Sterrekunde

'N Kamera en tydverwyding?

'N Kamera en tydverwyding?


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As ek naby 'n swart gat sou reis, sou my tyd stadiger vorder in vergelyking met iemand op aarde. Dit is duidelik genoeg. Maar sê nou ons stuur 'n sonde met 'n kamera na 'n swart gat? Sal ons tyd deur die kamera se perspektief sien as ons na die skerm kyk, dit wil sê, lyk dit asof die heelal vinniger vorder soos die sonde al hoe nader aan die swart gat kom?


As ek naby 'n swart gat sou reis, sou my tyd stadiger vorder in vergelyking met iemand op aarde. Dit is duidelik genoeg.

Ja, geen probleem met die swaartekragverwyding nie.

Maar sê nou ons stuur 'n sonde met 'n kamera na 'n swart gat? As ons na die skerm kyk, sou ons tyd deur die kamera se perspektief sien - dit wil sê, lyk dit asof die heelal vinniger vorder soos die sonde al hoe nader aan die swart gat kom?

Nee. Ons sou sien dat die heelal normaal vorder, omdat ons nie aan die swaartekragtydverwyding onderwerp is nie. (Ek neem aan ons is op 'n veilige afstand). Gestel dit was 'n TV-kamera wat 25 keer per sekonde 'n foto geneem het en na ons teruggestuur het, wat voldoende geskik was vir rooi verskuiwing. Die kamera begin 25 foto's per sekonde neem soos ons meet. Maar na 'n ruk sien ons dat ons net 24 foto's per sekonde kry, dan 23, ensovoorts. Ons sien hoe gebeure in die breër heelal teen hul normale tempo vorder, maar uiteindelik begin die film rukkerig raak namate die beeldsnelheid verminder. Uiteindelik verminder die raamkoers tot nul, en dit is die einde van die show.


Kom ons sê vir die eenvoud dat die swart gat geïsoleer en nie-draaiend (en nie gelaai) is nie, sodat die situasie beskryf word deur die relatief eenvoudige Schwarzschild-ruimtetyd. Laat ons ook veronderstel dat die kamera radiaal in die swart gat val.

Waarna kyk die kamera? Veronderstel dit kyk na een of ander stilstaande voorwerp wat iets met 'n bekende frekwensie doen. U vraag is basies hoe gereeld dit op die videostroom van die kamera waargeneem word.

Sonder verlies aan algemeenheid, kan ons aanvaar dat die kamera kyk ons, en dat ons 'n laserstraal daarop skyn: die 'iets met 'n bekende frekwensie' sou die ossillasies in die elektromagnetiese golf van die laserstraal wees. Ons kan dit doen omdat tydsverruiming elke fisiese proses beïnvloed, dus ons kan net sowel een kies wat geriefliker is om na te dink.

Op hierdie stadium is dit eenvoudig waarom die kamera-toevoer geen tydverwyding sal vertoon nie: gelykstaande aan 'n gereflekteerde laserstraal, sal die gravitasie-blueshift wanneer dit na binne gaan, gekanselleer word deur die swaartekrag-rooi skuif na buite.


'N Kamera en tydverwyding? - Sterrekunde

Ek is 'n hoërskoolonderwyser. In boeke oor tydverspreiding sien ek baie voorbeelde van voltooide probleme van wat sou gebeur tydens sulke reise na die ruimte. 'N Voorbeeld is die tweelingparadoks - is daar 'n formule waarin ek kan bereken hoeveel tyd daar op die aarde verloop het terwyl die reisiger in die ruimte vlieg? Ander voorbeelde wat ek in programme gesien het: "Dit is moontlik om na die middel van ons sterrestelsel te reis, 'n vlugtyd van 50 jaar (?). As u terugkeer, het daar 4 miljoen jaar verbygegaan." OF "12 jaar reis en die broer is nou 80 jaar oud". Ek word vertel dat so 'n formule bestaan ​​- wat is dit en wat is die veranderlikes wat ek kan bereken?

Lengtekrimping en tyddilatasie is beide die gevolge van spesiale relatiwiteit, wat plaasvind wanneer 'n voorwerp naby die snelheid van die lig beweeg. Dit word regtig nie as tydreis beskou nie, behalwe in die mate dat ons almal onverbiddelik deur die tyd reis na die toekoms. Nietemin is hierdie effekte beslis werklik. U kan inderdaad vir 'n kort tydjie baie naby die ligsnelheid reis en terugkeer na die aarde, waar miljoene jare verby is. Die verklaring hiervoor is 'n volledige fisikakursus op sy eie, en kan gevind word in inleidende tekste oor spesiale relatiwiteit. In wese is dit 'n onmiddellike gevolg van die ligsnelheid wat konstant is vir alle waarnemers, ongeag hul eie snelheid.

Bewegende horlosies loop stadig en bewegende stokke word met 'n faktor verkort

Laat ons sê ons dink aan die "tweelingparadoks" en dat ons onverskrokke reisiger teen 'n snelheid v gelyk is aan 0,9 keer die ligspoed, c. In hierdie geval,

gamma = 1 / Sqrt (1 - 0.9 2) = 2.29.

Die tweeling op aarde sien dus dat die klok van die ruimteskip 2.29 keer stadiger loop as sy eie, dit wil sê elke 2.29 jaar op aarde stem ooreen met een jaar volgens die ruimteskip se klok. Die Earthbound-tweeling merk ook op dat die ruimteskip wat 0,9c beweeg, 2,29 keer korter is as voor die lansering. Hoe vinniger die ruimteskip beweeg, hoe meer word die effek uitgespreek. Cool, nè?

Hierdie bladsy is laas op 28 Januarie 2019 hersien.

Oor die skrywer

Dave Kornreich

Dave was die stigter van Ask an Astronomer. Hy het in 2001 'n doktorsgraad aan Cornell behaal en is nou 'n assistent-professor aan die Departement Fisika en Natuurwetenskap aan die Humboldt State University in Kalifornië. Daar bestuur hy sy eie weergawe van Ask the Astronomer. Hy help ons ook met die vreemde kosmologievraag.


Tydsverruiming

Die feitlike tipe tydreise is deur die konsep van tydsverruiming - 'n verskil van verstreke tyd tussen twee gebeurtenisse. Dit is vir ons sterflinge 'n uiters moeilike ding om kop uit te steek - dit wil sê mense wat nie goed vertroud is met die fisika en sterrekunde nie. Dit is omdat Einstein se relatiwiteitsteorie 'n rol speel.

Kortom, as ruimtevaarders om die aarde wentel, is hulle opvallend verder van die planeet af as diegene wat op die oppervlak woon. Dit beteken dat hul gravitasietyddilatasie minder is omdat swaartekrag minder is en dat alles wat hulle doen vinniger is (selfs die horlosies loop stadiger op ruimtestasies). Wanneer hulle na die aarde terugkeer, reis hulle letterlik terug in die tyd. Dit is geensins 'n groot aantal nie, want die tydverwyding word veroorsaak deur swaartekrag wat 'n swak krag is. (Soos die aantrekkingskragte in die heelal gaan). Daar is bereken dat die Russiese ruimtevaarder Sergei Konstantinovich Krikalev die meeste tyd gereis het. Hier is 'n kort opsomming van hoe hy dit gedoen het.


Tyddilatasie rigting afhanklik?

Dit was 'n baie lang dag, maar laat my 'n lawwe vraag vra. Ek het die ruimtevaart op hierdie forum besin en vorendag gekom met iets wat ek nie formeel gesien het nie.

