vishisht aapekshikta

vishisht aapekshikta siddhaant athva aapekshikta ka vishisht siddhaant (jarman : Spezielle Relativitäatstheorie, angreji: special theory of relativity or STR) gatisheel vastuon mein vaidyutasthitiki par apne shodh-patra mein albart aainsteen ne 1905 mein prastaavit jadtveeya nirdesh tantr mein maapan ka ek bhautik siddhaant diya.

gaileeliyo gailili ne abhigruheet kiya tha ki sabhi samaan gatiyaaain saapekshik hain aur yahaaain kuchh bhi nirpeksh naheen hai tatha kuchh bhi viraam avastha mein bhi naheen hai, jise ab gaileeliyo ka aapekshikta siddhaant kaha jaata hai. aainsteen ne is siddhaant ko vistaarit kiya, jiske anusaar prakaash ka veg nirpeksh va niyat hai, yeh ek aisi ghatna hai jo maaikalasan-morale ke prayog mein haal hi mein drushtigochar hui thi. unhone ek abhigruheet yeh bhi diya ki yeh sabhi bhautik niyam, yaantriki va sthirvaidyutiki ke sabhi niyamon, vo jo bhi hon, samaan rahate hain.

is siddhaant ke parinaamon ki sankhya vruhat hai jo praayogik roop se prekshit ho chuke hain, jaise- samay vistaaran, lambaai sankuchan aur samakshanikta. is siddhaant ne nishchar samay antaraal jaisi avadhaarana ko badalkar nishchar dik-kaal antaraal jaisi nai avadhaarana ko janm diya hai. is siddhaant ne krantikaari dravyamaan-oorja sambandh E=mc2 diya, jahaan c nirvaat mein prakaash ka veg hai, yeh sootr is siddhaant ke do abhigruheeton sahit anya bhautik niyamon ka sayunkt roop se vyutpan hai. aapekshikta siddhaant ki bhavishyavaaniyaaain nyootaneeya bhautiki ke parinaam ko sahaj hi ullekhit karte hain, visheshat: jab prekshaniya vastu ka veg, prakaash ke veg ki tulana mein naganya ho. vishisht aapekshikta siddhaant ke anusaar prakaash ka veg c kisi parikalpana ka veg maatr naheen hai jaise vidyutachumbakeeya vikirn (prakaash) ka veg balki samashti va samay ke ekeekaran ka dik-kaal (space-time) ke roop mein karne ke liye ek moolabhoot lakshan hai. is siddhaant ka ek parinaam yeh bhi hai ki aisi koi bhi vastu athva kan jiska viraam dravyamaan shoonya naheen hai kisi bhi paristhiti mein prakaash ke veg tak tvarit naheen kiya ja sakta.

is siddhaant ko vishisht (special) kehne ka kaaran yeh hai ki yeh siddhaant keval jadtveeya nirdesh tantron mein hi laagoo hota hai. iske kuchh varshon pashchaat saamaanya aapekshikta naamak vyaapak siddhaant diya gaya, jo vyaapak nirdeshaankon par kaarya karta hai aur isse gurutvaakarshan samajhne mein bhi sahaayata milti hai.

anukram

abhigruheet

hindi anuvaad: is tarah ke kuchh vichaaron ne kai varshon poorv san 1900 ke pashchaat, arthaat plaank ke bhaari kaarya ki na to yaantriki aur na hi vidyutagatiki (keval seemaant sambandhon ko chhodakar) yathaarth vaidhata tak gyaat kiya ja sakta hai, ke turant baad yeh spasht kar diya tha. dheere-dheere main satya niyamon ke aavishkaar matlab gyaat tathyon par aadhaarit prayaason ki rachanaatmakata ki sambhaavana ko lekar niraash ho gaya. lambe samay tak aur adhik niraasha ke saath mainne koshish ki aur mera vishvaas aur drudh hota gaya ki keval saarvabhaumik aupachaarik siddhaant ka aavishkaar hi hamein aashvast parinaamon tak pahuaincha sakta hai.... kaise, tab, kya ek aisa saarvabhaumik siddhaant praapt kiya ja sakta hai?

—aalbart aainsteen : aatmakathaatmak tippaniyaaain[1]

aainsateen ne do moolabhoot prastaav diye jo sabse adhik sahi prateet hote hain, jo tatkaaleen yaantriki aur vidyutgaatiki ke niyamon ki paripoorn vaidhata ki anadekhi karke diye gaye. yeh prastaav prakaash ke veg par nirbhar aur bhautik niymo (us samay ke prakaash ke veg se sambandhit bhautik niyamon) va jadtveeya nirdesh tantr se svatantr the. unhonne 1905 mein apni pratham prastuti mein in abhigrihiton ka ullekh kiya[2]

  • aapekshikta ka siddhaant - bhautik ghatanaaeain ek jadtveeya nirdesh tantr se doosare mein jaane par parivrtit naheen hoti chaahe vo ek doosare ke saapeksh kisi niyat veg se gatisheel kyon na hon.[2]
  • prakaash ke veg ki nishcharata ka siddhaant - "...prakaash hamesha khaali samashti (nirvaat) mein veg (chaal) c se sanchaarit hota hai jo utsarjan pind (srot) ki gati par nirbhar naheen karta.[2] arthaat prakaash ka nirvaat mein veg c (ek sthaayi niytaank jo disha par nirbhar naheen karta) hota hai jo nirdesh tantr par nirbhar naheen karta.[3]

vishisht aapekshikta ki vyutpatti na keval uparokt do abhigruheeton par hai balki samashti (dik) ki samadaishikta va samaroopata, chhad maapan ki svatantrata aur apne ateet ke itihaas se ghadiyaaain (samay) sahit vibhinn nihit pariklpanaaon (lagbhag sabhi bhautik siddhaanton mein bante hain.) par nirbhar karti hai.[4]

vishisht aapekshikta par 1905 mein aainsateen ki mool prastuti ke anusaar, vibhinn parivrti vyutpan vidhiyon dvaara praapt vibhinn abhigruheet diye ja chuke hain.[5]

nirpeksh nirdesh tantr ka abhaav

vishisht aapekshikta siddhaant ke anusaar koi bhi nirdesh tantr nirpeksh naheen hoti. pruthvi par sthir nirdesh tantr jadtveeya nirdesh tantr naheen hai kyonki yeh pruthvi ki ghoornan gati ke saath yeh bhi ghoornan karta hai. ek jadtveeya nirdesh tantr ke saapeksh niyat veg se gatisheel nirdesh tantr bhi jadtveeya hota hai. at: nirpeksh jadtveeya nirdesh tantr ki parikalpana niraadhaar hai.

nirdesh tantr, nirdeshaank aur lorenj roopaantaran

yahaaain do nirdesh tantr pradarshit hain jinmein ek ka mool bindu O hai tatha kaale rang se pradarshit hai aur doosare ka O' jiska rang neela hai. yahaaain kaale nirdesh tantr par par sthit prekshak ke liye, neela nirdesh tantr, kaale nirdesh tantr ke saapeksh x-aksh ki disha mein niyat veg v se gatisheel hai. vishisht aapekshikta ke siddhaant se neele nirdesh tantr par sthit prekshak ke liye vaisi hi parightanaaeain prekshit hongi keval antar yeh hoga ki yahaaain veg -v hoga. anyonya kriya ke sancharan ki chaal mein parivartan nirpeksh (aapekshikta se poorv) prakriya mein anant tak sambhav thi jiska ek nishchit maan tak simit hona rupaantaran sameekaranon mein sanshodhan ki aavashyakta ki aur dhyaan kheenchati hai.

maana nirdesh tantr S mein dik-kaal nirdeshaank (t,x,y,z) hain aur nirdesh tantr S′ mein nirdeshaank (t′,x′,y′,z′) hain. tab lorenj roopaantaran ke anusaar in nirdeshaankon ko nimn sambandhon dvaara gyaat kiya ja sakta hai :

'"`UNIQ--postMath-00000001-QINU`"'

jahaaain

'"`UNIQ--postMath-00000002-QINU`"'

lorenj gunak hai aur c nirvaat mein prakaash ka veg hai aur nirdesh tantr S′ ka veg v x-aksh ke samaantar hai. y aur z nirdeshaank prabhaavit naheen hain; keval x aur t nirdeshaankon ka sthaanaantaran hota hai. yahaaain x-aksh mein kuchh vishesh naheen hai, sthaanaantaran y athva z akshon par bhi laagoo ho sakta hai, athva kisi bhi disha mein jo disha gati ki disha ke samaantar aur lambavat ho.

