07. Interpreting Special Relativity Topics 1.Two Interpretations 1....
Transcript of 07. Interpreting Special Relativity Topics 1.Two Interpretations 1....
07.InterpretingSpecialRelativity
BasicQuestion:Whatwouldtheworldbelikeifspecialrelativityweretrue?
1.TwoInterpretationsofSpecialRelativity
I.SpacetimeSubstantivalistInterpretation
Claims:
(a) SpecialRelativityisatheoryaboutthestructureofspacetime.ItsaysthatthisstructureisgivenbyMinkowskispacetime.
(b) Minkowskispacetimeisarealsubstancethataffectsthebehaviorofobjectsmovingthroughit(substantivalism).
Topics:1. TwoInterpretations2. PhilosophicalConsequences
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Rocketundergoingnon-inertialmotion(accelerating)
yelp!
WhyClaim(b)?Offersanexplanationofinertialforces:
Inertialforce = forcefeltbyanobjectwhenitdeviatesfrominertialmotion
SpacetimeSubstantivalistExplanationofInertialForces
Rocketundergoinginertialmotion(constantvelocity)
slurp!
- Minkowskispacetimeis"resistence-free"toobjectsundergoinginertialmotion (straight-line,constantvelocity).
- It"resists"objectsundergoingnon-inertialmotion (acceleratedmotion).
- This"resistence"manifestsitselfasinertialforces.
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Spacetime"resists"deviantnon-inertialtrajectories,pushingthembacktowardinertialnorm.
Privilegedstraightinertialtrajectory
Deviantcurvednon-inertialtrajectory
x
t
FurtherClaims:(i) Lengthcontractionandtimedilationarepurely kinematical effectsdueto
thestructureofMinkowskispacetime.- Duetodisagreementsoverhowineritalobserverstakespatialandtemporalcross-sectionsoftheworld-tubeofaphysicalsystem.
(ii) Spaceandtimearedifferentinertial-frame-dependentaspectsoftheinvariantframe-independentpropertyofspatiotemporallength.
(iii) Massandenergyaredifferentinertial-frame-dependentaspectsoftheinvariantframe-independentpropertyofenergy-momentum.
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Claims:(a) SpecialRelativityisatheoryabouttheformthatdynamicallaws
musttake.ItsaysthatsuchlawsmustbeLorentzinvariant.
(b) Spacetimedoesnotexistindependentlyofphysicalobjects;rather,itconsistsmerelyinthedynamical relationsbetweenphysicalobjects(relationalism).
WhyClaim(b)?• Whatkindofsubstancewouldspacetimebe?• Whatisthemechanismbywhichitinteractswith(resists)movingobjects?• Ifitactsonobjectswithoutobjectsactingonit,wouldn'titviolateNewton's3rdLaw(foreveryactionthereisanequalandoppositereaction)?
But: Whataboutinertialforces?Howcaninertialforcesbeexplainedrelationally?
II.DynamicalRelationalistInterpretation.
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FurtherClaims:(i) Timedilationandlengthcontractionarereal dynamical effects.
- Movingobjectscontractandmovingclocksslowdownduetophysicalmolecularforcesthatgoverntheirconstituents.
- ArealdynamicaleffectduetoLorentz-invariantlaws.- Notduetomotionwithrespecttoastationaryphysicalrestframe(liketheaether);norisitduetothe(kinematic)structureofMinkowskispacetime.
(ii) Timeandspacearedistinctquantities.Soaremassandenergy.
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2.PhilosophicalConsequencesofSpecialRelativity
A.OntologicalStatusofObjectswithrespecttoTime
BasicQuestion:Howdoobjectsexistwithrespecttotime?
(a) Endurantism:Objectsare3-dimensionalandendurethroughtime.(b) Perdurantism:Objectsare4-dimensionaland"perdure"(extend)overtime.
4-dimJoeextendsoveraspatialregionandatemporalinterval.
t
y
x
Perdurantism
3-dimJoeextendsoveraspatialregiononly.
3-dimJoeat t =ti
Endurantism
3-dimJoeat t =tf
t
y
x
A. OntologicalStatusofObjectsWithRespecttoTime
B. OntologicalStatusofTimeC. OntologicalStatusofChange
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BabyJoeatti−50 Joeatti CoffinJoeatti +50
• Endurantism:WhatidentifiesJoe-at-tiwithJoe-at-tf?- AretheythesameJoe:IsBabyJoethesame3-dimobjectasCoffinJoe?