As ek aan tydsverwyding dink, gaan ek altyd terug na die voorbeeld van 'n trein wat vinnig deur die stasie ry met een waarnemer op 'n vlagpaal van 100 voet wat aan 'n plat kar vas is. Hy laat val 'n bal en hy sien hoe die bal binne 1 sekonde 100 voet val. 'N Waarnemer wat in die stasie stilstaan, sal die bal skuins sien beweeg en gedurende dieselfde sekonde sal die bal 133 voet beweeg. Dus sou een horlosie dieselfde gebeurtenis vinniger sien plaasvind.

Ek het nog nooit daaraan gedink om die waarnemer te beweeg nie. As die waarnemer in die stasie onmiddellik op die spore spring net toe die trein verbygaan en die bal deur die tweede waarnemer op die vlagpaal val, sal albei waarnemers sien dat die bal dieselfde afstand binne dieselfde tydraamwerk deurkruis. As die trein dus direk van die waarnemer op die stasie beweeg, sou daar 'n tydsverskil in die stilstaande waarnemer teenoor die waarnemer in beweging wees?

(As dit regtig dom is, vra ek 'n vriend!)

# 2 LesB

# 3 LesB

Dit voorbeeld moet nie 'n bal wees nie, maar 'n ligstraal, en die pad van die ligstraal soos dit vir die waarnemer op die trein, meer spesifiek, 'n treinwa lyk. Die ander waarnemer wat die spoorwa sien verbygaan, sien 'n ander pad vir die ligstraal en die pad is langer as gevolg van die beweging van die treinwa. Dit is hier waar tydverspreiding plaasvind.

Die aanvaarding dat die snelheid van die lig in alle rigtings dieselfde is, ongeag die snelheid of rigting van die bron, is sentraal in die begrip van hierdie verskynsel. Hierdie begrip word bevorder deur die Pythagorese verhouding wat die formule ontleen. Alhoewel die pad van die bal wat weerkaats, analoog kan wees aan die pad van die ligstraal, breek die analogie af omdat die pad van die bal om voor die hand liggende redes parabolies is.

Die uiteindelike pad van lig word bepaal deur die kromming van die ruimte wat deur gravitasievelde verwring word. Die ligweg vir hierdie voorbeeld word plaaslik as 'n reguit lyn behandel.

# 4 JerryWise

Dit voorbeeld moet nie 'n bal wees nie, maar 'n ligstraal, en die pad van die ligstraal soos dit vir die waarnemer op die trein, meer spesifiek, 'n treinwa lyk. Die ander waarnemer wat die spoorwa sien verbygaan, sien 'n ander pad vir die ligstraal en die pad is langer as gevolg van die beweging van die treinwa.

# 5 LesB

# 6 JerryWise


Waarom word die GPS-satelliete dan aangepas vir tyddilatasie as hulle nie teen die ligspoed beweeg nie?

# 7 JerryWise

Dit voorbeeld moet nie 'n bal wees nie, maar 'n ligstraal, en die pad van die ligstraal soos dit vir die waarnemer op die trein, meer spesifiek, 'n treinwa lyk. Die ander waarnemer wat die spoorwa sien verbygaan, sien 'n ander pad vir die ligstraal en die pad is langer as gevolg van die beweging van die treinwa. Dit is hier waar tydverspreiding plaasvind.

# 8 LesB

Daar is een waarnemer op die bewegende spoorwa en die ander waarnemer staan ​​stil. U het dit verwar deur te sê dat die stilstaande waarnemer agter die trein loop.

Die waarnemer op die treinwa ervaar tydverspreiding, maar voel dit nie. Die stilstaande waarnemer ervaar tyd op 'n ander manier, want die ligpad van wat hy op die spoorwa waarneem, neem 'n langer pad vanaf die oorsprong tot by die bestemming. As die spoorwa stilstaan, sal albei waarnemers dieselfde ervaring hê.

Hoekom? Omdat c dieselfde is in alle rigtings en in alle traagheidsraamwerke. Die analogie van die bal kan dit illustreer, maar eintlik verwys alles na c. Die analogie van die bal breek af wanneer die wiskunde van die ligpad geanaliseer word.

# 9 JerryWise

Ek het dit nie verwar nie, dit is die vraag. Laat sak die bal as jy wil. Die ligpad werk ook. Ek het verstaan ​​dat die opmerking was dat die waarnemer op die platform ''n langer ligpad sou sien' '.

Voeg 'n derde waarnemer by as die waarnemer wat agter die trein beweeg verward is. Ons het een op die perron, een op die trein en een agter die trein. Die trein se beweging sal dieselfde wees vir die twee waarnemers wat nie in die trein is nie. Die waarnemer agter die trein sal 'n ander ligpad sien as die op die perron. Ons het dieselfde treinsnelheid vir albei treinwaarnemers, ons het 'n langer ligpad vir die waarnemer langs die trein as die waarnemer agter die trein.

Ek verstaan ​​die C- en traagheidsraamwerke. Moet ons ligsnelheid en ligweë gebruik as verwysing wanneer eksperimentering tydverspreiding op minder as C bevestig? Die vraag oor die GPS-satelliete is steeds oop en baie relevant om dit te illustreer.

# 10 LesB

Voeg 'n derde waarnemer by as die waarnemer wat agter die trein beweeg verward is. Ons het een op die perron, een op die trein en een agter die trein. Die trein se beweging sal dieselfde wees vir die twee waarnemers wat nie in die trein is nie. Die waarnemer agter die trein sal 'n ander ligpad sien as die op die perron. Ons het dieselfde treinsnelheid vir albei treinwaarnemers, ons het 'n langer ligpad vir die waarnemer langs die trein as die waarnemer agter die trein.

Ek het nooit betwis dat tyddilatasie by snelhede van minder as c plaasvind nie. Die toevoeging van 'n derde stilstaande waarnemer in u voorbeeld is egter onnodig omdat die spoed van lig is dieselfde in alle rigtings, ongeag die bron en die posisie van die waarnemer. Albei stilstaande waarnemers sal dieselfde resultaat sien. Die waarnemer, wat in die trein is, sal 'n vertraging van die tyd ervaar. Die toevoeging van 'n ander waarnemer in dieselfde stilstaande raam sal 'n ander waarnemer oplewer wat dieselfde gevoel van tyd ervaar.

As ek onthou, tyddilatasie was die onderwerp van hierdie draad. Dink daaraan dat die spoorwa in beweging is relatief tot beide waarnemers wat stilstaan. Die spoorwa is die traagheidsraam wat relatief tot albei stilstaande waarnemers beweeg.

# 11 JerryWise

.. Ek het nooit betwis dat tyddilatasie by snelhede van minder as c plaasvind nie.

Ek stem saam dat jy dit nooit betwis het nie. Ek neem aan dat u dit nou erken. Miskien as ons terugkom na die bal noudat dit erken word?

U noem 'n waarnemer wat 'n langer ligpad waarneem. Bly daarmee reg vir die betekenis van die draad. Sou die hoekverskil van twee stilstaande waarnemers 'n ander "langer" ligpad sien? Of is dit nie meer relevant nie? Net 'n ja of nee sal werk. Sê nee en ek sal gelukkig wees met u mening.

..As ek onthou, was tyddilatasie die onderwerp van hierdie draad.

Nie nodig om te snip en te snip nie. U wen as dit die punt is.

Verskoon asb. Ek bedoel nie om hieroor uit te sny nie, maar 'Freddie vs Jason' kom aan en. wel. .

# 12 LesB

Verskoon asb. Ek bedoel nie om hieroor uit te sny nie, maar 'Freddie vs Jason' kom aan en. wel. .

# 13 JerryWise

Verskoon asb. Ek bedoel nie om hieroor uit te sny nie, maar 'Freddie vs Jason' kom aan en. wel. .

# 14 Jarad

Goed hier is 'n paar verskillende dinge aan die gang.

