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WelcometoSpecialRelativity!
Physics2BRelativity&Electromagnetism,Semester22018
SPECIALRELATIVITY
Week6
Mon3Sep10.30-11.30EN303 Class1:FramesandEventsTues4Sep1.30-2.30EW301 Class2:Einstein’sPostulateWed5Sep3.30-4.30ATC421 Tut1:SpecialRelativitySet1Thurs6Sep3.30-4.30BA702 Class3:LorentzTransformations
ReadingWeek
Week7
Mon17Sep10.30-11.30EN303 Class4:Space-timeDiagramsTues18Sep1.30-2.30EW301 Class5:EnergyandMomentumWed19Sep3.30-4.30ATC421 Tut2:SpecialRelativitySet2(assessed)Thurs20Sep3.30-4.30BA702 Class6:RelativisticPhenomena
ELECTROMAGNETISM
Week8
Mon24Sep10.30-11.30EN303 Class1:ElectricForcesTues25Sep1.30-2.30EW301 Class2:ComputingtheElectricFieldWed26Sep3.30-4.30ATC421 Tut1:ElectrostaticsSet1Thurs27Sep3.30-4.30BA702 Class3:ElectrostaticPotential
Week9
Mon1Oct10.30-11.30EN303 Class4:Maxwell’sEquationsforElectrostaticsTues2Oct1.30-2.30EW301 Class5:ConductorsandCapacitorsWeds3Oct12.30-2.30AD207 Lab1:SolvingPoisson’sEquation(Group1)Weds3Oct3.30-4.30ATC421 Tut2:ElectrostaticsSet2(assessed)Thurs4Oct3.30-4.30BA702 Class6:InsulatingMaterials
Week10
Mon8Oct10.30-11.30EN303 Class7:ElectricCurrentTues9Oct1.30-2.30EW301 Class8:MagneticFieldsandForcesWeds10Oct12.30-2.30AD207 Lab1:SolvingPoisson’sEquation(Group2)Wed10Oct3.30-4.30ATC421 Tut3:Current/MagnetismSet1Thurs11Oct3.30-4.30BA702 Class9:ComputingtheMagneticField
Week11
Mon15Oct10.30-11.30EN303 Class10:Maxwell’sEquationsforMagnetismTues16Oct1.30-2.30EW301 Class11:MagneticMaterialsWeds17Oct12.30-2.30AD207 Lab2:TheBiot-SavartLaw(Group1)Wed17Oct3.30-4.30ATC421 Tut4:Current/MagnetismSet2(assessed)Thurs18Oct3.30-4.30BA702 Class12:ElectromagneticForces
Week12
Mon22Oct10.30-11.30EN303 Class13:InductionTues23Oct1.30-2.30EW301 Class14:CompletingMaxwell’sEquationsWeds24Oct12.30-2.30AD207 Lab2:TheBiot-SavartLaw(Group2)Wed24Oct3.30-4.30ATC421 Tut5:Time-VaryingFieldsSetThurs25Oct3.30-4.30BA702 Class15:ElectromagneticWaves
InWeeks6and7wewillstudySpecialRelativity
ChrisBlakeE-mail:[email protected]:92148624Office:AR303
Class1:FramesandEvents
Inthisclasswewilldescribetheframeworkofrelativity:events,inertialreferenceframes,
synchronizedclocksandco-ordinatetransformations
Class1:FramesandEvents
Attheendofthissessionyoushouldbeableto…
• … outlinetheframeworkofevents,referenceframesandsynchronizedclocks usedforrelativityanalysis
• … befamiliarwithinertialframes,andwhytheyarespecial
• … statetheprincipleofrelativity,relatingtheresultsofexperimentswhichtakeplaceindifferentinertialframes
• … describetheclassicalGalileantransformation betweeninertialframes,withitsconceptofabsolutetime,andtheexperimentalevidencecontradictingtheseideas
Space-time
• Inthenextfewclasseswewillstudythespecialtheoryofrelativity,acrowningachievementofmodernphysics
• Relativityre-framesourbasicunderstandingofspaceandtime
• Relativityisaunifyingtheory,whichgovernshowalllawsofphysicsmustbeconstructed
• [Oursubjectiscalled“special”relativitybecauseitexcludesgravity– thatrequiresgeneralrelativity!]
