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Staan Gravitasie-tyddilatasie bo-op die tyddilatasie wat veroorsaak word deur snelheid?

Staan Gravitasie-tyddilatasie bo-op die tyddilatasie wat veroorsaak word deur snelheid?


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Gebruik 1 CM van die Event Horizon of Super Massive Black Hole, SGR A, as verwysingspunt. Die deeltjies binne die aanwasskyf beweeg teen uiters hoë snelhede. Neem aan dat hierdie snelheid toeneem namate die deeltjies al hoe nader aan die EH wentel.

Is die deeltjies binne die aanwasskyf van Super Massive BH SGR A onderhewig aan tyddilatasie vanaf 1) die swaartekragveld van SGR A op 1 cm vanaf Event Horizon ... en 2) van die versnelling van deeltjies wat om die BH beweeg terwyl hulle die EH nader?

Werk die versnelling van deeltjies as 'n steuring in die gevolge van die swaartekragtydverwyding? En as dit nie die geval is nie, of as hierdie twee soorte tydsverruiming die tydsintervalle vir hierdie groep deeltjies beïnvloed, wanneer sou 'n waarnemer 1 ligjaar vanaf die EH sien dat die deeltjies die EH binnegaan? A) Voordat u die EH beïnvloed, B) Nadat u die EH beïnvloed het, of C) Nooit?


Die ontdekking dat kwasars nie tydverspreiding toon nie, maak sterrekundiges verbeeld

Hierdie X-straalbeeld toon die kwasar PKS 1127-145, 'n baie ligbron van X-strale en sigbare lig wat ongeveer 10 miljard ligjare van die aarde af geleë is. Sy X-straalstraal strek minstens 'n miljoen ligjare vanaf die kwasar. Krediet: NASA.

(PhysOrg.com) - Die verskynsel van tyddilatasie is 'n vreemde, maar eksperimentele bevestigde effek van relatiwiteitsteorie. Een van die implikasies daarvan is dat dit gebeur dat gebeure wat in verafgeleë dele van die heelal voorkom, stadiger moet voorkom as wat gebeure nader aan ons is. Byvoorbeeld, by die waarneming van supernovas het wetenskaplikes gevind dat ontploffings in die verre stadiger lyk of dit vervaag as die supernovas in die omgewing.

Die effek kan verklaar word omdat (1) die snelheid van die lig konstant is (onafhanklik van hoe vinnig 'n ligbron na of van 'n waarnemer beweeg) en (2) die heelal met 'n versnelde tempo uitbrei, wat veroorsaak dat afstandsvoorwerpe na rooi verskuiwing (dws die golflengtes wat langer word) in verhouding tot hoe ver die voorwerpe van waarnemers op Aarde af is. Met ander woorde, namate die ruimte vergroot, word die interval tussen ligpulse ook verleng. Aangesien uitbreiding dwarsdeur die heelal plaasvind, blyk dit dat tyddilatasie 'n eienskap van die heelal moet wees wat oral geld, ongeag die spesifieke voorwerp of gebeurtenis wat waargeneem word. 'N Nuwe studie het egter bevind dat dit nie die geval blyk te wees nie - kwasars, lyk dit, gee ligpulse in dieselfde tempo af, ongeag hul afstand van die aarde af, sonder 'n wenk van tydverruiming.

Sterrekundige Mike Hawkins van die Royal Observatory in Edinburgh het tot hierdie gevolgtrekking gekom nadat hy na byna 900 kwasars oor periodes van tot 28 jaar gekyk het. By die vergelyking van die ligpatrone van kwasars wat ongeveer 6 miljard ligjare van ons af geleë was en dié wat 10 miljard ligjare weg was, was hy verbaas om te ontdek dat die ligtekeninge van die twee monsters presies dieselfde was. As hierdie kwasars soos die supernovas was wat vroeër waargeneem is, sou 'n waarnemer verwag om langer, 'uitgerekte' tydskale te sien vir die verre, 'gestrekte' hoë-rooiverskuiwingskwasars. Maar alhoewel die verre kwasars sterker as die nouer kwasars, rooi verskuif is, was daar geen verskil in die tyd wat dit die lig geneem het om die aarde te bereik nie.

Dit lyk asof hierdie kwasar-raaisel nie 'n voor die hand liggende verklaring het nie, hoewel Hawkins 'n paar idees het. Vir sommige agtergronde is kwasars op baie maniere ekstreme voorwerpe: dit is die mees stralende en energieke voorwerpe wat in die heelal bekend is, en ook een van die verste (en dus oudste) bekende voorwerpe. Amptelik "kwasi-sterre radiobronne" genoem, is kwasars digte streke rondom die sentrale supermassiewe swart gate in die sentrums van massiewe sterrestelsels. Hulle voer 'n aanwas-skyf af wat elke swart gat omring, wat die uiterste helderheid van die kwasars dryf en dit vir die aarde sigbaar maak.

Een van Hawkins se moontlike verklarings vir kwasars se gebrek aan tyddilatasie is dat die lig van die kwasars gebuig word deur swart gate wat deur die heelal versprei is. Hierdie swart gate, wat kort na die oerknal gevorm het, sou 'n swaartekragvervorming hê wat die tydverwyding van verre kwasars beïnvloed. Hierdie idee van "swaartekrag-mikrolensing" is egter 'n kontroversiële voorstel, want dit vereis dat daar genoeg swart gate moet wees om al die donker materie van die heelal te kan verantwoord. Soos Hawkins uitlê, voorspel die meeste fisici dat donker materie bestaan ​​uit onontdekte subatomiese deeltjies eerder as primêre swart gate.

Daar is ook 'n moontlikheid dat die verklaring nog ingrypender kan wees, soos dat die heelal nie uitbrei nie en dat die oerknalteorie verkeerd is. Of kwasars is miskien nie geleë op die afstande wat deur hul rooi verskuiwings aangedui word nie, hoewel hierdie voorstel voorheen gediskrediteer is. Alhoewel hierdie verklarings kontroversieel is, beplan Hawkins om voort te gaan met die ondersoek na die kwasar-raaisel en miskien 'n paar ander probleme onderweg op te los.

Hawkins se referaat sal in 'n komende uitgawe van die Maandelikse kennisgewings van die Royal Astronomical Society.


Antwoorde en antwoorde

Ek veronderstel dat dit die tydsenergie-verhouding tussen die energie van die aantrekkende massa en die hoeveelheid tyd wat uitgebrei word, modelleer. Ek het in die formule hierbo gekies om een ​​sekonde minus x * planck-tyd te doen, en ek het dit gedoen om te ondersoek of u die tyd met 'n sekere hoeveelheid sou vertraag, dan sou dit 'n effek op energie hê.

Om 'n bietjie duideliker te wees, kan ons sê dat ons saam op 'n tandemfiets is (dit is geen rede nie, behalwe dat jy 'n persoon lyk wat dit sal geniet :)) en ons het 'n vliegwiel op die fiets. Ons ry 10 meter per sekonde en dan vertraag ek die fiets tot 9 meter per sekonde met 'n vliegwiel. Ek het dus my spoed vertraag, maar energie van die vliegwiel opgetel.

Dit is presies wat ek probeer formuleer. Behalwe nie die verband tussen snelheid deur die ruimte en vliegwielenergie nie, bereken ek eerder die verband tussen snelheid deur die tyd en energie van die massa.

Wat my hieroor aan die dink gesit het, was die verbeelding van 'n kubieke sentimeter tyd wat stadiger gaan deur te sê vir elke sekondes wat ons 50 jaar verloop het. Laat ons nou sê dat u 'n potlood op hierdie klein kubus sentimeter moes laat val, en die massamiddelpunt van die potlode is nie perfek met die kubus nie. Ek glo dat die potlood sal optree asof dit 'n massa tref en eenkant toe spring. Aangesien massa van energie bestaan, het ek hieruit geïnterpreteer dat 'n verandering in tyd geassosieer moet word met 'n verandering in energie. Wat my dan by die swaartekragverwyding en hierdie forum gebring het.