# 1 - Tyddilatasie word gewoonlik gedefinieer as gemeet deur 'n stilstaande waarnemer parallel aan die gebeurtenis wat gemeet word. Met ander woorde, die formule bereken die tyddilatasie-effek as die waarnemer langs die trein is op die oomblik van die gebeurtenis wat hy meet, en die trein kom dus nie nader nie. Dit is die 'ware' tydsverruimingsfaktor.

# 2 - As die waarnemer in plaas daarvan of agter die trein is (sodat hy van hom afneem) of voor die trein (dit kom nader), is daar 'n bykomende faktor as gevolg van die rooi-of blue-shift.

'N Trein wat aan die gang is, sal die latere gebeure verder laat plaasvind. Daarom sal dit langer neem van die gebeure om die waarnemer te bereik, sodat dit selfs stadiger lyk as die "ware" uitbreidingsfaktor. Vir 'n waarnemer agter die trein lyk dit asof dinge selfs meer vertraag as die normale uitbreidingsfaktor.

'N Trein wat naderkom, sal later gebeure nader aan die waarnemer plaasvind, daarom sal die lig van hierdie gebeure gouer opdaag as wat dit andersins sou gebeur, en dit lyk of die tyd sal versnel. Hierdie effek sal die dilatasie-effek teenstaan ​​en ook groter wees as dit, sodat 'n waarnemer voor die trein dinge in die trein vinniger as normaal sal sien plaasvind, ondanks die tydsverwidingsfaktor.

Die lorentz-transformfaktor vir 90% van die spoedlig is byvoorbeeld sqrt (1-0.9 ^ 2) = 0.141. Die tyd loop dus op 1/7 op 'n skip wat teen 0,9C relatief tot die aarde beweeg. Maar as die skip van ons af wegbeweeg, neem die lig wat dit by T + 0,141 sekondes uitstuur, 0,9 sekondes langer om ons te bereik as die lig wat by T uitgestraal word. Dit sal dus vir 0.141 op die skip 1,9 sekondes neem (1 tweede vir die verwydingsfaktor, plus 0,9 sekondes sedert dit 0,9 ligsekondes verder weg geëindig het), vir 'n totale skynbare tydverwidingsfaktor van 0,141 / 1,9 = 0,074, of net minder as 1/13 so vinnig as wat dit lyk asof dit op aarde gaan.

As dieselfde skip nader kom, sal die lig wat op T + 0,141 sekondes uitgestraal word, 1 sekonde later aardtyd uitgestraal word, maar vanaf 0,9 ligsekondes nader. Dit sal dus 0,1 sekonde later aankom, vir 'n tydsverruimingsfaktor van 0,141 / 0,1 = 1,41. Dit lyk dus asof die tyd 1,41 keer vinniger gaan op die naderende skip.


Relatiwiteit en die "Triplet Paradox"

Omlope, die werklike fisiese tyd wat die skip geneem het om die reis te voltooi, dit is ook feite. As die klok op die skip 17 jaar gesê het en die skip 20 geneem het, sien ek baie interessante moontlikhede (is die skip 17 jaar ouer of 20 vanaf die lansering).

Absoluut. Ek stem 100% saam. Waar ek hierheen gegaan het, is die een 'n persepsie teweeg gebring deur waarnemings in 'n traagheidsraamwerk, die ander waarnemings in die stelsel van koördinate in rus in verhouding tot die bewegende liggaam. Die metings wat in die traagheidsraamwerk geneem word, moet in 'n stelsel van koördinate in rus relatief tot die liggaam in beweging verander word om afsnitte en wentelbane te bepaal. Dit plaas probleme (noodgeval vir die skepping van die skip, ens.) In die optika van bewegende liggame na 'n reeks probleme in die optika van stilstaande liggame. (1)

Albei metings is baie werklik. Die een meting moet getransformeer word vir fisiese afsnitte en baanberekenings, terwyl die ander geen transformasie van die berekeningparameters benodig nie. Uit die aard van die transformasievereiste is hierdie stel waarnemings 'n persepsie wat voortgebring word deur 'n ligte weg te beweeg wat vanaf punt A (planeet) na punt B (planeet) voortbrei teen beduidende persentasies van C.

En dit bring die punt van die nadink. Waarom word alle lesings in 'n traagheidsraamwerk teruggevoer na die stelsel van koördinate in rus wanneer die skip staak (beweeg uit 'n traagheidsraamwerk), behalwe die ouderdom van die drieling aan boord van die skip? Watter spesiale traagheidsraamwerk laat hierdie waarneming toe terwyl alle ander waarnemings omgeskakel moet word? Dit in 'n stelsel wat onder die wet werk en geen spesiale verwysingsraamwerk het nie?

(1) "Oor die elektrodinamika van bewegende liggame" deur A. Einstein, 30 Junie 1905. Artikel 8, laaste paragraaf.

# 27 Jarad

Omdat dit nie net 'n optiese effek was nie.

Die afgelegde afstand gaan nie terug as die skip stop nie. Nadat die skip gestop het, sal hulle die afstand as 20 ligjaar sien as hulle agtertoe kyk, en hulle sal sien dat die horlosies in dieselfde tempo beweeg. Maar die verstreke tyd verander nie, en as die skip 'n kilometerteller gehad het, sal dit steeds 17,3 ligjare toon, nie 20 nie.

# 28 JerryWise

Omdat dit nie net 'n optiese effek was nie.

Die afgelegde afstand gaan nie terug as die skip stop nie. Nadat die skip gestop het, sal hulle die afstand as 20 ligjaar sien as hulle agtertoe kyk, en hulle sal sien dat die horlosies in dieselfde tempo beweeg. Maar die verstreke tyd verander nie, en as die skip 'n kilometerteller het, sal dit steeds 17,3 ligjare toon, nie 20 nie.

# 29 Jarad

Die stokke is nie so styf nie. As hulle die stokke meet, sou hulle dit korter meet as wat die mense op die planete sou doen (met ander woorde, die instrumente aan boord moet steeds omskakel om afsnitte te bereken).

# 30 JerryWise

# 31 Jarad

Dit is nodig as hulle in 'n ander verwysingsraamwerk is. Terwyl die skip dus relatief tot die planete beweeg, meet hulle dinge anders. As hulle stilstaande is ten opsigte van die planete, meet hulle dinge dieselfde.

# 32 JerryWise

# 33 HiggsBoson

Ek wil graag 'n gedagte-eksperiment plaas wat blyk dat die tydverwyding 'n permanente effek is. As daar vanuit hierdie perspektief na 'n reis gekyk word, kan ek nie sien hoe tyddilatasie anders kan wees as 'n waarneming binne 'n verwysingsraamwerk eerder as 'n permanente effek op die insittendes van die skip in beweging nie. (Tydsverwidingsbewyse uit Muon-eksperimente en die GPS-kompensasie word as feit beskou, maar ter wille van hierdie een voorbeeld wil ek die volgende stel omstandighede verwys.) In hierdie voorbeeld word drie meisies op dieselfde oomblik gebore, 2 op aarde en 1 op 'n verre planeet.

Wat u hier gedoen het, is soos volg 'n postulaat:

Tydsverwydings as gevolg van relatiewe beweging is die gevolg van ligte reistyd en duur nie voort wanneer die reisiger en verwysingswaarnemer na dieselfde verwysingsraamwerk teruggestuur word nie.

Die tweelingparadoks is nie 'n "gedagte" -eksperiment nie. Dit is met regte horlosies gedoen. In 1971 vlieg Hafele en Keating ooreenstemmende sesium-atoomklokke om die aarde. Die verwysingsklokke was by die Amerikaanse marine-sterrewag. Wanneer die horlosies herenig is, stem die horlosies wat gevlieg het, nie meer met die verwysingshorlosie ooreen met 'n bedrag wat nie aan meetfoute toegeskryf kan word nie.

