riti se hamari samayaganana dikh‌ athava lnbaee ki ganana par avalnbit rahati hai. at: apekshikata siddhant ke anusar yadi lnbaee ke mapan men veg ke karan parivartan hota hai to veg ke karan samay ke mapan men bhi parivartan hona avashyak hai.

oopar nirdisht rootantaran samikaran (2) keval kshanik binduon ke lie yatharth hote hain, kintu kisi bhi sthan ke lie samay se svatntr nahin hote. isaka arth yah hua ki in samikaranon men jo samay ka kshan s ata hai usaka vastavik svaroop ek nirdeshank jaisa hai. kisi sthan ko nishchit karane ke lie jis prakar (y,r,l) in tin nirdeshanko ki avashyakata hoti hai; usi prakar kisi ghatana ko nishchit karane ke lie samay ki avashyakata hoti hai. at: in tin nirdeshankon ke sath samay s bhi yukt karana padega. yadi paddhati p me kisi ghatana ke nirdeshank (y,r,l,s) hon to paddhati p' men unake sngat nirdeshank (y',r',r',s') hongen jinamen kramanusar y',r',l', ke y, r, l se snbndh samikaran (2) dvara prapt hote hain. s tatha s' ka paraspar snbndh nikalane ke lie pun: apekshikata siddhant ki sahayata leni hogi. maikelasan-maaurle ke prayog ka phal moolabhoot samajhakar chalana adhik saral hoga. maikelasan-maaurle ke prayog ke anusar prakash ki gati sarvanirdeshank paddhatiyon men (udaharanarth poovokt paddhatiyon p, p' men) saman hoti hai.

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

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

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

maikelasan-morle ke prayoganusar in donon paddhatiyon men prakash ka veg saman hoga. at:Relativity-Theory-4.gif

is samikaran men s tatha s' ka jo paraspar snbndh nishchit hota hai usamen v bhi ata hai. ab samikaran (2) tatha (3) ko ekatrit karane se, dikh‌ ke tin nirdeshank aur samay, in charon, in charon, ken snbndh ke lie nimnalikhit char samikaran milate hain :Relativity-Theory-5.gif

samikaran (4) ko lorentz ka roopantaran samikaran athava sootr kahate hain lorents ke samikaran apekshikata siddhant ke pahale hi prapt kie ge the, kintu unaka poora mahatv us samay logon ne nahin samajha tha.

(3) lorentz ke roopantaran samikaranon se dalaplar parinam (daauplar efekt), prakashavipathan ityadi any phal pramanit kie ja sakate hain. phir fijon ne pravahit pani men prakash ka jo veg prayog se napa tha, usake man ka samarthan apekshikata siddhant se saralata se hota hai. veg tatha tvaran ke lie bhi roopantaran sootron ki avashyakata hoti hai. larentz ke roopantaran samikaranon se ye sootr saralata se prapt ho sakate hain.

apekshikata siddhant men dravyaman tatha oorja-yantriki men apekshikata siddhant ka upayog karane se ek aur mahatvapoorn phal milata hai. dikh‌ tatha samay ke sath-sath bhautiki men dravyaman ka bhi mahatvapoorn sthan hai. veg tatha samay apekshik hain aur unake snbndh samikaran (4) se prapt hote hain. apekshikata siddhant ke mool tatvon ka yantriki men upayog karane se (visheshat: aise prayogon men jahan dravyaman ka snbndh ata hai-udaharanarth, do adarsh pratyasth golon ke snghat men) yah phal prapt hota hai ki jaise lnbaee veg par nirbhar hai vaise hi dravyaman bhi veg par nirbhar hai. kisi ek nirdeshapaddhati ke sapeksh vishranpi sthiti men ek pind ka dravyaman yadi m. ho, to jab pind veg v se chalata rahata hai jab usake dravyaman men nimnalikhit samikaran ke anusar vriddhi hoti hai Relativity-Theory-6.gif samikaran (5) se yah spasht hai ki dravyaman pind ka achar gun nahin hai, kyonki usamen veg ke anusar parivartan hota hai. apekshikata siddhant ke pahale dravyaman ke vishay men jo dharana thi usamen gnbhirata se vichar karane ki avashyakata samikaran (5) se utpann huee.

