
ekakaalapu saapekshata

bhouthika saastramlo, ekakaalikata yokka saapekshata anedi "suduura ekakaalikata"-rendu praadesikamgaa vaeru cheyabadina sanghatanalu oke samayamlo jarugutaya-anedi sampuurnamainadi kaadu, conny pariseelakudi suuchana chatrampai aadharapadi untundi. eee avakaasaanni 1900loe ganita shaastravetta henry paayinkaare levanettaaru, aaa taruvaata pratyeka saapekshata siddhaantamlo idhi oka kendra aalochanagaa maarindi.
vivarana.
albert inestein pravesapettina pratyeka saapeksha siddhaantam prakaram, aaa sanghatanalanu antarikshamlo vaeru chesthe oke samayamlo rendu vibhina sanghatanalu jarugutaayani "sampoorna" konamlo cheppadam asadhyam. oka reference frame antarikshamlo ververu paayintla vadda unna rendu eeventlaku khachitamgaa oke samayanni ketayinchinatlayite, modatidaaniki sambandhinchi kadulutunna reference frame saadhaaranamgaa rendu eeventlaku ververu samayaalanu ketayistundi (rendu eeventla sthaanaalanu anusandhaaninche rekhaku kadalika sarigga lambamgaa unnappudu matrame minahaayimpu).
udaaharanaku, londonlo jarigina kaaru pramaadam mariyu newyorklo jarigina maroka kaaru pramaadam, bhoomipai unna pariseelakudiki oke samayamlo jariginatlu kanipistuu, london mariyu newyork madhya egurutunna vimaanamlo unna pariseelakudiki konchem bhinnamaina samayaallo jariginatlu kanipistundi. antekakunda, rendu sanghatanalanu kaaranamgaa anusandhaaninchalekapothe, chalana sthithini batti, londonlo pramaadam icchina framelo modata sambhavinchinatlu anipinchavacchu, mariyu newyork pramaadam maroka framelo modata sambhavinchinatlu kanipinchavacchu. ayithe, sanghatanalu kaaranamtho anusandhaaninchabadinatlayite, anni frame off referencelalo praadhaanyata kramam bhadraparachabadutundi.
charitra.
1892 mariyu 1895loe, hendrick lorentz pratikuula eethar drift prayogaalanu vivarinchadaaniki "lokal time" t '= t-vx/c "2 anae ganita paddhatini upayoginchaaru. ayithe, lorentz eee prabhavam gurinchi etuvanti bhouthika vivarana ivvaledu. idhi 1898loe ekakaalapu sampradaaya swabhaavaanni nokkicheppina henry paayinkaare chetha cheyabadindi, mariyu anni disalalo kaanti vegam yokka sthirathvaanni pratipaadinchadam soukaryavantamgaa untundani vaadinchaaru. ayithe, eee kaagitamlo lorentz siddhaantam gurinchi ledhaa vividha kadalika sthithulalo pariseelakulaku ekakaalaanni nirvachinchadamlo saadhyamayye vyatyaasam gurinchi etuvanti charcha ledhu.
1900loe, eethar lopala kaanti vegam asthiramgaa undani bhaavinchi sthaanika samayanni paayinkaare pondinappudu idhi jarigindi. saapeksha kadalika suutram" kaaranamgaa, eethar lopala kadile pariseelakulu vaaru visraantigaa unnaarani mariyu kaanti vegam anni disalalo sthiramgaa undani ("v/c" loe modati kramamlo matrame) bhaavistaaru. anduvalla, vaaru kaanti sankethaalanu upayoginchadam dwara tama gadiyaralanu samakaaleekaristhe, vaaru sankethaalaku ravana samayanni matrame pariganistaaru, conny eetharku sambandhinchi vaati kadalikanu pariganincharu. kabatti kadile gadiyaralu samakaaleekarinchabadavu mariyu "nijamaina" samayanni suuchimchavu. eee samakaaleekarana lopam lorentz yokka sthaanika samayaniki anugunamgaa undani paayinkaare lekkinchaaru.
