
samvartita kii saapekshata

bhautiki mein, samvartita kii saapekshata yeh avadharana haye kii "door kii samvartita"-kyaa dou sthaanik roop seey alag ghatanaaen ack hii samay mein hoti hain-nirpeksh naheen haye, lekin paryavekshak key sandarbh dhaanche parr nirbhar karati haye. iss sambhavana koo 1900 mein ganitshastri heinry poinkere dwara uthaaya gayaa thaa, aur usake baad saapekshata key vishesh siddhant mein ack kendriya vichaar bunn gayaa.
varnan.
albert einstein dwara prastut saapekshata key vishesh siddhant key anusaar, "nirpeksh" arth mein yeh kahana asambhav haye kii dou alag-alag ghatanaaen ack hii samay mein hoti hain yadi una ghatnaaon koo antariksh mein alag kiya jaataa haye. yadi ack sandarbh frame dou ghatnaaon koo thheek ack hii samay nirdhaarit kartaa haye joe antariksh mein alag-alag binduon parr hain, tou ack sandarbh frame joe pahale key saapeksh chala rhaa haye, aam taur parr dou ghatnaaon koo alag-alag samay nirdhaarit karega (ekmatra apavaad taba haye jaba gati donon ghatnaaon key sthaanon koo jodane vaali rekha key thheek lambavat hoe).
udaaharan key liye, landan mein ack kaar durghatana aur newyork mein ack anya durghatana, joe prithvi parr ack paryavekshak key saath ack hii samay mein hoti dikhaai detee haye, landan aur newyork key beach udaan bharane vaale havaai jahaaj parr ack paryavekshak key liye thode alag samay parr hui hogi. isake alawa, yadi donon ghatnaaon koo kaaran seey jodaa naheen jaa sakata haye, tou gati kii sthiti key aadhar parr, landan mein durghatana pahale ack diye gaye frame mein hoe sakati haye, aur newyork durghatana pahale dusare mein hoe sakati haye. haalaanki, yadi ghatanaaen kaaran seey judee hui hain, tou sandarbh key sabhi frames mein vareeyata crum sanrakshit haye.
itihas.
1892 aur 1895 mein, hendrick lorentz ney nakaratmak eather drift prayogon koo samajhaane key liye "sthaaniya samay" t '= t-v x/c "2 naamak ack ganitiya vidhi kaa upayog kiya. haalaanki, lorentz ney iss prabhaav kaa koee bhautik spashteekaran naheen diyaa. yeh heinry poinkere dwara kiya gayaa thaa, jinhone pahale seey hii 1898 mein samkaaleentaa kii paaramparik prakriti parr jore diyaa thaa aur jinhone tark diyaa thaa kii sabhi dishaaon mein prakaash kii gati kii sthirata koo sthaapit karna suvidhajanak haye. haalaanki, iss pepper mein lorentz key siddhant yaa gati kii vibhinn sthitiyon mein paryavekshakon key liye samvartita koo paribhaashit karane mein sambhaavit antar kii koee charcha naheen thee.
yeh 1900 mein kiya gayaa thaa, jaba sanket sthaaniya samay koo yeh maanate hue praapt kiya gayaa thaa kii prakaash kii gati eather key bheetar aparivartaniya haye. saapeksh gati key siddhant" key kaaran, eather key bheetar chalane vaale paryavekshak yeh bhee maanate hain kii way aaraam parr hain aur prakaash kii gati sabhi dishaaon mein sthir haye (kewal "v/c" mein pahale crum mein). isaliye, yadi way prakaash sanketon kaa upayog karke apani ghadiyon koo samkaalik karate hain, tou way kewal sanketon key liye pargaman samay parr vichaar karenge, lekin eather key sambandh mein unaki gati parr naheen. isaliye chalati ghadiyaan samkaalik naheen hoti hain aur "sahee" samay kaa sanket naheen detee hain. poinkere ney ganana kii kii yeh samkraman truti lorentz key sthaaniya samay seey mell khaati haye.
1904 mein, poinkere ney saapekshata key siddhant, "sthaaniya samay" aur prakaash gati aparivartaniyata key beach sambandh parr jore diyaa; haalaanki, usa pepper mein tark koo gunaatmak aur anumanatmak tareeke seey prastut kiya gayaa thaa.
albert einstein ney 1905 mein "v/c", i mein sabhi aadeshon key liye samay parivartan praapt karane key liye ack samaan vidhi kaa upayog kiya.ee., poorna lorentz parivartan. poinkere ney 1905 mein pahale poorna parivartan praapt kiya thaa, lekin usa varsh key patron mein unhone apani samkraman prakriya kaa ullekh naheen kiya thaa. yeh vyutpatti poori tarah seey prakaash gati avyaavaran aur saapekshata siddhant parr adharit thee, isaliye einstein ney nott kiya kii gatishil nikaayon key vidyut gatiki key liye eather anaavashyak haye. iss prakaar, lorentz aur poinkere key "sahee" aur "sthaaniya" samay mein algaav gayab hoe jaataa haye-sabhi samay samaan roop seey maanya hotey hain aur isaliye lambai aur samay kii saapekshata ack praakritik parinam haye.