• Perdurantism:Howtemporallyextendedis4-dimJoe?- Doesheextendonlyovertheinterval[ti , tf]?Alarger/smallerinterval?
BabyJoeslice
CoffinJoeslice
TheComplete4-dimJoe?
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TypicalClaim:SpecialRelativitysupportsperdurantism.
Why?- Minkowskispacetimeis4-dim.- TheLorentz-invariantquantitiesassociatedwithMinkowskispacetime(likespatiotemporallengthandenergy-momentum)are4-dimquantities.
Conclusion:Byitself,SpecialRelativitysaysnothingabouttheontologicalstatusofobjectswithrespecttotime.- Inordertosayitdoes,wehavetoprovideitwithanintepretation,andwemayhavetoengageinspeculativemetaphysicswithrespecttopropertiesanddimensionality.
But:- DynamicalrelationalistinterpretationofSRiscompatiblewithendurantism.- Newtonianphysicscanbeformulatedina4-dimspacetime("Galilean"spacetime);hencethereisnothingspecialaboutSpecialRelativitywithrespectto4-dimspacetimes.
- Perhaps3-dimobjectscanhave4-dimproperties(spatiotemporallength,energy-momentum,etc)andstill remain3-dimensional.
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GalileanSpacetime
privilegedfamilyofabsolutetimeslices
noprivilegedfamilyofstraights
1. Manyinertialframes;noneprivileged.2. Velocityisrelative.3. Accelerationisabsolute.4. Simultaneityisabsolute.
noabsolutetimeslices
noprivilegedfamilyofstraights
1. Manyinertialframes;noneprivileged.2. Velocityisrelative.3. Accelerationisabsolute.4. Simultaneityisrelative.5. Light-conestructureateachpoint.
MinkowskiSpacetime
Howthe4-dimspacetimeofNewtonianphysics(Galileanspacetime)differsfromthe4-dimspacetimeofSpecialRelativity(Minkowskispacetime).
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BasicQuestion:Whatistheontologicalstatusoftimesotherthanthepresent?
(a)Presentism:Onlythepresentisreal.(b)Eternalism:Alltimes,past,presentandfuture,areequallyreal.
B.OntologicalStatusofTime
present
time
Presentism Eternalism
present
past
future
equallyreal
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Argument#1• SpecialRelativityentailsspaceandtimearenotseparatebutcombinedintospacetime.
• Inspacetime,alleventshavethesameontologicalstatus.
Accordingtopresentism(andcommonintuition)...
TypicalClaim:SpecialRelativitysupportseternalism.
The"Present"advancesandproducesdeterminatefactsoutofindeterminatestates.Earth
2020
Earth2024
Present
Bidenwins
determinatefact
indeterminatestate
?wins
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Claim:SpecialRelativitydeniesthisview...
Earth2020
Earth2024
Botheventsareequallydeterminateinspacetime(i.e.,botharepresentinaspacetimediagram).
x
t
Argument#1• SpecialRelativityentailsspaceandtimearenotseparatebutcombinedintospacetime.
• Inspacetime,alleventshavethesameontologicalstatus.
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TypicalClaim:SpecialRelativitysupportseternalism.
BUT!• ThedynamicalrelationalistinterpretationofSRiscompatiblewithpresentism.• SRisnotuniqueinitsuseofspacetimediagrams.(CanbeusedinNewtonianphysics,too.)
Argument#1• SpecialRelativityentailsspaceandtimearenotseparatebutcombinedintospacetime.
• Inspacetime,alleventshavethesameontologicalstatus.
TypicalClaim:SpecialRelativitysupportseternalism.
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Claim:Therelativityofsimultaneity entailsthatalleventsinspacetimecoexistwitheachother.
(3) So:TheEarthat2024coexistswiththeEarthat2020!
(2) RocketjudgesEarth2024assimultaneouswithher20thB-Day.Therefore,Earth2024coexistswiththerocket's20thB-Day.
rocket'slineofsimultaneity
worldlineofrocketmovingatconstantspeedwithrespecttoEarth
(1) Earthjudgesrocket's20thB-Dayashappeningin2020.Therefore,therocket's20thB-DaycoexistswithEarth2020.