is vicharadhara ko age badhane se dravyaman tatha oorja ke snbndh men bhi vilakshan parinam milata hai. yantriki ke anusar yadi m dravyaman ka pind v veg se gatiyukt ho to usaki gatij oorja 1/2 mav2 hoti hai. apekshikata siddhant ke anusar veg ke karan dravyaman men 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 pind ka dravyaman m hai usaki snpoorn oorja m´pr2 hoti hai, arthat

oo= m.pr2

[E=mc2]

dravyaman tatha oorja ka paraspar snbndh samikaran (6) se spasht hota hai. at: dravyaman tatha oorja ye ek hi vastu ke keval do vibhinn svaroop hain aur dravyaman ka oorja men athava oorja ka dravyaman men 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 men keval dravyaman ki avinashita athava keval oorja ki avinashita manana apoorn hoga, kintu samikaran (6) ka upayog karake ghatana ke poorv aur ghatana ke pashchat usaki snpoorn oorja athava snpoorn dravyaman avinashita ke niyam ke anusar saman rahega.

dravyaman men veg ke karan jo parivartan hota hai vah samany vegon ke lie atynt upekshaniy hota hai; at: nity vyavahar men yah parivartan anubhav men nahin ata hai. oorja tatha dravyaman ki samanata bhi nity vyavahar ke lie nirupayogi hai. jahan vishal vegon ka snbndh ata hai, keval vahin samikaran (5) aur (6) ka upayog ho sakata hai. jab dravyaman hai men nyoonata hoti hai tab samikaran (6) ke anusar is nasht dravyaman se itani prachnd oorja prapt hoti hai ki avashisht dravyaman ko vishal gati milati hai (dr.paramanviy oorja).

apekshikata siddhant ke parinam ke prayogik tatha any praman-maikelasan'maaurle ke prayog ke phal ka akalan tatha spashtikaran karane ke lie apekshikata siddhant prastut kiya gaya tha. kintu is vad ko vistrit karane ke pashchath‌ samikaran (4)(5)evn(6) ke anusar jo atirikt phal milate hain unako pramanit karane ke lie vishesh prayogon ki avashyakata thi. upakaranon ke nirman men jaise-jaise pragati huee vaise-vaise yatharth mapan ke lie uchit upakaran upalabdh hone lage. aise upakaranon dvara kie ge prayogon se samikaran (4),(5) aur (6) yatharthata se pramanit hue aur apekshikata siddhant ko adhik pushti mili. bhautiki men, visheshat: nabhikiy bhautiki men, katipay prayogon ke phal apekshikata siddhant ke drishtikon se hi sntusht hote hain. apekshikata siddhant ke apavad ka ek bhi udaharan vartaman kal tak bhautiki men nahin mila hai. keval di.si. milar ke prayogon men eethar ke sapeksh prithvi ki gati ka abhas milata hai. ye prayog maikelasan-morle ke prayog ke saman the. parntu milar ke prayog ke phal vaigyanikon men sarvamany nahin hai.