1908 mein, herman minkowski ney brahmand key apane model mein ack kann kii vishva rekha kii avadharana pesh kii jise minkowski space kahaa jaataa haye. minkowski key vichaar mein, wegg kii saral dhaarana koo teji seey badal diyaa jaataa haye, aur samvartita kii samanya bhavna teji seey judee vishva rekha key liye sthaanik dishaaon kii atee-maukhik orthogonality parr nirbhar hoe jaati haye. phir sandarbh key pratyek jadatviya frame mein ack teji aur ack saath hyperplane hotaa haye.
1990 mein robbert goldblatt ney "orthogonality aur spacetime jyaamiti" likhi, joe seedhe minkovsky kii sanrachana koo sambodhit karati haye joe ack saath rakhane key liye rakhee gaee thee. 2006 mein max jammer ney project muse key madhyam seey "samkaaleentaa kii avadhaaranaaenh pracheen kaal seey laker einstein aur usase aage" prakaashit kii. pustak adhyaay 6 mein samaapt hoti haye, "samkaaleentaa kii saapeksh avadharana mein sankraman". jammer ingit kartaa haye kii ernst mack ney neutonian bhautiki key poorna samay koo demytholose kiya.
swabhavik roop seey ganitiya dhaaranaaen bhautik vyakhya seey pahale kii jaati theen. udaaharan key liye, ack atidhruv key sanyugmit vyaas, sthaan aur samay key roop mein sambandhit hain. saapekshata key siddhant koo usa manmaanepan key roop mein vyakt kiya jaa sakata haye jisaki jodee koo ack tala mein sthaan aur samay kaa pratinidhitva karane key liye liya jaataa haye.
vichaar prayog.
einstein kii train.
einstein key prayog key sanskaran mein yeh anuman lagaaya gayaa thaa kii ack paryavekshak tej gati seey chalane vaale trainker key beach mein baithaa thaa aur doosara ack platform parr khadaa thaa kyonki train aage badh rahee thee. jaisa kii khade paryavekshak dwara maapa jaataa haye, train ack saath bijli key dou boult seey takaraati haye, lekin train kii gati key aksh (train kaar key peechhe aur saamane) key saath alag-alag sthitiyon mein hoti haye. sthaayi paryavekshak key jadatviya dhaanche mein, teen ghatanaaen hoti hain joe sthaanik roop seey visthaapit hoti hain, lekin ack saathah sthaayi paryavekshak gatishil paryavekshak kaa saamana curr rhaa hotaa haye (i.ee., train key kendra mein), train kaar key saamane bijli girati haye, aur kaar key peechhe bijli girati haye.
choonki ghatnaaon koo train kii gati key aksh key saath rakhaa jaataa haye, isaliye unake samay nirdeshank chalati train key jadatviya frame mein alag-alag samay nirdeshank key liye prakshepit hoe jaate hain. train kii gati kii disha mein antariksh nirdeshank parr honey vaali ghatanaaen train kii gati kii disha key vipareet nirdeshank parr honey vaali ghatnaaon kii tulanaa mein "pahale" hoti hain. chalati train key jadatviya frame mein, iska matlab haye kii bijli train kaar key saamane "isase pahale" takaraayegi kii donon paryavekshak sanrekhit hoe jaaen (ack dusare kaa saamana karein).
train aur platform.
iss vichaar koo samajhane key liye ack lokpriya tasveer 1910 mein daniel frost comstock aur 1917 mein einstein dwara sujhaae gaye vichaar prayog key samaan ack vichaar prayog dwara pradaan kii gaee haye. isamen ack paryavekshak bhee hotaa haye joe ack tej gati vaale trenkar key beach mein hotaa haye aur ack anya paryavekshak ack munch parr khadaa hotaa haye kyonki train aage badhati haye. 
jaise hii dou paryavekshak ack dusare seey gujarate hain, tranker key kendra mein prakaash kii ack chamak dee jaati haye. train mein savaar paryavekshak key liye, trenkar kaa aage aur peechhe prakaash srot seey nishchit doori parr hotaa haye aur iss paryavekshak key anusaar, prakaash ack hii samay mein trenkar key saamane aur peechhe taka pahunch jaayega.
