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1、 WHATISLIFE?ERWINSCHRODINGERFirstpublished1944Whatislife?ThePhysicalAspectoftheLivingCell.BasedonlecturesdeliveredundertheauspicesoftheDublinInstituteforAdvancedStudiesatTrinityCollege,Dublin,inFebruary1943.TothememoryofMyParentsPrefaceAscientistissupposedtohaveacompleteandthoroughIofknowledge,atfir
2、sthand,ofsomesubjectsand,therefore,isusuallyexpectednottowriteonanytopicofwhichheisnotalife,master.Thisisregardedasamatterofnoblesseoblige.ForthepresentpurposeIbegtorenouncethenoblesse,ifany,andtobethefreedoftheensuingobligation.Myexcuseisasfollows:Wehaveinheritedfromourforefathersthekeenlongingforu
3、nified,all-embracingknowledge.Theverynamegiventothehighestinstitutionsoflearningremindsus,thatfromantiquitytoandthroughoutmanycenturiestheuniversalaspecthasbeentheonlyonetobegivenfullcredit.Butthespread,bothinandwidthanddepth,ofthemultifariousbranchesofknowledgebyduringthelasthundredoddyearshasconfr
4、onteduswithaqueerdilemma.Wefeelclearlythatweareonlynowbeginningtoacquirereliablematerialforweldingtogetherthesumtotalofallthatisknownintoawhole;but,ontheotherhand,ithasbecomenexttoimpossibleforasinglemindfullytocommandmorethanasmallspecializedportionofit.Icanseenootherescapefromthisdilemma(lestourtr
5、uewhoaimbelostforever)thanthatsomeofusshouldventuretoembarkonasynthesisoffactsandtheories,albeitwithsecond-handandincompleteknowledgeofsomeofthem-andattheriskofmakingfoolsofourselves.Somuchformyapology.Thedifficultiesoflanguagearenotnegligible.Onesnativespeechisacloselyfittinggarment,andoneneverfeel
6、squiteateasewhenitisnotimmediatelyavailableandhastobereplacedbyanother.MythanksareduetoDrInkster(TrinityCollege,Dublin),toDrPadraigBrowne(StPatricksCollege,Maynooth)and,lastbutnotleast,toMrS.C.Roberts.Theywereputtogreattroubletofitthenewgarmentonmeandtoevengreatertroublebymyoccasionalreluctancetogiv
7、eupsomeoriginalfashionofmyown.Shouldsomeofithavesurvivedthemitigatingtendencyofmyfriends,itistobeputatmydoor,notattheirs.Thehead-linesofthenumeroussectionswereoriginallyintendedtobemarginalsummaries,andthetextofeverychaptershouldbereadincontinuo.E.S.DublinSeptember1944Homolibernulladereminusquamdemo
8、rtecogitat;etejussapientianonmortissedvitaemeditatioest.SPINOZASEthics,PtIV,Prop.67(Thereisnothingoverwhichafreemanponderslessthandeath;hiswisdomis,tomeditatenotondeathbutonlife.)CHAPTER1TheClassicalPhysicistsApproachtotheSubjectThislittlebookarosefromacourseofpubliclectures,deliveredbyatheoreticalp
9、hysicisttoanaudienceofaboutfourhundredwhichdidnotsubstantiallydwindle,thoughwarnedattheoutsetthatthesubject-matterwasadifficultoneandthatthelecturescouldnotbetermedpopular,eventhoughthephysicistsmostdreadedweapon,mathematicaldeduction,wouldhardlybeutilized.Thereasonforthiswasnotthatthesubjectwassimp
10、leenoughtobeexplainedwithoutmathematics,butratherthatitwasmuchtooinvolvedtobefullyaccessibletomathematics.Anotherfeaturewhichatleastinducedasemblanceofpopularitywasthelecturersintentiontomakeclearthefundamentalidea,whichhoversbetweenbiologyandphysics,toboththephysicistandthebiologist.Foractually,ins
11、piteofthevarietyoftopicsinvolved,thewholeenterpriseisintendedtoconveyoneideaonly-onesmallcommentonalargeandimportantquestion.Inordernottoloseourway,itmaybeusefultooutlinetheplanverybrieflyinadvance.Thelargeandimportantandverymuchdiscussedquestionis:Howcantheeventsinspaceandtimewhichtakeplacewithinth
12、espatialboundaryofalivingorganismbeaccountedforbyphysicsandchemistry?Thepreliminaryanswerwhichthislittlebookwillendeavortoexpoundandestablishcanbesummarizedasfollows:Theobviousinabilityofpresent-dayphysicsandchemistrytoaccountforsucheventsisnoreasonatallfordoubtingthattheycanbeaccountedforbythosesci