Laat weet my as dit help om te verduidelik wat ek probeer formuleer.

Die energie van die aanloklike massa is net die massa daarvan. Dit verander nie. Die & kwotasie van die tyd wat verwyd word & quot is net die tydverwydingsformule in terme van die massa (die eerste formule in u OP).

Dit het niks met swaartekrag of tyddilatasie te make nie.

Die enigste betekenis wat ek hieraan kan toeken, is die tydverwydingsformule (die eerste formule in u OP), soos hierbo.

Ek is nie seker of ek verstaan ​​wat dit beteken nie. Is dit 'n voorwerp van 1 kubieke sentimeter in volume, wat diep in die swaartekrag van 'n massa is, sodat dit tydverruim word? Of is dit net 'n kubieke sentimeter leë ruimte wat diep in die swaartekrag is?

Die energie van die aanloklike massa is net die massa daarvan. Dit verander nie. Die & kwotasie tyd wat verwyd word & quot sou net die tydverwydingsformule wees in terme van die massa (die eerste formule in u OP).

ok, ek weet dat jy dit weet, maar ek bereken vir E in E / c ^ 2 = m. Ek het die massa vervang met energie bo c ^ 2. dit is hoe ek energie hierin bring.

Dit het niks met swaartekrag of tyddilatasie te make nie

Ek weet, ek wys jou net hoe ek tyd met energie probeer vergelyk op 'n eenvoudige manier om jou te help verstaan.


Ek is nie seker of ek verstaan ​​wat dit beteken nie. Is dit 'n voorwerp van 1 kubieke sentimeter in volume, wat diep in die swaartekrag van 'n massa is, sodat dit tydverruim word? Of is dit net 'n kubieke sentimeter leë ruimte wat diep in die swaartekrag is?

Dit is nou net 'n kubieke sentimeter leë ruimte in die palm van u hand, die enigste verskil is dat die tyd binne die grens van die grens ongelooflik stadig is. Gebruik jou verbeelding 'n bietjie.

As dit 'n voorwerp van een kubieke sentimeter is, sal dit natuurlik wees. As dit net 'n kubieke sentimeter leë ruimte is, sal die potlood nie optree soos met enige ander kubieke sentimeter leë ruimte nie. Leë ruimte is steeds leë ruimte, selfs al is dit diep in 'n swaartekragput. [/ QUOTE]

Gebruik weer u verbeelding, selfs in die aarde se swaartekrag as iets versnel / daal op 9,8 meter per sekonde ^ 2 en 'n deel daarvan val in 'n deel van die ruimte waar een sekonde regtig stadig is, sou ek argumenteer dat dit nie net eenvoudig gaan val nie daardeur asof niks daar is nie. Dit is nie in 'n swaartekragput nie.


Antwoorde en antwoorde

Ek het die nuwe program & quotInto the Universe saam met Stephen Hawking & quot gekyk, en ek was effens geïrriteerd oor sy kontras van swaartekrag en snelheidsverspreiding. Daar word gesê dat as u 'n ruimteskip neem en om 'n super massiewe swart gat wentel, u slegs 'n 2: 1 keer-uitbreiding sal kry. As u egter 'n ruimteskip neem en vinnig in 'n reguit lyn beweeg, sal u 'n onbeperkte verhouding tot tydverwyding kry.

Nou, ek is geen fisikus nie, maar ek is redelik seker dat die twee dinge een en dieselfde was, en ek het dit op my geneem om dit te bewys.

Ongelukkig het ek 'n syfer 2 ontbreek, wat 'n fout van my kant moet wees. Hopelik kan iemand die fout in my wiskunde wys.

Definisies:
[tex] m_ <1> [/ tex] = Planeet (of swart gat) massa
[tex] m_ <2> [/ tex] = Ruimteskipmassa
[tex] v_ <1> [/ tex] = Ruimteschip snelheid relatief tot [tex] m_ <1> [/ tex]
[tex] T_ <1> [/ tex] = Tyd, soos waargeneem op die oppervlak van [tex] m_ <1> [/ tex]

'N Ruimteskip wat om 'n supermassiewe swart gat (of ander liggaam) wentel, moet die snelheid hê:
[tex] v_ <1> = sqrt <> / r> [/ tex]

Lorentz-transformasie gebruik
[tex] T_ <1> = T_ <2> sqrt <1->/> [/ tex]

Vervang v met [tex] v_ <1> [/ tex]:
[tex] T_ <1> = T_ <2> sqrt <1-/> [/ tex]

Die probleem is dat ek 'n 2 nodig het om aan te pas by die formule vir swaartekragtydverwyding:
[tex] T_ <1> = T_ <2> sqrt <1- <2Gm_1> /> [/ tex]

Moet die tyddilatasie as gevolg van swaartekrag bygevoeg word by die tyddilatasie as gevolg van snelheid? IE, GPS-satelliete - moet hulle albei verantwoord?

Waar die eerste term die tydverspreiding is as gevolg van die snelheid van die sirkelbaan, en die 2de as gevolg van swaartekrag. Ek dink steeds daar is 'n probleem in my formule vir sirkelbane en dat die twee terme moet ooreenstem.

Of is ek net ver weg, en ek moet nog 'n bietjie RTFM gaan

jammer, het daardie laaste sin gemis.

Ek verstaan ​​dit, maar ek is steeds verlore met my vervanging van my formule. Hulle moet saam vermenigvuldig word, dus my laaste formule is basies 'n herskikking van pos 35 waarna u my gewys het. Die enigste verskil is dat ek v vervang het met die sirkelvormige wentelsnelheidsformule. My vraag dan, het ek my vervanging korrek uitgevoer? Ek word nog steeds afgegooi deur die ooreenkoms tussen die twee formules, die enigste verskil is daardie dom 2.

jammer, het daardie laaste sin gemis.

Ek verstaan ​​dit, maar ek is steeds verlore met my vervanging van my formule. Hulle moet saam vermenigvuldig word, dus my laaste formule is basies 'n herskikking van pos 35 waarna u my gewys het. Die enigste verskil is dat ek v vervang het deur die sirkelformule vir die wentelbaan. My vraag dan, het ek my vervanging korrek uitgevoer? Die ooreenkoms tussen die twee formules laat my nogsteeds weggooi, die enigste verskil is daardie dom 2.

Miskien verrassend, die derde wet van Kepler:

hou steeds algemene relatiwiteit in vanuit die oogpunt van 'n koördinaatwaarnemer by oneindigheid in die Schwarzschild-maatstaf.

Bogenoemde vergelyking kan weer gerangskik word om die koördinaat wentelsnelheid te verkry:

(Rhenetta was dus op die regte pad). Dinge raak ingewikkelder vir nie-sirkelbane, maar vir eers hou ek by sirkelbane.

Die plaaslike snelheid word verkry deur die gravitasietydverspreidingsfaktor toe te pas sodat:

As R op die fotonbaanradius 3GM / c ^ 2 ingestel is, is die plaaslike wentelsnelheid v = c.

Die tydverwidingsverhouding van 'n deeltjie met 'n sirkelvormige wentelbaan van radius R en plaaslike wentelsnelheid v is:

Die vergelyking wat vroeër vir v verkry is, kan direk in die bostaande uitdrukking ingevoeg word om die tydverwidingsverhouding van die wenteldeeltjie te verkry wanneer die enigste bekende veranderlikes die massa van die swart gat (M) en die baanradius (R) is:

waar T die tyd is volgens 'n waarnemer by oneindigheid en T 'die tyd volgens die wentelende deeltjie. Dit is baie maklik om te sien dat die tyddilatasie van die wentelende deeltjie onbegrens is.

1) 'n vuurpyl kan uit hierdie streek ontsnap

2) lig opwaarts gerig kan uit die streek ontsnap

3) 'n bofbal wat na bo gegooi word, kan uit hierdie streek ontsnap.