Die uitkoms van die eksperiment is voldoende om aan te toon dat die postulaat waarop u voorbeeld gebaseer is, vals is. 'N Mens hoef nie relatiwiteit op enige manier te verwys nie. Die natuur ondersteun nie die postulaat nie. Die eksperiment is herhaal met beter horlosies met soortgelyke resultate.

Dit is belangrik om te onthou dat dit die uitkoms van eksperimente is wat bepaal watter teorieë nuttiger is. Einstein het Quantum nie aanvaar nie, maar hy het nooit voorgestel dat eksperimente wat Quantum ondersteun nie geldige resultate is nie. Hy wou eenvoudig meer uit die teorie hê.

In hierdie geval het ons 'n teorie wat voorspel dat die resultate akkuraat rekening hou met die vertraagde kloksnelheid as gevolg van beweging en die versnelling as gevolg van 'n groter afstand van die middelpunt van die aarde. Alhoewel 'n mens kan voorstel dat 'n nuwe, tans onbekende teorie meer korrek kan wees, is daar eintlik geen ruimte om aan te dui dat die uitbreidings nie plaasvind nie.

As die muondata en die kloktoets nie oortuig nie, is die GPS-data oorweldigend. Daar is

2-dosyn satelliete met 2 dosyn sesiumklokke. Daar is honderdmiljoene ontvangers wat elkeen 'n navigasie-oplossing per sekonde lewer, solank hulle aangedryf word en seine ontvang. Daar is min toepassings van tegnologie wat so 'n groot hoeveelheid data verifieer. As hierdie uitbreidings nie werklik was nie, sou die hele stelsel nie so akkuraat wees as wat dit blyk uit tien miljoen van voorbeelde nie. Soos ek verstaan, moes die horlosies in die oorspronklike stelsel twee keer per dag vir Relativistiese effekte gekorrigeer word om die horlosies voldoende gesinkroniseer te hou om aan die akkuraatheidsvereistes te voldoen. Dit blyk dat die uitbreidings in hierdie geval 'n baie aanhoudende effek was.

# 34 Joad

[snip] "En dit bring die punt van die nadink oor. Waarom word alle lesings in 'n traagheidsraamwerk teruggevoer na die stelsel van koördinate in rus wanneer die skip staak (beweeg uit 'n traagheidsraamwerk), behalwe die ouderdom van die drieling aan boord van die skip? ' [snip]

Jarad en HiggsBoson het die tegniese kant van die vraag beantwoord, en llanitedave het die sielkundige kant genoem. Maar ek is bly dat u dit gevra het, omdat u ons goed ingeligte lede in staat gestel het om weer huis toe te ry wat 'n vreemde ding is wat relatiwiteit is.

# 35 JerryWise

Ek wil graag 'n gedagte-eksperiment plaas wat blyk dat die tydverwyding 'n permanente effek is. As daar vanuit hierdie perspektief na 'n reis gekyk word, kan ek nie sien hoe tyddilatasie anders kan wees as 'n waarneming binne 'n verwysingsraamwerk eerder as 'n permanente uitwerking op die insittendes van die skip wat in beweging is nie. (Tydsverwidingsbewyse uit Muon-eksperimente en die GPS-kompensasie word as feit beskou, maar ter wille van hierdie een voorbeeld wil ek die volgende stel omstandighede verwys.) In hierdie voorbeeld word drie meisies op dieselfde oomblik gebore, 2 op aarde en 1 op 'n verre planeet.

Wat u hier gedoen het, is soos volg 'n postulaat:

Tydsverwydings as gevolg van relatiewe beweging is die gevolg van ligte reistyd en duur nie voort wanneer die reisiger en verwysingswaarnemer na dieselfde verwysingsraamwerk teruggestuur word nie.

Die tweelingparadoks is nie 'n "gedagte" -eksperiment nie. Dit is met regte horlosies gedoen. In 1971 vlieg Hafele en Keating ooreenstemmende sesium-atoomklokke om die aarde. Die verwysingsklokke was by die Amerikaanse marine-sterrewag. Wanneer die horlosies herenig is, stem die horlosies wat gevlieg het, nie meer met die verwysingshorlosie ooreen met 'n bedrag wat nie aan meetfoute toegeskryf kan word nie.

Die uitkoms van die eksperiment is voldoende om aan te toon dat die postulaat waarop u voorbeeld gebaseer is, vals is. 'N Mens hoef nie relatiwiteit op enige manier te verwys nie. Die natuur ondersteun nie die postulaat nie. Die eksperiment is herhaal met beter horlosies met soortgelyke resultate.

Dit is belangrik om te onthou dat dit die uitkoms van eksperimente is wat bepaal watter teorieë nuttiger is. Einstein het Quantum nie aanvaar nie, maar hy het nooit voorgestel dat eksperimente wat Quantum ondersteun nie geldige resultate is nie. Hy wou eenvoudig meer uit die teorie hê.

In hierdie geval het ons 'n teorie wat voorspel dat die resultate akkuraat rekening hou met die vertraagde kloksnelheid as gevolg van beweging en die versnelling as gevolg van 'n groter afstand van die middelpunt van die aarde. Alhoewel 'n mens kan voorstel dat 'n nuwe, tans onbekende teorie meer korrek kan wees, is daar eintlik geen ruimte om aan te dui dat die verwyding nie plaasvind nie.

As die muondata en die kloktoets nie oortuig nie, is die GPS-data oorweldigend. Daar is

2-dosyn satelliete met 2 dosyn sesiumklokke. Daar is honderdmiljoene ontvangers wat elkeen 'n navigasie-oplossing per sekonde lewer, solank hulle aangedryf word en seine ontvang. Daar is min toepassings van tegnologie wat so 'n groot hoeveelheid data verifieer. As hierdie uitbreidings nie werklik was nie, sou die hele stelsel nie so akkuraat wees as wat dit blyk uit tien miljoen van voorbeelde nie. Soos ek verstaan, moes die horlosies in die oorspronklike stelsel twee keer per dag vir Relativistiese effekte gekorrigeer word om die horlosies voldoende gesinkroniseer te hou om aan die akkuraatheidsvereistes te voldoen. Dit blyk dat die uitbreidings in hierdie geval 'n baie aanhoudende effek was.


So Micheal, jy haal my aan dat ek binne die eerste drie sinne van hierdie berig gesê het dat ek glo in tydsverwidering en 'n gedagte-oefening wil doen. (Tydsverwidingsbewyse van Muon-eksperimente en GPS-kompensasies word as feit beskou, maar ter wille van hierdie een voorbeeld wil ek die volgende stel omstandighede verwys.) Ek het in 'n aantal vorige poste gesê ek glo in die tydsverwyding van die GPS-stelsel en gebruik dit gereeld tydens nagnavigasie in mariene navigasie. Maar tog wil u vir my sê dat wat ek gesê het, waar is. Ek stem saam met u en my daaroor. Ek respekteer u vorige boodskap op CN baie en hoop op effektiewe insig oor 'n eenvoudige gedagte-oefening?

Dit is bewerkstellig deur 'n stelling van Einstein te oordink

Alle probleme in die optika van bewegende liggame kan opgelos word volgens die metode wat hier gebruik word. Wat noodsaaklik is, is dat die elektriese en magnetiese krag van die lig wat deur 'n bewegende liggaam beïnvloed word, in 'n stelsel van koördinate in rus relatief tot die liggaam getransformeer word. Hierdeur sal alle probleme in die optika van bewegende liggame verminder word tot 'n reeks probleme in die optika van stilstaande liggame.

in sy referaat "Oor die elektrodinamika van bewegende liggame", afdeling 8, laaste paragraaf.

Ek verstaan ​​nie heeltemal wat Einstein daarmee bedoel nie. Miskien kan u kundigheid uithelp.