Space-time
• Inrelativity,wefindthattheconceptsofspace andtime– whichareseparateinclassicalphysics– becomeinextricablyconnected
• Takeafewminutestothinkofsome(everydayorphysics)waysinwhichspaceandtimearedifferent andsimilartoeachother https://xkcd.com/1524/
Events
• Inrelativity,weanalysetheworldintermsofevents
• Aneventisanoccurrenceataparticularplaceandtime
• Anobject’spathcanbeanalysedasasequenceofevents
https://www.nabo.com.au/whats-on/event/western-flat-fireworks https://spaceandperspective.com/2013/02/07/motion-photography/
Referenceframes
• Todophysicsweneedtoassignco-ordinatestoevents
• Wedosobycreatingareferenceframe, whichallowsthelocationandtimeoftheeventstoberecorded
• Thesameeventscanbeviewedfromdifferentreferenceframes,whichwouldassignthemdifferentco-ordinates!
Event
𝑥′
𝑦′
𝑥
𝑦
Referenceframes
• Wecanthinkofareferenceframeasbeinglikea“junglegym”fillingspace!
• Theeventsthatoccurateachvertex(positioninspace)arerecordedbyalocalobserveratthatvertex
• Eachlocalobserveriscarryingasynchronizedclock(whichticksimultaneously,intheframe)
http://w
ww.skywalkertrampo
lines.com
/sho
p/mod
ular-ju
ngle-gym
-playgroun
d/
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_principles
Synchronizedclocks
• Canyouthinkofanymethodswhichlocalobserversateachvertexofthereferenceframemightusetosynchronizetheirclocks?
Referenceframes
• Whydoesareferenceframehavetobeconstructedusingmanylocalobservers,ratherthanasingleobserversittingattheorigin?
• Weneedtorecordeventsattheirspace-timelocation,ratherthanworryingaboutthetraveltimeoflight
Event
Event
Thisisbadbecausesimultaneouseventswouldnotappeartobesimultaneous!
Inertialframes
• Somereferenceframesarespecial
• Inaninertialframe,afreely-movingobject– thatis,anobjectexperiencingnoexternalforces– moveswithconstantvelocity(i.e.,Newton’sFirstLawholds)
• Inertialframesmoveuniformly withrespecttoeachother
https://www.gizmodo.com.au/2016/04/what-happens-when-you-cook-french-fries-in-space/ https://en.wikipedia.org/wiki/Special_relativity
NoteintheWorkbook
Inertialframes
• Inanon-inertialframe,observerswillnotice“pseudo-forces” – thatis,effectsnotcausedbyreal,physicalforces
https://xkcd.com/123/
https://www.thinglink.com/scene/877700809561735169https://www.pinterest.com.au/bestonamusement/
Inertialframes
• Agoodexampleistocomparewhatyouexperienceinanaeroplane(1)stationaryontheground,(2)takingoff,and(3)duringsmoothflight
• Youexperienceaforceduringtake-off,butsmoothflightfeelslikebeingontheground!
https://www.flysfo.com/newsletter/sfo-community-newsletter-spring-2009https://www.adelaidenow.com.au/news/national/problems-hit-qantas-a380-london-take-offhttps://www.ausbt.com.au/qantas-to-start-airbus-a380-flights-to-dallas-from-september
Principleofrelativity
• Theprincipleofrelativityassertsthatthelawsofnatureareidenticalinallinertialframes,orinotherwords,noexperimentcandistinguishoneinertialframefromanother
• “Withoutlookingoutoftheaeroplanewindow,wecan’ttellwhetherwe’reinsmoothflightorontheground”
https://owlcation.com/stem/What-Were-Galileos-Contributions-to-Astronomy
• Thisisanoldidea,usuallyassociatedwithGalileo.WewillsoonseeEinstein’stwist!
NoteintheWorkbook
Principleofrelativity
• “Thelawsofnatureareidenticalinallinertialframes”
• Alawofnatureisamathematicalrelationrelatingdifferentphysicalquantities
• AnexampleisNewton’sSecondLaw:�⃗� = 𝑚�⃗�
• Whathappensifwetransformtoadifferentinertialframe,�⃗�* 𝑡 = �⃗� 𝑡 + 𝑉./012302?