Die vergelyking wat vroeër vir v verkry is, kan direk in die bostaande uitdrukking ingevoeg word om die tydverwidingsverhouding van die wenteldeeltjie te verkry wanneer die enigste bekende veranderlikes die massa van die swart gat (M) en die baanradius (R) is:

Ek het die nuwe program & quotInto the Universe saam met Stephen Hawking & quot gekyk, en ek was effens geïrriteerd oor sy kontras van swaartekrag en snelheidsverspreiding. Daar word gesê dat as u 'n ruimteskip neem en om 'n super massiewe swart gat wentel, u slegs 'n 2: 1 keer-uitbreiding sal kry. As u egter 'n ruimteskip neem en vinnig in 'n reguit lyn beweeg, kry u 'n onbeperkte tydverwidingsverhouding.

Nou, ek is geen fisikus nie, maar ek is redelik seker dat die twee dinge een en dieselfde was, en daarom het ek dit op my geneem om dit te bewys.

Daar is 'n soort verband tussen snelheid en gravitasietyddilatasie, maar dit is die ontsnap snelheid in 'n gegewe radius wat benodig word. Die Newtonse ontsnappingssnelheid is:

Dit is die snelheid wat bereik word deur 'n deeltjie wat aanvanklik in rus by oneindigheid is (losweg) wanneer dit tot 'n radius R val, aangesien die potensiële energie daarvan omgeskakel word na kinetiese energie. Die invoeging van hierdie snelheid in die SR-tydverwyderingsvergelyking gee:

Dit is die tydverwidingsverhouding van 'n deeltjie wat by R sweef. Vir 'n deeltjie wat om R wentel, moet die gravitasietydverwyding by R vermenigvuldig word met die tyddilatasie as gevolg van die plaaslike wentelsnelheid van die deeltjie.

Daar is 'n soort verband tussen snelheid en gravitasietyddilatasie, maar dit is die ontsnap snelheid in 'n gegewe radius wat benodig word. Die Newtonse ontsnappingssnelheid is:

Dit is die snelheid wat 'n deeltjie aanvanklik in rus by oneindigheid (losweg) bereik wanneer dit in 'n radius R val, aangesien die potensiële energie daarvan omgeskakel word na kinetiese energie. Die invoeging van hierdie snelheid in die SR-tydverwydingsvergelyking gee:

Dit is die tydverwidingsverhouding van 'n deeltjie wat by R sweef. Vir 'n deeltjie wat om R wentel, moet die gravitasietydverwyding by R vermenigvuldig word met die tyddilatasie as gevolg van die plaaslike wentelsnelheid van die deeltjie.

Ek sien nie hoe ons snelheid en gravitasietyddilatasie van 'n waarnemer in 'n gravitasieveld langs die r-rigting kan beweeg nie, deur die definisie van die regte tyd uit spesiale relatiwiteit te gebruik.

As 'n waarnemer in die r rigting beweeg, verminder die Schwarzschild-maatstaf tot (sferiese simmetrie):

Die foton sfeer is die naaste wat mens ooit sou kon hoop om 'n swart gat te wentel.

Tussen die fotonfeer en die gebeurtenishorison is dit moontlik om te ontsnap, maar selfs teen ligsnelhede moet u binne 'n kegel na buite beweeg vanaf die radiale as wat na 'n piek naby die gebeurtenishorison draai.

As u tussen die fotonfeer en die gebeurtenishorison is, kan u versnel tot waar u snelheid binne die escapre-kegel is en die gebied verlaat. As u vrylik in hierdie streek val, sal u moet versnel om die gebeurtenishorison te bereik.

Op my ruimtereise wil ek meer as 10 R van die geleentheidshorison bly, net om veilig te wees :)

Ek kan nie sien hoe ons snelheid en gravitasietyddilatasie van 'n waarnemer in 'n gravitasieveld in die r-rigting kan beweeg deur die definisie van die regte tyd uit spesiale relatiwiteit te gebruik nie.

As 'n waarnemer in die r rigting beweeg, verminder die Schwarzschild-maatstaf tot (sferiese simmetrie):

In # 10 het ek 'n vergelyking gegee wat aandui dat die koördinaat-tydverwyding van 'n deeltjie wat in 'n gravitasieveld beweeg die produk is van die tydverwyding as gevolg van sy plaaslike snelheid [itex] v_L [/ itex] en tydverwyding as gevolg van swaartekrag, dit wil sê:

Nou gebruik ek die vergelyking in die konteks van die horisontale wentelsnelheid, maar laat ons kyk of dit ook in die radiale rigting werk. As ons dit met die Schwarzschild-maatstaf wil vergelyk, moet ons die plaaslike snelheid [itex] v_L [/ itex], soos gemeet deur 'n stilstaande waarnemer by R, omskakel na 'n koördinaat snelheid v soos gemeet deur die Schwarzschild-waarnemer op oneindig met behulp van die relasie:

Die vervanging hiervan in Vgl 1 gee:

wat vereenvoudig met die vergelyking wat u gegee het:

As die lokaal gemete radiale snelheid van 'n deeltjie wat aanvanklik in rus val van oneindigheid nou die Newtonse ontsnappingssnelheid [itex] sqrt <(2GM / R)> = R_s c ^ 2 [/ itex] is, dan is die koördinaatverruimingstyd van die vryvalpartikel met behulp van Eq1 is:

[tex] d tau = dt sqrt <1-R_s / R> sqrt <1-R_s / R> = dt (1-R_s / R) [/ tex] (Vgl5)

Daar kan gesien word dat die grootte van die snelheidstyddilatasie van die vryvalpartikel gelyk is aan die grootte van die gravitasietyddilatasie van die vryvalpartikel (maar dit is onderworpe aan albei effekte). By 'n plaaslike waarneming by R is die tydverwyding van die vryvalpartikel slegs te danke aan snelheid en numeries gelyk aan [itex] sqrt <(1-v ^ 2 / c ^ 2)> [/ itex] of [itex] sqrt <(1-R_s / R)> [/ itex].

Volgens wiskunde-bladsye http://www.mathpages.com/rr/s6-07/6-07.htm is die koördinaatsnelheid van 'n dalende deeltjie met behulp van G = c = 1:

Uit wiskunde-bladsye kan gesien word dat die parameter K eenheid is wanneer die deeltjie aanvanklik in oneindige rus is. Die plaaslike snelheid wat my Eq2 gebruik, is dan:


Antwoorde en antwoorde

Die volgende berekening kan help. Ons begin met die regte tyd τ vir 'n wêreldlyn C

Kom ons gebruik nou die Schwarzschild-maatstaf vir die gravitasieveld van die aarde, en gebruik die regte tyd τ en koördinate (t, r, Ω):

[tex] d tau ^ 2 = f , dt ^ 2 - f ^ <-1> , dr ^ 2 - r ^ 2 , d Omega ^ 2 [/ tex]

rs is die sogenaamde Schwarzschild-radius.

Laat ons aanneem dat radiale snelheid verdwyn, dit wil sê dr = 0, en konstante hoeksnelheid ω op vaste hoogte r. Die regte tyd word

[tex] d tau ^ 2 = dt ^ 2 links (f (r) - r ^ 2 , omega ^ 2 regs] [/ tex]

b / c al die terme is tydonafhanklik, die integraal is eenvoudig

'N Mens vind dat die gravitasie-effek in die vierkantswortel is

1 / r terwyl die effek as gevolg van die snelheid is

Nou kan 'n mens die regte tye vir verskillende waarnemers vergelyk volgens verskillende wêreldlyne. Elke wêreldlyn word gespesifiseer deur 'n vaste radius r, 'n vaste hoeksnelheid ω en 'n & quotduur & quot t. Hierdie koördinaatstyd t is die regte tyd van 'n stilstaande waarnemer met ω = 0 by r = ∞:

Net FYI, ek kan u nie 'n skakel of wiskunde gee om dit te ondersteun nie, maar ek onthou dat ek op hierdie forum gelees het dat die GPS-stelsel verantwoordelik is vir beide effekte om te verhoed dat u deur mielielande ry, en die resultaat is ongeveer dit: spesiale relatiwiteit (spoed) het 'n effek van 7 mikrosekondes per dag en algemene relatiwiteit (swaartekrag) het 'n effek van 45 mikrosekondes per dag.