Earth2020'slineofsimultaneity
NOWismy20thbirthday!Earth
2020
Earth2024
Argument#2
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TypicalClaim:SpecialRelativitysupportseternalism.
BUT!• Thisconflates"beingsimultaneouswith"with"coexistingwith".- IsitthecasethatifEventAissimultaneouswithEventB,thenBcoexistswithA?
- Whatdoesitmeanforoneeventtocoexistwithanother?
Claim:Therelativityofsimultaneity entailsthatalleventsinspacetimecoexistwitheachother.
Argument#2
TypicalClaim:SpecialRelativitysupportseternalism.
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• LightconestructureinMinkowskispacetimeentailsthatnotwoeventswillagreeonthetotality ofeventsthatcountasthefuture,thetotality thatcountasthepast,andthetotality thatcountasthepresent.
• Ifthe"present"istheboundarybetweenpastandfuture,thenthepresentexistsonlyatapointinMinkowskispacetime!
Claim:Presentismminimallyrequireseveryonetoagreeonwhatthepresentisatanygiventime.Butsincesimultaneityisrelativeinspecialrelativity,thereisnowaythiscanbedone.
• •A B
eventsthatareinthefutureforAbutnotforB
overlapoffuturelightcones=eventsthatareinthefutureforbothAandB
eventsthatareinthefutureforBbutnotforA
Argument#3
TypicalClaim:SpecialRelativitysupportseternalism.
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ConstrastwithGalileanspacetime:
• •A B
Argument#3Claim:Presentismminimallyrequireseveryonetoagreeonwhatthepresentisatanygiventime.Butsincesimultaneityisrelativeinspecialrelativity,thereisnowaythiscanbedone.
TypicalClaim:SpecialRelativitysupportseternalism.
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ConstrastwithGalileanspacetime:
• •A B
Argument#3Claim:Presentismminimallyrequireseveryonetoagreeonwhatthepresentisatanygiventime.Butsincesimultaneityisrelativeinspecialrelativity,thereisnowaythiscanbedone.
TypicalClaim:SpecialRelativitysupportseternalism.
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ConstrastwithGalileanspacetime:
commonpast
commonfuture
commonpresent
• "Flatteningout"lightconescorrespondsmathematicallytotakingthe"Newtonianlimit":lettingc→∞ (orv/c→ 0).
• Newtonianpresent= globalinstantaneoussurfaceofsimultaneity.
• •A B
Argument#3Claim:Presentismminimallyrequireseveryonetoagreeonwhatthepresentisatanygiventime.Butsincesimultaneityisrelativeinspecialrelativity,thereisnowaythiscanbedone.
TypicalClaim:SpecialRelativitysupportseternalism.
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BUT!• Whatexactly areourintuitionsaboutthepresent?• Isthe"manifestimage"ofoureverydayexperienceofthepresentreallyincompatiblewiththe"scientificimage"givenbySpecialRelativity?
• IsthemanifestimageofoureverydayexperienceofthepresentreallythesameastheNewtonianglobalpresent?Dowereallyexperiencethepresentasaninstant?
Argument#3Claim:Presentismminimallyrequireseveryonetoagreeonwhatthepresentisatanygiventime.Butsincesimultaneityisrelativeinspecialrelativity,thereisnowaythiscanbedone.
TypicalClaim:SpecialRelativitysupportseternalism.
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Whatdoesoureverydayexperienceofthe"present"suggest?
• Claim:Thepresentisnotexperiencedasinstantaneous,butratherextendedovertime,andhowit'sexperiencedmaydependonthingslikethemetabolismoftheexperiencingorgranism.
• Specious present =Presentasexperiencedbyalivingorganism.
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0.2sec(singlethought)
0.02sec
human
gnat
brachiosaurus 2.0sec
organism speciouspresent
Def.1. NOW =temporallyextendedspacetimeregionoccupiedbyanobjectduringitsspeciouspresent.Def.2. Stein-presentofNOW =RegionboundedbypastlightconeoffutureboundaryofNOW,andfuturelightconeofpastboundaryofNOW.
60,000km
• TheStein-presentofJoe'sNOW extendsveryfarinspace(60,000km =distancelighttravelsin0.2s),butit'snotglobal.
futureboundaryofJoe'sNOW
pastboundaryofJoe'sNOW
Stein-presentofJoe'sNOW
• ItencompassesmosthumansJoecomesintocontactwith,allofwhomcanagreeonitsstatusasthe"present".