# 36 JerryWise

[snip] "En dit bring die punt van die bepeinsing oor. Waarom word alle lesings in 'n traagheidsraamwerk teruggevoer na die stelsel van koördinate in rus wanneer die skip staak (beweeg uit 'n traagheidsraamwerk), behalwe die ouderdom van die drieling aan boord van die skip? ' [snip]

Jarad en HiggsBoson het die tegniese kant van die vraag beantwoord, en llanitedave het die sielkundige kant genoem. Maar ek is bly dat u dit gevra het, want deur dit te vra, het u ons ingeligte lede in staat gestel om weer huis toe te ry wat 'n vreemde ding is wat relatiwiteit is.

# 37 JerryWise

Ek het weer hieroor nagedink en wil dit in 'n bietjie ander perspektief stel. Soos Joad hierbo genoem het, is die wetenskap verduidelik en dit is voor die hand liggend. Ek vermoed dat ek en baie ander hier studente is wat kennis soek (dit lyk asof baie dit volg volgens die aantal sienings). Ek verstaan ​​die formules en die logika agter Relativistiese voorbeelde. Voorbeelde soos die bal van 'n vlagpaal in 'n bewegende trein met 'n platformwaarnemer en die arme eksperiment wat vinnig op die vlagpaal sit. Ons het 'n eenvoudige voorbeeld hierbo in die OP voorgestel. Ons verstaan ​​die figure en tot 'n mate die Wetenskap. As studente moet ons toegelaat word om te vra: 'Waarom is dit?'. Ek weerlê nie die wetenskap nie (ek sou dit nooit waag nie) en vra net: "waarom is dit?".

Aangesien Higgsbosen die woord 'postulaat' noem, laat my een formuleer (of ekstrapoleer).

âDie ligsnelheid is in alle verwysingsraamwerke dieselfde. Aangesien die spoed van lig in alle verwysingsraamwerke dieselfde is, is die proporsionele ligspoed in alle verwysingsraamwerke dieselfde. .5C (1/2 die snelheid van die lig) is in alle verwysingsraamwerke dieselfde, net soos die snelheid van die lig dieselfde is.â €

As dit nie volledig in die wetenskap bewus is nie, sê dan 'dit is verkeerd'. Maar asseblief, as dit verkeerd is, verduidelik die 'waarom' nie net die 'verkeerde' nie.

Laat ons dus ons voorbeeld na enkele basiese beginsels neem. Ignoreer die optiese weersprekings in die eerste boodskap. Ons spreek nou slegs die skip aan op die reis onder 'Spesiale Relatiwiteit', wat die voorwaardes weerspieël wat Jarad hierbo bereken het.

1. Die skip reis vanaf Planeet A na Planeet B hierbo by .5C. Planeet A en Planeet B hierbo is tien ligjare van mekaar. Die skip ry teen die ligspoed en neem 20 jaar (10 x 2) om die reis te onderneem. As u die reis binne minder of meer tyd aflê, beteken dit dat u nie by .5C reis nie.

2. Die skip is onderhewig aan Relativistiese Tydverwyding wat van Planeet A na Planeet B gaan .5C. Die berekeninge hierbo bewys dat die skip 17,25 jaar sal neem om van Planeet A na Planeet B by .5C te gaan, onderhewig aan tyddilatasie.

Lyk dit buite lyn?

As daar na hierdie stellings gekyk word, is daar 'n teenstrydigheid? Indien wel, wat dink jy sou die rede daarvoor wees? Ek dink ek sien sommige.

Eerstens het die skip 20 jaar geneem om die reis te onderneem (2). Maar die horlosies op die skip, die ouderdom van die insittendes en die ouderdom van die skip is 17,25 jaar, dus het die skip 17,25 jaar geneem om die reis te onderneem. Dit lyk dus of die skip 17,25 en 20 jaar geneem het om die reis te onderneem. Ons kan Lorentz-transformasies gebruik om die tyd wat 17,25 jaar tot 20 jaar uitgebrei is, te transformeer. (Ons kan ondersoek instel na hoe die transformasie op beide maniere sal werk, maar ons moet verstaan ​​watter waarneming die raam "met rus" is en watter 'n traagheids- of 'in beweging' raamwerk onderhewig is aan tydsverwyding. Maar ons kan nie aanneem dat die Die 20-jaar-figuur is die rusraam, aangesien dit vermeld word, en dit word ook bepaal deur die snelheid van die lig (onveranderlik). Ek dink albei tydsraamwerke werk goed, want ons het 'n omskakelingsfaktor (Lorentz Transform) en die wetenskap is gesond. Ek verstaan ​​nie die wetenskap of definisie nie, net een aspek van die resultaat. Ons moet 'n Lorentz-transform gebruik vir presiese plek-afsnitte op die reis vir die fisiese ligging van die skip, sodat dit die tydverruimde lesings omskakel na die onderliggende rusraam. Aan die einde van die reis moet ons 'n Lorentz-transform op die skeepsklok gebruik om dit dieselfde te laat lees as die 20-jarige periode van die reis. Waarom doen ons nie dieselfde transformasie op die ouderdom van die inwoner nie? Lyk 'n eenvoudige vraag. As student vra ek waarom dit is.

Tweedens, as die skip van planeet A na planeet B beweeg tydens .5C en .5C 'n invariant is (C / 2), sal die skip 20 jaar neem om die reis te onderneem. As die insittendes van die skip binne iets anders as 20 jaar vaar, sal hulle die afstand fisies deurkruis het op 'n ander figuur as .5C. Dit lyk asof dit binne 'n onveranderlike verskil het. As ons die Lorentz Transform op die ouderdomme van die insittende aan die einde van die reis gebruik om hulle in lyn te bring met die onveranderlike .5C, is hul ouderdomme nie meer tydverruim nie. Sien iemand hier 'n teenstrydigheid? As student vra ek hulp met 'n verduideliking, nie die berekeninge nie (dit is heeltemal korrek soos hierbo deur Jarad gegee).

Enige hulp hieromtrent sal ten volle waardeer word.

# 38 Meneer T

Dave, ek het my kop hieroor probeer draai.

Maar ek het gedink is die effek van tydverspreiding as gevolg van versnelling nie snelheid nie?

maybe it is is not traveling at c that distorts space-time, but the acceleration needed to get there.

acceleration is a result of a force

which is why gravity also distorts space-time.

#39 Jarad

Because space is dilated as well. To the ship, it was moving at 0.5 C for 17.33 years,and only travelled 8.66 light years. It's odometer would show 8.66 light years, and it's clocks will show 17.33 real years (and the ages of the passengers are just more clocks). When it stops, none of those previous measurements change, even though the distance and clock rates reset.

#40 JerryWise

.
But I was thinking isn't the time dilation effect due to acceleration not velocity??
.

#41 Joad

I can think of two things, Jerry (which is no guarantee that the thoughts are any good ), but here goes:

1. Planet A and Planet B are not 10 light years apart, as such. Their distance is always relative to the situation of some measuring point. Mathematical transforms can bring the measurements together but do not establish an "actual" distance between the planets because there is no actual distance: there is only distance as measured, and that is always relative. Thus, to the moving ship, the distance is less than it is to the underlying frame measurement. Both measurements are right, just as I weigh 135 pounds on earth but would weigh a lot less on the moon: both measurements are my "real" weight.

2. The three sisters aged 17.3 years on the voyage. They would have aged 20 years if they had stayed home, but time, and their bodies, changed (aged) at a different rate on the voyage. When they land, mathematics can restore a measurement equilibrium of sorts, but their bodies are younger relative to what they would have been if they had stayed "home" because the time in which their lives took place got foreshortened for a while.

In other words, there is no absolute time for their bodies to age.