ek raashi jo lorenj roopaantaran mein nishchar rahati hai lorenj nishchar kahalaati hai.

bhinn nirdeshaankon mein lorenj roopaantaran aur iske vyutkram likhne par, jahaaain ek ek ghatna ke nirdeshaank (x1, t1) aur (x1, t1) hain tatha doosari ghatna ke nirdeshaank (x2, t2) aur (x2, t2) tab unke antaraal nimn tarah se paribhaashit kiye jaate hain :

'"`UNIQ--postMath-00000003-QINU`"'

at: ham likh sakte hain

'"`UNIQ--postMath-00000004-QINU`"'

lorenj roopaantaran se vyutpann parinaam

vishisht aapekshikta ke parinaam lorenj sameekaranon se vyutpann kiye ja sakte hain.[6] ye roopaantaran aur vishisht aapekshikta bhi, nyootaneeya parinaamon se bhinn parinaam dete hain jab saapeksh veg ka maan prakaash ke veg ki koti ka ho. prakaash ka veg maanav nirmit kisi bhi samaagam se bahut adhik hai jo vishisht aapekshikta dvaara kuchh prabhaav praapt kiye gaye. samakshanikta, samay vistaaran, lambaai sankuchan jaise udaaharan praayogik roop se siddh kiye ja chuke hain. [7]

samakshanikta ki aapekshikta

hare (chitr mein pradarshit rang) nirdesh tantr mein ghatna B ghatna A ke saath ghatit hoti hai arthaat samakshanik hai lekin neele nirdesh tantr mein yeh pehle ghatit ho chuki hai aur laal nirdesh tantr mein baad mein prekshit hoti hai.

do bhinn ghatanaaeain jo ek jadtveeya nirdesh tantr mein samakshanik hain, ho sakta hai doosare jadtveeya nirdesh tantr mein sthit prekshak ke liye samakshanik naheen hain (nirpeksh samakshanikta ka aabhaav).

bhinn nirdeshaankon mein lorenj roopaantaran ki pratham sameekaran

'"`UNIQ--postMath-00000005-QINU`"'

yahaaain yeh spasht hai ki jo ek nirdesh tantr S mein samakshanik hain (Δt = 0 sahi hai), aavashyak naheen ki anya nirdesh tantr S′ mein bhi samakshanik hon (Δt′ = 0 sahi hai). yadi ye ghatanaaeain nirdesh tantr S mein samasthaaneek hain (Δx = 0 sahi hai), tab vo doosare nirdesh tantr S′ mein bhi samakshanik hongi.

samay vistaaran

ek prekshak se doosare prekshak tak kinheen do ghatanon ke madhya samay nishchar naheen hai, balki prekshakon ki gati par nirbhar karta hai (udaaharan ke liye yamal virodhaabhaas dekhein jismein do judvaanon ke baare mein vichaar karta hai jo samashti mein prakaash ke veg ke samakaksh veg vaale antarikshayaan se udte hain aur vaapas aane par dekhte hain ki usaka/usaki judva bhaai/bahin ki aayu bahut adhik ho gayi hai.)

maana ki ek ghadi nirdesh tantr S mein viraamaavastha mein hai. is ghadi ke do bhinn tik-tik ko Δx = 0 dvaara pradarshit kiya ja sakta hai. in donon tik ke madhya samay ka maapan donon tantron mein kiya jaata hai, iske liye pratham sameekaran nimn prakaar praapt hua :

'"`UNIQ--postMath-00000006-QINU`"' ghatanaaeain jinke liye '"`UNIQ--postMath-00000007-QINU`"' hai.

isse pradarshit hota hai ki do tik ke madhya ka samayaantar (Δt') nirdesh tantr (S) jismein ghadi viraam avastha mein thi ki tulana mein nirdesh tantr (S') jismein ghadi gatisheel thi mein adhik tha. samay vistaaran ki sahaayata se ham kai bhautik pariklpanaaon ko samajh sakte hain jaise pruthvi ke vaayumandal mein brahmaand kirnon se janit myuonno ki kshaya dar.[8]

lambaai sankuchan

ek prekshak dvaara kisi vastu ki vima (udahaaran ke liye lambaai) ka maapan anya prekshak dvaara prekshit maapan se bhinn ho sakti hai. (udaaharan ke liye seedhi virodhaabhaas dekhein, jismein prakaash ke veg ke tulya veg se gatisheel vastu ko isse kam aakar vaale myaan mein rakha ja sakta hai.)

isi prakaar, maana rekhak (skel) viraamaavastha mein nirdesh tantr S mein x-aksh ki taraf sanrekhit hai. is tantr mein rekhak ki lambaai Δx likhi jaati hai. rekhak ki lambaai ka maapan S' nirdesh tantr mein karne par jismein ghadi gatisheel hai jahaan chhad ke chhoron par x′ ka maapan S' tantr mein samakshanik kiya jaata hai. anya shabdon mein, is maapan ko Δt′ = 0 mein kiya gaya, jise chaturth sameekaran dvaara yugmit kiya ja sakta hai ke liye lambaaiyon Δx aur Δx′ mein nimn samband sthaapit kiya jaata hai:

'"`UNIQ--postMath-00000008-QINU`"' un ghatnaaon ke liye jinmein '"`UNIQ--postMath-00000009-QINU`"'hai.

isse spasht hota hai ki nirdesh tantr jismein chhad gatisheel thi mein chhad ki lambaai (Δx') ka maan iske swayam ke viraam nirdesh tantr (S) se kam hai.

vegon ka sanyojan

vegon (chaalon) ke sayonjan ke liye inhein saadhaaran roop se naheen joda jaata. yadi nirdesh tantr S mein prekshak ke anusaar koi vastu x aksh ki or veg u se gatisheel hai, to nirdesh tantr S′ jo nirdesh tantr S ke saapeksh x-aksh ki aur v veg se gati kar rahi hai mein sthit prekshak dvaara prekshit gatisheel vastu ka veg u' hai jahaan (upar likhit lorenj roopaantaranon ki sahaayata se) :

'"`UNIQ--postMath-0000000A-QINU`"'

anya nirdesh tantr (S) mein prekshit :

'"`UNIQ--postMath-0000000B-QINU`"'

yahaaain dhyaan dene yogya baat yeh hai ki vastueain jo nirdesh tantr S mein prakaash ke veg se gatisheel hain (arthaat u=c) tab vah vastu nirdesh tantr S′ mein bhi prakaash ke vag se gatisheel hogi. yadi u aur v ke maan prakaash ke veg ke saapeksh bahut nyoon hain to hamein vegon ke sahaj gaililiyeeya roopaantaran praapt hote hain

'"`UNIQ--postMath-0000000C-QINU`"'

saamaanya udahaaran jo diya jaata hai vah yeh hai ki ek train (nirdesh tantr S) poorv disha ki aur patariyon (nirdesh tantr S′) ke saapeksh v veg se gati kar rahi hai. ek bachcha jo train ke andar baitha hai ne ek geind poorv disha ki aur train ke saapeksh veg u se feinka. chirsammat bhautiki mein, patariyon par viraamaavastha mein par sthit prekshak geind ka veg ka maan poorv disha mein u = u′ + v prekshit karega, jabki vishisht aapekshikta yeh satya naheen hai; balki geind ka veg poorv disha mein doosari sameekaran dvaara diya jaata hai : u = (u′ + v)/(1 + uv/c2). pun:, yahaaain x athva poorv disha ke liye kuchh vishesh naheen hai. ye sootr kisi bhi disha mein laagoo hogein jiske liye hamein saapeksh veg v ke paraspar samaantar va lambavat gatiyon ka dhyaan rakhana hoga.

aainsateen ka vegon ke sanyojan ka niyam fijaaoo prayog (Fizeau experiment) mein sahi paaya gaya, jisne prakaash ke veg ka maapan prakaash ke veg ke samaantar gatisheel taral ke saapeksh kiya tha. lekin aaj tak kisi bhi prayog ne asamaantar gati ke vyaapak roop ke liye sootr ka parikshan naheen kiya.[9]

anya parinaam

Thomas agragaman

Thomas agragaman ko Thomas ghurnan ke naam se bhi jaana jaata hai, yeh kanon ke prachakran par laagoo hone wala aapekshik shodhan hai. kisi vastu ka abhivinyaas (arthaat iski akshon ka prekshak ki akshon ke saapeksh sanrekhan) vibhinn prekshakon ke liye bhinn ho sakta hai. anya aapekshik prabhaavon ke vipreet, yeh prabhaav ati nimn vegon par bhi saarthak hai, jaisa gatisheel kanon ke prachakran mein dekha ja sakta hai.[10][11]

dravyamaan-oorja samatulyata

jaise-jaise kisi vastu ki chaal prekshak ke drushtikon se prakaas ke veg ke samakaksh pahunchati hai, to iske aapekshik dravyamaan bhi badhta hai jisse iska tvarit hona aur adhik kathin ho jaata hai, yeh sab prekshak ke nirdesh tantr se prateet hota hai.