1904loe, paayinkaare saapekshataa suutram, "sthaanika samayam" mariyu kaanti vegam asthirata madhya sambandhaanni nokki chepparu; ayithe, aaa kaagitamlooni tarkam gunaatmaka mariyu oohaatmaka paddhatiloo pradarsinchabadindi.
albert inestein 1905loe "v/c", i looni anni kramaalaku samaya parivartananu pondadaaniki idhe vidhamaina paddhatini upayoginchaaru.ii., puurti lorentz parivartana. 1905loe praarambhamlo paayinkaare puurti parivartananu pondaadu, conny aaa samvatsaram patraalalo athanu thana samakaaleekarana vidhananni prastaavinchaledu. eee utpannam puurtigaa kaanti vegam asthirata mariyu saapekshata suutrampai aadharapadi undhi, kabatti kadile vastuvula electrodynamics kosam eethar anavasaram anie inestein paerkonnaadu. anduvalla, lorenz mariyu paayinkaare yokka "nijamaina" mariyu "sthaanika" samayaluga vibhajana adrusyamavutundi-anni samayalu samanamga chellubaatu avtayi mariyu anduvalla podavu mariyu samayam yokka saapekshata sahaja parinaamam.
1908loe, herman minkovsky thana vishwa namoonaalo minkovsky space anie piluvabade kanaala prapancha rekha anae bhavananu pravesapettaadu. minkovsky drushtilo, vegam yokka amayaka bhavana vegamtho bharti cheyabadutundi, mariyu ekakaalapu saadhaarana bhavana vaegaaniki sambandhinchina prapancha rekhaku praadaesika disala yokka hyperbolic orthogonalitypy aadharapadi untundi. appudu prati jadatva frame off reference vegaanni mariyu ekakaala hyper plain kaligi untundi.
1990loe robbert goldblatt "orthogonality und space time jyaamiti" nuu vraasaaru, minkovsky ekakaalamlo unchina nirmaanaanni neerugaa prastaavinchaaru. 2006loe maaks jammer, project muse dwara, "ekakaalikata yokka bhaavanalanu puraatana kaalam nundi inestein varaku mariyu antaku minchi" prachurinchaadu. eee pustakam 6va adhyaayamlo mugustundi, "ekakaalapu saapeksha bhavanaku parivartana". ernst maak neutonian bhouthika shaastram yokka sampoorna samayanni demythologies chesinatlu jammer suuchistaadu.
sahajamgaane ganita bhavanalu bhouthika vivaranaku mundu undevi. udaaharanaku hyperbolaku chendina samyoga vyasalu, sthalam mariyu samayamgaa sambandham kaligi untaayi. saapekshataa suutraanni oka samatalamlo sthalam mariyu samayanni suuchimchadaaniki yea jatha yokka ekapakshamgaa teesukobadutundo vyakteekarinchavachhu.
aalochana prayogaalu.
inestein yokka railu.
inestein prayogam yokka samskaranalo oka pariseelakudu vegavantamaina trainakar lopala madhyalo kuurchunnaadani, railu munduku saagutunnappudu marokaru platformpy nilabadi unnaarani bhaavinchaaru. nilabadi unna pariseelakudu kolichinatlugaa, railu ekakaalamlo rendu boltla merupu debbatintundi, conny railu kadalika aksham venta (railu kaaru venuka mariyu mundu) ververu sthaanaalalo untundi. nilabadi unna pariseelakudi jadatva chatramlo, moodu sanghatanalu unnaayi, ivi praadesikamgaa sthaanabhramsham chendutaayi, conny ekakaalamlo untayih kadulutunna pariseelakudiki edurugaa nilabadi unna pariseelakudu (i.ii., railu madhyalo), railu kaaru mundu bhaagamlo merupu taakindi, mariyu kaaru venuka bhaagamlo merupu taakindi.
sanghatanalu railu kadalika aksham venta unchabadinanduna, vaati samaya akshaamsaalu kadulutunna railu yokka jadatva chatramlo ververu samaya akshaamsaalaku anchanaa vaeyabadataayi. railu kadalika disalo antariksha akshaamsaala vadda sambhavinche sanghatanalu railu kadalika disaku vyatiraeka disalo unna akshaamsaala vadda jarige sanghatanala kante mundugaane jarugutaayi. kadulutunna railu yokka jadatva chatramlo, iddaru pariseelakulu samalekhanam cheyadaaniki (okarinokaru edurkonadaaniki) mundu railu kaaru mundu bhaagamlo merupu taakindi anie dheeni ardham.
railu mariyu platfam.
eee aalochananu ardham chesukovadaniki oka prasiddha chitram 1910loe daniel fraast comstock mariyu 1917loe inestein suuchimchina maadirigaane oka aalochanaa prayogam dwara andinchabadindi. indulo oka pariseelakudu vegavantamaina trainakar lopala madhyalo mariyu railu munduku saagutunnappudu maroka pariseelakudu platformpy nilabadi untaaru. 
