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



12


BUT!• ThedynamicalrelationalistinterpretationofSRiscompatiblewithpresentism.• SRisnotuniqueinitsuseofspacetimediagrams.(CanbeusedinNewtonianphysics,too.)




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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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BUT!• Thisconflates"beingsimultaneouswith"with"coexistingwith".- IsitthecasethatifEventAissimultaneouswithEventB,thenBcoexistswithA?

- Whatdoesitmeanforoneeventtocoexistwithanother?

Claim:Therelativityofsimultaneity entailsthatalleventsinspacetimecoexistwitheachother.

Argument#2


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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


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ConstrastwithGalileanspacetime:

• •A B

Argument#3Claim:Presentismminimallyrequireseveryonetoagreeonwhatthepresentisatanygiventime.Butsincesimultaneityisrelativeinspecialrelativity,thereisnowaythiscanbedone.


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• •A B



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commonpast

commonfuture

commonpresent

• "Flatteningout"lightconescorrespondsmathematicallytotakingthe"Newtonianlimit":lettingc→∞ (orv/c→ 0).

• Newtonianpresent= globalinstantaneoussurfaceofsimultaneity.

• •A B



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BUT!• Whatexactly areourintuitionsaboutthepresent?• Isthe"manifestimage"ofoureverydayexperienceofthepresentreallyincompatiblewiththe"scientificimage"givenbySpecialRelativity?

• IsthemanifestimageofoureverydayexperienceofthepresentreallythesameastheNewtonianglobalpresent?Dowereallyexperiencethepresentasaninstant?



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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


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.


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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.


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Conclusion:Byitself,SpecialRelativitysaysnothingabouttheontologicalstatusofchange.- Inordertosayitdoes,wehavetoprovideitwithanintepretation,andwemayhavetoengageinspeculativemetaphysicswithrespecttotheconceptofbecoming.

07. interpreting special relativity topics 1.two interpretations 1....

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