viraam avastha mein kisi vastu ki oorja ka maan mc2 hota hai jahaan m vastu ka dravyamaan hai. oorja sarankshan ke niyam se kisi bhi kriya mein dravyamaan mein kami kriya ke pashchaat iski gatij oorja mein vruddhi ke tulya honi chaahiye. isi prakaar, kisi vastu ka dravyamaan ko iski gatij oorja ko ismein lekar badhaaya ja sakta hai.

iske alaava uparokt ke sandarbh - lorenj roopaantaran ko vyutpann karte hain aur vishisht aapekshikta ki vyaakhya - tulyata (aur kraantik vichaar) ke liye sv aanubhavik tark dete hue aainsteen ne bhi kam se kam chaar pepar likhe.

dravyamaan-oorja samatulyata vishisht aapekshikta ka ek parinaam hai. nyootaneeya yaantriki mein jahaan oorja aur sanveg bhinn bhautik raashiyaaain hain vishisht aapekshikta mein ek chatursadish ka nirmaan karte hain aur yeh samay ghatak (oorja ghatak) ko samashti ghatak (sanveg) se sambandhit karta hai. viraam avastha mein sthit ek vastu, oorja dravyamaan chatursadish (E,0,0,0) hota hai : iska samay ghatak oorja hai aur anya teen samashti (dik) ghatak hain jo shoonya hain. x-aksh disha mein alp veg v ke saath lorenj roopaantaran ke saath nirdesh tantr badalne par oorja-sanveg chatursadish (E,Ev/c2, 0, 0) hoga. saveg ka maan oorja va veg ke gunanafal ko c2 se vibhaajit karne par praapt maan ke saamaan hoga. jaise kisi vastu ka nyootaneeya dravyamaan, jo nimn vegon ke liye sanveg va veg ke anupaat ke saamaan hota hai, E/c2 ke baraabar hoga.

oorja va sanveg, dravya va vikirn ka naij gunadharm hai aur yeh parinaam niklana asambhav hai ki vishisht aapekshikta ke do moolabhoot abhigrihiton se ve apne aap chatursadish roop mein praapt honge, kyonki ye (abhigruheet) padaarth athva vikirn ke vishay mein naheen bataate, balki samashti (dik) va samay (kaal) ke baare mein bataate hain. at: iski vyutpati ke liye adhik bhautik gyaan ki aavashyakta hai. iske liye aainsteen ne atirikt siddhaant ka upayog kiya jiske anusaar nimn vegon par nyootaneeya yaantriki se sahi parinaam milte hain, at: nimn vegon par keval oorja adish va teen-sanveg sadish hote hain. isse aage unhonne parikalpana di ki prakash ki oorja aur aavruti samaan dauplar visthaapan ghatak se roopaantarit hoga, jise usane Maxwell sameekaranon dvaara pehle hi satya siddh kar diya tha[2] aainsateen dvaara 1905 mein prakaashit pratham pepar ka vishay "kya kisi pind ka jadtv us oorja par nirbhar karta hai? (Does the Inertia of a Body Depend upon its Energy Content?)" tha.[12] yadyapi pepar mein aainsateen ka tark bhautik vijnyaaaniyon dvaara satya ke roop mein bina kisi pramaan ke lagbhag saarvabhaumikta se sveekaar kiya jaata hai aur bahut lekhakon ne pichhle kuchh varshon tak sujhaavit kiya ki yeh galat hai.[13] anya lekhakon ke anusaar yeh kathan kaafi anirnaayak tha kyonki yeh kuchh antarnihit maanyataaon par aadhaarit tha.[14]

aainsateen ne sveekaar kiya ki vishisht aapekshikta par unke 1907 ke aalekh mein usaki vyutpati par vivaad hue. vahaan unhonne mahasoos kiya ki anumaanit oorja-dravyamaan tark ke liye Maxwell sameekaranon par bharosa karna samasyaatmak hai. unke 1905 mein prakaashit pepar mein tark tha ki dravyamaan rahit kan ka utsarjan kiya ja sakta hai, lekin Maxwell sameekaranon ke anusaar ise nisandeh pratyeksh banaaya ki keval kaarya ke parinaamasvaroop prakaash ka utsarjan praapt kiya ja sakta hai. vidyutachumbakeeya tarangon ke utsarjan ke liye, kisi aaveshit kan ki halachal hi prayaapt hai aur yeh nishchit hi kaarya hai, at: yeh oorja ka utsarjan hai.[15][16]

pruthvi se kitni door yaatra sambhav

chooainki prakaash ke veg se tej gati sambhav naheen hai, jiska nishkarsh nikaala ja sakta hai ki maanav pruthvi se 40 prakaash varshon se adhik door yaatra naheen kar sakta yadi yaatri 20 se 60 varsh ki aayu mein sakreeya rahe. yeh bhi saralata se socha ja sakta hai ki yaatri kuchh hi sauramandalon tak pahuainch paane mein saksham ho sakta hai jo pruthvi se 20-40 prakaash varshon ki doori par sthit hain. lekin yeh ek galat parinaam hai. kyonki samay-vistaaran ki parikalpana ke anusaar pilot ke sakreeya 40 varsh ke dauraan kaalpanik antarikshayaan saikadon prakaashavarsh yaatra kar sakta hai. yadi ek aisa antarikshayaan banaana sambhav ho paaya jiska tvaran 1g (pruthvi ka gurutveeya tvaran) ho, to ek varsh se bhi kam samay mein pruthvi se lagbhag prakaash ke veg ke saamaan veg se gatisheel prekshit hoga. samay vistaaran ki vajah se pruthvi par sthit nirdesh tantr se prekshit usaka jeevan vistaar badhega, lekin uske saath yaatra kar rahi ghadi mein yeh parivartan naheen hoga. usaki yaatra ke dauraan, pruthvi par sthit vyakti yaatri ki tulana mein adhik samay anubhav karega. yaatri dvaara prekshit 5 varsh bhraman yaatra pruthvi ke 6½ varsh ke tulya hogi aur 6 prakaashavarsh duri tay karega. ek 20 varsh ki bhraman yaatr (5 varshon tak tvarit aur 5 varshon tak mandit) ke pashchaat yadi pruthvi par vaapas aata hai to vah pruthvi ke 335 varsh vyateet kar chuka hai aur 331 prakaashavarsh doori tay kar chuka hai.[17] 1 g tvaran ke saath 40 varsh ki yaatra pruthvi ke 58,000 varshon ke tulya hogi aur 55,000 prakaashavarsh doori tay hogi. 1.1 tvaran ke saath 40 varsh ki yaatra pruthvi ke 148,000 varshon ke tulya hogi aur 140,000 prakaashavarsh doori tay hogi. isi vistaaran kaaran se ek myuon jo prakaash ke veg c ke lagbhag saamaan veg se gatisheel hota hai c×aviraam arddh-aayu doori se bahut aage bhi prekshit hota hai.[18]

prakaash ka veg sabse teevr aur kaaranata

chitr 2 : prakaash shanku

chitr 2 mein antaraal AB 'samay-samaroop' hai; jaise yahaaain nirdesh tantr hai jismein A aur B do ghatanaaeain samashti mein ek hi bindu par ghatit hoti hain keval alag samay par ghatit hone par hi alag ki ja sakti hain. yadi is nirdesh tantr mein ghatna A, ghatna B, se pehle ghatit hoti hai to sabhi nirdesh tantron mein ghatna A, B se pehle hi ghatit hogi. yeh dravya ke liye sambhav hai ki vah ek sthaan se doosare sthaan par gati kare, at: yahaaain ek kaarantv sambandh sthaapit ho jaata hai. (A ke saath kaaran va B par prabhaav)

chitr mein antaraal AC samashti-samaroop (space-like) arthaat yahaaain ek nirdesh tantr aisa hai jismein ghatna A aur C ek hi samay par ghatit hoti hain keval samashti (dik) alag-alag hota hai. yahaaain par aise nirdesh tantr bhi praapt kar sakte hain jinmein A, C se pehle (jaisa ki chitr mein dikhaaya gaya hai) ghatit hoti hai aur nidesh tantr jinmein C, A se pehle ghatit hoti hai. yadi yeh kaaran-aur-prabhaav sambandh ke liye sambhav hota ki kuchh ghatanaaeain A aur C ke beech ghatit ho jaayein tab kaaranata ka virodhaabhaash iska parinaam hoga. udahaaran ke liye, yadi A kaaran tha aur C prabhaav hai to kuchh nirdesh tantr aise bhi hain jinmein prabhaav kaaran se pehle ghatit hua. yadyapi yeh apne aap mein virodhaabhaash naheen hai, isse pradarshit kiya ja sakta hai[19][20] ki prakaash ke bhi veg se tej gati se swayam ke nirdesh tantr ke bhoot mein bhej ja sakta hai. kaaranata virodhaabhaash ka signal bhejkar nirmaan kiya ja sakta hai yadi aur keval yadi poorv mein koi signal naheen mila tha.