iddaru pariseelakulu okaripai okaru daatinatle trainkar madhyalo kaanti kaanti vidudala cheyabadutundi. railulo unna pariseelakudiki, trainkar mundu mariyu venuka kaanti muulam nundi nirneeta dooraalalo untaayi mariyu eee pariseelakudi prakaram, kaanti adhe samayamlo trainkar mundu mariyu venukaku cherukuntundi.
platformpy nilabadi unna pariseelakudiki, marovaipu, trainkar venuka bhaagam flash off cheyabadina sthaanam vaipu kadulutondi (paiki pattukuntundi), mariyu trainkar mundu bhaagam daani nundi dhooramgaa kadulutondi. kaanti vegam parimitamainadi mariyu anni pariseelakulaku anni disalalo okela untundi kabatti, railu venuka vaipu velle kaanti mundu vaipu velle kaanti kante takkuva dhooram untundi. anduvalla, kaanti yokka merupu ververu samayaallo trainkar chivaralanu taakutundi.
antariksha kaala rekhaachitraalu.
antariksha kaala rekhaachitraalanu upayoginchi eee paristhitini oohinchadam sahaayapadavachhu. icchina pariseelakudiki, "t"-aksham anedi praadaesika coordinate "x" yokka muulam dwara kalakramena gurtinchabadina binduvugaa nirvachinchabadindi mariyu niluvugaa geeyabadutundi. x"-aksham anedi "t" = 0 samayamlo antarikshamloni anni binduvula samitigaa nirvachinchabadindi mariyu addamgaa geeyabadutundi. pariseelakulandarikee kaanti vegam okate anae prakatana pariseelakudi vaegaaniki sambandhinchi muulam yokka vegamtho sambandham lekunda, kaanti kiranaanni 45° rekhagaa geeyadam dwara suuchimchabadutumdi.
modati rekhaachitramlo, railu yokka rendu chivaralanu budidarangu rekhalagaa geestaaru. railu yokka chivaralanu pariseelakudiki sambandhinchi niluvugaa untaayi kabatti, eee panktulu kevalam niluvu panktulu, ivi samayam dwara vaati kadalikanu chuuputaayi conny sthalam kaadu. kaanti yokka kaanti 45° errati rekhalagaa choopabadindi. rendu kaanti merupu railu chivaralanu taakina paayintlu rekhaachitramlo oke sthaayilo untaayi. antey sanghatanalu ekakaalamlo jarugutaayi.
rendava rekhaachitramlo, railu kudi vaipuku kadulutunna rendu chivaralanu samaantara rekhala dwara chuupimchaaru. railu yokka rendu chivarala madhya sarigga sagam dhooramlo kaanti yokka flash off cheyabadutundi, mariyu mallii rendu 45° linelanu yerparustundi, idhi kaanti vegam yokka sthirathvaanni vyaktam chestundi. ayithe, eee chitramlo, railu chivaralanu kaanti merustunna binduvulu oke sthaayilo "kaadu"; avi ekakaalamlo "kaadu".
lorenz parivartana.
ekakaalikata yokka saapekshatanu lorenz parivartananu upayoginchi pradarsinchavacchu, idhi oka pariseelakudu upayoginche coordinatelanu modatidaaniki sambandhinchi ekareeti saapeksha kadalikalo marokaru upayoginche coordinatelaku sambandhinchinadi.
modati pariseelakudu "t", "x", "y" mariyu "z" anie label cheyabadina coordinatelanu upayogistaadani anukundam, rendava pariseelakudu "t′", "x′", "y′" mariyu "z′" anie label cheyabadina coordinatelanu upayogistaadani anukundam. ippudu modati pariseelakudu rendava pariseelakudu "x"-disalo "v" vegamtho kadulutunnatlu chuustaadani anukundam. mariyu pariseelakula samanvaya akshalu samaantaramgaa unnayani mariyu vatiki oke muulam undani anukundam. appudu lorenz parivartana akshaamsaalu elaa sambandham kaligi unnayo vyakteekaristundih
suutram _ 1
suutram _ 2
suutram _ 3
suutram _ 4
ikkada "c" anedi kaanti vegam. modati pariseelakudi chatramlo oke samayamlo rendu sanghatanalu jarigithe, avi "t"-samanvaya viluvalanu kaligi untaayi. ayithe, avi "x"-samanvayaaniki ("x"-disalo ververu sthaanaalu) ververu viluvalanu kaligi unte, avi "t" samanvayaaniki ververu viluvalanu kaligi untaayi, kabatti avi aaa framelo ververu samayaallo jarugutaayi. sampoorna ekakaalika vaiphalyaaniki kaaranamayye padam "vx"/"c" 2.