1) Dit kan nanosekondes wees, nie mikrosekondes nie. Ek kan dit nie onthou nie --- ek het op die verhouding 7 tot 45 gefokus
2) Hierdie spesifieke figure hang af van die snelheid en afstand vanaf die middelpunt van die aarde van die GPS-satelliete.

Dit is mikrosekondes. Maar 'n belangrike punt is dat die twee effekte in teenoorgestelde rigtings is: die SR-effek laat GPS-horlosies stadig loop ten opsigte van horlosies op die aardoppervlak, terwyl die GR-effek hulle vinniger laat loop. Die gesamentlike effek is dat GPS-horlosies 45 - 7 = 38 mikrosekondes per dag vinnig hardloop as dit nie vergoed word nie, vergeleke met horlosies op die aardoppervlak. (Ek sê & quotif word nie vergoed nie & quot, want daar is 'n ekstra ossillator aan boord van elke satelliet wat sy kloksnelheid regstel om by die tempo van die grondhorlosies te pas, deur 'n frekwensieversetting op die basiese kloksein toe te pas.)

Die beste inligting wat ek ken oor relativistiese effekte in die GPS-stelsel, is hierdie artikel van Neil Ashby:

Daar is eintlik 'n aantal ander, kleiner effekte, benewens die twee wat ons bespreek het. Dit is u korrek dat al hierdie effekte afhang van die presiese baanparameters, wat effens vir elke satelliet verskil (en wat ook met verloop van tyd verander na aanpassing van die wentelbane).

As u 'n horlosie oplig, kan dit vinniger tik naby die aardoppervlak. Maar namate u verder van die aarde se oppervlak af kom, word dinge ingewikkelder, afhangende van die presiese verhouding snelheid / hoogte. As u voorwerpe beskou wat lyk asof dit nie relatief tot die aardoppervlak beweeg nie, byvoorbeeld, op 'n sekere hoogte, sal die snelheid van die voorwerp r * omega die snelheid van die lig nader, en die tydsverruiming sal oneindig nader

Dus, die antwoord wat korrek en voldoende is in die konteks van 'n vergelyking tussen die oppervlak en die bergtop & quot, is miskien nie van toepassing op die situasie van & quotsatellite v satelliet & quot of & quotmy berg is regtig 'n ruimtetuig & quot.

Ek het al gewonder .. As 'n persoon (A), sê maar, bo-op Mt. Everest, sou hy vinniger beweeg as 'n man (B) aan die voet van die berg, aangesien A verder van die middelpunt van die aarde af is, maar hy sal ook 'n swakker swaartekrag as B ervaar.
Dus, vir wie van die individue lyk dit asof die tyd stadiger reis?

Met ander woorde, kan daar gesê word dat gravitasie 'n groter of mindere impak op tyddilatasie het as relatiewe beweging?

Hoop die vraag is nie heeltemal onsinnig nie ..

'N Foton wat na die top van Mt. Everest verloor energie weens die swaartekrag.

'N Foton wat na die top van die berg klim. Everest kry bietjie energie as gevolg van die sentrifugale krag. Hierdie wins is ongeveer 3/1000 van die verlies.

Die foton se frekwensie word verander, 0,3% van die verandering word veroorsaak deur die beweging, 99,7% word deur die swaartekrag veroorsaak.

Die antwoord is dus dat 99,7% van die kloksnelheidsverandering deur die swaartekrag is.

Ek het aangeneem dat g 10 m / s is, en dat Mt. Everest is aan die ewenaar, waar die sentrifugale versnelling 0,03 m / s is

Ja, dit is regtig wat dit maklik kan oplos.

As ons aanneem dat die OP se vraag gebaseer is op albei waarnemers wat dieselfde hoeksnelheid rondom die middelpunt van die Aarde het, sal daar 'n spesifieke hoogte wees waar die swaartekrag- en snelheidseffekte ophou (dit gee geen tydverwyding w.r.t. Aardoppervlak). Ter wille van eenvoud kan aanvaar word dat die waarnemer op die aardoppervlak nul snelheid het sonder om die resultaat veel te beïnvloed.

Onder die nul-tydverruimingshoogte sal hoër horlosies vinniger tik as op die aarde. Hierbo sal hoër horlosies stadiger tik.

'Domineer' (dit wil sê groter of minder impak) is eerder 'n subjektiewe woord in hierdie konteks, maar op die hoogtepunt van Mt. Gravitasie-effekte sal 'domineer' in Everest (dws snelheidsverwyding sal in vergelyking weglaatbaar wees).

Ek het nie die calc gedoen nie, maar dit moet redelik maklik wees. As u nie omgee nie, plaas tom.stoer, stuur die antwoord op die nul tydverruiming.

Eerstens maak ons ​​'n Taylor-uitbreiding vir die vierkantswortel wat beteken dat ons aanneem

[tex] frac ll [/ tex]
[tex] r ^ 2 , omega ^ 2 ll 1 [/ tex]

[tex] tau = t links (1- frac <1> <2> links ( frac + r ^ 2 , omega ^ 2 reg) regs] [/ tex]

Dan stel ons die radius van die aarde inE en die hoogte h:

en maak nog 'n Taylor-uitbreiding in h / rE

[tex] tau = t links (1- frac <1> <2> links ( frac + r ^ 2 , omega ^ 2 regs regs) = t links (1- frac <1> <2> links ( frac links (1 - frac right) + r ^ 2 , omega ^ 2 right) right) [/ tex]

Onthou dat die koördinaat t die regte tyd is vir 'n stilstaande = nie-korotasie-waarnemer by r → ∞. Vir 'n nie-korotasie-waarnemer by h = 0 (sy sal op h = 0 sit en 'n vinnig bewegende oppervlak van die aarde sien !!) is die resultaat

[tex] tau (h = 0, , omega = 0) = t links (1- frac <2r_E> regs] [/ tex]

[tex] tau (h, , omega) = tau (h = 0, , omega = 0) + Delta tau (h, , omega) [/ tex]

waar ek c weer ingedring het om eksplisiete berekeninge toe te laat

Die ontbrekende stuk is die Schwarzschild-radius

In die volgende stap raak ons ​​van die onwaarneembare koördinaat t ontslae en druk ons ​​uit in terme van die regte tyd van die waarnemer wat nie koroteer nie by h = 0, en gebruik ook (weer) die benadering

Dit is die finale resultaat vir klein snelhede v = rω en klein hoogte h.

Soos u kan sien is daar toenemende (Delta van) regte tyd τ met toenemende h (swakker gravitasieveld) en afname (Delta van) regte tyd met toenemende v = rω, die tweede term v² / 2c² is bekend van SR. Die noemer is 'n regstelling vanweë die feit dat ons al by h = 0 een of ander gravitasieveld het wat die tyd vertraag.

Hierdie formule moet van toepassing wees op 'n lughawe op h = 0 en 'n vliegtuig op bv. h = 10 km wat klein is in vergelyking met rE. Onthou asseblief dat ω = 0 wel van toepassing is op 'n nie-korotasie-waarnemer. Om die formule vir lughawens en vliegtuie te gebruik, stel 'n mens die snelhede in

waar Δv die snelheid van die lugvlakte is w.r.t. die lughawe, bv. ± 800 km / h vir westelike / oostelike rigting is hierdie snelheid natuurlik klein vergeleke met c = 300000 km / h. Met behulp van hierdie formule kan u die Hafele – Keating-eksperiment onmiddellik ontleed

opmerking: natuurlik is daar in beginsel geen benadering nodig wat 'n mens kan gebruik nie

Ja, dit is regtig wat dit maklik kan oplos.