#42 HiggsBoson

Jerry, it seems that I missed the point of your post. You are asking why the age dialation sticks and other apparent contradictions go away. Some of the confusion here may be due to language.

First, the ship took 20 years to make the journey (2). But the clocks on the ship, the age of the occupants and the ship’s age read/are 17.25 years so the ship took 17.25 years to make the journey. So it looks like the ship took both 17.25 and 20 years to make the journey.

In these types of problems one must always make sure that the meaning is unambiguous. The trip took 20 years as measured in the reference frame of Planet A. This is a calculation. There is no way for anyone on Planet A to know that this is true. It will take at least 10 years for that information to return to Planet A.

In the statement of the problem and the outcome of experiments one must keep in mind the limitations of each frame. No one can actually know some of the things that are ‘given’ in the statement of the problem.

One of my hobbies is film making. Film directors have the ability to show the audience what is ‘really’ going on in two or more locations at a time. This is called ‘parallel action’. Imagine a house husband having a rough day with the kids and the wife having a hard time at work. A director can cut between activities going on at the home and work location with reckless abandon. One can even include a home to work phone conversation between the two to clearly show that the views are near simultaneous. The camera can cut to any location in the universe just in time to show the audience relevant information that will propel the story developing in the mind of the audience. Called the ‘omnipotent camera‘, it sees all, it knows all and it gets there just in time to see important events happen. In some cases it will actually show you the same action from more than one point of view ‘explosions are expensive they tend to get used 2 or 3 times’.

The challenge with a thought experiment is to avoid observing the experiment from an omnipotent camera. The mind creates an ‘absolute’ reference frame ( Point of View to film makers ) to which everything else is compared. The omnipotent camera is allow to have points of view that do not correspond to any real point of view ( no one actually views people talking in a car from the POV of the hood ornament ).

The two reckonings of the trip time are both valid when the ship reaches Planet B. There is no absolute frame from which one can say what really happened. When the ship returns to planet A, there is a difference in time experience by those who traveled vs those who did not. The dilations that stick are those experienced by those who experience acceleration during the interval in question. Because the travelers had to accelerate to change from moving toward planet B to moving toward planet A they will experience a sticky dilation compared to those who remained in the Planet A reference frame.

#43 Joad

Jerry's thread has helped me grasp more fully (I think) the often-cited observation in this forum that time does not exist for a photon. I think I can understand better, now, desitter's observation that space doesn't really exist for a photon. It makes sense: if space/time compresses as C is approached, at C space/time would compress to, well, nothing. Right?

But that doesn't mean that there is no space/time. Relative to poky old earth that photon from M51 I looked at last night came a long way baby, and took a long time to get here. So that photon both crossed a lot of space/time (relative to me) and is suspended in its own relativistic "now" relative to its own C movement. And both are real.

#44 HiggsBoson

Joad, I think that the short answer here is ‘yes‘. Photons do not experience the passage of time as we know it. However, one result of Relativity is we lost the classical concept of time. In the Relativistic view space and time are a part of an inseparable thing called space-time. A singular noun describing that stuff that contains the universe.

In General Relativity we learn that space-time is flexible enough to twist and form interesting shapes. It is very hard to understand the results of Relativity using the classical concept of time. Unfortunately, the concept is so intuitive to us that it is hard to let it go and embrace this new space-time stuff prior to attempting to understand a problem.

To quote Feynman ‘no one understands quantum, we just get use to it.’ Every quantum mechanical wave function I have ever seen for a real object was non-zero everywhere in the universe. What am I to make of this? The wave function for an electron in the ground state of the hydrogen atom is non-zero everywhere in the universe.(1) Yes, I can talk about what this means from a mathematical standpoint. But as a person with a mind I do not understand why such functions provide accurate predictions of the behavior of electrons.

In the case of that M51 photon, from the reference frame of the Earth, the wave function that describes the probability of an observation of that photon has a maxima that took 23 million years to get here. However, in the reference frame of the photon, no time has passed. While I understand the math this does not conform with anything within my personal experience.

Allow me to express my gratitude for this forum. It helps me blow the dust off of the few remaining brain cells that I have.

1) With the exception of a singularity at the center of the nucleus. The function is zero at the origin and has radial symmetry. Because the Proton is centered at this point and has non-zero radius the probability of the electron collapsing, (being observed), into the Proton is non-zero.

#45 JerryWise

Jerry's thread has helped me grasp more fully (I think) the often-cited observation in this forum that time does not exist for a photon. I think I can understand better, now, desitter's observation that space doesn't really exist for a photon. It makes sense: if space/time compresses as C is approached, at C space/time would compress to, well, nothing. Right?

But that doesn't mean that there is no space/time. Relative to poky old earth that photon from M51 I looked at last night came a long way baby, and took a long time to get here. So that photon both crossed a lot of space/time (relative to me) and is suspended in its own relativistic "now" relative to its own C movement. And both are real.

HiggsBosen absolutely is on track with the concepts. And I think Joad is on track with what I've tried to understand.

What I did in the OP was present a scenario which tended to free the thought exercise from some conventional thoughts on Relativity. This by placing the motion of the three observers in a common "Omnipotent Camera" (thanks for that Micheal) observational mode. This was done by giving all three observers visual access to the other's clock faces. Note I said clock faces and not "time". This is the clock face "information" and it is conveyed by the one absolute we can’t refute by definition. The speed of light ©. The special optical device (large binoculars?) at each location could observe the clock faces at each of the other observers locations. This Omnipotes (made that up) the observers.

Is it possible to do this? Yes or much of what we have learned about light and distances to galaxies, stars and the edge of the Universe is flawed (possibly a valid assumption but not one we can take based on present knowledge). Here we are looking at light as a carrier of information (what we discern in the image of the clock face or the time it shows at the distant location and not a photon’s characteristics). This information is moving between these locations at C and in the omnipotent camera's eye (visual perception of all three locations) this would make the three observers frames of reference available to each observer in real time minus the necessary transit time of light (the carrier of the information). Light does propagate at a given rate and we can transit along that path. This is why we see Red and Blue shifts indicating a motion relative to the emission source. This is also why I suggest in the OP the clock face information is valid visually between all observers at each stage of the journey. We would also see the light from the clock face of the approaching planet B as slightly blue tinted (blue shift of the light frequency indicating an approach to the light source) and the clock face of planet A slightly red tinted (indicating a move away from that light source). It is how these readings contradict with how some calculations are applied that is a concern. (I hope I'm making this clear. I have it thought out but putting something this involved to pen is rough.)

As Joad says, "time does not exist for a photon". But that Photon has a given set of physical characteristics that define its behavior. It moves at "C" in all frames of reference and moving from an emitting location to a perceiving location it moves along a physical path at "C" which is a given and fixed speed/time span. So time does not exist for the Photon but time does exist for any journey a photon will make. Photons are worthless to us without bringing a shape in their group presentation (what we see). If they bring the shape of a distant clock face we can read that face just as the observer at that location. So the camera doesn't need to relocate and we become the omnipotent observers at each location.

I am not saying there is a problem with Relativity. Nor am I saying there is a problem with the intuitive visual scenario in the original post. I am proposing a mental exercise that appears to show a contradiction. If we can make a visual observation of an approaching and receding light source traveling between the light sources at the same instant (did not say simultaneously) we can compare the information as presented. If this information does not agree with the calculations then we have a "Triplet Paradox". To say the visual indications of the omnipotent binoculars is flawed disputes the nature of light propagation. To say it is valid disputes the application of some Relativistic calculations. Peculiar.

I’d like to post up a suggestion of why there might be a misconception using the moving train, dropped ball and flagpole scenario so common in discussing Relativity. But first need to run put out a fire.


What Will An Action Camera Record If It Falls Into A Black Hole?