t" = sthiraamkam anedi rendava (kadile) pariseelakudiki ("x′", "t′") samanvaya vyavasthalo "ekakaalika rekha" nuu nirvachistundi, adhe vidhamgaa sameekaranam "t" = sthiraamkam ("x", "t") samanvaya vyavasthalo modati (sthira) pariseelakudiki "ekakaalika rekha" nii nirvachistundi. lorentz parivartana kosam paina perkonna sameekaranaala nundi "t" − "vx"/"c" 2 = sthiramgaa unte matrame "t" sthiramgaa untundani chudavachu. anduvalla "t" nii sthiramgaa chese paayintla samiti "t" nii sthiramgaa chese paayintla samitiki bhinnamgaa untundi. antey, ekakaalamlo pariganinchabade sanghatanala samiti poolika cheyadaaniki upayoginche suuchana framepy aadharapadi untundi.
ekakaalamlo pariganinchabade paayintla samiti yokka plaat pariseelakudipai aadhaarapade oka geetanu utpatti chestundi anae vaastavam dwara dheenini graphicalga, antariksha kaala rekhaachitramlo suuchimchavachchu. antariksha kaala rekhaachitramlo, dashed line anedi kaanti vegamlo naaluginta oka vanthu vegamtho kadulutunna pariseelakudi dwara muulamtoe ekakaalamlo pariganinchabade paayintla samitini suuchistumdi. chukkala kshitija samaantara rekha anedi sthira pariseelakudu muulamtoe ekakaalamlo pariganinche paayintla samitini suuchistumdi. eee rekhaachitram sthira pariseelakudi ("x", "t") akshaamsaalanu upayoginchi geeyabadutundi mariyu kaanti vegam okati, i gaa undela scale cheyabadutundi.ii., tadwara kaanti kiranaanni "x" aksham nundi 45° konamtho oka rekha dwara suuchistaaru. mana munupati vislaeshanha nundi, "v" = 0.25 mariyu "c" = 1 ichinatlayithe, ekakaalikata yokka dashed line yokka sameekaranam "t" − 0.25 "x" = 0 mariyu "v" = 0 thoo, chukkala line yokka sameekaranam "t" = 0.
saadhaaranamgaa rendava pariseelakudu "t" = "x"/"v" dwara varninchabadina modati pariseelakudi antariksha samayamlo oka prapancha rekhanu kanugontaadu mariyu rendava pariseelakudiki (muulam vadda) ekakaala sanghatanala samitini "t" = "vx" rekha dwara vivaristaaru. hyperbolic orthogonality suutraaniki anugunamgaa, prapancha rekha yokka vaalulu mariyu ekakaala sanghatanala yokka gunakaara viloma sambandhaanni gamaninchandi.
vegavantamaina pariseelakulu.
paina perkonna lorentz-transform ganana podiginchina-ekakaala nirvachanam (i.ii. meeru laeni chota") eppudu, ekkada sanghatanalu jarugutaayi anedaanini koo-moving ledhaa "tangent free-float-frame" nirvachanam anie suuchimchavachchu. eee nirvachanam sahajamgaa gurutvakarshana-vakra sthala samayaalloni sanghatanalaku mariyu vegavantamaina pariseelakulaku, radar-samayam/dhoora nirvachananni upayoginchadam dwara (vegavantamaina framelaku tangent free-float-frame nirvachanam vale kakunda) edainaa sanghatanaku pratyaekamaina samayam mariyu sthaanaanni ketayistundi.
podiginchina-ekakaalamu yokka radar-samaya nirvachanam, yea gurutvakarshana vastuvulu lenappudu prayaanikulaku tvaranam antariksha samayanni vakrapariche vidhananni drushyamaanam cheyadaaniki marinta sulabhataram chestundi. idhi kudivaipuna unna chitramlo vivarinchabadindi, idhi sthiramaina saraina-vegavantamaina roundtripnu teesukune yaatrikudu (erra patham) anubhavinchinatlugaa chadunaina antariksha samayamlooni sanghatanalaku radar samayam/sthaanam iso kaantuurlanu chooputundi. eee vidhanam yokka oka heccharika emitante, atuvanti sanghatana nundi vachhe kaanti mana prayaanikudini cherukune varaku maarumuula sanghatanala samayam mariyu pradaesam puurtigaa nirvachinchabadavu.