• Acceleration�⃗� = 𝑑�⃗�/𝑑𝑡,so�⃗�* =�⃗� andthelawisunchanged!
Transformingbetweenframes
• Acentralquestionofrelativityiscomparingmeasurementsofeventsindifferentinertialreferenceframes
• Wewilloftenrefertoastandardarrangementoftwoinertialreferenceframes,𝑆 and𝑆′,withconstantrelativespeed𝑣,orientedsuchthatthe𝑥- and𝑥′-axescoincide
𝑆 𝑆′
Event Eachframeisoutfittedwithastandardlatticeofobserverswithsynchronizedclocks
Transformingbetweenframes
• The“oldanswer”forconvertingtheco-ordinatesofeventsbetweenframesisprovidedbytheGalileantransformations
• AccordingtotheGalileantransformationsthereisanabsolutetime,onwhichbothframescanagree(𝑡* = 𝑡)
𝑆 𝑆′
Event
𝑥* = 𝑥 − 𝑣𝑡𝑦* = 𝑦𝑧* = 𝑧𝑡* = 𝑡
Transformingbetweenframes
• “Absolutetime”isadeeply-ingrainedclassicalidea,whichweareabouttooverthrow– braceyourself!
https://www.azquotes.com/quote/1342652 https://store.moma.org/magnetic-sand-hourglass/124546-124546.html
Transformingbetweenframes
• TheGalileantransformationsmakeanimportantpredictionthatvelocitiesindifferentframessimplyaddandsubtract
• Alittleoverahundredyearsago,physicistsrealizedthatthisisnotexactlythecase
10m/s
10m/s 20m/s
Michelson-Morleyexperiment
• Oneofthekeypiecesofevidenceagainstthisworld-viewwasprovidedbytheMichelson-Morleyexperiment(1887)
• Thisexperimentwasfocussedontheroleoflight,whichisacriticalingredientofrelativity
• Inthelate19th century,physicistsbelievedthatlightwavestravelledatfixedspeedinamedium,fixedinspace,calledtheluminiferous aether
• SincetheEarthorbitstheSun,ourspeedrelativetotheaether wouldchange,whichwouldcauseachangeinthespeedoflightwemeasure
https://en.wikipedia.org/wiki/Luminiferous_aether
Michelson-Morleyexperiment
• MichelsonandMorleysetouttodetectthischangeinspeedusingatwo-beaminterferometer
• Hereisaschematic:
𝐿
𝐿
Source
Beam-splitter,angledat45°
Mirror
Mirror
Detector
Usinginterference,theapparatuscandetectifthelighthastravelledadifferentnumberofwavelengthsalong
thetwobeams
Michelson-Morleyexperiment
• SupposetheEarthismovingthroughtheaetherwithspeed𝑣
• Thespeedofthelightbeamswouldbechanged!
𝐿
𝐿
Luminiferousaether
𝑣
𝑐 𝑐𝑐 − 𝑣
𝑐 + 𝑣Interferometermovingthisway
atspeed𝑣
𝑣𝑡/2
Michelson-Morleyexperiment
• Whatisthetimedifferencebetweenthetwobeams?
𝐿
𝑐 − 𝑣
𝑐 + 𝑣
𝑐 𝑐 𝐿
𝑣
𝑐𝑡/2𝐿
Michelson-Morleyexperiment
• TheMichelson-Morleyexperimentproducedanullresult–therewasnophasedifferencebetweenthetwobeams
• Thisresultsupportstheideathatthespeedoflightisthesameinallframes,andisnotmodifiedbyrelativemotion
• [MichelsonandMorleyarguedthatthenullresultwasproducedbecausetheEarthdraggedalongtheluminiferous ether!]
10m/s
𝑐 𝑐
Class1:FramesandEvents
Attheendofthissessionyoushouldbeableto…
• … outlinetheframeworkofevents,referenceframesandsynchronizedclocks usedforrelativityanalysis
• … befamiliarwithinertialframes,andwhytheyarespecial
• … statetheprincipleofrelativity,relatingtheresultsofexperimentswhichtakeplaceindifferentinertialframes
• … describetheclassicalGalileantransformation betweeninertialframes,withitsconceptofabsolutetime,andtheexperimentalevidencecontradictingtheseideas