samikaran (4) ke anusar lnbaee tatha samay donon vegasnbaddh hain. in samikaranon ka pratyaksh phal napane ke lie veg v prakash ke veg pr se tulaniy hona chahie. jaisa pahale bataya gaya hai, vyavahar ke samany vegon ke lie lnbaee tatha samay men jo parivartan hota hai vah upekshaniy hai. paramanu bhautiki men adhunik kal men jo pragati huee aur prachnd oorja prapt karane ka avishkar hua, unaki sahayata se pr se tulaniy veg prayogashala men ab mil sakata hai. isi prakar prithvi par antariksh kiranon (kaausmik rez) ki jo varsha hoti hai, usamen prachnd veg tatha oorja ke kan hote hain. inamen ek vishesh prakar ke kan, mesan, hote hain. jo akash men prithvi se 10 kilomitar ki oonchaee par nirmit hote hain. inaka jivanakal lagabhag 3´10-6 sekend hota hai. samany ganana ke anusar prithvi par pahunchane ke lie inaka veg pr se bahut adhik hoga, kintu vishisht apekshikata siddhant ke anusar yah asnbhav hai. yadi vishisht apekshikata siddhant ka yahan upayog kiya jay to yah jivanakal pratyek mesan ke sath usake hi veg se chalanevali ghadi ka samay hai. prithvi par ke prekshak ke lie yah ghadi vilnbit (mnd gati) chalegi. at: samay ke sootr men uchit snshodhan karane par in mesanon ka veg 0.99 pr ata hai aur jivanakal bhi thik ata hai. dravyaman ka veg ke oopar avalnban (samikaran 5) to anek prayogon men pramanit hua hai. ilektran ko prachnd vibhav (potenshiyal) 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 padati hai. dvitiy vishvayuddh ko jisane shighr samapt kiya aur vartaman kal men 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 prachnd tap men haidrojan ke paramanu ekatrit hote hain aur hiliyam ke ne paramanu banate hain, us samay adhik dravyaman nasht hone ke karan paramanu bam se sahasraguni adhik oorja utpann hoti hai. soory anek koti shatabdiyon se satat prachnd 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 hain ki vishisht apekshikata siddhant ke sab phal pratyaksh athava apratyaksh riti se pramanit ho chuke hain aur unaki yatharthata men koee sndeh nahin raha hai.

vyapak apekshikata siddhant (janaral riletiviti thyori)-vyapak apekshikata siddhant (1)apekshikata niyam aur (2)gurutvakarshaniy tatha jadata (inarshiya) par ashrit dravyamanon ki samanata, in do parikalpanaon par adharit hai. lnbaee, dikh‌,kal, snhati, oorja ityadi ke vishay men bhotiki men jo dharanaen thin unamen vishisht apekshikata siddhant ne sudhar kiya. inake atirikt bhautiki ke kshetr men any vishay hain jo utane hi mahatvapoorn hain, kintu unaka samavesh vishisht apekshikata siddhant men nahin hai. bal tatha vidyuchchunbakiy kshetron men vishisht apekshikata siddhant ka jaisa upayog ho sakata hai jaisa gurootvakarshaniy kshetr men nahin ho sakata. gurootvakarshan bhautiki ka ek atynt mahatvapoorn vibhag hai, at: vishisht apekshikata siddhant ko vyapak banane ki avashyakata spasht hai.

dravyaman ka snbndh bhautiki men do prakar se ata hai. kisi pind par jab bal kary karata hai tab pind ka sthan badalata hai aur usaka veg badalata hai. jab tak bal kary karata hai tab tak pind ko tvaran milata hai. yantriki ke niyamon ke anusar bal (p), pind ka dravyaman (m) aur tvaran (ph) men nimnalikhit snbndh hai :

p=m´ph . . . (7)

samikaran (7) men jo dravyaman m hai usako jadata ya ashrit (athava avasthititviy) dravyaman kahate hain. dravyaman ka doosara snbndh nyootan ke gurutvakarshaniy kshetr men ata hai. nyootan pranit gurutvakarshan ke siddhant ke anusar yadi do dravyaman, m' tatha m, doori d par hon, to unake bich men nimnalikhit gurutvakarshaniy bal p' kam karega :