In the whole universe, there is only one place where our modern technology cannot survive, and obviously, it is a Black Hole. But just for a minute, suppose that scientists have made a powerful and strong action camera that can survive any threat in the universe and dropped it into a black hole. What will it record for us?

The action camera falling into a black hole may transmit a signal to us up to the intersection of the event horizon. As you approach a black hole, the time for the camera will slow down, which will lead to a shift of its signal to the region of long waves (gravitational redshift), and the shift will noticeably increase every second.

Schematic representation of the gravity wells of the Sun, a neutron star and a black hole

The redshift is a consequence of the time dilation for the action camera in the frame of reference of an observer located far from the black hole. That is, the camera in its frame of reference of 60 frames per second will still shoot and send us its records, but 1 second for the camera can turn into hours, years and ultimately billions of years for us.

That means that huge intervals of time will pass for an observer on the earth between the arrival of frames, and the picture will change very slowly.

Therefore, soon after starting the camera, the usual technique will not be able to catch this signal and restore the video from it, but if necessary, you can create devices that can capture the long-wave signal and turn it into a video.

Another, more significant problem will be the noise of the signal and the huge temperature, because a huge amount of substance usually falls into a black hole, which, when dropped, heats up to hundreds of millions of degrees

Nevertheless, let’s say that we were able to protect the camera from high temperature and filter the signal, so what will we see?

The view that the camera records depends on how massive the black hole will be. In black holes of stellar mass, the gravitational field is very heterogeneous, huge tidal forces appear in it that will tear the camera apart long before it approaches the black hole. All that we will see in this situation is a hot accretion disk and darkness in the middle of horizon events. To see something more interesting, you need to send the camera into a supermassive black hole, where the tidal forces are much weaker.

Near a black hole, space-time is strongly curved, and the closer to the singularity, the greater the curvature of space-time. When the camera begins to “sink” into the gravitational well of the black hole, the field of view of the camera will begin to narrow, in fact, the light on one side (right or left) of the camera will cease to reach it, and eventually all the light of the universe will degenerate into a small blue dot (due to gravitational blue shift). Before passing the event horizon, total darkness will come, however, we will not have time to see this, because for us, by that time, billions of years will pass.


Time Dilation Examples

The effects of time dilation are used often in science fiction stories, dating back to at least the 1930s. One of the earliest and most well-known thought experiments to feature time dilation is the famous Twin Paradox, which demonstrates the curious effects of time dilation at its most extreme.

Time dilation becomes most apparent when one of the objects is moving at nearly the speed of light, but it manifests at even slower speeds. Here are just a few ways we know time dilation actually takes place:


Was time dialation understood before 1905?

I seem to recall the concept going back before Einstein's Special Theory of Relativity. In fact, I believe Galileo knew of time dilation in an early form of relativity he proposed.

#3 jayhall0315

There were a number of physicists playing around with different dimensions and the ether including Poincare and Lorentz but none really made note of variable time (it simply did not occur to them that something so fundamental could be based on the observer reference frame). The only person I am aware of who actually looked at variant time was the polymath Fredrick Carl Gauss. He was the first I am aware to look at the ancient equation d=vt on a curving surface and realize that time might actually be distorted by curvature. (this is really more in the general relativity realm) So, the short answer is no. Einstein really was the first to see the whole picture from special relativity including the variable passage of time depending upon the observer's reference frame.

#4 astro_NC

Others did in fact hit upon some of the ideas central to relativity theory, but Einstein's way of thinking about it is what revolutionized physics.

This video contains perhaps the most beautiful visual demonstration of how special relativity works. Darren, your question is also discussed and answered in a most profound way. One must pay close attention to the video, but it is well worth it.

Edited by astro_NC, 08 January 2017 - 12:49 AM.

#5 GJJim

There were a number of physicists playing around with different dimensions and the ether including Poincare and Lorentz but none really made note of variable time (it simply did not occur to them that something so fundamental could be based on the observer reference frame). The only person I am aware of who actually looked at variant time was the polymath Fredrick Carl Gauss. He was the first I am aware to look at the ancient equation d=vt on a curving surface and realize that time might actually be distorted by curvature. (this is really more in the general relativity realm) So, the short answer is no. Einstein really was the first to see the whole picture from special relativity including the variable passage of time depending upon the observer's reference frame.

Leibniz, and later Mach argued that the concept of time could be cast in terms of relations between physical events (order, simultaneity, etc.) and there was no need for the absolute framework championed by Newton. Time and space are more akin to a relational database than a giant aquarium. Einstein's stroke of genius was to condense these largely philosophical arguments into a mathematically consistent model that was acceptible to scientists of his day.

Edited by GJJim, 08 January 2017 - 11:38 AM.

#6 JonNPR

Ja. Fitzgerald in 1889, followed by Lorentz in 1892 devised the contraction equations in order to explain the Michelson-Morley aether experiment. But as the Wiki explains, there's depended upon ad hoc assumptions and only an hypothesis. Einstein was the first to show a better explanation, in 1915. He demonstrated that contraction wasn't necessary due to traveling through a hypothetical aether, in an attempt to save the aether idea. Instead, it was directly due to special relativity, a full fledged (scientific, formal) theory.


Is Time Dilation Real?

Is time dilation real? Such as when something speeds up or when nearing a black hole, like in Interstellar?

Some supermassive black holes at the centre of galaxies are devouring the surrounding material. They . [+] also divert part of it away through powerful winds and jets. This artist's impression shows how the black hole accretes the surrounding matter through a disc (orange). Part of the accreted material is pushed away in a wind (blue), which in turn powers a large-scale galactic outflow of molecular gas (red). Image credit: ESA/ATG medialab

Time dilation is real! And anyone who uses a GPS, or the “My Location” option on Google Maps, is making direct use of the fact that time dilation is real.

The idea behind time dilation is just as you describe, where your perception of time is dependent on how fast you’re going, or how close to a very large object you are. Interstellar actually did a remarkably good job of discussing time dilation in general, especially given how counter-intuitive ideas to do with relativity can be.

In Interstellar, the major plot points surrounding time dilation are the difference between time passing in two different locations, where the astronauts sitting near the black hole felt time passing at a slower rate than their families back home on Earth. Similarly, when some of them head down to the water world, they feel time passing at a slower rate than the astronaut left on the spacecraft. Now, ignoring the exact numbers of this difference, which depends on things like how big the black hole is, how far you are from it, and how much movie magical math you’re willing to go for, this kind of time dilation does happen.

The principle is this: the deeper you find yourself in a strong gravitational field, the slower your clock will run, relative to someone who is not in as strong a gravitational field. This can be translated into meaning the closer you are to something large, the slower your clocks will run. However, it also means that if your two clocks are the same distance from two objects, one which has a much stronger gravitational pull than the other (say, a planet for one clock, and a black hole for the other), the clock around the more massive object (the black hole) will run slower, even though both clocks are the same distance away.

Artist's illustration of a Navstar-2F satellite of the Global Positioning System (GPS). Image use: . [+] public domain.

A GPS satellite, which orbits about 12,500 miles above the surface of the earth, is further away from the Earth than those of us who live on its surface, which means that our clocks on the surface will appear to progress more slowly, relative to the clock on the GPS. Unfortunately, we really need these two clocks to operate in sync with each other, or the location information you get back starts to be increasingly inaccurate, defeating the point of having the GPS in the first place. This effect can be mathematically calculated, so we can correct for this slight difference in clock speed by setting the GPS clock to run a little slower than normal. Just a little slower this effect is only nanoseconds in size near the Earth.

But for a GPS, another form of time dilation is also in effect, because the fact that the satellite is in motion changes the clocks as well. This form of time dilation goes such that the faster you’re moving, the slower your clocks appear to move, relative to someone who is not moving. This effect gets more and more dramatic the closer to the speed of light you travel, so the offset in your clocks would get more severe.