13、ences.STATISTICALPHYSICS.THEFUNDAMENTALWDIFFERENCEINSTRUCTUREThatwouldbeaverytrivialremarkifitweremeantonlytostimulatethehopeofachievinginthefuturewhathasnotbeenachievedinthepast.Butthemeaningisverymuchmorepositive,viz.thattheinability,uptothepresentmoment,isamplyaccountedfor.Today,thankstotheingeni
14、ousworkofbiologists,mainlyofgeneticists,duringthelastthirtyorfortyyears,enoughisknownabouttheactualmaterialstructureoforganismsandabouttheirfunctioningtostatethat,andtotellpreciselywhypresent-dayphysicsandchemistrycouldnotpossiblyaccountforwhathappensinspaceandtimewithinalivingorganism.Thearrangemen
15、tsoftheatomsinthemostvitalpartsofanorganismandtheinterplayofthesearrangementsdifferinafundamentalwayfromallthosearrangementsofatomswhichphysicistsandchemistshavehithertomadetheobjectoftheirexperimentalandtheoreticalresearch.YetthedifferencewhichIhavejusttermedfundamentalisofsuchakindthatitmighteasil
16、yappearslighttoanyoneexceptaphysicistwhoisthoroughlyimbuedwiththeknowledgethatthelawsofphysicsandchemistryarestatisticalthroughout.Foritisinrelationtothestatisticalpointofviewthatthestructureofthevitalpartsoflivingorganismsdifferssoentirelyfromthatofanypieceofmatterthatwephysicistsandchemistshaveeve
17、rhandledphysicallyinourlaboratoriesormentallyatourwritingdesks.Itiswell-nighunthinkablethatthelawsandregularitiesthusdiscoveredshouldhappentoapplyimmediatelytothebehaviourofsystemswhichdonotexhibitthestructureonwhichthoselawsandregularitiesarebased.Thenon-physicistcannotbeexpectedeventograspletalone
18、toappreciatetherelevanceofthedifferenceinstatisticalstructurestatedintermssoabstractasIhavejustused.Togivethestatementlifeandcolour,letmeanticipatewhatwillbeexplainedinmuchmoredetaillater,namely,thatthemostessentialpartofalivingcell-thechromosomefibremaysuitablybecalledanaperiodiccrystal.Inphysicswe
19、havedealthithertoonlywithperiodiccrystals.Toahumblephysicistsmind,theseareveryinterestingandcomplicatedobjects;theyconstituteoneofthemostfascinatingandcomplexmaterialstructuresbywhichinanimatenaturepuzzleshiswits.Yet,comparedwiththeaperiodiccrystal,theyareratherplainanddull.Thedifferenceinstructurei
20、softhesamekindasthatbetweenanordinarywallpaperinwhichthesamepatternisrepeatedagainandagaininregularperiodicityandamasterpieceofembroidery,sayaRaphaeltapestry,whichshowsnodullrepetition,butanelaborate,coherent,meaningfuldesigntracedbythegreatmaster.Incallingtheperiodiccrystaloneofthemostcomplexobject
21、sofhisresearch,Ihadinmindthephysicistproper.Organicchemistry,indeed,ininvestigatingmoreandmorecomplicatedmolecules,hascomeverymuchnearertothataperiodiccrystalwhich,inmyopinion,isthematerialcarrieroflife.Andthereforeitissmallwonderthattheorganicchemisthasalreadymadelargeandimportantcontributionstothe
22、problemoflife,whereasthephysicisthasmadenexttonone.THENAIVEPHYSICISTSAPPROACHTOTHESUBJECTAfterhavingthusindicatedverybrieflythegeneralidea-orrathertheultimatescope-ofourinvestigation,letmedescribethelineofattack.Iproposetodevelopfirstwhatyoumightcallanaivephysicistsideasaboutorganisms,thatis,theidea
23、swhichmightariseinthemindofaphysicistwho,afterhavinglearnthisphysicsand,moreespecially,thestatisticalfoundationofhisscience,beginstothinkaboutorganismsandaboutthewaytheybehaveandfunctionandwhocomestoaskhimselfconscientiouslywhetherhe,fromwhathehaslearnt,fromthepointofviewofhiscomparativelysimpleandc
24、learandhumblescience,canmakeanyrelevantcontributionstothequestion.Itwillturnoutthathecan.Thenextstepmustbetofcomparehistheoreticalanticipationswiththebiologicalfacts.Itwillthenturnoutthat-thoughonthewholehisideasseemquitesensible-theyneedtobeappreciablyamended.Inthiswayweshallgraduallyapproachthecor
25、rectview-or,toputitmoremodestly,theonethatIproposeasthecorrectone.EvenifIshouldberightinthis,Idonotknowwhethermywayofapproachisreallythebestandsimplest.But,inshort,itwasmine.Thenaivephysicistwasmyself.AndIcouldnotfindanybetterorclearerwaytowardsthegoalthanmyowncrookedone.WHYARETHEATOMSSOSMALL?Agoodm