isliye, yadi kaaranata ko parirkshit kiya jaae, tab vishisht aapekshikta ke parinaamasvaroop nirvaat mein koi soochana athva padaarth prakaash ke veg se tej gati naheen kar sakta. tathaapi, kuchh vastuen prakaash ke veg se bhi teji se gati karti hain jaise : sthaan jahaan bijli ki chamak ke kaaran kirnein baadal ke nichle hisse se takaraati hai to us samay yeh kiran prakaash ke veg se bhi adhik gati se doori tay kar sakti hai jab yeh sheeghrata se mudti hai.[21]

kaaranata ko dhyaan mein rakhe bina yahaaain aur bhi bahut prabal kaaran hain prakaash ke veg se teevr gati vishisht aapekshikta dvaara nisheddh hai. udaaharan ke liye ek niyat bal aseemit samay ke liye ek vastu par laagoo kiya jaaye to nimn vyanjak ka bina seema ke samaakalan karne par F = dp/dt saralata se sanveg praapt kiya jaata hai lekin yeh keval isliye kyonki '"`UNIQ--postMath-0000000D-QINU`"' anant ki aur agrasar hota hai jaise-jaise '"`UNIQ--postMath-0000000E-QINU`"', c ki agrasar hota hai. ek prekshak le liye jo tvarit naheen hai ko yeh drushtaant hota hai yadyapi vastu ka jadtv badhta hai, at: saamaan bal ke prabhaav mein ek laghu tvaran utpann hota hai. yeh vyavahaar vaastav mein kan tvarakon mein prekshit hote hain, jahaan pratyek aaveshit kan vidyutachumbakeeya bal dvaara tvarit hota hai.

guntar nimtj (Güanter Nimtz) aur petrissa ekkle dvaara pratipaadit saiddhaantik aur praayogik surangan adhyayan ne[22] galat daava kiya ki vishesh paristhitiyon mein signal prakaash ke veg se bhi adhik gati se chal sakta hai.[23][24][25][26] yeh maapan kiya gaya ki faaibar ankeekaran signal c se 5 guna veg tak gati karta hai aur shoonya samay surangan ilektraan dvaara le jaane waali soochana ki parmaanu ka foton se aayaneekaran aur iske baavajood bhi ilektraan surangan mein shoonya samay lagaata hai. nimtj aur ekkle ke anusaar, is ati-pradeepan prakriya mein keval aainsteen kaaranata aur vishisht aapekshikta lekin praacheen kaaranata naheen, ka ullanghan hota hai : ati-pratideept sanchaar kisi bhi tarah ki samay yaatra ka parinaam naheen hota.[27][28] vibhinn vaigyaaniko ke anusaar na keval nimtj ki vyaakhyaaeain galat hain balki prayog vaastav mein vishisht aapekshikta siddhaant ka saamaanya praayogik satyaapan hai.[29][30][31]

dik-kaal ki jyaamiti

samatal yooklideeya va minkosaki samashti mein tulana

lamb koneeya aur ghoornan nirdeshaank tantr, baaen: vruteeya kon ke maadhyam se φ yooklideeya samashti aur daayein: ati-paravalayik kon φ (c dvaara ankit laal rekhaayein prakaash signal ki jagat rekha ko nirdeshit karaati hain aur ek sadish iske lamb koneeya sthiti mein hota hai yadi yeh rekha par sthit hai) ke maadhyam se minkosaki samashti.[32]

vishisht aapekshikta mein 4-vimeeya minkovasaki samashti ka upayog kiya jaata hai; - yeh dik-kaal ka udahaaran hai. minkovasaki dik-kaal maanak trivim yooklideeya samashti ke bahut samaan prateet hoti hai, lekin samay ke saath ismein kraantik parivartan aa jaata hai.

trivim samashti mein avakal rekha alpaansh ds nimn prakaar se paribhaashit hota hai

'"`UNIQ--postMath-0000000F-QINU`"'

jahaan dx = (dx1, dx2, dx3) trivim samashti mein avakal alpaansh hain. minkovaasaki jyaamiti mein, samay se vyutpan nirdeshaank x0 adhi-vima hoti hai at: doorik avakal nimn hai

'"`UNIQ--postMath-00000010-QINU`"'

jahaaain dx = (dx0, dx1, dx2, dx3) chaturvim dik-kaal mein avakal alpaansh hai. yeh ek gahari saiddhaantik antardrushti ka sujhaavit karta hai: vishesh aapekshikta dik-kaal mein saamaanya ghoornan samamiti ke tulya hai, jo yooklidiyn samashti (daayaaain chitr) mein ghoornan samamiti ke anuroop.[33] yooklidiyn samashti ki tarah yooklidiyn doorik ka bhi upayog hota hai at: dik-kaal minkovasaki doorik ko upayog karta hai. mool roop se vishisht aapekshikta ko "dik-kaal antaraal ki nishcharata" (kinheen do ghatnaaon ke madhya chaturvim duri hai) ke roop mein dekha jaata hai jab ise "kisi jadtveeya nirdesh tantr" mein dekha jaata hai. vishisht aapekshikta ki sabhi sameekaranon va prabhaavon ko minkosaki dik-kaal ki ghoornan samamiti (poinakeyar samooh) se vyutpan kiya ja sakta hai.

uparokt "ds" ka vaastavik roop doorik par aur x0 nirdeshaank ke chunaav par nirbhar karta hai. samay nirdeshaank ko samashti nirdeshaank ke sadrush banaane ke liye, ise kaalpanik ki tarah upayog kiya jaata hai : x0 = ict (ise viks ghoornan kaha jaata hai). misnar, thorne aur vheelar (1971, §a2.3) ke anusaar, antat: vishisht va saamaanya aapekshikta donon ki gahari samajh minkosaki doorik (neeche ullikhit) ke adhyayan se praapt hoti hai aur abhedya yooklidiyn doorik samay nirdeshaank ict ke sthaan par x0 = ct lete hain.

kuchh lekhak x0 = t ka upayog karte hain jahaan c ke gunak ko anyatr samaahit kar lete hain; udahaaran ke liye, samashti nirdeshaankon ko c se vibhaajit kiya jaata hai athva c±a2 ke gunak ko doorik pradish mein prayukt karte hain.[34] yahaaain vibhinn prathaaon ko praakrut ikaai se pratisthaapit kiya ja sakta hai jahaaain c=1. ismein samay va samashti donon ki ikaaiyaaain samatulya hoti hain aur koi c ka gunak bhi kaheen bhi prakat naheen hota.

trivim dik-kaal

shoonya goleeya samashti

yadi ham samashtiya vima ko ek kam kar dein (arthaat 2 rakhein), jisse ki bhautiki ko trivim mein nirupit kar sakein

'"`UNIQ--postMath-00000011-QINU`"'

tab dvait shanku ki disha mein shoonya parivartan milega, sameekaran ke roop mein

'"`UNIQ--postMath-00000012-QINU`"'

ya

'"`UNIQ--postMath-00000013-QINU`"'

jo c adt trijya vaale vrut ka sameekaran hai.[35]

chaturvim dik-kaal

jab ham teen dik-vimaaon mein iski vruddhi karte hain, tab yeh raashi chaturvima shanku mein drushtaant hoti hai :

'"`UNIQ--postMath-00000014-QINU`"'

at:

'"`UNIQ--postMath-00000015-QINU`"'

yeh ashakt dvait-shanku, samashti mein ek bindu ko ek-vima ke roop mein pradarshit karta hai. yeh jab ham taaron ka adhyayan karte hain aur kehte hain ki "is taare se aapatit prakaash jo main ab dekh raha hooain vah amuk varsh puraana hai", ham is bindu ko vima ke roop mein dekhte hain : ek ashakt jiyodesik hai. ham is ghatna ko doori '"`UNIQ--postMath-00000016-QINU`"' par sthit va d/c samay poorv ghatit ho chuki thi. is kaaran se ashakt dvait shanku ko 'prakaash shanku' ke roop mein bhi jaana jaata hai. (yahaaain pradarshit chitr mein taar pradarshit hai, mool bindu prekshak ko nirupit karta hai aur rekha ashakt jiyodesik mein bindu vima ko nirupit karti hai.)

shanku mein -"t" kshetr ka matlab bindu se soochana praapt kar raha hai aur shanku ke +"t" kshetr mein bindu soochana bhej raha hai.

minkosaki samashti ki jyaamiti minkosaki aarekhon ke upayog se chitrit kar sakte hain, jo vishisht aapekshikta mein vibhinn praayogik vichaaron ko samajhne mein upayogi bhi hain.[36]

dik-kaal mein bhautik vigyaan

vishisht aapekshikta ki sameekaranon ko vyakt parivrti roop mein likha ja sakta hai. kisi ghatna ki dik-kaal mein sthiti pratiprivrti chatursadish dvaara di jaati hai jiske ghatak nimn hain :

'"`UNIQ--postMath-00000017-QINU`"'

ham x0 = ct paribhaashit karte hain taaki samay nirdeshaank ki vima bhi doori ke samaan ho jaisa ki anya dik-vimaaeain hain; at: dik va kaal samaan roop se sambandhit hain[37][38][39] sheershaank pratiprivrti soochakaank ke liye upayog kiye hain na ki unki ghaat ke liye (yeh prasang se spasht ho jaana chaahiye) aur paadaank parivrti soochakaank hain jo shoonya se teen tak ki paraas mein hain jaise ki adish kshetr φ ki chaturpravanata ko likha jaata hai :

'"`UNIQ--postMath-00000018-QINU`"'

bhautik raashiyon ka nirdesh tantron mein parivartan

jadtveeya nirdesh tantron mein nirdeshaank roopaantaran lorenj roopaantaran Λ dvaara diye jaate hain. gati ki vishesh avastha ke liye jab yeh x-aksh ki disha mein ho :

'"`UNIQ--postMath-00000019-QINU`"'

jo x va ct nirdeshaankon ke madhya abhivrdhan (veg vardhak) maitriks (ghoornan ke samaan) hai, jahaan μ' panktiyon ko tatha ν sthambh ka soochak hai aur

'"`UNIQ--postMath-0000001A-QINU`"'

yeh kisi bhi disha mein veg ke liye vyapkikrut kiya ja sakta hai aur aage ghoornan ko bhi shaamil kiya ja sakta hai, adhik jaankaari ke liye lorenj roopaantaran sambandhi vishay dekhein.

ek jadtveeya nirdesh tantr se doosare mein chatursadish ka roopaantaran (saralata ke liye sthaanaantaran rahit) lorenj roopaantaran dvaara diye jaate hain:

'"`UNIQ--postMath-0000001B-QINU`"'

yahaaain par μ' aur ν' par 0 se 3 tak ke liye joda jaata hai. vyutkram roopaantaran nimn hain :

'"`UNIQ--postMath-0000001C-QINU`"'

jahaaain '"`UNIQ--postMath-0000001D-QINU`"', '"`UNIQ--postMath-0000001E-QINU`"' ki vyutkram maitriks kahalaati hai.

lorenj roopaantaran ki sthiti mein uparokt x-aksh ki disha mein liya gaya hai :

'"`UNIQ--postMath-0000001F-QINU`"'

adhik vyaapak roop mein, adhiktar bhautik raashiyon ko pradish ke ghatakon ke roop mein paribhaashit kiya jaata hai. at: ek nirdesh tantr se doosare mein roopaantaran, vyaapak pradish roopaantaran niyamon ka paalan kar sakein[40]

'"`UNIQ--postMath-00000020-QINU`"'

yahaaain '"`UNIQ--postMath-00000021-QINU`"', '"`UNIQ--postMath-00000022-QINU`"' ki vyutkram maitriks hai. sabhi pradish niymaanusaar rupaantarit hote hain.

doorik

dik-kaal ki chaturvim prakruti ka minkosaki durik η ke ghatakon (sabhi nirdesh tantron mein vaidh) ko 4 × 4 ke aavyooh (maitriks) ke roop mein likha ja sakta hai :

'"`UNIQ--postMath-00000023-QINU`"'

jo un nirdesh tantron mein apne vyutkram '"`UNIQ--postMath-00000024-QINU`"' ke saamaan hai.

poinakeyar samooh roopaantaran ka vruhat vyaapak samooh hai jismein minkovasaki doorik samaahit hota hai

'"`UNIQ--postMath-00000025-QINU`"'

aur yeh vishisht aapekshikta ki aadhaarbhoot bhautik samamiti hai.

nishcharata

chatursadish sthiti mein lambai mein alp parivartan '"`UNIQ--postMath-00000026-QINU`"' ke varg ko nimn prakaar likha jaata hai

'"`UNIQ--postMath-00000027-QINU`"'

yeh ek nishchar raashi hai. nishchar se matlab sabhi jadtveeya nirdesh tantron mein iska maan samaan rahata hain kyonki yeh ek adish (shoonya koti ka pradish) raashi hai at: iske saamaanya roopaantaran mein koi Λ prakat naheen hota. jab rekhaansh dx2 ka maan rinaatmak hota hai

'"`UNIQ--postMath-00000028-QINU`"'

tab maanak samay ka avakalaj hai, jabki dx2 dhanaatmak hai, (dx2) maanak duri ka avakalaj hai.

prasish roop mein bhautik sameekaranon ka praathamik maan piyonakeyar samooh mein nishchar rahata hai, at: yeh prabhaav kalit karne ke liye hamein vishisht va kathin gananaaen naheen karni padti.

chaturvim mein veg va tvaran

pradish ke roop mein parichit anya bhautik raashiyaaain bhi roopaantaran niyamon ka paalan karti hain. chaturveg sadish Uμ nimn sameekaran dvaara diya jaata hai

'"`UNIQ--postMath-00000029-QINU`"'

iske pashchaat ham kan ke ek nirdesh tantr se doosare nirdesh tantr mein chaturvegon ke roopaantaran se sambandhit saral vaakya mein vegon ke sanyojan par vichaar karte hain. Uμ ka bhi ek nishchar roop hota hai :

'"`UNIQ--postMath-0000002A-QINU`"'

at: sabhi chaturveg sadish ka parimaan c hota hai. yeh sameekaran yeh saabit karti hai ki aapekshikta mein sthaayi nirdesh tantr ki parikalpana ko asatya siddh karti hai : kyonki ham kam se kam samay mein hamesha agragaami hain. chaturtvaran sadish nimn sameekaran dvaara diya jaata hai :

'"`UNIQ--postMath-0000002B-QINU`"'

iske pashchaat uparokt sameekaran ko τ ke saapeksh avakalit karne par

'"`UNIQ--postMath-0000002C-QINU`"'

at: aapekshikta mein, tvaran chatursadish aur veg chatursadish lanb koneeya hote hain.

chaturvim mein sanveg

sanveg va oorja ko covariant 4-sadish mein sammilit kiya jaata hai :

'"`UNIQ--postMath-0000002D-QINU`"'

jahaaain m nishchar dravyamaan hai.

chatursanveg sadish ka nishchar maan sanveg-oorja sambandh vyutpan karta hai :

'"`UNIQ--postMath-0000002E-QINU`"'

yeh nishchar kya hai ham siddh kar sakte hain jiske liye hamein yeh siddh karna hoga ki yeh ek adish hai, yeh is par nirbhar naheen karta ki ham kis nirdesh tantr mein ganana kar rahe hain aur nirdesh tantr ke roopaantaran se hamein kul sanveg shunya praapt hota hai.