A GPS satellite, which has to travel in a circle 12,500 miles above the Earth’s surface every 12 hours, is therefore going around 8,670 miles per hour. The speed of light is about 670,000,000 miles per hour, so our GPS is only going about 13 millionths of the speed of light. Dit is nie a significant fraction of light speed, but it’s enough that we can calculate and measure the impact that it has on the onboard clocks on the GPS.

The speedy motion of a satellite in space slows down its clocks relative to ours on earth, while its . [+] distance out of the earth's gravitational well makes satellite clocks go a bit faster. Thus shuttle pilots age less than a couch potato at the south pole, while geosynchronous orbiters (as well as interstellar dust particles) age more rapidly. This also means that the surface of the earth may be more than a year older than the earth's center, assuming that both were formed at the same time. Although the resulting errors in satellite timing are measured in nanoseconds, lightspeed is 30 centimeters (1 foot) per nanosecond so that the combined effects can result in GPS errors as large as 15 meters if not taken into account. Image credit: P. Fraundorf, CC BY-SA 3.0

As it happens, the gravitational time dilation has a more significant impact on the clock than the speed of the GPS relative to us on the ground. While the speed-up due to gravity is partially canceled out by the slow-down imposed by its 8,670 mph speed, there’s still some residual extra speed on those clocks because they’re so far away from the most concentrated part of the Earth's gravitational field. It’s this slightly diluted speed-up that’s calibrated into the clocks that we send up onto our satellites for the GPS network. (You’ll notice from the chart above that the space shuttle’s orbit was so close to the Earth that the gravitational effect wasn’t a big one, so the only clock-altering effect they were dealing with was due to their orbital speed around our planet.)

Anytime you pull your phone out to get directions to a restaurant, or to check how far you have left to walk, and your phone accurately figures out where you are, the GPS connection that underlies that software is relying on our understanding of relativity, and the time dilation the satellite is undergoing, to do its job properly.


Antwoorde en antwoorde

Hi All. I have a little bit of a strange question I'm trying to figure out.

If a human body was undergoing time dilation relative to another object, we believe that their brain, and therefore mind would slow down along with the rest of their body, correct?

If this is so, and light continues to hit a time-dilated person's eyes at a constant rate (because c is constant), would light accumulate on their retina and cause their vision to become blurred or brighter than usual because it's hitting their eyes faster than their brain can process it?

I suppose the same question applies to sound as well, though the speed of sound is not constant.

I may be off base here and have some incorrect assumptions. Thanks for humoring me!

How can the light be hitting their eyes both at a constant rate and faster?

And why are you concerned that a human body is undergoing time dilation relative to just one other object--there are billions of objects out there, which one is going to make a difference to the human body?

Sorry, I know my question wasn't very clear.

Say there is a light source, and I am far away from it. I begin moving towards it, and as I do so, time dilates for me (though it seems constant to me) and my body slows down relative to the light source. Even though my body has slowed down, the light hitting my eyes remains at a constant speed from my perspective due to the time dilation I'm undergoing. However, my brain is moving more slowly and taking longer to process the light hitting my eyes.

Would there be some sort of "build up" of light caused by my eyes not being able to process the light quickly enough?

Basically what I'm wondering is if things get brighter as you move towards a light source, and therefore more slowly when moving away. I know that they red/blue shift, but I'm wondering about brightness or some blurring due to not being able to process the light as quickly as it's coming in due to your body being slowed down.

I'm just using a single light source/object in this example to make it as simple as possible. I know that at the speeds we travel at in our human experiences that time dilation is largely negative, so I'm guessing this affect would be as well, but I'm curious about the principal of it.

I'm pretty sure the answer is "no," or, "this is an invalid question," but I don't understand why.

Sorry, I know my question wasn't very clear.

Say there is a light source, and I am far away from it. I begin moving towards it, and as I do so, time dilates for me (though it seems constant to me) and my body slows down relative to the light source. Even though my body has slowed down, the light hitting my eyes remains at a constant speed from my perspective due to the time dilation I'm undergoing. However, my brain is moving more slowly and taking longer to process the light hitting my eyes.

Would there be some sort of "build up" of light caused by my eyes not being able to process the light quickly enough?

Basically what I'm wondering is if things get brighter as you move towards a light source, and therefore more slowly when moving away. I know that they red/blue shift, but I'm wondering about brightness or some blurring due to not being able to process the light as quickly as it's coming in due to your body being slowed down.

I'm just using a single light source/object in this example to make it as simple as possible. I know that at the speeds we travel at in our human experiences that time dilation is largely negative, so I'm guessing this affect would be as well, but I'm curious about the principal of it.

I'm pretty sure the answer is "no," or, "this is an invalid question," but I don't understand why.

Your brain doesn't slow down due to time dilation nor do your bodily processes take any longer to process light coming into your eye. Time dilation is something OTHER people see you experiencing. You don't experience it at all. You WILL see light coming into your eyes differently than if you were not traveling a substantial fraction of c, but that's not due to any change in your mental processes.

Although I don't have a link handy, there are "movies" on the internet that show what incoming light would look like as you increase in speed, and similarly as you go into a black hole and "experience" time dilation due to gravity.

It's my understanding that time dilation is an objective phenomenon, but that the subject(s) of the time dilation wouldn't know it because their brain is slowed down along with their body, so they wouldn't see themselves as moving in slow motion, but they would see other people moving quickly, relative to them.

Given this, and that the stimuli hitting their senses (e.g. Light) is NOT slowed down, wouldn't their brains "fall behind" and not be able to process the sensations as quickly as they would be coming in?

Maybe I'm just reasking the same question again.

It's my understanding that time dilation is an objective phenomenon, but that the subject(s) of the time dilation wouldn't know it because their brain is slowed down along with their body, so they wouldn't see themselves as moving in slow motion, but they would see other people moving quickly, relative to them.

Given this, and that the stimuli hitting their senses (e.g. Light) is NOT slowed down, wouldn't their brains "fall behind" and not be able to process the sensations as quickly as they would be coming in?

I think I know what you are getting at and I think you are on the right tracks once we unravel which reference frames you are talking about. It is a good idea with relativity subjects to always be clear about which reference frame you are talking about.

OK, I will use the example of a camera rather than a human brain and eye, because it is simpler to analyse, but the principles are the same.

Consider:
A laser light source that emits 10 photons per second (in its rest frame).
A camera that has a fixed shutter speed of one second (in its rest frame).
The camera and laser source are moving towards each other at 0.8c as measured in the rest frame of either.

As seen in the camera reference frame:
Taking only the simple classical Doppler effect into account, about 50 photons would arrive at the camera film in the the one second the shutter is open, due to the light source going towards the camera. On top of this the light source is subject to time dilation, so it actually only emits 60 photons per second in this reference frame and the nett result is that about 30 photons per second arrive at the camera film in the one second the shutter is open. All this produces a blue shift and a brighter image than if the source was stationary with respect to the camera.
As seen in the laser source reference frame:
In this reference frame the camera appears to be moving towards the laser source. The laser is now not subject to time dilation and emits its regular 10 photons per second. The fact that the camera is going towards the source means that it would receive 18 photons per second if we consider only simple classic Doppler shift. However, due to time dilation the camera shutter is actually open for 1.6666 seconds in this reference frame and the end result is that 30 photons arrive at the film in the time the shutter is open. (Note that this is the same result as for the camera reference frame but the explanation is different.)

Now if you liken your eye and brain to the camera and its control circuits, then yes, in the reference frame of another observer moving relative to you, he explains why you see the blue shift and brighter image, partly in terms of your slowing brain processes just as if your brain was a mechanical device. However, in your own rest frame you do not experience any brain slow down and you explain everything in terms of Doppler shift and the slowing down of the emission rate of the light source.