Physics- The Modern Revolution in Physics

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Whenthetravelingtwingetshome,shehasagedonlyafewyears, whilehersisterisnowoldandgray. RobertHeinleinevenwrote asciencectionnovelonthistopic,althoughitisnotoneofhis betterstories. Theparadox"arisesfromanincorrectapplicationoftheprincipleofrelativitytoadescriptionofthestoryfromthetraveling twin'spointofview. Fromherpointofview,theargumentgoes, herhomebodysisteristheonewhotravelsbackwardonthereceding earth,andthenreturnsastheearthapproachesthespaceshipagain, whileintheframeofreferencexedtothespaceship,theastronaut twinisnotmovingatall.

Itwouldthenseemthatthetwinonearth istheonewhosebiologicalclockshouldtickmoreslowly,notthe oneonthespaceship.


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Theawinthereasoningisthattheprinciple ofrelativityonlyappliestoframesthatareinmotionatconstant velocityrelativetooneanother,i. Theastronauttwin'sframeofreference,however,isnoninertial,becauseherspaceshipmustacceleratewhenitleaves,deceleratewhen itreachesitsdestination,andthenrepeatthewholeprocessagain onthewayhome. Theirexperiencesarenotequivalent,because theastronauttwinfeelsaccelerationsanddecelerations.

Acorrect treatmentrequiressomemathematicalcomplicationtodealwiththe changingvelocityoftheastronauttwin,buttheresultisindeedthat it'sthetravelingtwinwhoisyoungerwhentheyarereunited. First, there'snoclearcutwaytodecidewhetherthetimedistortionhappensduring theaccelerationsanddecelerations,orduringthelongperiodsofconstant-speed cruisinginbetween.

Thisisbecausesimultaneityisn'twelldened,sothere'sno well-denedanswerifEarth-boundEmmaasks,Ismysister'stimedistorted rightnow? Itmayevenbe apartofyourordinarylife. Theeectwasrstveriedexperimentallybysynchronizingtwoatomicclocksinthesameroom,andthen sendingoneforaroundtriponapassengerjet. Theyboughtthe clockitsownticketandputitinitsownseat.

Theclocksdisagreed whenthetravelingonegotback,andthediscrepancywasexactly theamountpredictedbyrelativity. Theeectsarestrongenough tobeimportantformakingtheglobalpositioningsystemGPS workcorrectly. Ifyou'veevertakenaGPSreceiverwithyouona hikingtrip,thenyou'veusedadevicethathasthetwinparadox" programmedintoitscalculations. YourhandheldGPSboxgetssignalsfromasatellite,andthesatelliteismovingfastenoughthatits timedilationisanimportanteect. Sofarnoastronautshavegone fastenoughtomaketimedilationadramaticeectintermsofthe humanlifetime.

TheeectontheApolloastronauts,forinstance, wasonlyafractionofasecond,sincetheirspeedswerestillfairly smallcomparedtothespeedoflight. AsfarasIknow,noneofthe astronautshadtwinsiblingsbackonearth! Anexampleoflengthcontraction Figurepshowsanartist'srenderingofthelengthcontractionfor thecollisionoftwogoldnucleiatrelativisticspeedsintheRHICacceleratorinLongIsland,NewYork,whichwentonlinein The goldnucleiwouldappearnearlysphericalorjustslightlylengthened likeanAmericanfootballinframesmovingalongwiththem,butin thelaboratory'sframe,theybothappeardrasticallyforeshortened astheyapproachthepointofcollision.

Thelaterpicturesshowthe nucleimergingtoformahotsoup,inwhichexperimentershopeto observeanewformofmatter. Sarah,however,saysthatsheherselfisnormal,andthatEmmais theonewhosoundsslow. Eachtwinexplainstheother'sperceptionsasbeing duetotheincreasingseparationbetweenthem,whichcausestheradiosignals tobedelayedmoreandmore. Theotherthingtounderstandisthat,evenif wedodecidetoattributethetimedistortiontotheperiodsofaccelerationand deceleration,weshouldexpectthetime-distortingeectsofaccelerationsand decelerationstoreinforce,notcancel. Thisisbecausethereisnocleardistinction betweenaccelerationanddecelerationthatcanbeagreeduponbyobserversin dierentinertialframes.