'"`UNIQ--postMath-0000002F-QINU`"'

yahaaain yeh spasht hai ki sthaayi dravyamaan svatantr va nishchar hai. sthir dravyamaan ki ganana gatisheel kanon va nikaayon ke liye bhi ki jaati hai, iske liye inka roopaantaran us nirdesh tantr mein kiya jaata hai jismein inka sanveg shunya ho.

sthir oorja ka sambandh dravyamaan se hai aur yeh chirparichit sambandh sameekaran upar ullekhit ki gayi :

'"`UNIQ--postMath-00000030-QINU`"'

yahaaain dhyaan rahe nikaaya ka dravyamaan unke dravyamaan kendra nirdesh tantr mein kalit kiya jaata hai (jahaaain sanveg shunya ho) jo is nirdesh tantr mein iski kul oorja dvaara diya jaata hai. yeh anya nirdesh tantr mein maapan kiye gaye niji nikaaya dravyamaanon ke yog ke samaan ho aavashyak naheen.

chaturvim mein bal

nyootan ke gati ke truteeya niyam ka upayog karne ke liye, donon balon ko samaan samay nirdesh tantr mein veg mein parivartan ki dar ke roop mein paribhaashit hone chaahiyen. jahaaain, upar paribhaashit trivim balon ka hona aavashyak hai. durbhaagyavash, chaturvim mein aisa koi pradish naheen hai jo trivim bal sadish ke ghatakon ko apne ghatakon mein samaahit karta ho.

yadi kan ka veg c naheen hai tab kan ke sahagaami nirdesh tantr se prekshak nirdesh tantr mein trivim balon ka roopaantaran sambhav hai. isse 4-sadish ka nirmaan hota hai jise chaturbal kaha jaata hai. yeh uparokt maanak samay ke saapeksh upar paribhaashit oorja sanveg chatursadish mein parivartan ki dar hai. chaturbal ka covariant sanskaran:

'"`UNIQ--postMath-00000031-QINU`"'

jahaaain τ maanak samay kahalaata hai.

vastuon ke sthir nirdesh tantr mein, tab tak chaturbal ka samay ghatak shunya rahata hai jab tak vastu ka nishchar dravyamaan parivrtit (ismein khule nikaaya ki aavashyakta hoti hai jahaaain oorja/dravyamaan ko vastu se aasaani se joda athva hataya ja sake) naheen hota jis paristhiti mein dravyamaan mein parivartan ki dar ka rinaatmak maan se c guna hota hai. vyaapak roop mein, yadyapi, chaturbal ke ghatak trivim bal ke ghatakon ke samaan naheen hote kyonki trivim balon ko sanveg mein parivartan ki dar ke roop mein nirdesh tantr samay ke saapeksh paribhshit kiya jaata hai jo dp/dt hota hai balki chaturvim bal ko maanak samay mein parivartan ki dar se paribhaashit kiya jaata hai arthaat dp/dτ.

ek satat maadhyam mein, trivim balon ka ghanatv covariant 4-sadish roop mein shakti ke ghanatv ke roop mein sammilit hota hai. samashtiya bhaag laghu kaksh (trivim samashti mein) par balon ko kaksh ke sampoorn aayatan dvaara vibhaajit karne ka parinaam hai. samay ghatak kaksh ke aayatan se vibhaajit kaksh ke shakti roopaantaran ka -1/c ke gunak ke baraabar hota hai. iska upayog nimnalikhit vaidyutachumbakatv ke anuchhed mein kiya gaya hai.

aapekshikta aur vaidyutachumbakatv samekak

chirsammat vaidyutachumbakeeki mein saiddhaantik anveshan se tarang sancharan ka aavishkaar hua. sameekaranein vaidyutachumbakeeya prabhaav ko vyaapak roop mein se praapt kiya ja sakta hai ki E va B kshetron ke vegon ke parimit sancharan ke liye aaveshit kan par nishchit vyavahaar aavashyak hai. aaveshit kanon ka vyaapak adhyayan linaard-vichrt vibhv ke roop mein hota hai, jo vishisht aapekshikta ki taraf ek star adhik hai.

sthir prekshak nirdesh tantr mein gatisheel aavesh ke vidyut kshetr ka lorenj roopaantaran ke parinaamasvaroop chumbakeeya kshetr naamak ganiteeya vyanjak prakat hoti hai. isi prakaar gatisheel aavesh se vyutpan chumbakeeya kshetr sahagaami nirdesh tantr mein lupt ho jaata hai aur keval sthirvaidyut bal mein badal jaata hai. at: Maxwell sameekaranein brahmaand ke chirsammat pratimaan mein vishisht aapekshik prabhaav saralata va aanubhaavik roop se uchit hain. jaise vidyut va chumbakeeya kshetr nirdesh tantr par nirbhar hain aur ek doosare mein samaahit hain at: inhein vaidyutachumbakeeya bal bhi kehte hain. vishisht aapekshikta ke maadhyam se ham ek jadtveeya nirdesh tantr se doosare jadtveeya nirdesh tantr mein inke roopaantaran niyam praapt hote hain.

trivim roop mein Maxwell sameekaran vishisht aapekshikta ke bhautik gunon ke samaroop hain yadyapi inhein saralata se prakat sahaparivrti roop mein antarveshit karte hain.[41] adhik jaankaari ke liye mukhya sootr dekhein.

(praayogik) sthiti

apne minkosaki dik-kaal mein vishisht aapekshikta keval usi sthiti mein yarthaath hai jab gurutveeya vibhv ka nirpeksh maan adhyayan ke kshetr mein c2 se bahut kam ho[42] prabal gurutvaakarshan kshetr mein, saamaanya aapekshikta ka upayog karna chaahiye. saamaanya aapekshikta durbal kshetr ki seema mein vishisht aapekshikta ke tulya ho jaati hai. atisukshm paimaane par jaise plaank lambaai aur isse bhi nimn, kvaantam prabhaavon ko kvaantam gurutvaakarshan ke adheen lena chaahiye. yaddapi sukshm (micro) star ke paimaanon par aur prabal gurutveeya kshetr ke abhaav mein, vishisht aapekshikta poorn roop se parikshan uchch shuddhata ke saath (10−20) kiya ka chuka hai.[43] aur at: bhautik vijnyaaaniyon dvaara pramaanit hai. iske virodhaabhaash mein praapt praayogik parinaam pun:praapt naheen ho paate hain at: inhein vyaapak roop se praayogik truti maana jaata hai.

vishisht aapekshikta ganit mein svat:tarkasangat hai aur aadhunik siddhaanton ka saamaanya bhaag ban gaya hai, mukhya roop se kvaantam kshetr siddhaant, string siddhaant aur aapekshikta (naganya gurutveeya kshetr ki seema ke saath).

nyootaneeya yaantriki ganiteeya roop se nimn vegon (prakaash ke veg ki tulana mein) par vishisht aapekshikta ka paalan karti hai - at: nyootaneeya yaantriki ko dheeme veg waali vastuon ki vishisht aapekshikta ke roop mein dekha jaata hai. adhik jaankaari ke liye chirsammat yaantriki dekhein.

vibhinn prayog aainsteen ke san 1905 ke pepar ko aaj aapekshikta ke pramaan ke roop mein ullekhit karte hain. inmein se yeh jaana jaata hai ki san 1905 mein aainsateen ko fijaaoo prayog (Fizeau Experiment) ke baare mein pehle se jaankaari thi[44] aur itihaasakaar maanate hain ki aainsateen 1999 se kam se kam Michael morle prayog se avagat hone ke baavajood unhone baad ke varshon mein koi saiddhaantik vikaas naheen kiya[45]

  • fijaaoo prayog (Fizeau experiment) (1851, 1886 mein maaikalasan va morle dvaara punavrurti) ne gatisheel maadhyam mein prakaash ke veg ka maapan kiya, jo rekheek vegon ke aapekshik sanyojan se mel khaati hain.[46]
  • prasiddh maaikalasan morle prayog (1881, 1887) ne nirpeksh prakaash ke veg ke sansoochan ke abhigruhit ko bhaavi sahaara diya. yeh yaha aarambh hona chaahiee ki anya kai daavon ke vipreet tha, isne alp maatra mein srot va prekshak ke veg ke saapeksh prakaash ke veg ki nishcharata ke baare mein kaha tha jahaaain sabhi srot va prekshak samaan veg se sabhi samayon par ekasaath gatimaan the.
  • troutan-Nobel prayog (1903) ne pradarshit kiya ki ek sandhaaritr par laga balaaghoorn nirdesh tantr va sthiti se svatantr hota hai.
  • rele va bres ke prayogon (1902, 1904) ne darshaaya ki lambaai mein sankuchan sah-gatisheel prekshak ke liye vishisht aapekshikta siddhaant ke anusaar vipaatit ho jaata hai.