Joe'sNOW(4-dimJoeextending0.2s)
22Gibson,I.&O.Pooley(2006)'RelativisticPersistence',Phil.Perspectives20,157-98;Stein,H.(1991)'OnRelativityTheoryandOpennessoftheFuture',Phil.Sci.58,147-67.
• Claim:TheStein-presentofahuman'sNOW issufficienttogroundtheintuitionsofthepresentist,whileatthesametimebeingcompatiblewithSpecialRelativity.
pastboundaryofJoe'sNOW
60,000km
futureboundaryofJoe'sNOW
Stein-presentofJoe'sNOW
Joe'sNOW(4-dimJoeextending0.2s)
Def.1. NOW =temporallyextendedspacetimeregionoccupiedbyanobjectduringitsspeciouspresent.Def.2. Stein-presentofNOW =RegionboundedbypastlightconeoffutureboundaryofNOW,andfuturelightconeofpastboundaryofNOW.
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Conclusion:Byitself,SpecialRelativitysaysnothingabouttheontologicalstatusoftime.- Inordertosayitdoes,wehavetoprovideitwithanintepretation,andwemayhavetoengageinspeculativemetaphysicswithrespecttothenotionofthepresent.
BasicQuestion:Ischange(becoming)real?
(a)Heracliteanism:Becoming(change)isfundamentallyreal.(b)Parminedeanism:Beingisfundamentallyreal;changeisanillusion.
C.OntologicalStatusofChange
TypicalClaim:SpecialRelativitysupportsParminedeanism.
- OurmanifestimageofBecomingindicatesthatthereshouldbeanabsolutedistinctionbetween:(i) Eventsthathavebecome(ii) Eventsthatcoexistandareintheprocessofbecoming(iii) Eventsthathaveyettobecome
Why?
- And:Ifthisdistinctionismadeintermsof(i)eventsinthepast,(ii)eventsinthepresent,and(iii)eventsinthefuture,theninSpecialRelativitythereisnosuchabsolutedistinction!
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ManifestImageofBecoming(?)
- A andB coexist(co-presentevents).- C hasbecome(pastevent).- D hasyettobecome(futureevent).
commonpast
commonfuture
commonpresent
•
•
A B
C
D
• •
••A B
•
•
C
D
ImcompatiblewithMinkowskispacetimestructure
- A andB donotcoexist.- C hasbecomeforB butnotforA.- D hasyettobecomeforA butnotforB.
Can the manifest image of Becoming be made compatible with Minkowski spacetime?
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Let's replace the absolute present with the Stein-Present of NOW...
pastlightconeofStein-presentofJoe'sNOW
futurelightconeofStein-presentofJoe'sNOW
• Becausemost(all?)humanswillagreeontheStein-present ofanygivenhuman'sNOW,theywillalsoagreeonthefuturewithrespecttothisSteinpresent,andonthepastwithrespecttothisStein-present.
• So:Most(all?)humanswillagreeonwhicheventshavebecome,whichcoexist,andwhichareyettobecome.
C•
- ObjectX hasbecomewithrespecttoobjectY justifX isinthepastlightconeoftheSteinPresentofY'sNOW.
B•
- ObjectsX andY coexist justifX fallswithintheSteinPresentofY'sNOW andY fallswithintheSteinPresentofX'sNOW.
D•
- ObjectX hasyettobecomewithrespecttoobjectY justifX isinthefuturelightconeoftheSteinpresentofY'sNOW.
Stein-presentofJoe'sNOW
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pastlightconeofStein-presentofJoe'sNOW
futurelightconeofStein-presentofJoe'sNOW
C•
- ObjectX hasbecomewithrespecttoobjectY justifX isinthepastlightconeoftheSteinPresentofY'sNOW.
B•
- ObjectsX andY coexist justifX fallswithintheSteinPresentofY'sNOW andY fallswithintheSteinPresentofX'sNOW.
D•
- ObjectX hasyettobecomewithrespecttoobjectY justifX isinthefuturelightconeoftheSteinpresentofY'sNOW.
Stein-presentofJoe'sNOW
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Conclusion:Byitself,SpecialRelativitysaysnothingabouttheontologicalstatusofchange.- Inordertosayitdoes,wehavetoprovideitwithanintepretation,andwemayhavetoengageinspeculativemetaphysicswithrespecttotheconceptofbecoming.