objectsinightImaginethefamiliarscenariowhereaheavystewardessfallsfromanairplaneandthenKalElinterceptsandcatcheshermidightThisSceneisillustratedingure2IfSupermanobeyedthelawsofphysicswewouldex ID: 185948
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2PhysicalPowersInthissectionwearguethatthereisevidencethatSupermancanalterthemomentofinertiaorinertialmassofmacroscopicobjects.2.1SuperStrengthSuperman'sextraordinarystrengthissomewhatofamystery,sinceitseemsattimestonotsatisfyNewton'slaws.ImagineKalElliftingano cebuildingoverHishead,onehanded,whilewalkingdownthestreet.Thefeatofstrengthitselfisnotjustunbelievable,butalsounphysical.Consider gure1.Ifweweretopositionamulti-storiedo cebuildingupononapostonastreet,tobeheldfromthesamepositionasweimagineSupermanholdingit:thebuildingabovethepostwouldcrackfromtheenormouspressure;aswouldthepavementbeneaththepost.Sincethepostwouldnotliebeneaththebuilding'scenterofmass,wewouldexpecttoseethebuildingeithertumbleforward,orwewouldseethebuildingcrackfromtheshearstresseswhichcomefrombeingheldbythecorner.Incontrast,weseenoneoftheseeectswhenKalElliftsanobject.WecanonlyconjecturethatSupermanhastheabilitytomovethecenterofmass(bycontrollingthemomentofinertia)oftheo cebuilding.Inaddition,thelackofdeformationofthepavement(thoughthepressurebeneathHisfeetasHewalksmustbeintense),andthelackofdamageatthepointofcontactofthebuildingtellusthatHemusthavealsosomehowreducedtheeectivemassofthebuilding.2 objects,in ight.Imaginethefamiliarscenariowhereaheavystewardessfallsfromanairplane,andthenKalElinterceptsandcatchesher,mid ight.ThisSceneisillustratedin gure2.IfSupermanobeyedthelawsofphysicswewouldexpectthat,onceSupermancaughtthestewardess,theircollectivetrajectorywouldsuerasaresultofhermonstrousinitialmomentum.Additionallywewouldgenerallyexpecthertobecrushedunderthelargeacceleration,andtornintopiecesbytheconsiderableimpulse.However,fromexperience,KalElrarelydipsaftercatchingsomeonemidair.Thisseemsonlypossibleif,somehow,Supermanwereabletoreducethemo-mentumofthecaughtperson.Furthermore,thecaughtpersonreportsfeelingmuchpressureoraccelerationfromSuperman'sarms.Ifthestewardess'mo-mentofinertiaweredramaticallyreducedpriortotheimpactofKalEl'sarm,herbodywouldsuerlessfromtheimpulse,asitwouldbelightlyfelt. 4 2.3SuperSpeedWhileKalEl'shighrunningspeedandheavyaccelerationcouldbeexplainedintermsofextremephysicalstrength;wewouldexpect,ifthiswerethecase,thestreetbeneathHisfeettowarporshatterundertheintensepressure.Sincethisisrarelyinevidence,wededucethatHishighaccelerationcomesnotfromHisexertinganalmostin niteforce,butratherfromHishavinganarbitrarilysmallmass.3SuperSensesInadditiontoHisfeatsofstrength,KalElalsopossessessuper-senses.Hecanhearabroaderrangeofsoundsandseeawiderspectrumofelectromagneticwavesthanwe(humans)can.WefeelthatthesecanbebestexplainedinthecontextofourconjectureasanabilitytoaltertheinertialmassofpartsofHisownsensoryorgans.Wenote,however,thatthefollowingexplanationsareconjecture;sinceKalEl'shighlytunedsensesmightsimplybeamatterofKryptonianphysiology.3.1SuperHearingSupermancanhearsoundsacrossabroaderfrequencythanwehumanscan,andHecanalsohearsoundswhicharemuchquieterandtoleratesoundswhicharemuchlouderthancanhumans.Thoughthespeci