aapekshikta siddhaant

saamaanya aapekshikta mein varnit trivimeeya space-samay karvechar ki enaalauji ke ka dvivimeeyaprakshepan.

aapekshikta siddhaant athva saapekshikta ka siddhaant (angreji: thiori of railetiviti), ya keval aapekshikta, aadhunik bhautiki ka ek buniyaadi siddhaant hai jise albart aainsteen ne viksit kiya aur jiske do bade ang hain - vishisht aapekshikta (spaishal railaitiviti) aur saamaanya aapekshikta (jainairal railaitiviti).[1] fir bhi kai baar aapekshikta ya riletiviti shabd ko gaileeliyn invairiyns ke sandarbh mein bhi prayog kiya jaata hai. theory of riletiviti naamak is shabd ka prayog sabse pehle san 1906 mein maiks plaink ne kiya tha. yeh angreji shabd samooh "riletiv theory" (jarman : Relativtheorie) se liya gaya tha jismein yeh bataaya gaya hai ki kaise yeh siddhaant principle of riletiviti ka prayog karta hai. isi pepar ke charcha sanbhaag mein alfred bukarar ne pratham baar "theory of riletiviti" (jarman : Relativitäatstheorie) ka prayog kiya tha.[2][3]

anukram

parichay

aapekshikta siddhaant (riletiviti theory ) sankshep mein yeh hai ki 'nirpeksh' gati tatha 'nirpeksh' tvaran ka astitv asambhav hai, arthaat 'nirpeksh gati' evam 'nirpeksh tvaran' shabd vastut: nirrthak hain. yadi 'nirpeksh gati' ka arth hota to vah anya pindo ki charcha kiye bina hi nishchit ho sakti. parantu sab prakaar se cheshta karne par bhi kisi pind ki 'nirpeksh' gati ka pata nishchit roop se prayog dvaara pramaanit naheen ho saka hai aur ab to aapekshikta siddhaant bataata hai ki aisa nishchit karna asambhav hai. aapekshikta siddhaant se bhautiki mein ek nae drushtikon ka praarambh hua. aapekshikta siddhaant ke aane se bhautiki ke katipya puraane siddhaanton ka drudh sthaan dig gaya aur anek maulik kalpanaaon ke vishay mein sookshm vichaar karne ki aavashyakta dikhaai dene lagi. vigyaan mein siddhaant ka kaarya praaya: gyaat falon ko vyavasthit roop se sootrit karna hota hai aur uske baad us siddhaant se nae falon ka anumaan karke prayog dvaara un falon ki pareeksha ki jaati hai. aapekshikta siddhaant in donon kaaryon mein safal raha hai.

19veen shataabdi ke ant tak bhautiki ka vikaas nyootan praneet siddhaanton ke anusaar ho raha tha. pratyek nae aavishkaar athva praayogik fal ko in siddhaanton ke drushtikon se dekha jaata tha aur aavashyak nai pariklpanaaeain banaai jaati theen. inmein sarvavyaapi ithar ka ek vishisht sthaan tha. ithar ke astitv ki kalpana karne ke do pramukh kaaran the. pratham to vidyutachumbakeeya tarangon ke kanpan ka ek sthaan se doosare sthaan tak prasaran hone ke liye ithar jaise maadhyam ki aavashyakta thi. dviteeya, yaaaintriki mein nyootan ke gati vishyak sameekaranon ke liye, aur jis paarshvabhoomi par ye sameekaran aadhaarit the uske liye bhi, ek praamaanik nirdeshak (standard of refreins) ki aavashyakta thi. prayogon ke falon ka yathaarth aakalan hone ke liye ithar par vishisht gunadharmon ka aaropan kiya jaata tha. ithar sarvavyaapi samjha jaata tha aur sampoorn dishaaon mein tatha pindon mein bhi usaka astitv maana jaata tha. is sthir ithar mein pind bina pratirodh ke bhraman kar sakte hain, aisi kalpana thi. in gunon ke kaaran ithar ko nirpeksh maanak samajhne mein koi baadha naheen thi. prakaash ki gati 3x108 mi. prati second hai, yeh gyaat hua tha aur prakaash ki tarangein 'sthir' ithar ke saapeksh is gati se vikeerit hoti hain, aisi kalpana thi. yaaaintriki mein veg, tvaran, bal ityaadi ke liye bhi ithar nirpeksh maanak samjha jaata tha.