kan tvarakon mein niymat: tvarit aur lagbhag prakaash ke veg se gatisheel kanon ke gunadharm prekshit kiye jaate hain, jahaaain inka vyavahaar aapekshikta siddhaant ke sangat hota hai aur nyootaneeya yaantriki se asangat. ya yantr keval unhi paristhitiyon mein sugamata se kaarya karte hain jab abhiyaantriki roop se aapekshikta ke siddhaanto ke anusaar banaaya jaata hai. paryaapt sankhya mein aadhunik prayog vishisht aapekshikta ke parikshan ke liye taiyaar kiye gaye. kuchh udaaharan nimn hain:

  • aapekshik oorja va sanveg ke parikshan – kanon ki seemaant chaal ka parakh
  • stilvel prayog (Ives–Stilwell experiment) – aapekshik daupalar prabhaav va samay vistaaran ka parikshan
  • gatisheel kan ka samay vistaaran – teevr gatisheel kanon ki arddh-aayu par aapekshikta ka prabhaav
  • thorndik prayog (Kennedy–Thorndike experiment) – lorenj roopaantaran ke anusaar samay vistaaran
  • hughej-drevar prayog (Hughes–Drever experiment) – samashti va dravyamaan ki samadaishik
  • lorenj ullanghan ke liye aadhunik khoj – vibhinn aadhunik parikshan
  • utsarjan siddhaant par prayog : yeh siddh kiya utsarjak par prakaash ka veg nirbhar naheen karta.
  • ithar maadhyam ki parikalpana – ithar maadhyam naheen hai, ke liye parikshan.

aapekshikta ke siddhaant aur kvaantam yaantriki

vishisht aapekshikta ko kvaantam yaantriki ke saath milaakar aapekshik kvaantam yaantriki ka vikaas kiya ja sakta hai. yeh bhautiki mein anasulajhi paheliyon ki soochi mein shaamil hai, saamaanya aapekshikta va kvaantam yaantriki ko samekak kaise kiya jaae; kvaantam gurutvaakarshan aur sarvatatv siddhaant, jiske liye ekeekaran ki aavashyakta hai aur saiddhaantik shodh ka sakriya va vartamaan mein pragatisheel vishay hai.

poorv bor model dvaara us samay ke kvaantam yaantriki gyaan va vishisht aapekshikta ke upayog se kshaar dhaatu paramaanuon ki uttam sanrachana ki vyaakhya ki gayi.[47]

1928 mein, paul diraik ne prabhaavashaali aapekshik tarang sameekaran ka pratipaadan kiya, jise unke samaan ke roop mein aaj diraak sameekaran ke naam se jaana jaata hai,[48] jo vishisht saapekshikta va 1926 ke pashchaat tak ki antim kvaantam siddhaant donon ke anukool hai. yeh sameekaran na keval ilektraanon naij koneeya sanveg (intrinsic angular momentum) jise prachakran kehte hai ki vyaakhya karti hai balki isne ilektraan ke prati-kan (pojeetraun) ke asthitv ki bhavishyavaani bhi ki.[48][49] aur uttam sanrachana keval vishisht aapekshikta ke saath hi pallavit kiye gaye. yeh aapekshik kvaantam yaantriki ka pratham aadhaash tha. saamaanya kvaantam yaantriki mein, prachakran ek nai ghatna hai aur isko samajhaaya naheen ja sakta.

anya udaaharan ke taur par dekhein to, prati-kanon ki khoj se siddh hota hai ki in ghatnaaon ko aapekshik kvaantam yaantriki samajhaane mein saksham naheen hai aur yeh kanon ki anyonya kriya ke liye ek poorn siddhaant naheen hai. balki aavashyak roop se un kanon ka siddhaant hai jo kvaanteekrut kshatron se sambandhit hain at: ise kvaantam kshetr siddhaant kaha jaata hai; jismein kanon ka dik-kaal ke saath nirman va vilopan kiya ja sakta hai.

ye bhi dekhein

luaa truti package.lua mein pankti 80 par: module 'Module:Portal/images/other' not found.

log:heindrik laareinj | aanri paankare | albart aainsteen | maiks plaank | maaks vaan lo | maaks born
aapekshikta: aapekshikta ka siddhaant | prakaash ka veg | nirdesh tantr |
bhautik vigyaan: chirsammat yaantriki | dik-kaal | prakaash ka veg | dauplar prabhaav
ganit: jyaamiti | pradish
virodhaabhaas: yamal virodhaabhaas