samikaran (8) men g gurutvakarshan sthirank hai. yadi ham m' ko prithvi ka dravyaman samajhen aur m ko samikaran (7) men ke kisi pind ka dravyaman samajhen to samikaran (8) dravyaman m ka bhar vyakt karega. nyootan ki yantriki men gativigyan tatha gurutvakarshan svatntr aur bhinn hain, kintu donon men hi dravyaman ka snbndh ata hai. dravyaman ke in do svatntr tatha bhinn vibhagon men prayukt kalpanaon ka ekikaran ainstain ne apane vyapak apekshikata siddhant men kiya. yah gyat tha ki jadata par ashrit dravyaman (samikaran 7) aur gurutvakarshaniy dravyaman (samikaran 8) saman hote hain. ainstain ne dravyaman ki is samanata ka upayog karake gativigyan aur gurutvakarshan ko ekaroop kiya aur sanh‌ 1915 ee. men vyapak apekshikata siddhant prastut kiya.

vyapak apekshikata siddhant ko ganit men sootrit karane ki jo paddhati hai vah any paddhatiyon se bhinn hai. isamen vishesh jyamiti ka upabhog kiya jata hai, jo yooklid ki tri-ayamiy jyamiti se bhinn hai. minkovski ne yah bataya ki yadi vishisht apekshikata siddhant men dikh‌ ke tin ayam tatha samay ka chaturth ayam, in charon ayamon ko lekar ek 'chaturayam satati' (for daimenshanal kaauntinuam), ki kalpana ki jae to apekshikata siddhant adhik saral ho jata hai. samakshanikata nirapeksh nahin hai, yah pramanit kiya ja chuka hai. isase nyootan pranit dikh‌ tatha samay ki nirapekshata aur svatntrata 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 ainstain ne adhik upayog kiya. dikh‌ tatha samay ki is chaturayam satati men bhaumiki ke siddhant jyamitiy roop se vyapak apekshikata siddhant men rakhe ge. is chaturayam satati ka (athava 'vishv' ka) yuklid ke tin ayam ke dikh‌ se samy hai. tin ayam ki satati men (y, r, l) in tin nirdeshankon se (athava ayamon se) jis prakar bindu athava ek sthan nishchit hota hai, vaise hi do bindu (y1, r1, l1) aur (y2, r2, l2) ke bich ki lnbaee bhi nishchit hoti hai. chaturayam satati men dikh‌ ke (y, r, l) in tin ayamon ke sath jab samay bhi joda jata hai tab samay ka ayam roop Ö(-1) s pr ata hai, jahan s=samay aur pr=prakash ka veg hai. ek prekshak ke lie ek vishvaghatana ke nirdenshank (y, r, l, s) hon to us prekshak ke sapeksh gatiman doosare prekshak ke lie usi ghatana ke nirdeshnk (y', r', l', s') honge. lorentz ke roopantarana niyam yadi yatharth hon to siddh kiya ja sakata hai ki (9). samikaran (9) men chaturth nirdeshank Ö(-1) pras, ata hai jisamen Ö(-1) kalpanik snkhya hai.

samikaran (9) ka vikas karake kisi bhi prakar ki gati ke lie isi prakaraki kintu atyadhik snmishr padasnhatiyan milati hain. isake lie nishchalon (invairients) aur atanakon (tensars) ke siddhanton ki avashyakata hoti hai. maulik kalpanaon ka is riti se vistar karane par vyapak apekshikata siddhant men gurutvakarshan svabhavat: ata hai. usake lie vishisht parikalpanaon ki avashyakata nahin hati hai.

vyapak apekshikata siddhant ke phalon ka praman-anek ghatanaon ke phal ainstain pranit vyapak apekshikata siddhant ke anusar tatha nyootan pranit pratishthit yantriki ke anusar saman hi hote hen. kintu khagoliki men jab vyapak apekshikata siddhant ka upayog kiya gaya tab tin ghatanaon ke phal pratishthit yantriki ke anusar nikale phalon se kuchh bhinn rahe. in phalon se vyapak apekshikata siddhant ki kasauti ka kam le sakate hain. ye tin phal is prakar hain:

(1) anek varshon se yah gyat tha ki budh grah ki pratyaksh kaksha nyootan ke siddhanton ke anusar nahin rahati. ganana ke pashchath‌ yah pramanit hua ki vyapak apekshikata siddhant ke kshetr samikaranon ke anusar budh grah ki jo kaksha ati hai vah prekshit kaksha ke anuroop hai. usi prakar prithvi ki pratyaksh kaksha bhi nyootan ke siddhanton ke anusar nahin hain, kintu prithvi ki kaksha men truti budh grah ki kaksha ki truti se bahut kam hai. to bhi kaha ja sakata hai ki prithvi ki kaksha ki ganana men vyapak apekshikata siddhant saphal raha. at: is vishal mapakramon ki ghatanaon men jahan pratishthit yantriki asaphal thi vahan vyapak apekshikata siddhant saphal raha.

(2) vyapak apekshikata siddhant ki doosari kasauti prakash ki vakriyata hai. prakash ki kiranen jab tivr gurutvakarshan kshetr men se hokar jati hain, tab vyapak apekshikata siddhant ke anusar unaka path alp matra men vakr ho jata hai. prakash oorja ka hi ek svaroop hai. at: oorja evn dravyaman ke snbndh ke anusar (samikaran 6) prakash men bhi dravyaman hota hai aur dravyaman ko akarshit karana gurutvakarshan kshetr ka gun hone ke karan prakashakiran ka path aisi sthiti men svalp matra men 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 men 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 varshon men sarv sooryagrahan ke samay kiya gaya. pata chala ki prakashakiran ke path ki mapit vakrata aur vyapak apekshikata siddhant ke anusar nikali vakrata men itana sookshm antar hai ki ham yah kah sakate hain ki ye prekshan vyapak apekshikata siddhant ka samarthan karate hain.

(3) vyapak apekshikata siddhant ki tisari pariksha gurutvakarshaniy kshetr ke karan varn-kram-rekhaon (spektraauskopik lains) ka sthanantaran hai. is vad ke anusar jo tare tivr gurutvakarshaniy kshetr men hain unake kisi vishesh tatv ke paramanuon se nikale prakash ka tarngadairdhy prithvi ke usi tatv ke paramanuon ke prakash-tarng-dairdhy se adhik hoga. at: tare ke kisi ek tatv ke prakash ke varnakram aur prayogashala men prapt usi tatv ke varnakram ki tulana se tarngadairdhy ke parivartan ka mapan ho sakata hai. anek nirikshanon ke phal vyapak apekshikata siddhant ke anuroop hain, yadyapi kuchh prakshakon (phhऱaendalikh adi) ke anusar sab phal vyapak apekshikata siddhant ke anuroop nahin hain.[1][2]

apekshikata siddhant aur gurutvakarshan-apekshikata ke siddhant ke anusar yah vichar ki bhautik vastuen ek doosar ko akarshit karati hain, ek bhram hai, jo prakriti snbndhi galat yantrik dharanaon ke karan paida hua hai. vastut: gurutvakarshan jadata ka ek bhag matr hai, tare aur grahon ki gatividhiyan, unaki svabhavagat jadata (inarshiya) se utpann hoti hai aur unaka marg dikh‌-kal-satati (spes-taim-kaauntinuam) ke vrittiy tatvon par nirbhar karata hai. jis prakar chunbak ke charon or chunbakiy kshetr hota hai usi prakar khagoliy vastu apane charon or ke akash men ek kshetr bikherati hai. jis tarah chunbakiy kshetr men ek lohe ke tukade ki gatividhi kshetr ki banavat se nirdeshit hoti hai usi tarah gurutviy kshetr men kisi vastu ka marg us kshetr ki jyamitik avastha se nirdharit hota hai.

ainstain ka gurutvakarshan snbndhi niyam dikkal satati ke kshetriy tatvon ki janakari deta hai. mukhyat: is niyam ka ek bhag gurutvakarshanajany vastu ke charon or ke kshetr ke dhanche se snbndh vyakt karata hai.