munch parr khade paryavekshak key liye, doosari or, tranker kaa pichla hissa usa bindu kii or badh rhaa haye (pakad rhaa haye) jiss parr flashes diyaa gayaa thaa, aur tranker kaa agala hissa isase door jaa rhaa haye. choonki prakaash kii gati sabhi paryavekshakon key liye sabhi dishaaon mein seemit aur samaan haye, isaliye train key peechhe kii or jaane vaale prakaash mein aage kii or jaane vaale prakaash kii tulanaa mein cumm doori hogi. iss prakaar, prakaash kii chamak vibhinn samay parr trenkar key siron parr prahaar karegi.
antarikshakaal aarekh.
spacetime aarekh kaa upayog karke iss sthiti kii kalpana karna sahayak hoe sakata haye. kissy diye gaye paryavekshak key liye, "tii"-aksh koo sthaanik nirdeshank "aiks" kii utpatti dwara samay mein pataa lagaaya gayaa ack bindu key roop mein paribhaashit kiya gayaa haye, aur ise urdhvaadhar roop seey kheencha gayaa haye. x"-aksh koo "t" = 0 key samay sthaan mein sabhi binduon key samooh key roop mein paribhaashit kiya gayaa haye, aur kshaitij roop seey kheencha gayaa haye. yeh kathan kii prakaash kii gati sabhi paryavekshakon key liye samaan haye, paryavekshak kii gati key saapeksh srot kii gati kii parwah kiye binaa, 45° rekha key roop mein ack prakaash kiran kheenchkar darshaaya jaataa haye.
pahale aarekh mein, train key dou chhor dhusar rekhaaon key roop mein kheenche gaye hain. kyonki train key chhor train parr paryavekshak key sambandh mein sthir hotey hain, yeye laainen kewal urdhvaadhar rekhaaen hoti hain, joe samay key madhyam seey apani gati dikhaati hain lekin sthaan naheen. prakaash kii chamak koo 45° laal rekhaaon key roop mein dikhaaya gayaa haye. jinn binduon parr dou prakaash chamak train key siron seey takaraate hain, way aarekh mein ack hii star parr hotey hain. iska matlab haye kii ghatanaaen ack saath hoti hain.
dusare aarekh mein, train key dou chhor daaeen or badhate hue, samanantar rekhaaon dwara dikhaae gaye hain. train key dou siron key beach thheek aadhe raaste parr prakaash kii chamak koo bund curr diyaa jaataa haye, aur phir seey dou 45° rekhaaen banati hain, joe prakaash kii gati kii sthirata koo vyakt karati hain. haalaanki, iss tasveer mein, jinn binduon parr prakaash train key siron seey takaraata haye, way ack hii star parr "naheen" hain; way ack saath "naheen" hain.
lorentz parivartan.
samvartita kii saapekshata koo lorentz parivartan kaa upayog karke pradarshit kiya jaa sakata haye, joe ack paryavekshak dwara upayog kiye jaane vaale nirdeshank koo pahale key sambandh mein samaan saapeksh gati mein dusare dwara upayog kiye jaane vaale nirdeshank seey sambandhit haye.
maan leejiye kii pahala paryavekshak "t", "x", "y" aur "z" label vaale nirdeshank kaa upayog kartaa haye, jabaki doosara paryavekshak "t′", "x′", "y′", aur "z′" label vaale nirdeshank kaa upayog kartaa haye. abb maan leejiye kii pahala paryavekshak dusare paryavekshak koo "x"-disha mein "v" wegg seey aage badhate hue dekhta haye. aur maan leejiye kii paryavekshakon key nirdeshank aksh samanantar hain aur unakaa mool ack hii haye. phir lorentz parivartan vyakt kartaa haye kii nirdeshank kaise sambandhit hainh
sootra _ 1
sootra _ 2
sootra _ 3
sootra _ 4
jahan "c" prakaash kii gati haye. yadi dou ghatanaaen pahale paryavekshak key frame mein ack hii samay mein hoti hain, tou unake paas "tii"-samanvaya key samaan moolya honge. haalaanki, yadi unake paas "x"-nirdeshank ("x"-disha mein alag-alag sthiti) key alag-alag maan hain, tou unake paas "t" nirdeshank key alag-alag maan honge, isaliye way usa frame mein alag-alag samay parr honge. poorna samvartita kii viphalata key liye jimmedaar shabd "vx"/"c" 2 haye.