cmechanismbywhichKalElhearsisnotunderstood,itisreasonabletoexpectthatitfunctionsinternallyinawayanalogoustoourownears.Anincreaseinsensitivity,aswellasaresistanceagainsthearinglosscouldbeexplainedifHeweretomakethevariouscomponentsofHisearslighterorheavieralternatively,withoutalteringthemechanismofhearing.Anincreasedfrequencyrangeofhearingcouldbecreatedbygeneratingtemperatureordensitygradientsintheair,orwithinthecomponentsofHisear,shiftingthesoundsintoHisaudiblerange.3.2SuperSightSimilarlythespeci cmechanismthroughwhichSuperman'snervesperceivelightisnotclear.WhileHisabilitytoseeawiderspectrumoflightthanwecanmayjustbeamatterofKryptonianphysiology,itseemsstrangethatHiseyesshouldbeabletoseeintothex-raypartofthespectrum.Indeed,wewonderwhereallthex-raysKalElcanseecomefrom.Wewouldexpectthatinmostsituations,itwouldbetoodimtoseemuchinthex-rayspectrum.Ourconjectureprovidesanalternateexplanation.IfSupermanwereabletoalterinertialmassonthescaleatomsandmolecules,wewouldexpectthatHecouldaltertheemission/absorptionspectrumofatomsormolecules.Considerthesimplecaseofthehydrogenatom.Ordinarily,theenergycontributionfromthegravitationalpotentialisneglected;howeveritcaneasilybere-introduced.Thepotentialenergyinthehamiltoniangoesfrom5 4Freeze-BreathandHeatVisionKalEl'smostexoticpowerscouldbeHisabilitytofreezeobjectswithHisbreath,oralternativelyemitheatbeamsfromHiseyes.Thesetwopowershavebeenthemostdi culttoexplain,butthey twellwithourconjecturethatKalElcanaltertheinertiaofthemoleculesofagaswithwhichHeisincontact.InadditiontoHisFreeze-BreathandHeatVision,KalElhasindirectlyprovidedevidenceofHisabilitytocontrolthetemperatureofthegasaroundhim.HisfrequentvisitstotheSunandtheEarth'spolarregionswithouthavingtochangehisclothing,forexample.Wecannotcountthisasconclusiveevidenceforourconjecture,though,sinceotherexplanationscouldbeimagined.Thus,wefocusourattentionsonattemptingtoprovideamechanismforhisabilitytoglare re,andbreathice.4.1FreezeBreathIngasses,thetemperatureofthegasisrelatedtotheaveragekineticenergyoftheparticlesinthegas.IfSupermanwereabletoreducetheinertialmassoftheairmoleculesinHislungs,asHeexhaled,theairwouldbecolderthanwhenitwentin.Tin=1 3kBminv2&#x-277;1 3kBmoutv2&#x-278;=ToutTofacilitateexpirationofthecoldgas,theprocesscouldbeisobaric.Thusforanidealgas,P3V mv2&#x-277;=NweseethatthenumberofgasmoleculesinKalEl'slungsmustincreaseinverse-proportionallywiththedecreasedmass.7 targetwillinitiallybeTi=1 3kmv2&#x-278;=1 3kMmiv2&#x-278; Mwheremiistheoriginalinertialmassofthegasmolecules.IfthesebecomesmfafterhittingSuperman'seye;thenafterHe'sengagedHisheatvisionthetemperatureofthetargetwillbe:T=1 3kmv2&#x-278;=1 3k(M�Nt)miv2&#x-278;+Ntmfv2&#x-278; MT=MTi�NtTi+Ntmf miTi M=Ti+tN M(mf mi�1)TiSowecanroughlyestimatethatthetemperatureoftheobjectKalElisheatingwithHisheatvisionwillincreaselinearlywithtime. 9 5ConclusionWeconjecturethatallofSuperman'spowerscomefromHisabilitytoaltertheinertialmassofobjectsinHisimmediatevicinityorwithwhichHeisinpersonalcontact;althoughthemechanismisunknown.Ourconjectureofasingleuni edpowercouldbetestedinafewsimpleways.Wecould,forinstance,determinewhetherSupermancouldaccelerateifHeweresurroundedbyanearlyperfectvacuum.Alternatively,WecoulddeterminewhetherHehastheabilitytoemitx-rays,andwhetherHecanactivelychangeHistransparencytox-rays.WecouldtestHisheatvisiontodeterminewhethertherearelimitstotheratiomf mi;andtowhatdegreethechangeshemakeswillpersist.shutup.10