ThisisafactaboutplainoldGalileanrelativity,not Einstein'srelativity. Inthe asphalt'sframeofreference,thisisadeceleration. DiscussionQuestions A Apersoninaspaceshipmovingat Whatwoulditlookliketoan observeronEarth? B Aquestionthatstudentsoftenstrugglewithiswhethertimeand spacecanreallybedistorted,orwhetheritjustseemsthatway.

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Compare withopticalillusionsormagictricks. Howcouldyouverify,forinstance, thatthelinesinthegureareactuallyparallel? Arerelativisticeffectsthe sameornot? C Onaspaceshipmovingatrelativisticspeeds,wouldalectureseem evenlongerandmoreboringthannormal? D Mechanicalclockscanbeaffectedbymotion. Forexample,itwas asignicanttechnologicalachievementtobuildaclockthatcouldsail aboardashipandstillkeepaccuratetime,allowinglongitudetobedetermined.

E WhatwouldtheshapesofthetwonucleiintheRHICexperiment lookliketoamicroscopicobserverridingontheleft-handnucleus? To anobserverridingontheright-handone? Cantheyagreeonwhatis happening? Ifnot,whynotafterall,shouldn'ttheyseethesamething iftheybothcomparethetwonucleiside-by-sideatthesameinstantin time? F Ifyoustickapieceoffoamrubberoutthewindowofyourcarwhile drivingdownthefreeway,thewindmaycompressitalittle.

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Doesitmake sensetointerprettherelativisticlengthcontractionasatypeofstrain thatpushesanobject'satomstogetherlikethis? Howdoesthisrelateto discussionquestionE? Thesimplestargumentofthis kindisasfollows. SupposeJanettakesatripinaspaceship,and acceleratesuntilsheismovingat0.

Shethenlaunchesaspaceprobeintheforward directionataspeedrelativetohershipof0. Isn'ttheprobethen movingatavelocityof1.

Objectivity versus subjectivism

TheproblemwiththislineofreasoningisthatalthoughJanet saystheprobeismovingat0. Velocitiestherefore don'taddthesamewaytheydoinGalileanrelativity. Supposewe expressallvelocitiesasfractionsofthespeedoflight. Thederivationofthecorrectrelativisticresultrequiressometedious algebra,whichyoucanndinmybook SimpleNature ifyou're curious.

I'lljuststatethenumericalresultshere: Janet'sprobe,forexample,ismovingnotat1. Thedierencebetweenthe twotablesismostevidentaroundtheedges,wherealltheresults areequaltothespeedoflight. Thisisrequiredbytheprincipleof relativity. Forexample,ifJanetsendsoutabeamoflightinstead Section1. Thegreenovalnearthecenterofthetabledescribesvelocitiesthatarerelativelysmallcomparedtothespeedoflight,and theresultsareapproximatelythe sameastheGalileanones. The edgesofthetable,highlightedin blue,showthateveryoneagrees onthespeedoflight.

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Physicist Lee Smolin On Einstein's Unfinished Revolution in Quantum Physics: Author Q&A

On theotherhand,thecorrespondenceprinciplerequiresthattherelativisticresultshouldcorrespondtoordinaryadditionforlowenough velocities,andyoucanseethatthetablesarenearlyidenticalinthe center. Momentum Here'sanotherawedschemefortravelingfasterthanthespeed oflight. Theyseparateslightlyinmid-air,andthebaseballthereforehastime tohittheoorandreboundbeforeitcollideswiththeping-pong ball,whichisstillonthewaydown.