sameekaran "t′" = sthiraank dusare (gatishil) paryavekshak key liye ("x′", "t′") samanvaya pranali mein "samvarti rekha" koo paribhaashit kartaa haye, thheek usee tarah jaise sameekaran "t" = sthiraank ("x", "t") samanvaya pranali mein pahale (sthir) paryavekshak key liye "samvarti rekha" koo paribhaashit kartaa haye. lorentz parivartan key liye uparokt samikaranon seey yeh dekhaa jaa sakata haye kii "t" sthir haye yadi aur kewal tabhi jaba "t" − "vx"/"c" 2 = sthir haye. iss prakaar "tii" koo sthir banaane vaale binduon kaa samooh una binduon key sett seey alag hotaa haye joe "tii" koo sthir banaate hain. arthaat, ghatnaaon kaa samooh jise ack saath maanaa jaataa haye, tulanaa karane key liye upayog kiye jaane vaale sandarbh key dhaanche parr nirbhar kartaa haye.
graphical roop seey, ise ack spacetime aarekh parr iss tathya seey darshaaya jaa sakata haye kii ack saath maane jaane vaale binduon key samooh kaa ack plot ack rekha utpann kartaa haye joe paryavekshak parr nirbhar kartaa haye. antariksh kaal aarekh mein, dashes rekha prakaash kii gati key ack chauthai key wegg "v" key saath aage badhane vaale paryavekshak dwara mool key saath ack saath maane jaane vaale binduon key ack samooh kaa pratinidhitva karati haye. binduon vaali kshaitij rekha ack sthir paryavekshak dwara mool key saath ack saath maane jaane vaale binduon key samooh kaa pratinidhitva karati haye. iss aarekh koo sthir paryavekshak key ("x", "t") nirdeshank kaa upayog karke kheencha gayaa haye, aur ise iss tarah seey maapa gayaa haye kii prakaash kii gati ack, i hoe.ee.taaki prakaash kii ack kiran koo "x" aksh seey 45° konn vaali rekha dwara darshaaya jaa sakey. hamaare pichhale vishleshan seey, yeh dekhate hue kii "v" = 0.25 aur "c" = 1, samvartita kii dashes rekha kaa sameekaran "t" − 0.25 "x" = 0 haye aur "v" = 0 key saath, samvartita kii bindidar rekha kaa sameekaran "t" = 0 haye.
samanya taur parr doosara paryavekshak pahale paryavekshak key antariksh kaal mein ack vishva rekha kaa pataa lagaata haye jiska varnan "t" = "x"/"v" dwara kiya gayaa haye, aur dusare paryavekshak (mool mein) key liye ack saath honey vaali ghatnaaon key samooh kaa varnan rekha "t" = "vx" dwara kiya gayaa haye. hyperbolic orthogonality key siddhant key anusaar, vishva rekha kii dhalanon aur ack saath honey vaali ghatnaaon key gunak vyutkram sambandh koo nott karein.
twarit paryavekshak.
oopar dee gaee lorentz-parivartan ganana vistaarit-samvarti (i.ee. kaba aur kahaan ghatanaaen hoti hain "jiss parr aap maujood naheen they") jise saha-gatishil yaa "sparshrekha mukt-tair-frame" paribhasha key roop mein sandarbhit kiya jaa sakata haye. yeh paribhasha swabhavik roop seey gurutvaakarshan-ghumaavdaar sthaankaal mein ghatnaaon key liye bahishkrit haye, aur twarit paryavekshakon key liye, radar-samay/doori paribhasha key upayog key madhyam seey joe (twarit frame key liye sparshrekha mukt-tair-frame paribhasha key vipareet) kissy bhee ghatana key liye ack advitiya samay aur sthiti nirdhaarit karati haye.
vistaarit-ack saath kii radar-samay paribhasha aage usa tareeke key drishya kii suvidha pradaan karati haye joe kissy bhee gurutvaakarshan vastuon key abhaav mein yaatriyon key liye twaran antariksh samay koo modata haye. yeh daaeen or key chitra mein sachitra haye, joe sapaat antariksh kaal mein ghatnaaon key liye radar samay/sthiti isocontore koo darshaata haye jaisa kii ack yatri (laal prakshepavakra) dwara nirantar uchit-twaran roundtrip lete hue anubhav kiya jaataa haye. iss drishtikon kii ack chetavani yeh haye kii doorasth ghatnaaon kaa samay aur sthaan taba taka poori tarah seey paribhaashit naheen haye jaba taka kii aisee ghatana seey prakaash hamaare yatri taka pahunchane mein saksham naheen hoe jaataa haye.