As ons aanneem dat die OP se vraag gebaseer is op albei waarnemers wat dieselfde hoeksnelheid het rondom die middelpunt van die Aarde, sal daar 'n spesifieke hoogte wees waar die gravitasie- en snelheidseffekte opgehef word (wat geen tydverruiming w.r.t. Aardoppervlak gee). Ter wille van eenvoud kan aanvaar word dat die waarnemer op die aardoppervlak nul snelheid het sonder om die resultaat veel te beïnvloed.

Onder die nul-tydverruimingshoogte sal hoër horlosies vinniger tik as op die aarde. Hierbo sal hoër horlosies stadiger tik.

'Domineer' (dit wil sê groter of minder impak) is eerder 'n subjektiewe woord in hierdie konteks, maar op die hoogtepunt van Mt. Gravitasie-effekte sal 'domineer' in Everest (dws die snelheidsverwyding sal in vergelyking weglaatbaar wees).

Ek het nie die calc gedoen nie, maar dit moet redelik maklik wees. As u nie omgee nie, plaas tom.stoer, stuur die antwoord op die nul tydverruiming.

Op ongeveer 150000 km hoogte is die kinetiese energie en die potensiële energie ongeveer dieselfde, so dit is die hoogte waar die twee tydverwidings kanselleer.


Ek het amper 'n fout gemaak deur te sê dat die geosinchrone hoogte, 36000 km, die hoogte is, maar dit is net die hoogte waar die veranderinge in die twee tydsverwidings kanselleer as u op of af beweeg.


Intuïtiewe uiteensetting van die effekte van tydsverruiming op waarnemings van swart gate

Vanuit 'n eksterne waarnemersperspektief blyk dit dat voorwerpe wat 'n horison van swart gate en # x27 nader, vertraag as gevolg van swaartekragverwyding, en dit nooit in 'n beperkte tyd raak nie.

Daar word egter gesê dat swaartekrag-rooi verskuiwing die voorwerp effektief onopspoorbaar maak in 'n eindige tyd vir 'n eksterne waarnemer, en die kombinasie van swart gat en voorwerp wat nie onderskei kan word van die gegroeide swart gat wat die gevolg is van die perspektief van die voorwerp wat val nie.

Ek het nog nooit 'n intuïtiewe verklaring / visualisering / intrige gevind vir die eindige tydsaspek hiervan nie.

Dieselfde geld vir samesmeltings van swart gate, wat, weer vanuit 'n eksterne waarnemersperspektief, nooit in 'n beperkte tyd sou gebeur nie. Die LIGO / Virgo-samewerking vind egter gereeld gekwetter van binêre stelsels op soos dit in mekaar val:

Hoe beïnvloed die tydverwyding die frekwensie en amplitude van hierdie sein?

Soos ek dit verstaan, is die verander in frekwensie van die gravitasiegolwe moet afneem totdat die frekwensie 0 bereik het (omdat die voorwerp wat val, al hoe meer stilstaan), in plaas daarvan om oneindig te benader. Miskien so: https://i.imgur.com/FwHE3Id.png

Of stem die frekwensie in hierdie grafieke nie eintlik ooreen met die rotasiefrekwensie van die binêre stelsel nie?

Of beteken rooi verskuiwing in terme van gravitasiegolwe iets anders?

Is hierdie frekwensies buite die meetvermoë van die interferometers?

Edit: Hierdie antwoord: https://physics.stackexchange.com/a/332510/236187 blyk dit baie aanneemlik te maak dat hoewel 'n voorwerp stilstaan ​​as dit naby die horison kom, dit hul baie vinnig sodra dit binne drie keer die Schwarzschild-radius is, binne breuke van 'n millisekonde

Eerlikwaar, GR (en by uitbreiding van swaartekraggolwe, swart gate, ens.) Is ver bo my vlak, maar ek dink ek kan dalk help, alhoewel daar 'n baie moontlike moontlikheid is dat ek net verkeerd is.

Volgens een of ander vraag wat ek by stapeluitruiling gevind het, kan gravitasiegolwe & verskuif word & quot.

Die saak is, sover ek weet, meet ons oor die algemeen nie die punt van kruising nie. Ons meet die baie vinnige rotasie net voordat hulle mekaar se gebeurtenishorison oorsteek. Dit is waarom ons in werklikheid 'n meetbare sein kry.

Die rede waarom 'n voorwerp vir ons stilstaan ​​by die kruispunt, is omdat die lig wat van die voorwerp af kom, teruggesleep & word deur swaartekrag. Dit sal basies stilstaan ​​by die geleentheidshorison - dink ek.

Weereens wil ek herhaal dat hierdie vraag bo my vlak is, dus kan ek net BS rn uitspuug. Stel my asseblief reg as ek & # x27m verkeerd is.

Ons meet die baie vinnige rotasie net voordat hulle mekaar se gebeurtenishorison oorsteek

Ja, dit verstaan ​​ek. Maar vanuit ons perspektief, in plaas van om oneindig te benader, is die verander in frekwensie van die gravitasiegolwe moet afneem totdat die frekwensie 0 bereik het (omdat die voorwerp wat val, al hoe meer stilstaan). Miskien so: https://i.imgur.com/FwHE3Id.png

Of stem die frekwensie in hierdie grafieke nie eintlik ooreen met die rotasiefrekwensie van die binêre stelsel nie?

Of beteken rooiverskuiwing in terme van gravitasiegolwe iets anders?

Is hierdie frekwensies buite die meetvermoë van die interferometers?

KLIK HIERDIE SKAKEL om 'n PM te stuur om ook daaraan herinner te word en om strooipos te verminder.

Ek voel dat ek nie regtig 'n goeie antwoord kan gee nie, want dit is dinge wat 'n mens in 'n papier sal dek, nie op reddit nie. Vir konteks is ek 'n astrofisikus wat besig is met swart gate (wel, röntgenbinaries en aktiewe galaktiese kerne), en het nie die vaagste idee hoe om 'n noukeurige antwoord te gee nie, want swaartekraggolwe is ver van my kundigheidsgebied af, neem dit dus met 'n korreltjie sout.

Eerstens is die sein wat ons op aarde sien, al beïnvloed deur spesiale en relativistiese effekte. Tydsverwyding is reeds gebak in die frekwensie en amplitude wat LIGO / VIRGO opspoor, en dit word ingereken wanneer mense die golfvorm modelleer om samesmeltingsmassas, draai, ens.

Tweedens neem die hele & quotobjects oneindige tyd om op 'n swart gat te val & quot argumente wat u in GR hoor, beskou 'n puntmassa van weglaatbare massa wat die gebeurtenishorison oorsteek, wat nie regtig van toepassing is op 'n kompakte samesmelting nie. Intuitively, I would guess that during the pre-merger phase when the two compact objects are approaching each other, they do so on a timescale that is finite for any reasonable choice of frame of reference (ie, both the one here on Earth and some sort of observer co-moving with the binary), because they are still far enough apart to catch most of the in-spiraling. That results in measurable amplitudes and frequencies. The post-merger/ringdown phase is more complicated to visualize in my mind, but I suspect the decay of the amplitude and frequency is driven simply by the fact that the post-merger object is "settling down" for lack of a better word, rather than some weird GR effect where things from one frame of reference to the other stop being sensible.

Finally, to clarify a bit, gravitational redshift applies to any kind of wave, electromagnetic, gravitational, you name it. The end result is always the same. For example, it's important to account for it to make sure GPS signals are accurate. It's also quite common to detect gravitationally redshifted emission from luminous plasma near a black hole.