sandarbh

  1. aainsteen aatmakathaatmak lekh, 1949
  2. a aa i E albart aainsteen (1905) "Zur Elektrodynamik bewegter Köarper", annaalein der fysik 17: 891; angreji anuvaad gatisheel vastuon ki vaidyutagatiki ka George baarkar jefri aur vilfrid perrett ne 1923 mein kiya; meghanaad saaha dvaara (1920) mein anya angreji anuvaad gatisheel vastuon ki vaidyutagatiki
  3. edavin efa॰ Taylor aur John aarkibld vheelar (1992). dik-kaal bhautiki : vishisht aapekshikta ka ek parichay (Spacetime Physics: Introduction to Special Relativity). dablyoo॰ echa॰ freemaan. aai॰aऍsa॰abee॰aऍna॰ 0-7167-2327-1.
  4. aainsateen, "vishisht aapekshikta ke moolabhoot vichaar aur pranaaliyaaain (Fundamental Ideas and Methods of the Theory of Relativity)", 1920
  5. aise vyutpanon ke sarvekshan ke liye lukaas aur hodgasan dvaara rachit dik-kaal aur vidyut-chumbakatv, 1990 (Spacetime and Electromagnetism, 1990) dekhein.
  6. Robert resanik (1968). vishisht aapekshikta ka parichay (Introduction to special relativity). Wiley. pp. 62–63. http://books.google.com/books?id=fsIRAQAAIAAJ.
  7. Tom robarts aur siyegmar sklif (October 2007). "vishisht aapekshikta ka praayogik aadhaar kya hai? (What is the experimental basis of Special Relativity?)". yoojnet fijiks FAQ (aksar poochhe jaane vaale prashn). http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html. abhigman tithi: 2008-09-17.
  8. Daniel klepanar aur David koleinkov (1973). yaantriki ka parichay (An Introduction to Mechanics). pp. 468–70. aai॰aऍsa॰abee॰aऍna॰ 0070350485.
  9. Phillip Gibbs aur Don koks. "asamaantar vegon ke liye asamaantar veg sanyojan sootr (The velocity addition formula for non-parallel velocities)". http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html.
  10. L. H. Thomas, "Motion of the spinning electron", Nature 117, 514, 1926
  11. Relativistic velocity space, Wigner rotation and Thomas precession, John A. Rhodes, Mark D. Semon (2005)
  12. Does the inertia of a body depend upon its energy content? alabart aainsateen, Annalen der Physik. 18:639, 1905 (dablyoo॰ perret aur jee॰abee॰ jefferi dvaara angreji mein anuvaadit)
  13. maiks jaimar (1997). chirsammat aur aadhunik bhautiki mein dravyamaan ki avadhaarana (Concepts of Mass in Classical and Modern Physics). kooriyr dover pablikeshans. pp. 177–178. aai॰aऍsa॰abee॰aऍna॰ 0-486-29998-8. http://books.google.com/?id=lYvz0_8aGsMC&pg=PA177.
  14. John je॰ staachel (2002). B se Z tak aainsateen (Einstein from B to Z). springar. pa॰ 221. aai॰aऍsa॰abee॰aऍna॰ 0-8176-4143-2. http://books.google.com/?id=OAsQ_hFjhrAC&pg=PA215.
  15. aapekshikta siddhaant ke anusaar oorja ke jadatv aavashyak hai. (On the Inertia of Energy Required by the Relativity Principle), alabart aainsateen, annaalein der fijiks 23 (1907): 371–384
  16. 1955 mein kaarl seelig ke ek patra (In a letter to Carl Seelig in 1955), aainsateen ne likha "I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity. (hindi anuvaad : mainne pehle hi dekha tha ki Maxwell siddhaant vikirn ki sthool-saranchana ke liye naheen hai aur at: iski koi vyaapak vaidhata naheen hai.)", Einstein letter to Carl Seelig, 1955.
  17. Phillip Gibbs aur Don koks. "aapekshik raaket (The Relativistic Rocket)". http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html. abhigman tithi: 30 August 2012.
  18. vishisht aapekshikta ke anusaar samay va samashti gati se prabhaavit hote hain. (The special theory of relativity shows that time and space are affected by motion). Library.thinkquest.org. abhigman tithi 24 April 2013
  19. aara॰ see॰ tolman, gati ki aapekshikta ka siddhaant (The theory of the Relativity of Motion), (Berkeley 1917), prushth. 54
  20. jee॰ e॰ benford, dee॰ ela॰ book aur dablyoo ॰ e॰ nyookomb (1970). "the tekyonik enteeteleefon". fijikl rivyu di 2 (2): 263. doi:10.1103/PhysRevD.2.263.
  21. vesle see॰ salmon (2006). vaigyaanik vyaakhya ke chaar dashak (Four Decades of Scientific Explanation). university of pitsabarg. pa॰ 107. aai॰aऍsa॰abee॰aऍna॰ 0-8229-5926-7. http://books.google.com/books?id=FHqOXCd06e8C. , Section 3.7 page 107
  22. aadhunik bhautiki ke kuchh hal (Answers of Morden Physics)
  23. efa॰ lonv aur pee॰ mende (1991). "surangan samay samasya par ek tippani (A Note on the Tunneling Time Problem)". enals of fijiks 210: 380–387. doi:10.1016/0003-4916(91)90047-C.
  24. e॰ endars aur jee॰ nimtj (1992). "ati-pratideept chakraman avarodhak (On superluminal barrier traversal)". je॰ fijiks aaya॰ France 2: 1693–1698. doi:10.1051/jp1:1992236.
  25. esa॰ longhi ityaadi (2002). "dvi-avarodh fotoneeya band antaraal mein ati-pratideept prakaasheeya surangan ka maap (Measurement of superluminal optical tunneling times in double-barrier photonic band gaps)". fijikl rivyu E 65 (4): 046610. arXiv:physics/0201013. doi:10.1103/PhysRevE.65.046610. PMID 12006050. http://www.researchgate.net/publication/11365120_Measurement_of_superluminal_optical_tunneling_times_in_double-barrier_photonic_band_gaps.
  26. pee॰ ekkle ityaadi, heeliym mein eto-saikand aayaneekaran aur surangan vilamb samay maapan (Attosecond Ionization and Tunneling Delay Time Measurements in heeliym), vigyaan, 322, 1525–1529 (2008)
  27. jee॰ nimtj, do evaanesseint mods Violate Relativistic Causality? (2006). "Do Evanescent Modes Violate Relativistic Causality?". Lect. Notes Phys.. Lecture Notes in Physics 702: 506–531. doi:10.1007/3-540-34523-X_19. aai॰aऍsa॰abee॰aऍna॰ 978-3-540-34522-0.
  28. G. Nimtz (2010). Tunneling Violates Special Relativity. arXiv:1003.3944v1.
  29. harbart vinful (2007-09-18). Comment on "Macroscopic violation of special relativity" by Nimtz and Stahlhofen.
  30. kris li (2007-08-16). "Latest "faster than the speed of light" claims wrong (again)". http://arstechnica.com/news.ars/post/20070816-faster-than-the-speed-of-light-no-i-dont-think-so.html.
  31. harbart jee॰ vinful (December 2006). "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox". Physics Reports 436 (1–2): 1–69. Bibcode 2006PhR...436....1W. doi:10.1016/j.physrep.2006.09.002. http://sitemaker.umich.edu/herbert.winful/files/physics_reports_review_article__2006_.pdf.
  32. je॰ e॰ vheelar, see॰ misnar, ke॰aesa॰ thorne (1973). gurutvaakarshan. dablyoo॰ echa॰ freemain & company. pa॰ 58. aai॰aऍsa॰abee॰aऍna॰ 0-7167-0344-0.
  33. je॰ aara॰ forshaav, e॰ jee॰ smith (2009). gatiki aur aapekshikta. vili. pa॰ 247. aai॰aऍsa॰abee॰aऍna॰ 978-0-470-01460-8.
  34. aara॰ peinrose (2007). the road too reality (The Road to Reality). vintej books. aai॰aऍsa॰abee॰aऍna॰ 0-679-77631-1.
  35. [Volkov, Yu.A. (2001), "Geodesic line", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4.]
  36. Mermin (1968) Chapter 17
  37. jeen-bernaard juber & Claude Itzykson, kvaantam kshetr siddhaant (Quantum Field Theory), pg 5, ISBN 0-07-032071-3
  38. Charles dablyoo॰ misnar (Charles W. Misner), kip esa॰ thorn (Kip S. Thorne) & John e॰ vheelar (John A. Wheeler),gurutvaakarshan (Gravitation), pg 51, ISBN 0-7167-0344-0
  39. George sterman (George Sterman), kvaantam kshetr siddhaant ka ek parichay (An Introduction to Quantum Field Theory), pg 4, ISBN 0-521-31132-2
  40. Sean M. Carroll (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley. pa॰ 22. aai॰aऍsa॰abee॰aऍna॰ 0-8053-8732-3. http://books.google.com/books?id=1SKFQgAACAAJ.
  41. i॰ je॰ post (1962). vidyutachumbakiki ka saamane roop : vyaapak sahaparivrtan aur vidyutachumbakatv (Formal Structure of Electromagnetics: General Covariance and Electromagnetics). dovar pablikeshan Inc.. aai॰aऍsa॰abee॰aऍna॰ 0-486-65427-3.
  42. Grøan, Øaayvind; Hervik, Sigbjøarn (2007). Einstein's general theory of relativity: with modern applications in cosmology. Springer. pa॰ 195. aai॰aऍsa॰abee॰aऍna॰ 0-387-69199-5. http://books.google.com/books?id=IyJhCHAryuUC. , Extract of page 195 (with units where c=1)
  43. The number of works is vast, see as example:
    Sidney Coleman, Sheldon L. Glashow, Cosmic Ray and Neutrino Tests of Special Relativity, Phys. Lett. B405 (1997) 249-252, online
    An overview can be found on this page
  44. Norton, John D., John D. (2004), "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905", Archive for History of Exact Sciences 59: 45–105, Bibcode 2004AHES...59...45N, doi:10.1007/s00407-004-0085-6, http://philsci-archive.pitt.edu/archive/00001743/
  45. Dongen, Jeroen van (2009). "On the role of the Michelson–Morley experiment: Einstein in Chicago". Eprint arXiv:0908.1545 0908: 1545. arXiv:0908.1545. Bibcode 2009arXiv0908.1545V. http://philsci-archive.pitt.edu/4778/1/Einstein_Chicago_Web2.pdf.
  46. volfagaing raaindlar (1977). aavashyak aapekshikta (Essential Relativity). Birkhäauser. pa॰ §a1,11 p. 7. aai॰aऍsa॰abee॰aऍna॰ 3-540-07970-X. http://books.google.com/?id=0J_dwCmQThgC&pg=PT148.
  47. aara॰ resanik, aara॰ aaisabarg (1985). parmaanu, anu, thos, naabhik aur kanon ki kvaantam yaantriki (Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles) (dviteeya san॰). John vile & sans. pp. 114–116. aai॰aऍsa॰abee॰aऍna॰ 978-0-471-87373-0.
  48. a aa diraak, pee॰ e॰ ema॰ (1930). "ilektraanon va protonon ka siddhaant (A Theory of Electrons and Protons)". Proc. R. Soc. A126: 360. Bibcode 1930RSPSA.126..360D. doi:10.1098/rspa.1930.0013. JSTOR 95359.
  49. see॰ dee॰ aindarasan: dhanaatmak ilektraan. Phys. Rev. 43, 491-494 (1933)

vishay se sambandhit pustakein

patrika lekh

baahari kadiyaaain

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special relativity ko vikshanari,
ek mukt shabdakosh mein dekhein.

maulik kaarya

samaanya shrota ke liye vishisht aapekshikta (ganiteeya gyaan aavashyak naheen)

  • vikeebuks: special rileteeviti
  • aainsateen laait ek sammaan-praapt, gair-takaniki (chalachitr bhaag va pradarshan) parichay, ganiteeya star sahit va rahit, vyaakhya va enimeshan ke saath darjanon prushthon ke saath.
  • aainsateen online gurutveeya balon ke liye maiks plaank sansthaan (Max Planck Institute for Gravitational Physics) dvaara aapekshikta siddhaant ka parichay.
  • audio : kain/gay (2006) (Audio: Cain/Gay (2006)) - khagol paatravarg. aainsateen ka vishisht aapekshikta ka siddhaant.

vishisht aapekshikta ki vyaakhya (saadhaaran va unnat ganit ke saath)

pratyaksh-darshan