apekshikata ke siddhant men pragati-apekshikata ke siddhant ke pratipadan ke bad bhi isamen kuchh pragatiyan huee hain. inamen se ek tathakathit 'brahmand-rachana-samasya' ke snbndh men hai. apekshikata ke siddhant se pahale aisa samajha jata tha ki dikroopi agadh sagar men brahmand tairate hue ek dvip ke saman hai. lekin achal taron ke prekshan se yah spasht ho gaya hai ki brahmand annt riktakash (dikroopi agadh sagar) men tairate hue dvip ke sadrish nahin hai aur jitana dravy brahmand men vidyaman hai us sab ke lie gurutvakendr (sentar aauv graiviti) jaise kisi bindu ka astitv nahin hai. apekshikata ke siddhant ke dvara brahmand ka jo roop samane aya usaki tulana sabun ke ek aise bulabule se ki gee hai jisaki satah par silavaten hon. antar itana hai ki sabun ke bulabule men keval do vistar hote hain jabaki brahmandiy bulabule ke char vistar hain-tin dikh‌ (spes) ke aur ek kal ka. shoony dikh‌ (jo ki shoony kal se snyukt hai) se is bulabule ka janm hota hai.

apekshikata ke siddhant ke anusar brahmand annt hai aur vah annt par yuklidiy hai. brahmand ko simit man lene par bhi usaka ek ayam asimit hi rahata hai.

apekshikata ke siddhant ki pragati ka ek bhag yah bhi hai ki prakash ke udgam ke (rinatmak) gurutviy vibhav ke karan honevale spektramiy rekhaon ke rakt visthapan (red shift) ka astitv prekshan dvara asndigdh roop se pramanit ho gaya hai. isaka praman tathakathit vaman taron ke avishkar se snbhav hua hai jinaka ghanatv jal ke ghanatv se lagabhag 10,000 guna adhik hai. prekshit visthapan ka man bhi apekshit simaon ke bhitar paya gaya.

apekshikata ke siddhant ke prarnbhik nirman ke gurutvakarshit kan ki gati ka niyam gurutviy kshetr ke niyam ke atirikt ek svatatr maulik snkalpanaon ke roop men mana gaya tha jisake anusar gurutvakarshit kan alpantari (jiyodesik) rekha par gaman karata hai. lekin bad men yah pramanit hua ki gati ke is niyam ka vishal dravyapunjon ke lie vyapakikrit roop bhi keval riktakash ke kshetr samikaranon men se hi kiya ja sakata hai jisaki vyutpatti ke anusar gati ka yah niyam is pratibndh se garbhit hai ki jin dravyabinduon se is kshetr ki utpatti hoti hai unase bahar kahin bhi kshetriy vichitrataon (singyulairitiz) ka astitv nahin hona chahie.[3]

ainstain ke vishisht apekshikata siddhant se prapt kee parinamon ko anek prayogon dvara parakha ja chuka hai aur usaki satyata siddh ki ja chuki hai. prakash se adhik tivr gativale kanon (taikyan) ka astitv ainstain ke siddhant ko asaty siddh nahin karata apitu aise kanon ke astitv ka snket deta hai. is bat se kee bhautikgyon ne sahamati jataee hai.[4]


panne ki pragati avastha
adhar
prarambhik
madhyamik
poornata
shodh

tika tippani aur sndarbh

  1. sn.grn.-ailbart ainstain : riletiviti, speshal aind d jenaral thyori; ailbart ainstain : di mining aauv riletiviti; sar arthar edingatan : d maithimaitikal thyori aauv riletiviti; si. molar : d thyori aauv riletiviti.
  2. daau. devidas raghunatharav bhavalakar
  3. hindi vishvakosh, khand 1 |prakashak: nagari pracharini sabha, varanasi |snkalan: bharat diskavari pustakalay |prishth snkhya: 383 |
  4. sn.grn.-uparyukt sn.grn. ke navinatam snskaran.

snbndhit lekh

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