12.Kant and Handedness - NYU Tandon School of...

• "ConcerningtheUltimateFoundationoftheDifferentiationofRegionsofSpace"(1768).

12.KantandHandedness

ImmanuelKant(1724-1804)

[Anincongruentcounterpartis]...anobjectwhichiscompletelylikeandsimilartoanother,althoughitcannotbeincludedexactlywithinthesamelimits."

Claim:Absolutespaceisnecessarytoexplaintheexistenceofincongruentcounterparts.

• Anincongruentcounterpartisacertaintype ofmirrorimage.

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1. IncongruentCounterparts2. Kant'sArgumentforAbsoluteSpace

1.IncongruentCounterparts

• Maps(1)and(2)reproducethesamerelationsbetweenobjects.• Arelationistmustsaytheyarethesame.• Anabsolutistcansaytheyaredifferent;namely,theydifferintheirlocationswithrespecttoabsolutespace.

Example1

(1) (2)

2

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

3

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

3

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

3

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

3

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

3

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

3

(2) O' isanincongruentcounterpart ofO ifitcannot bemadetocoincidewithObyrigidmotions.

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

4

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

(2) O' isanincongruentcounterpart ofO ifitcannot bemadetocoincidewithObyrigidmotions.

4

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

(2) O' isanincongruentcounterpart ofO ifitcannot bemadetocoincidewithObyrigidmotions.

4

ImportantFact:Whetherornotamirrorimageisanincongruentcounterpartdependsonthepropertiesofthespaceitislocatedin.

TwotypesofmirrorimageLetO beanobjectandletO' beitsmirrorimage.(1) O' isacongruentcounterpart ofO ifitcanbemadetocoincidewithO byrigid

motions.

(2) O' isanincongruentcounterpart ofO ifitcannot bemadetocoincidewithObyrigidmotions.

5

• Ifthespaceis3-dimensional,thenFanditsmirrorimagearecongruentcounterparts.

6

• Ifthespaceis3-dimensional,thenFanditsmirrorimagearecongruentcounterparts.

6

• Ifthespaceis3-dimensional,thenFanditsmirrorimagearecongruentcounterparts.

6

• Ifthespaceis3-dimensional,thenFanditsmirrorimagearecongruentcounterparts.

6

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.

7

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

y••

x

x'••

y'

• Ifthespaceis2-dimensionalandnon-orientable,thenFanditsmirrorimagearecongruentcounterparts.

Example:AMöbiusstrip.• Obtainedbyidentifyingedgepointsxwithx',andywithy' ona2-dimstrip.• Result:Aglobal"twist"thatallowsthemirrorimageofFtoberigidlytransportedaroundtheentirespacebackontoF.

8

Modifieddefinition:

Anobjectisanincongruentcounterpart ofanotheriftheycannotbemadetooccupythesameplacebyrigidmotionsinalocal(closelysurrounding)regionofspace.

• Anobjectissaidtopossesshandedness (chirality)justwhenitanditsmirrorimageareincongruentcounterparts.

• Anobjectissaidtolackhandedness (chirality)justwhenitanditsmirrorimagearecongruentcounterparts.

sphericalcow 9

2.Kant'sArgumentforAbsoluteSpace

"Letitbeimaginedthatthefirstcreatedthingwereahumanhand,thenitmustnecessarilybeeitherarighthandoralefthand."

• But:Arelationistcannotdeterminethehandednessofanobjectintheabsenceofotherobjects.

• So:Relationalismisnotadequate.

• Leftandrighthandsagreeonallrelationalproperties.• Absolutist:Theydisagreeontheirlocationswithrespecttoabsolutespace.

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LetterExampleAgain

• DoFanditsmirrorimagehavethesamerelationalproperties?• Dependsonhowmanypropertiesoneiswillingtoconsiderasrelational.

THEQUICKBROWNOXJUMPEDOVERTHELAZYDOG.

THEQUICKBROWNFOXJUMPEDOVERTHELAZYDOG.

• Fanditsmirrorimagedifferintheirrelationalpropertiestotheotherlettersinthesentence.- ThereisnowaytomakethemirrorimageofFfitintothesentenceinthesamewaythatFdoes.

- Similarly,thereisnowaytofitarighthandintoaleft-handed(FreddyKrueger)glove(andviceversa).