Inhoud

Length contraction was postulated by George FitzGerald (1889) and Hendrik Antoon Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment and to rescue the hypothesis of the stationary aether (Lorentz–FitzGerald contraction hypothesis). [2] [3] Although both FitzGerald and Lorentz alluded to the fact that electrostatic fields in motion were deformed ("Heaviside-Ellipsoid" after Oliver Heaviside, who derived this deformation from electromagnetic theory in 1888), it was considered an ad hoc hypothesis, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones. In 1897 Joseph Larmor developed a model in which all forces are considered to be of electromagnetic origin, and length contraction appeared to be a direct consequence of this model. Yet it was shown by Henri Poincaré (1905) that electromagnetic forces alone cannot explain the electron's stability. So he had to introduce another ad hoc hypothesis: non-electric binding forces (Poincaré stresses) that ensure the electron's stability, give a dynamical explanation for length contraction, and thus hide the motion of the stationary aether. [4]

Eventually, Albert Einstein (1905) was the first [4] to completely remove the ad hoc character from the contraction hypothesis, by demonstrating that this contraction did not require motion through a supposed aether, but could be explained using special relativity, which changed our notions of space, time, and simultaneity. [5] Einstein's view was further elaborated by Hermann Minkowski, who demonstrated the geometrical interpretation of all relativistic effects by introducing his concept of four-dimensional spacetime. [6]

First it is necessary to carefully consider the methods for measuring the lengths of resting and moving objects. [7] Here, "object" simply means a distance with endpoints that are always mutually at rest, d.w.s., that are at rest in the same inertial frame of reference. If the relative velocity between an observer (or his measuring instruments) and the observed object is zero, then the proper length L 0 > of the object can simply be determined by directly superposing a measuring rod. However, if the relative velocity > 0, then one can proceed as follows:

The observer installs a row of clocks that either are synchronized a) by exchanging light signals according to the Poincaré–Einstein synchronization, or b) by "slow clock transport", that is, one clock is transported along the row of clocks in the limit of vanishing transport velocity. Now, when the synchronization process is finished, the object is moved along the clock row and every clock stores the exact time when the left or the right end of the object passes by. After that, the observer only has to look at the position of a clock A that stored the time when the left end of the object was passing by, and a clock B at which the right end of the object was passing by op dieselfde tyd. It's clear that distance AB is equal to length L of the moving object. [7] Using this method, the definition of simultaneity is crucial for measuring the length of moving objects.

In Newtonian mechanics, simultaneity and time duration are absolute and therefore both methods lead to the equality of L and L 0 > . Yet in relativity theory the constancy of light velocity in all inertial frames in connection with relativity of simultaneity and time dilation destroys this equality. In the first method an observer in one frame claims to have measured the object's endpoints simultaneously, but the observers in all other inertial frames will argue that the object's endpoints were nie measured simultaneously. In the second method, times T and T 0 > are not equal due to time dilation, resulting in different lengths too.

The deviation between the measurements in all inertial frames is given by the formulas for Lorentz transformation and time dilation (see Derivation). It turns out that the proper length remains unchanged and always denotes the greatest length of an object, and the length of the same object measured in another inertial reference frame is shorter than the proper length. This contraction only occurs along the line of motion, and can be represented by the relation

L is the length observed by an observer in motion relative to the object L0 is the proper length (the length of the object in its rest frame) γ(v) is the Lorentz factor, defined as γ ( v ) ≡ 1 1 − v 2 / c 2 /c^<2>>>> > where v is the relative velocity between the observer and the moving object c is the speed of light

Replacing the Lorentz factor in the original formula leads to the relation

In this equation both L and L0 are measured parallel to the object's line of movement. For the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object. For more general conversions, see the Lorentz transformations. An observer at rest observing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero.

Then, at a speed of 13,400,000 m/s (30 million mph, 0.0447 c ) contracted length is 99.9% of the length at rest at a speed of 42,300,000 m/s (95 million mph, 0.141 c ), the length is still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes prominent.

The principle of relativity (according to which the laws of nature are invariant across inertial reference frames) requires that length contraction is symmetrical: If a rod rests in inertial frame S, it has its proper length in S and its length is contracted in S'. However, if a rod rests in S', it has its proper length in S' and its length is contracted in S. This can be vividly illustrated using symmetric Minkowski diagrams, because the Lorentz transformation geometrically corresponds to a rotation in four-dimensional spacetime. [9] [10]

Magnetic forces are caused by relativistic contraction when electrons are moving relative to atomic nuclei. The magnetic force on a moving charge next to a current-carrying wire is a result of relativistic motion between electrons and protons. [11] [12]

In 1820, André-Marie Ampère showed that parallel wires having currents in the same direction attract one another. To the electrons, the wire contracts slightly, causing the protons of the opposite wire to be locally denser. As the electrons in the opposite wire are moving as well, they do not contract (as much). This results in an apparent local imbalance between electrons and protons the moving electrons in one wire are attracted to the extra protons in the other. The reverse can also be considered. To the static proton's frame of reference, the electrons are moving and contracted, resulting in the same imbalance. The electron drift velocity is relatively very slow, on the order of a meter an hour but the force between an electron and proton is so enormous that even at this very slow speed the relativistic contraction causes significant effects.

This effect also applies to magnetic particles without current, with current being replaced with electron spin. [ aanhaling nodig ]

Any observer co-moving with the observed object cannot measure the object's contraction, because he can judge himself and the object as at rest in the same inertial frame in accordance with the principle of relativity (as it was demonstrated by the Trouton–Rankine experiment). So length contraction cannot be measured in the object's rest frame, but only in a frame in which the observed object is in motion. In addition, even in such a non-co-moving frame, direk experimental confirmations of length contraction are hard to achieve, because at the current state of technology, objects of considerable extension cannot be accelerated to relativistic speeds. And the only objects traveling with the speed required are atomic particles, yet whose spatial extensions are too small to allow a direct measurement of contraction.

However, there are indirek confirmations of this effect in a non-co-moving frame:

  • It was the negative result of a famous experiment, that required the introduction of length contraction: the Michelson–Morley experiment (and later also the Kennedy–Thorndike experiment). In special relativity its explanation is as follows: In its rest frame the interferometer can be regarded as at rest in accordance with the relativity principle, so the propagation time of light is the same in all directions. Although in a frame in which the interferometer is in motion, the transverse beam must traverse a longer, diagonal path with respect to the non-moving frame thus making its travel time longer, the factor by which the longitudinal beam would be delayed by taking times L/(c-v) & L/(c+v) for the forward and reverse trips respectively is even longer. Therefore, in the longitudinal direction the interferometer is supposed to be contracted, in order to restore the equality of both travel times in accordance with the negative experimental result(s). Thus the two-way speed of light remains constant and the round trip propagation time along perpendicular arms of the interferometer is independent of its motion & orientation.
  • Given the thickness of the atmosphere as measured in Earth's reference frame, muons' extremely short lifespan shouldn't allow them to make the trip to the surface, even at the speed of light, but they do nonetheless. From the Earth reference frame, however, this is made possible only by the muon's time being slowed down by time dilation. However, in the muon's frame, the effect is explained by the atmosphere being contracted, shortening the trip. [13]
  • Heavy ions that are spherical when at rest should assume the form of "pancakes" or flat disks when traveling nearly at the speed of light. And in fact, the results obtained from particle collisions can only be explained when the increased nucleon density due to length contraction is considered. [14][15][16]
  • The ionization ability of electrically charged particles with large relative velocities is higher than expected. In pre-relativistic physics the ability should decrease at high velocities, because the time in which ionizing particles in motion can interact with the electrons of other atoms or molecules is diminished. Though in relativity, the higher-than-expected ionization ability can be explained by length contraction of the Coulomb field in frames in which the ionizing particles are moving, which increases their electrical field strength normal to the line of motion. [13][17]
  • In synchrotrons and free-electron lasers, relativistic electrons were injected into an undulator, so that synchrotron radiation is generated. In the proper frame of the electrons, the undulator is contracted which leads to an increased radiation frequency. Additionally, to find out the frequency as measured in the laboratory frame, one has to apply the relativistic Doppler effect. So, only with the aid of length contraction and the relativistic Doppler effect, the extremely small wavelength of undulator radiation can be explained. [18][19]

In 1911 Vladimir Varićak asserted that one sees the length contraction in an objective way, according to Lorentz, while it is "only an apparent, subjective phenomenon, caused by the manner of our clock-regulation and length-measurement", according to Einstein. [20] [21] Einstein published a rebuttal:

The author unjustifiably stated a difference of Lorentz's view and that of mine concerning the physical facts. The question as to whether length contraction regtig exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer though it "really" exists, d.w.s. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer. [22]

Einstein also argued in that paper, that length contraction is not simply the product of arbitrary definitions concerning the way clock regulations and length measurements are performed. He presented the following thought experiment: Let A'B' and A"B" be the endpoints of two rods of the same proper length L0, as measured on x' and x" respectively. Let them move in opposite directions along the x* axis, considered at rest, at the same speed with respect to it. Endpoints A'A" then meet at point A*, and B'B" meet at point B*. Einstein pointed out that length A*B* is shorter than A'B' or A"B", which can also be demonstrated by bringing one of the rods to rest with respect to that axis. [22]

Due to superficial application of the contraction formula some paradoxes can occur. Examples are the ladder paradox and Bell's spaceship paradox. However, those paradoxes can be solved by a correct application of relativity of simultaneity. Another famous paradox is the Ehrenfest paradox, which proves that the concept of rigid bodies is not compatible with relativity, reducing the applicability of Born rigidity, and showing that for a co-rotating observer the geometry is in fact non-Euclidean.

Length contraction refers to measurements of position made at simultaneous times according to a coordinate system. This could suggest that if one could take a picture of a fast moving object, that the image would show the object contracted in the direction of motion. However, such visual effects are completely different measurements, as such a photograph is taken from a distance, while length contraction can only directly be measured at the exact location of the object's endpoints. It was shown by several authors such as Roger Penrose and James Terrell that moving objects generally do not appear length contracted on a photograph. [23] This result was popularized by Victor Weisskopf in a Physics Today article. [24] For instance, for a small angular diameter, a moving sphere remains circular and is rotated. [25] This kind of visual rotation effect is called Penrose-Terrell rotation. [26]

Length contraction can be derived in several ways:

Known moving length Edit

with respect to which the measured length in S is contracted by

According to the relativity principle, objects that are at rest in S have to be contracted in S' as well. By exchanging the above signs and primes symmetrically, it follows:

Thus the contracted length as measured in S' is given by:

Known proper length Edit

Conversely, if the object rests in S and its proper length is known, the simultaneity of the measurements at the object's endpoints has to be considered in another frame S', as the object constantly changes its position there. Therefore, both spatial and temporal coordinates must be transformed: [27]

Likewise, the same method gives a symmetric result for an object at rest in S':

Using time dilation Edit

Therefore, the length measured in S ′ is given by

Geometrical considerations Edit

Additional geometrical considerations show, that length contraction can be regarded as a trigonometric phenomenon, with analogy to parallel slices through a cuboid before and after a rotation in E 3 (see left half figure at the right). This is the Euclidean analog of boosting a cuboid in E 1,2 . In the latter case, however, we can interpret the boosted cuboid as the world slab of a moving plate.

Beeld: Left: a rotated cuboid in three-dimensional euclidean space E 3 . The cross section is langer in the direction of the rotation than it was before the rotation. Right: the world slab of a moving thin plate in Minkowski spacetime (with one spatial dimension suppressed) E 1,2 , which is a boosted cuboid. The cross section is thinner in the direction of the boost than it was before the boost. In both cases, the transverse directions are unaffected and the three planes meeting at each corner of the cuboids are mutually orthogonal (in the sense of E 1,2 at right, and in the sense of E 3 at left).

In special relativity, Poincaré transformations are a class of affine transformations which can be characterized as the transformations between alternative Cartesian coordinate charts on Minkowski spacetime corresponding to alternative states of inertial motion (and different choices of an origin). Lorentz transformations are Poincaré transformations which are linear transformations (preserve the origin). Lorentz transformations play the same role in Minkowski geometry (the Lorentz group forms the isotropy group of the self-isometries of the spacetime) which are played by rotations in euclidean geometry. Indeed, special relativity largely comes down to studying a kind of noneuclidean trigonometry in Minkowski spacetime, as suggested by the following table:


Inhoud

Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century. [2] [3] Joseph Larmor (1897), at least for electrons orbiting a nucleus, wrote ". individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio: 1 − v 2 c 2 >>>>>> ". [4] Emil Cohn (1904) specifically related this formula to the rate of clocks. [5] In the context of special relativity it was shown by Albert Einstein (1905) that this effect concerns the nature of time itself, and he was also the first to point out its reciprocity or symmetry. [6] Subsequently, Hermann Minkowski (1907) introduced the concept of proper time which further clarified the meaning of time dilation. [7]

Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the speed of light (299,792,458 m/s).

Theoretically, time dilation would make it possible for passengers in a fast-moving vehicle to advance further into the future in a short period of their own time. For sufficiently high speeds, the effect is dramatic. For example, one year of travel might correspond to ten years on Earth. Indeed, a constant 1 g acceleration would permit humans to travel through the entire known Universe in one human lifetime. [9]

With current technology severely limiting the velocity of space travel, however, the differences experienced in practice are minuscule: after 6 months on the International Space Station (ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than those on Earth. [10] The cosmonauts Sergei Krikalev and Sergei Avdeyev both experienced time dilation of about 20 milliseconds compared to time that passed on Earth. [11] [12]

Simple inference Edit

Time dilation can be inferred from the observed constancy of the speed of light in all reference frames dictated by the second postulate of special relativity. [13] [14] [15] [16]

This constancy of the speed of light means that, counter to intuition, speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by moving towards or away from the light source.

Consider then, a simple vertical clock consisting of two mirrors A and B , between which a light pulse is bouncing. The separation of the mirrors is L and the clock ticks once each time the light pulse hits mirror A .

In the frame in which the clock is at rest (diagram on the left), the light pulse traces out a path of length 2L and the period of the clock is 2L divided by the speed of light:

From the frame of reference of a moving observer traveling at the speed v relative to the resting frame of the clock (diagram at right), the light pulse is seen as tracing out a longer, angled path. Keeping the speed of light constant for all inertial observers requires a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the local clock, this clock will appear to be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:

The total time for the light pulse to trace its path is given by:

The length of the half path can be calculated as a function of known quantities as:

Elimination of the variables D en L from these three equations results in:

Because all clocks that have a common period in the resting frame should have a common period when observed from the moving frame, all other clocks—mechanical, electronic, optical (such as an identical horizontal version of the clock in the example)—should exhibit the same velocity-dependent time dilation. [17]

Reciprocity Edit

Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would perceive the other's clock as ticking at a slower rate than their own local clock, due to them both perceiving the other to be the one that is in motion relative to their own stationary frame of reference.

Common sense would dictate that, if the passage of time has slowed for a moving object, said object would observe the external world's time to be correspondingly sped up. Counterintuitively, special relativity predicts the opposite. When two observers are in motion relative to each other, each will measure the other's clock slowing down, in concordance with them being in motion relative to the observer's frame of reference.

While this seems self-contradictory, a similar oddity occurs in everyday life. If two persons A and B observe each other from a distance, B will appear small to A, but at the same time A will appear small to B. Being familiar with the effects of perspective, there is no contradiction or paradox in this situation. [18]

The reciprocity of the phenomenon also leads to the so-called twin paradox where the aging of twins, one staying on Earth and the other embarking on a space travel, is compared, and where the reciprocity suggests that both persons should have the same age when they reunite. On the contrary, at the end of the round-trip, the traveling twin will be younger than their sibling on Earth. The dilemma posed by the paradox, however, can be explained by the fact that the traveling twin must markedly accelerate in at least three phases of the trip (beginning, direction change, and end), while the other will only experience negligible acceleration, due to rotation and revolution of Earth. During the acceleration phases of the space travel, time dilation is not symmetric.


4 Answers 4

It's a great question, and I think the answer is no - you wouldn't be able to synchronize based on an event like that because of the precision required in determining when it happened. The issue actually comes down to determining waar that event occurred.

