Welcome to Special Relativity! - Swinburne

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


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


• The“oldanswer”forconvertingtheco-ordinatesofeventsbetweenframesisprovidedbytheGalileantransformations

• AccordingtotheGalileantransformationsthereisanabsolutetime,onwhichbothframescanagree(𝑡* = 𝑡)

𝑆 𝑆′

Event

𝑥* = 𝑥 − 𝑣𝑡𝑦* = 𝑦𝑧* = 𝑧𝑡* = 𝑡


• “Absolutetime”isadeeply-ingrainedclassicalidea,whichweareabouttooverthrow– braceyourself!

https://www.azquotes.com/quote/1342652 https://store.moma.org/magnetic-sand-hourglass/124546-124546.html


• 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


• MichelsonandMorleysetouttodetectthischangeinspeedusingatwo-beaminterferometer

• Hereisaschematic:

𝐿

𝐿

Source

Beam-splitter,angledat45°

Mirror

Mirror

Detector

Usinginterference,theapparatuscandetectifthelighthastravelledadifferentnumberofwavelengthsalong

thetwobeams


• SupposetheEarthismovingthroughtheaetherwithspeed𝑣

• Thespeedofthelightbeamswouldbechanged!

𝐿

𝐿

Luminiferousaether

𝑣

𝑐 𝑐𝑐 − 𝑣

𝑐 + 𝑣Interferometermovingthisway

atspeed𝑣

𝑣𝑡/2


• Whatisthetimedifferencebetweenthetwobeams?

𝐿

𝑐 − 𝑣

𝑐 + 𝑣

𝑐 𝑐 𝐿

𝑣

𝑐𝑡/2𝐿


• TheMichelson-Morleyexperimentproducedanullresult–therewasnophasedifferencebetweenthetwobeams

• Thisresultsupportstheideathatthespeedoflightisthesameinallframes,andisnotmodifiedbyrelativemotion

• [MichelsonandMorleyarguedthatthenullresultwasproducedbecausetheEarthdraggedalongtheluminiferous ether!]

10m/s

𝑐 𝑐


Attheendofthissessionyoushouldbeableto…

• … outlinetheframeworkofevents,referenceframesandsynchronizedclocks usedforrelativityanalysis

• … befamiliarwithinertialframes,andwhytheyarespecial

• … statetheprincipleofrelativity,relatingtheresultsofexperimentswhichtakeplaceindifferentinertialframes

• … describetheclassicalGalileantransformation betweeninertialframes,withitsconceptofabsolutetime,andtheexperimentalevidencecontradictingtheseideas

Welcome to Special Relativity! - Swinburne

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