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Chapter 6 Light space and time（第1页）

Chapter6Light，spadtime

&Grosseteste，BishopofLindthefirstcelloroftheUyofOxfordihtury，wasoheleadingthinkersofhisday，andapropoheworksoftheaGreeks。Forhim，asformanyphilosophers，thegelight’siderstandingthewrosseteste’streatiseo，entitledDeLuce，heextolstheprimaryimporta:‘Thefirst…isinmyopinionlight。Fhtofitsverynaturediffusesitselfiioninsuchaointoflightwillprodutaneouslyasphereoflightofasoever’。

Frosseteste，lightdefispropagationinstantlythroughouttheulight，thereishereforenoforumistakeplace。Matter，andthusthespatialextensios，arecoupledtolight，butotbeseparatelydefihisiio，spadmatter—ie’shaoquaiohedevelopmentologyinthesubsequeuries。

&ime

Foroheradmittednordemaioofspaceasapre-existiy，asortoftheatreisplayedthemselvese-scalemotioheheavenswasiohisideaofasetofuniversallaws。Einstein，bytrast，placeslightatthetreofspa，itdefiimebyvirtueofsettiffromooftheuher。Thefactthatthereisafinitemaximumspeedturnsouttomakespadtimeiein’stheoryofrelativityteachesusthatweotthithinkihisisbecauseourperofspadtimeisbasedosofdistaimeihesemeasuresappeardifferentlytothosemovious，becauseofthespeedlimitimposedbylight。

Howdoesthisstrawiningofspadtimebylightarise?Let’sstartwithoionofspathinkofthisasasortofscaffold—aaginaryrodsoffixedlengthallectedtogetherinathree-dimensionalframework，asshownionthoughtthatthissortofstructurepre-existeda，aalleventstookplaewhereinthisstructure。Eventsthereforebespecifiedbytheirdistanafixedpointintheframebygthenumberofrodstoreachthelooftheevent。Ofcourseeventsoccuratatime，too，sothesustbeequippedwitheasurethetime。Ifaclockisplacedatthejunofeachoftherods，theyallshowthesametimeeverywhereinspadweeasilydefinea‘uime’。

askseveralquestions。First，howshouldwebuildaclod，howshouldweeheyareallsynizedacrossspace?Third，howshouldwebuildaruler?Thesequestionsallhaveaareiedtothepropertiesoflight。Iothelastisthis:ohelengthofthepathtravelledbylightinavagatimeintervalof1299，792，458ofased。Itisthereforeliheahefirstquestion:howaccurateabebuilt。

28。Ascafspacemadeupofa3Dlattieasuringrods。Ateaterseisaclock，allsynized。

Clocks

Theprimarycharacteristicofaclockisthatit‘ticks’。Thatis，itsigervalsoftime。Bygtheicksbetwees，weatimeihem。Themorepreciseaclockis，themulartheiweeiagrandfatherclock，the‘ticks’areprovidedbytheregularsendulum。Ironicwristwatch，the‘ticks’aretheossofapieceofquartzcrystal。Thesearemuchmularthanthesendulum，whibeaffectedbythetemperatureandhumidityoftheplacewherethegrandfatherclockislocated。Thereforethequartzwatchissaidtokeepbettertimethaherclock。

&accuratetheworldarebasedonthehighlyregularclicksofeleovingaroundinatoms。We’veseenthatatomisjumpbetweeableehinanatom。Forsomeatoms，thediffereweentheselevelsisextremelywelldefiherateatwhipbetweewothereforebeusedtodefiicks，basedonthefrequeusedtopushtheelesupahetwystates。

Theideaissimpleenough:illumiomwithmicrowaves（recallthatmicrowavesarejustlikelight，butwithamuchlowerfrequensofossoftheelectricfieldpersedratherthanmillionsofbillionsasinthecaseofvisiblelight）。Thenslowlygethefrequenicrowavesuroheatylevelsmosteffitly。Thisdefihenumberofcyclesperseicrowaveradiatioicksofthetermsoftheenergylevelspagofeleaparti。

Therearemanyteicalgestobuildingsuicclogtheatthemiinitialstate，illuminatingwithmicrowavesiomaximizethesensitivity，detegthattheelesareihehigherstateatagiveclocksbasedoomsareaccuratewaytomeasuretime，witharateoftigthatdeviatesfrompleteandutterregularitybyohofaseehundredmillionyears。

TheseclocksprovideatimestandardthatisagreediionallyandmaintainedbygoverlaboratoriessuchastheNationalIandardsandTeology（NIST）iheNationalPhysicalLaboratory（NPL）intheUK，andPhysikalisisdesanstalt（PTB）iheyareposofmanyteologiesthatunderpinourdailylives。Foriheyarevitalflobalpositiohatisthebasisfation，ingthesatnavonlyusedincars。

ization

&geistosywoclocks，sothattheyarecalibrated。Oodothisisbysendingasignalfromooaartthefirstditotheotherclogitwhenyourfirst‘tick’occurred。Theperseofthatknowswhatfraoftickherclockisbehindyours（siheclocksarethesamestru，weassumetheytickatthesamerate）ahisinformatiohee。

&erestiothis。ImagitosynizeyourEarthtothatonadista，inafar-awaygalaxy。Yousendyourpulseoflightoffiio，andthenyoulaisfaraway，itmighttakeaverylohelighttiventhehighvelocityoflight。Meanwhileyolderahepersonwhoreceivesyoursynizationmessagewillhavereceiveditfromtheyoungyou—shewillseeyouasyouwerewhehemessage。

Likeelookatthenightsky，astars，weareseeihembyreglightthatlefttheirsurfag，longtimeago。Aalaxiesthatareevenfartheraway，sowelookintothedeepera，seeingtheuwasbillionso。Ihelightthatreachesusisalsobillionsofyearsold—ithasbeentravellingacrossspaagesihi。Lightistheoldestthingwetheuniverse。

Ourclocks，though，areabitclether。Aingfactisthatwhenyouputoheseanaeroplanemovingat800kphorso，youfindthatitticksslowerthaheground。Thatis，ifyousettheclockstotellthesametime，youwillfindthattheoheaeroplaneappearsfromthegrouigataslowerratethanthegrouhisisaaximumspeedatwhialsveyedbetweewoclocks—thespeedoflight。

Youseethisbylookiionihere，personAisonthegroundandpersonBisinanaeroplanemovingathighspeed。BwatchesasAsendsalightpulsetoamirrorsuspeHabovetheground。FromA’spoihelightpulsetravelsdistanceH。However，fromB’sperspectivethatsignalwilltravelaslightlyloahanHsiobemovingbackeedrelativetoB。Therefore，becausethesiglightspeedagtobothAandB，ahesameicksbetweensendihesigheoionisthatB’sclockistigslowerthanA’sseenfromA，andA’sclockistigslowerthanB’swhenseenfromB。Thiseffectiscalledtimedilation。

29。Timedilatioivemotion。ObserversAandBbothmeasurethetimeforapulsetoarriveatthesuspendedmirror。Theymeasuredifferenttimesbecausetheyaremoviooher。

&einarguedinasimilaraceshouldalsotract。Thatis，arodofB’simaginaryscaffoldshouldlooksmallertoAthaihispossession。Andviceversa:A’srodlooksshortertoBthanherown。