19veen shataabdi ke uttaraardh mein ithar ka astitv tatha uske gunadharm sthaapit karne ke anek prayatn prayog dvaara kiye gaye. inmein maaikelasanamaurle ka prayog vishesh mahatvapoorn tatha ullekhaneeya hai. pruthvi, soorya ki parikrama ithar ke saapeksh jis gati se karti hai us gati ka yathaarth maapan karna is prayog ka uddeshya tha. kintu yeh prayatn asafal raha aur prayog ke fal se yeh anumaan nikaala gaya ki ithar ke saapeksh pruthvi ki gati shoonya hai. iska yeh bhi arth hua ki ithar ki kalpana asatya hai, arthaat ithar ka astitv hi naheen hai. yadi ithar hi naheen hai to nirpeksh maanak ka bhi astitv naheen ho sakta. at: gati keval saapeksh hi ho sakti hai. bhautiki mein saamaanyat: gati ka maapan karne ke liye athva fal vyakt karne ke liye kisi bhi ek paddhati ka nirdesh (refreins) dekar kaarya kiya jaata hai. kintu in nirdeshak paddhatiyon mein koi bhi paddhati 'vishishtataapoorn' naheen ho sakti, kyonki yadi aisa hota to us 'vishishtataapoorn' nirdeshak paddhati ko ham vishraanti ka maanak samajh sakte. anek prayogon se aisa hi fal praapt hua.

in prayogon ke falon se keval bhautiki mein hi naheen, balki vigyaan tatha darshan mein bhi gambhir ashaanti utpann hui. 20veen shataabdi ke praarambh mein (1904 mein) prasiddh French ganitjnya H. pauinkaare ne aapekshikta ka praniym prastut kiya . inke anusaar bhautiki ke niyam aise svaroop mein vyakt hone chaahiye ki ve kisi bhi prekshak (dekhanevaale) ke liye vaastavik hon. iska arth yeh hai ki bhautiki ke niyam prekshak ki gati ke oopar avalanbit na rahein. is praniym se dik (space) tatha kaal (time) ki prachalit dhaaranaaon par naya prakaash pada. is vishay mein aainstaain ki vichaaradhaara, yadyapi vah kraantikaarak thi, prayogon ke falon ko samajhaane mein adhik safal rahi. aainstaain ne gati, tvaran, dik, kaal ityaadi maulik shabdon ka aur unase sanyukt prachalit dhaaranaaon ka vishesh vishleshan kiya. is vishleshan se yeh spasht hua ki nyootan ke siddhaanton par aadhaarit tatha pratishthit bhautiki mein trutiyaaain hain.

aainsteen praneet aapekshikta siddhaant ke do vibhaag hain :

  • (1) vishisht aapekshikta siddhaant, aur
  • (2) saamaanya aapekshikta siddhaant.

vishisht aapekshikta siddhaant mein bhautiki ke niyam is svaroop mein vyakt hote hain ki ve kisi bhi atvarit prekshak ke liye samaan honge. saamaanya aapekshikta siddhaant mein bhautiki ke niyam is prakaar vyakt hote hain ki ve prekshak ki gati se svatantr ya abaadhit honge. vishisht aapekshikta siddhaant ka vikaas 1905 mein hua aur saamaanya aapekshikta siddhaant ka vikaas 1915 mein hua.

vishisht aapekshikta

thumb|250px| E = m c 2 {\displaystyle E=mc^{2}} iska pratipaadan san 1905 mein aainsteen ne apne ek shodhapatr on the elektrodaainemiks of mooving baudeej mein ki thi. vishisht saapekshata do pariklpanaaon (pauschulets) par aadhaarit hai jo shaastreeya yaantriki (klaasikl mekainiks) ke sankalpanaaon ke viruddh (ulate) hain:

(1) bhautiki ke niyam ek doosare ke saapeksh ekasamaan (yoonifaarm) gati kar rahe sabhi nirikshakon ke liye samaan hote hain. (gaililiyo ka saapekshikta ka siddhaant)
(2) nirvaat mein prakaash ka veg sabhi nirikshakon ke liye samaan hota hai chaahe un sabki saapeksh gati kuchh bhi ho, chaahe prakaash ke srot ki gati kuchh bhi ho.

vishisht aapekshikta ke siddhaant se nikalne vaale parinaam aashcharyajanak hain; inmein se kuchh is prakaar hain:

  • kisi sthir ghadi ki apeksha ek gatisheel ghadi dheemi chalti hai. (time dileshan) (Time dilation)
  • kisi nireekshak ke saapeksh kisi disha mein gatisheel vastuon ki lambaai us disha mein ghat jaati hai. (Length contraction)
  • do ghatanaayein jinhein koi nireekshak 'k' ek saath (simultaneous) ghatit hota hua dekhta hai, kisi doosare nireekshak 'kh' ko ve ek saath ghatit hoti hui naheen dikheingi yadi doosra nireekshak pehle ke saapeksh gatisheel hai. (Relativity of simultaneity)
  • dravya aur oorja tulya hain; ek ko doosare ke roop mein badla ja sakta hai. is parivartan mein E = mc2 ka sambandh laagoo hota hai.

shaastreeya yaantriki mein gaililiyo ka roopaantaran (Galilean transformations) prayukt hota hai jabki vishisht saapekshata mein lorents roopaantaran (Lorentz transformations).

saamaanya aapekshikta

mukhya lekh: saamaanya aapekshikta

san 1907 se 1911 ke beech aainsteen dvaara viksit aapekshikta siddhaant hi 'saamaanya aapekshikta' ke naam se jaana jaata hai.yeh siddhaant nimnalikhit do pariklpanaaon par aadhaarit hai-

  • (1) aapekshikta niyam, aur
  • (2)gurutvaakarshaneeya tatha jadtv (inarshiya) par aashrit dravyamaanon ki samaanata.

lambaai, dik (space), kaal, dravyamaan, oorja ityaadi ke vishay mein bhotiki mein jo dhaaranaaeain theen unamein vishisht aapekshikta siddhaant ne sudhaar kiya. inke atirikt bhautiki ke kshetr mein anya vishay hain jo utane hi mahatvapoorn hain, kintu unka samaavesh vishisht aapekshikta siddhaant mein naheen hai. bal tatha vidyutachumbakeeya kshetron mein vishisht aapekshikta siddhaant ka jaisa upayog ho sakta hai vaisa gurutveeya kshetr mein naheen ho sakta. gurutvaakarshan bhautiki ka ek atyant mahatvapoorn vibhaag hai, at: spasht hai ki vishisht aapekshikta siddhaant ko vyaapak banaane ki aavashyakta hai.

dravyamaan ka sambandh bhautiki mein do prakaar se aata hai. kisi pind par jab bal kaarya karta hai tab pind ka sthaan badalta hai aur usaka veg badalta hai. jab tak bal kaarya karta hai tab tak pind ko tvaran milta hai. yaantriki ke niyamon ke anusaar bal (F), pind ka dravyamaan (m) aur tvaran (a) mein nimnalikhit sambandh hai :

F = ma -- (1)

is sameekaran mein jo dravyamaan m hai usako jadtv ya aashrit (athva avasthititveeya) dravyamaan kehte hain. dravyamaan ka doosra sambandh nyootan ke guruttveeya kshetr mein aata hai. nyootan dvaara diye gaye gurutvaakarshan ke siddhaant ke anusaar yadi do dravyamaan, m1 tatha m2, doori r par hon, to unke beech mein nimnalikhit gurutvaakarshaneeya bal F kaam karega :