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• But:Howcanarelationistdeterminethehandednessofanobjectwhentherearenootherreferenceobjectstodefinedistinguishingrelationalproperties?

• Moreover:Whatifsuchreferenceobjectsthemselveshavebeenreflected?

• SinceFanditsmirrorimageshareallrelationalpropertiesinthesesentences,arelationistwillnotbeabletodistinguishthem.

• Absolutistintuition:Aren'tFanditsmirrorimagedistinct,independentoftheirrelationstootherobjects?

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Relationist'sReflectionArgument

• Suppose:Absolutespaceexists.

• Anabsolutistmustclaimthereflectionproducesdistinctworlds.- Theydifferontheirvaluesofabsoluteposition.

• Arelationistwillclaimthatthereflectiondoesnotproducedistinctworlds.- Sincetherelationsbetweenmaterialobjectsareunaffected(andthere'snosuchthingasabsolutespace),theworldsarenotdistinct.

AB

Universe1

absolutespace

world1(unreflected)

Universe2

absolutespace

world2(reflected)

A

• Then:Thefollowingtwouniversesmustbepossible:

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PossibleAbsolutistRetort:

• Wouldareflectedworldbeindiscerniblefromanunreflectedworld?

Spock MirrorSpock

• ReplaceSpockwithadecayingCobalt-60atom:

Co60®Ni60 +e− +νe

Co60

e−

νe

Co60

e−

νe

Co60 decay MirrorCo60 decay

• Co60 decay(electronemittedindirectionofnuclearspin)isobservedmoreoftenthanMirrorCo60 decay(electronemittedinoppositedirectionofnuclearspin)(Wuetal.1957).

Chien-ShiungWu(1912-1997)

Designed, run by C-S Wu. 1957 Nobel prize to Lee & Yang (men). 1978 Wolf prize finally to Wu.• Evidencethattheweakforce(thatgovernsdecay)violates

mirrorsymmetry(i.e.,"parity").14

• AbsolutistClaim:Thereflectedandunreflectedworldsarenot observationallyindiscernible.- Inworld1,theCo60 atomdecayoccursmorefrequentlythaninworld2.

• Onusisnowontherelationisttoexplainthephysicaldifferencebetweenworlds1and2.- RecallClarke'sDynamicShift,withparity-violatingexperimentsnowreplacinginertialeffects.

B

Universe1

absolutespace

world1(unreflected)

Universe2

absolutespace

world2(reflected)

A A

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LetitbeimaginedthatthefirstcreatedthingwereaCo60 decayprocess,thenitmustnecessarilybeeitheraright-handedCo60decayprocess,oraleft-handedCo60 decayprocess...and there'salaw-likephysicaldifferencebetweenthetwo!

• Canarelationistbothground thedistinctionbetweenright- andleft-handedprocessesandexplainwhyoneismoreprobablethantheother?

(a) Claimthatthedifferenceisintrinsic:Co60 decayprocessespossessanintrinsicmonadic(non-relational)propertythatboth determinestheirhandednessand theirweak-force-governedbehavior.

(b) Claimthedifferenceisextrinsic:- WhatdetermineswhetherthefirstcreatedCo60 decayprocessisright- orleft-handedisitsrelationtoallsubsequentCo60 decayprocesses.

- And:Itisabrutelawlikefact(inneedofnofurtherexplanation)thatoneofthesedecayprocessesismoreprobablethantheother.

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ALingeringConcernaboutOption(b)

• WhatexplainsNewton'sFirstLaw?Howdoesaforce-freeobjectknowtomoveinertially?

• Similarly:Whatexplainstheparity-violatingweakforce?WhydoCo60 atomspreferdecaymodesofonechiralityratherthananother(givenchiralityisnotintrinsic)?

- Absolutist:Alocal interactionbetweenspacetimeandtheobject(localspacetime"feelers"?).

- Relationist:Anonlocal correlationbetweentheobjectandotherobjects(nonlocalinertial antennae?).

- Absolutist:Alocal interactionbetweenspacetimeandtheobject.

- Relationist:Anonlocal correlationbetweentheobjectandotherobjects(nonlocalweak-forceantennae).

• Isonesetofmysteriousantennae(absolutist)betterthantwo(relationist)?17