Theresultisasurpriseifyou haven'tseenitbefore:theping-pongballiesoathighspeedand hitstheceiling! Asimilarfactisknowntopeoplewhoinvestigate thescenesofaccidentsinvolvingpedestrians. Ifacarmovingat 90kilometersperhourhitsapedestrian,thepedestrianiesoat nearlydoublethatspeed,kilometersperhour. Nowsuppose thecarwasmovingat90percentofthespeedoflight. Toseewhynot,wehavetobackupalittleandthinkabout wherethisspeed-doublingresultcomesfrom. Foranycollision,there isaspecialframeofreference,thecenter-of-massframe,inwhich thetwocollidingobjectsapproacheachother,collide,andrebound withtheirvelocitiesreversed.

Inthecenter-of-massframe,thetotal momentumoftheobjectsiszerobothbeforeandafterthecollision. Beforethecollision,thelargeballismovingrelatively slowlytowardthetopofthepage,butbecauseofitsgreatermass, itsmomentumcancelsthemomentumofthesmallerball,whichis movingrapidlyintheoppositedirection.

Are There Revolutions In Physics?

Thetotalmomentumis zero. Afterthecollision,thetwoballsjustreversetheirdirectionsof motion. Themotionis shownasitwouldappearonthelmofanold-fashionedmoviecamera, withanequalamountoftimeseparatingeachframefromthenext. Film 1wasmadebyacamerathattrackedthecenterofmass,lm2byone thatwasinitiallytrackingthesmallball,andkeptonmovingatthesame speedafterthecollision. Saythesmallball hasamassof1kg,thebigone8kg. Inframe1,let'smakethe velocitiesasfollows: beforethecollision afterthecollision Tondallthevelocitiesinthis frame,wejustadd0.

Butwhatifallthesevelocitieswereinunits ofthespeedoflight? Nowit'snolongeragoodapproximation justtoaddvelocities. Weneedtocombinethemaccordingtothe relativisticrules. Forinstance,thetableonpage28tellsusthat combiningavelocityof0. Theresultsareverydierent: beforethecollision afterthecollision 0 0. Theballsappearforeshortened duetotherelativisticdistortionof space.

Thisisverynearlythewaythe scenewouldbeseenbyanantstandingonthebigball. According toanobserverinframet,however,bothballsaremovingatnearly thespeedoflightafterthecollision. Becauseofthis,theballs appearforeshortened,butthedistancebetweenthetwoballsisalso shortened. Tothisobserver,itseemsthatthesmallballisn'tpulling awayfromthebigballveryfast. Sohowcanthe dierent resultshowninguretbe possible? Theansweristhatrelativistically,momentummustnot equal mv. Theold,familiardenitionisonlyanapproximation that'svalidatlowspeeds.

Ifweobservethebehaviorofthesmall ballinguret,itlooksasthoughitsomehowhadsomeextrainertia.

It'sasthoughafootballplayertriedtoknockanotherplayerdown withoutrealizingthattheotherguyhadathree-hundred-poundbag fullofleadshothiddenunderhisuniform hejustdoesn'tseem toreacttothecollisionasmuchasheshould. Thisalsoexplainstheanswertoanotherparadoxoftenposed bybeginnersatrelativity. Supposeyoukeeponapplyingasteady forcetoanobjectthat'salreadymovingat0.

Whydoesn't itjustkeeponspeedinguppast c? Theansweristhatforceisthe rateofchangeofmomentum.

Einstein's Relativity and the Quantum Revolution: Modern Physics for Non-Scientists, 2nd Edition

Asitsvelocitygetscloserandcloserto c ,its approachesinnity. Tomoveat c ,itwouldneedaninnite momentum,whichcouldonlybecausedbyaninniteforce. Sofarwe'veonlyconsidered collisionsinwhichnoneofthekineticenergyisconvertedintoany otherformofenergy,suchasheatorsound. Let'sconsiderwhat happensifablobofputtymovingatvelocity v hitsanotherblob thatisinitiallyatrest,stickingtoit.

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