Let's say civilizations on planet A and planet B try to synchronize based on a supernova, which occurs at a time $ au$ and lies a distance $d_A$ from planet A and a distance $d_B$ from planet B. They observe the supernova at times $t_A$ and $t_B$ , respectively. Light takes a finite time to propagate through space, and so - not accounting for any delays because of travel through the interstellar medium - civilization A knows that the supernova occurred at $ au=t_A-d_Ac$ , and civilization B knows that the supernova occurred at $ au=t_B-d_Bc$ . Therefore, civilization A can calculate $ au$ if they know $d_A$ , and likewise for civilization B. They can then synchronize their clocks, right?

Here's the issue: This assumes that the distances are known to the requisite precision. In reality, this is quite difficult to do. The Uncertainties of distance measurements to stars are often in the range of

10-20%. Given that the supernova is (ideally!) hundreds of light-years away from both planets at the minimum, the civilizations may have measurement errors on the order of 10-20 light-years, meaning their clocks could be off from one another by 20-40 years. That's not great!

As an example, we don't have the distance to Betelgeuse - a luminous, important star - pinned down very well, with errors in the area of 25% or more in some cases (see e.g. Harper et al. 2008). The thing that's even more striking is that Betelgeuse can be observed continuously, and has been for decades - and yet, for various reasons, we still can't determine its location to a high precision. A one-off event like a supernova really doesn't given you the option of having more measurements, because the remnant is likely dim and difficult to observe at any wavelength.

A true galactic civilization, of course, will have to deal with a galaxy roughly 100,000 light-years across. This means that we're dealing with distance likely of several tens of thousands of light-years. Sure, technology has likely gotten much better than ours (and I very much envy those astronomers), but to have initial synchronization errors on the order of a year, you'd need distance measurements accurate to 0.01%, and that seems quite difficult. For example, say the event occurred near the center of the Milky Way. We don't even know that distance well it's around 25,000 light-years, but many of the measurement errors are around 1,000 light-years (Malkin 2013)!

You could also ask about whether time dilation will be an issue, due to both the gravitational field of the Milky Way and the motion of stars within it. We can do those calculations, and determine that the fractional difference in time between the inner regions and an observer at infinity is $Delta=7 imes10^<-6>$ due to gravity and the difference between an observer orbiting with the Sun and an observer at infinity $3 imes10^<-7>$ due to special relativity $^$ . Those are both at least 5 orders of magnitude lower than the discrepancies we'd be looking at due to measurement uncertainties - and they wouldn't change substantially if we compared any two star systems.

$^$ Time dilation due to a potential difference $DeltaPhi$ can be written as $Delta t_r=Delta t_sqrt<1-frac<2DeltaPhi>>$ for bodies at radii $r$ and $infty$ . From special relativity, we get that a star moving at a speed $v$ experiences $Delta t_v=Delta t_sqrt<1-v^2/c^2>$ For a typical galactic potential and a stellar speed typical of the Sun, you can check that you get the results I listed above.

1 year from the center to the outskirts would require a source about 400 million light-years away, which is certainly reasonable for detecting a supernova or GRB - but the two observers would still observe it happening a year apart. $endgroup$ &ndash HDE 226868 ♦ May 19 at 3:10

First I agree with the points made that this time synchronization would not be very important in a galactic "civilization" with such limited interaction. Also that time dilation would have a slight but not huge affect on planets in different solar systems because they're all in similar gravitational fields and all moving at far less than 1% the speed of light relative to each other.

Rather than half life of an element I would look to the oscillation period of a neutral hydrogen atom. The Hydrogen Line. This is what NASA used on the Golden Record on the Voyager Probe to indicate a recognizable unit of time to any aliens that might intercept it.

The easiest way to keep time between worlds would be to put atomic clocks on all the starships to keep time from the time they leave earth. These remain accurate to within one second after running for 300,000 years. However, assuming these starships travel at any notable fraction of the speed of light (anywhere near 1% or more) you'll worry about time dilation. If it was my galactic empire I would come up with some technology to receive the radio signal from some quasar, presumably the one with the strongest signal on average across the Milky Way. Quasars aren't found in the Milky Way but they would be detectable throughout it. Everyone would receive the same radio pulses from the same quasar but, for instance, if you were traveling at 10% the speed of light on a starship, you would observe the frequency to be lower than would observers living on a planet. Maybe time 0 is the time the first starship left earth and you count galactic time by the number of oscillations of the radio frequency of the selected pulsar since then.

This would be different periods of perceived time to different people and planets, but it would be a reliable galactic standard. This would be useful for galactic historical records like you mentioned but of course it wouldn't be relevant to the average citizen or even scientist on any given planet. More for record keeping and communications protocols than anything else I would think.

Also should be noted that there are other bodies in space that give off frequencies in the radio spectrum any many others. But, my understanding is that quasars are very powerful and would be reliable for this purpose. Google tells me that they tend to last 100-1000 million years. On some timelines it could take around this long for us to actually populate the galaxy but I would also think that that's plenty of time for us to come up with an artificial radio pulse powerful enough for everyone in the galaxy to pick up on. Once that is constructed the galaxy could be instructed to switch to this artificial frequency after some determined (upcoming) oscillation number of the pulsar. Alternatively, there may be another type of body with similar useful properties that also lives longer. It guess it all depends on how long it's been since first launch in your world.

P.S. If you haven't seen Sharkee's video on how we could feasibly populate the galaxy with reasonable limits like these you should check it out here. One of my all time favorite YouTube videos.

Edit: if you picked a quasar that is "off to the side" of the milky way, the close side would receive the pulse 52000 years before the far side. If you chose a quasar that is "above" the disk galaxy, then everyone would receive the pulse at closer to the same time in a sort of radio wall passing through the whole galaxy at once. Alternatively, if you picked an off to the side one, the receivers could just account for the difference because it would be well known where they are in relation to the rest of the galaxy and the pulsar.


6 antwoorde 6

The wikipedia entry you reference describes two opposing forms of time dilation, one that will make you age quicker and one that will make you age slower. Both have noticeable effect only on extremely extended or close to light speed movement. The ISS astronauts, for instance, said to have aged slower, by 0.007 seconds for every 6 months on the station.

Consider, however, that The Flash mostly runs around on Earth. The earth's circumference is about 40,000 kilometers. Even if the Flash runs at only 13% of light speed, he can go around the entire earth in one second. As I understand it, he spends 99% of his time in "normal speed", only gearing up for full speed when necessary. This means that to achieve a sizeable time dilation will take decades, probably. Maybe more.

(Disclaimer: I did not really run any numbers here, neither for time dilation or for aggregated time spent in near light speed. I'm going mostly by intuition here)

No, the Flash does not get any significant aging benefit because he is running at faster than light speeds. There are several limitations which need to be taken into account:

He spends the bulk of his life moving at a normal pace and thus does not utilize his relativistic movement except in extreme emergencies. His average pace around the city is only around 180-200 miles per hour.

Given the extremes of speed once you start reaching Mach 10 or more, the Flash, even with his speed aura is reluctant to approach relativistic speeds. More importantly, there are almost no reasons he would need to approach even ten percent of the speed of light while on Earth which would approach 6,706,166 miles per hour (circling the Earth 268 times in a hour).

When he is moving at a percentage of light speed which varies from writer to writer, his speed is so great whatever feat he is performing happens and ends within a few seconds and rarely lasts for more than a few minutes tops.

The Flash empties an entire city in North Korea (2 people at a time in a few seconds).

  • Relativistic aging benefits would only occur if he were maintaining a sustained top speed for a significant amount of time, say if he were moving from star to star. Depending on his top speed he might slow his aging considerable in comparison to the flow of time on Earth.

The Flash's powers are not clearly defined by the laws of physics, nor by the DC Comics franchise. We are left unfortunately to speculate as to how he defies or obeys the laws of physics as determined by the writer/editor team at the moment.


Kyk die video: ДИМАШ SOS. История выступления и анализ успеха. Dimash SOS (November 2022).