ProfessorJasperHalekasVanAllen70MWF12:30-1:20Lecture

¡  First,openthewebpage(https://rwpoll.comorhttps://account.turningtechnologies.com)ortheResponseWareapp§  EnterthesessionIDontheboard

¡  WaituntilIopenpolling(arrowchangestosquareonmyscreen)

¡  EnterA,B,C,D,orE§  Canchangeansweraslongaspollingstillopen

¡  AfterIclosepolling,wewillseeahistogramoftheresults

¡ Whatintrophysicsseriesdidyoutake?

A.  PhysicsI,II,&IIIhere

B.  IntroductoryPhysicsI&IIhere

C.  Anintrophysicsseriesatanotherinstitution

D.  Didnottakeanintrophysicsseries

E.  Other

¡  Whenyougraduate,doyouwantto:

A.  Getahigherdegreeinphysics?

B.  Getahigherdegreeinanothersubject?

C.  Workinengineering,industry,computerscience,

datascience,orothertechnicalfield?

D.  Workinanon-technicalfield?

E.  Fleethecountry?

¡  Areyoulookingforwardtobeingabletoexplainquantummechanicstoyourfriendsand/orsignificantother?

A.  Yes,Ienjoydemonstratingmyintellectualacumen

B.  No,Ihavebetterthingstotalkabout

C.  MysignificantotherwouldleavemeifIbroughtup

quantummechanics

D.  WhytheheckelsewouldIbetakingthisclass!!??

Attimet=0,thetwoframescoincide.AballisatrestinframeS.Itspositionis• x=2minS• x’=2minS’

...-3-2-10123...

...-3-2-10123...

u

FrameS’ismovingtotheright(relativetoS)atu=1m/s.Attimet=3sec,thepositionoftheballis• x=2minS• x’=-1minS’

...-3-2-10123...

...-3-2-10123...

u

Attime0,theballwasatx=x’.Attimetlater,theballisstillatxinSbutwhereisitinS’atthesametimet?a)x’=x b)x’=x+ut c)x’=x-ut

...-3-2-10123...

...-3-2-10123...

u

Attime0,theballwasatx=x’.Attimetlater,theballisstillatxinSbutwhereisitinS’atthesametimet?a)x’=x b)x’=x+ut c)x’=x-ut

...-3-2-10123...

...-3-2-10123...

u

ʹx = x −utʹy = yʹz = zʹt = t

vx ' =d ʹx (t)dt

=ddt

x(t)−ut( ) = dx(t)dt

−u = vx −u

Note:Assumesframesalignedatt=0

Thelawsofphysicsarethesameinallinertialframesofreference.

Thespeedoflightisthesameinallinertialframesofreference.

Anobserverat(0,0)hasaclock;eventstherearecovered.Anobserverat(3m,2m)hadbetterhaveaclocktoo,ifwewanttoknowabouteventsthere.And,thetwoclockshadbettershowthesametime.

Attheorigin,atthreeo’clock,theclocksendsoutalightsignaltotelleverybodyit’sthreeo’clock.Timepassesasthesignalgetstotheclockatx=3m.

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Whenthesignalarrives,theclockatx=3missetto3:00plusthe10nsdelay(whichiscalculatedbyknowingthespeedoflightc).

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Asecondframehasitsownclocks,andmovespastme.Whathappensnow?

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u

Cory

L R

Coryisthemiddleofarailroadcar,andsetsoffafirecracker.Lightfromtheexplosiontravelstobothendsofthecar.WhichenddoesitreachfirstaccordingtoCory?

a)bothendsatonceb)theleftend,Lc)therightend,R

u

Cory

L R

Coryisthemiddleofarailroadcar,andsetsoffafirecracker.Lightfromtheexplosiontravelstobothendsofthecar.WhichenddoesitreachfirstaccordingtoCory?

a)bothendsatonceb)theleftend,Lc)therightend,R

u

Cory

L R

Chrissieisstandingatrestnexttothetraintracks,watchingthetrainmovetotheright.AccordingtoChrissie,whichendofthetraincardoesthelightreachfirst?

a)bothendsatonceb)theleftend,Lc)therightend,R

L R

v

Chrissie

Chrissieisstandingatrestnexttothetraintracks,watchingthetrainmovetotheright.AccordingtoChrissie,whichendofthetraincardoesthelightreachfirst?

a)bothendsatonceb)theleftend,Lc)therightend,R

L R

v

Chrissie

u

...-3-2-10123...Chrissie

Cory

SupposeCory’sfirecrackerexplodesattheoriginofChrissie’sreferenceframe.

L R

ThelightspreadsoutinChrissie’sframefromthepointshesawitexplode.Becausethetraincarismoving,thelightinChrissie’sframearrivesattheleftendfirst.

uCory

L R

...-3-2-10123...Chrissie

uCory

L R

...-3-2-10123...Chrissie

Sometimelater,inChrissie’sframe,thelightcatchesuptotherightendofthetrain.

L R

0

uL R

uL R

uL R

uL R

Cory:inthetrain Chrissie:ontheplatform

0

EventL:(x=-3,t=3s)

EventR:(x=+3,t=3s)

EventL’:(x’=-2,t’=2s)

EventR’:(x’=+5,t’=4s)

x’x

uL R

Corysays:‘Simultaneous!’ Chrissiesays:‘Notsimultaneous!’

Mirror

Garethh u

Garethmeasuresthetimeinterval:Δt’=Δt0 = 2h/c

Mirror

h

Joey Brad

u

Note:Thisexperimentrequirestwoobservers.

Joey Brad

h

u · Δt/2

Joey Brad

h

u · Δt/2

JoeyandBradmeasurethetimeinterval:

ButGarethmeasuredΔt’=Δt0=2h/c!!

Δt = 2hcγ, γ =

1

1− u2

c2

¡  “ProperTime”=Δτ=Δt0§  Thetimeintervalmeasuredinaframewherethetwoeventsoccuratthesamespatialcoordinate–i.e.theframemovingwithyourclock

¡  ThetimeintervalΔtmeasuredinanyotherframemovingwithrespecttothisframewillbelonger§  Δt=γΔt0

¡  Amuonlifetimeis2.2μsinitsrestframe,butitisobservedtolivefor220μsintravelingfromtheupperatmospheretotheground.Whichisclosesttoitsvelocityaccordingtotheexternalobserver?

A.  v=√(0.9)cB.  v=√(0.99)cC.  v=√(0.999)cD.  v=√(0.9999)c

¡  Amuonlifetimeis2.2μsinitsrestframe,butitisobservedtolivefor220μsintravelingfromtheupperatmospheretotheground.Whichisclosesttoitsvelocityaccordingtotheexternalobserver?

A.  v=√(0.9)cB.  v=√(0.99)cC.  v=√(0.999)cD.  v=√(0.9999)c

β=v/c=√(0.9999)=0.99995

EveryonenowagreesthatthishalfofthelightmovesatcWhataboutthishalf?