F = G m1 m2 / r2 -- (2)

is sameekaran mein G gurutvaakarshan sthiraank hai. yadi ham m1 ko pruthvi ka dravyamaan samajhein aur m2 ko dharati ke paas sthit kisi anya pind ka dravyamaan samajhein to sameekaran (2) dravyamaan m2 ka bhaar vyakt karega. nyootan ki yaantriki mein gativijnyaaan tatha gurutvaakarshan svatantr aur bhinn hain, kintu donon mein hi dravyamaan ka sambandh aata hai. dravyamaan ke in do svatantr tatha bhinn vibhaagon mein prayukt kalpanaaon ka ekeekaran aainstaain ne apne saamaanya aapekshikta siddhaant mein kiya. yeh gyaat tha ki jadtv par aashrit dravyamaan (sameekaran 1) aur gurutveeya dravyamaan (sameekaran 2) samaan hote hain. aainstaain ne dravyamaan ki is samaanata ka upayog karke gativijnyaaan aur gurutvaakarshan ko ekaroop kiya aur san 1915 E. mein vyaapak aapekshikta siddhaant prastut kiya.

saamaanya aapekshikta siddhaant ko ganit mein sootrit karne ki jo paddhati hai vah anya paddhatiyon se bhinn hai. ismein vishesh jyaamiti ka upayog kiya jaata hai, jo yooklid ki tri-aayaami jyaamiti se bhinn hai. minkovski ne yeh bataaya ki yadi vishisht aapekshikta siddhaant mein dik ke teen aayaam tatha samay ka chaturth aayaam, in chaaron aayaamon ko lekar ek 'chaturaayaam satati' (for daaimeinshanal kauntinuam), ki kalpana ki jaae to aapekshikta siddhaant adhik saral ho jaata hai. samakshanikta, nirpeksh naheen hai - yeh pramaanit kiya ja chuka hai. isse nyootan praneet dik tatha samay ki nirpekshata aur svatantrata samaapt ho jaati hai. at: bhautik ghatna vyakt karne ke liye dik tatha samay ki chaturaayaam satati adhik svaabhaavik hai. reemaan ne 'chaturaayaam dik' ki kalpana karke usaki jyaamiti ka jo vikaas kiya tha usaka aainstaain ne adhik upayog kiya. dik tatha samay ki is chaturaayaam satati mein bhautiki ke siddhaant jyaamiteeya roop se saamaanya aapekshikta siddhaant mein rakhe gaye. is chaturaayaam satati ka (athva 'vishv' ka) yuklid ke teen aayaam ke dik se saamya hai. teen aayaam ki satati mein, (x, y, z) in teen nirdeshaankon se (athva aayaamon se) jis prakaar bindu athva ek sthaan nishchit hota hai, vaise hi do bindu (x1, y1, z1) aur (x2, y2, z2) ke beech ki lanbaai bhi nishchit hoti hai. chaturaayaam satati mein dik ke (x, y, z) in teen aayaamon ke saath jab samay bhi joda jaata hai tab samay ka aayaam (vima) roop t = x0.5c-1 aata hai, jahaaain t = samay aur c = prakaash ka veg hai. ek prekshak ke liye ek vishvaghatana ke nirdeinshaank (x, y, z, t) hon to us prekshak ke saapeksh gatimaan doosare prekshak ke liye usi ghatna ke nirdeshank (x', y', z', t') honge. loreinj ke roopaantaran ke niyam yadi yathaarth hon to siddh kiya ja sakta hai ki

--- (3)

sameekaran (3) ka vikaas karke kisi bhi prakaar ki gati ke liye isi prakaar ki kintu atyadhik sanmishr padasanhatiyaaain milti hain. iske liye nishchalon (invairiyeaints) aur pradishon (tensars) ke siddhaanton ki aavashyakta hoti hai. maulik kalpanaaon ka is reeti se vistaar karne par vyaapak aapekshikta siddhaant mein gurutvaakarshan svabhaavat: aata hai. uske liye vishisht pariklpanaaon ki aavashyakta naheen haati hai.

saamaanya aapekshikta siddhaant ke falon ka pramaan

anek ghatnaaon ke fal, aainstaain praneet vyaapak aapekshikta siddhaant ke anusaar tatha nyootan praneet pratishthit yaaaintriki ke anusaar, samaan hi hote hain. kintu khagoliki mein jab saamaanya aapekshikta siddhaant ka upayog kiya gaya tab teen ghatnaaon ke fal pratishthit yaaaintriki (klaasikl mekeniks) ke anusaar nikle falon se kuchh bhinn rahe. in falon se saamaanya aapekshikta siddhaant ki kasauti ka kaam le sakte hain. ye teen fal is prakaar hain:

  • (1) anek varshon se yeh gyaat tha ki budh grah ki pratyaksh kaksha nyootan ke siddhaanton ke anusaar naheen rahati. ganana ke pashchaat yeh pramaanit hua ki saamaanya aapekshikta siddhaant ke kshetr sameekaranon ke anusaar budh grah ki jo kaksha aati hai vah prekshit kaksha (observed orbit) ke anuroop hai. usi prakaar pruthvi ki pratyaksh kaksha bhi nyootan ke siddhaanton ke anusaar naheen hain, kintu pruthvi ki kaksha mein truti budh grah ki kaksha ki truti se bahut kam hai. to bhi kaha ja sakta hai ki pruthvi ki kaksha ki ganana mein saamaanya aapekshikta siddhaant safal raha. at: is vishaal maapakramon ki ghatnaaon mein jahaaain pratishthit yaaaintriki asafal thi vahaaain saamaanya aapekshikta siddhaant safal raha.
  • (2) saamaanya aapekshikta siddhaant ki doosari kasauti prakaash ki vakreeyata hai. prakaash ki kirnein jab teevr gurutvaakarshan kshetr mein se hokar jaati hain, tab saamaanya aapekshikta siddhaant ke anusaar unka path alp maatra mein vakr (tedha) ho jaata hai. prakaash, oorja ka hi ek svaroop hai. at: oorja evam dravyamaan ke sambandh ke anusar prakaash mein bhi dravyamaan hota hai aur dravyamaan ko aakarshit karna gurutvaakarshan kshetr ka gun hone ke kaaran prakaashakirn ka path aisi sthiti mein thodi maatra mein tedha ho jaata hai. is fal ki pareeksha keval sarvasooryagrahan ke samay ho sakti hai. kisi taare ka prakaash soorya ke nikat se hokar nikle to prakaash ke maarg ko alp maatra mein vakr ho jaana chaahiye aur isliye taare ki aabhaasi sthiti badal jaani chaahiye. saamaanya aapekshikta ke is fal ko naapane ka prayatn 1919, 1922, 1927, 1947 ityaadi varshon mein sarv sooryagrahan ke samay kiya gaya. pata chala ki prakaashakirn ke path ki maapit vakrata aur vyaapak aapekshikta siddhaant ke anusaar nikli vakrata mein itna sookshm antar hai ki ham yeh kah sakte hain ki ye prekshan saamaanya aapekshikta siddhaant ka samarthan karte hain.
  • (3) saamaanya aapekshikta siddhaant ki teesari pareeksha gurutvaakarshaneeya kshetr ke kaaran varn-kram-rekhaaon (spektrauskopik lines) ka sthaanaantaran hai. is vaad ke anusaar jo taare teevr gurutveeya kshetr mein hain unke kisi vishesh tatv ke paramaanuon se nikle prakaash ka tarangadairghya pruthvi ke usi tatv ke paramaanuon ke prakaash-tarang-dairghya se adhik hoga. at: taare ke kisi ek tatv ke prakaash ke varnakram aur prayogashaala mein praapt usi tatv ke varnakram ki tulana se tarangadairghya ke parivartan ka maapan ho sakta hai. anek nireekshanon ke fal saamaanya aapekshikta siddhaant ke anuroop hain, yadyapi kuchh prekshakon (fऱaaaeaindalikh aadi) ke anusaar sab fal saamaanya aapekshikta siddhaant ke anuroop naheen hain.

inhein bhi dekhein

sandarbh

  1. aainsteen, A (1916 (anuvaar 1920)), riletiviti: the special end general theory, new yaurk: H holt end company
  2. plaink, maiks (1906), "the mejrmeint of kaufamain on the diflektibiliti of beeta rej in deyar impaurtains faur the daayanemiks of the ilektrauns", Physikalische Zeitschrift 7: 753-761
  3. Miller, arthar, I (1981), albart aainshteens special theory of riletiviti. imarjens (1905) end arli intarpriteshan (1905-1911), reeding: edeesan-velesli, aai॰aऍsa॰abee॰aऍna॰ 0-201-04679-2

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