26、ethodofdevelopingthenaivephysicistsideasistostartfromtheodd,almostludicrous,question:Whyareatomssosmall?Tobeginwith,theyareverysmallindeed.Everylittlepieceofmatterhandledineverydaylifecontainsanenormousnumberofthem.Manyexampleshavebeendevisedtobringthisfacthometoanaudience,noneofthemmoreimpressiveth
27、antheoneusedbyLordKelvin:Supposethatyoucouldmarkthemoleculesinaglassofwater;thenpourthecontentsoftheglassintotheoceanandstirthelatterthoroughlysoastodistributethemarkedmoleculesuniformlythroughoutthesevenseas;ifthenyoutookaglassofwateranywhereoutoftheocean,youwouldfindinitaboutahundredofyourmarkedmo
28、lecules.Theactualsizesofatomsliebetweenabout1/5000and1/2000thewave-lengthofyellowlight.Thecomparisonissignificant,becausethewave-lengthroughlyindicatesthedimensionsofthesmallestgrainstillrecognizableinthemicroscope.Thusitwillbeseenthatsuchagrainstillcontainsthousandsofmillionsofatoms.Now,whyareatoms
29、sosmall?Clearly,thequestionisanevasion.Foritisnotreallyaimedatthesizeoftheatoms.Itisconcernedwiththesizeoforganisms,moreparticularlywiththesizeofourowncorporealselves.Indeed,theatomissmall,whenreferredtoourcivicunitoflength,saytheyardorthemetre.Inatomicphysicsoneisaccustomedtousetheso-calledAngstrom
30、(abbr.A),whichisthe10lOthpartofametre,orindecimalnotation0.0000000001metre.Atomicdiametersrangebetween1and2A.Nowthosecivicunits(inrelationtowhichtheatomsaresosmall)arecloselyrelatedtothesizeofourbodies.ThereisastorytracingtheyardbacktothehumourofanEnglishkingwhomhiscouncillorsaskedwhatunittoadopt-an
31、dhestretchedouthisarmsidewaysandsaid:Takethedistancefromthemiddleofmychesttomyfingertips,thatwilldoallright.Trueornot,thestoryissignificantforourpurpose.ThekingwouldnaturallyIindicatealengthcomparablewiththatofhisownbody,knowingthatanythingelsewouldbeveryinconvenient.WithallhispredilectionfortheAngs
32、tromunit,thephysicistpreferstobetoldthathisnewsuitwillrequiresixandahalfyardsoftweed-ratherthansixty-fivethousandmillionsofAngstromsoftweed.Itthusbeingsettledthatourquestionreallyaimsattheratiooftwolengths-thatofourbodyandthatoftheatom-withanincontestablepriorityofindependentexistenceonthesideofthea
33、tom,thequestiontrulyreads:Whymustourbodiesbesolargecomparedwiththeatom?Icanimaginethatmanyakeenstudentofphysicsorchemistrymayhavedeploredthefactthateveryoneofoursenseorgans,formingamoreorlesssubstantialpartofourbodyandhence(inviewofthemagnitudeofthesaidratio)beingitselfcomposedofinnumerableatoms,ism
34、uchtoocoarsetobeaffectedbytheimpactofasingleatom.Wecannotseeorfeelorhearthesingleatoms.Ourhypotheseswithregardtothemdifferwidelyfromtheimmediatefindingsofourgrosssenseorgansandcannotbeputtothetestofdirectinspection.Mustthatbeso?Isthereanintrinsicreasonforit?Canwetracebackthisstateofaffairstosomekind
35、offirstprinciple,inordertoascertainandtounderstandwhynothingelseiscompatiblewiththeverylawsofNature?Nowthis,foronce,isaproblemwhichthephysicistisabletoclearupcompletely.Theanswertoallthequeriesisintheaffirmative.THEWORKINGOFANORGANISMREQUIRESEXACTPHYSICALLAWSIfitwerenotso,ifwewereorganismssosensitiv
36、ethatasingleatom,orevenafewatoms,couldmakeaperceptibleimpressiononoursenses-Heavens,whatwouldlifebelike!Tostressonepoint:anorganismofthatkindwouldmostcertainlynotbecapableofdevelopingthekindoforderlythoughtwhich,afterpassingthroughalongsequenceofearlierstages,ultimatelyresultsinforming,amongmanyothe
37、rideas,theideaofanatom.Eventhoughweselectthisonepoint,thefollowingconsiderationswouldessentiallyapplyalsotothefunctioningoforgansotherthanthebrainandthesensorialsystem.Nevertheless,theoneandonlythingofparamountinteresttousinourselvesis,thatwefeelandthinkandperceive.Tothephysiologicalprocesswhichisre
38、sponsibleforthoughtandsensealltheothersplayanauxiliarypart,atleastfromthehumanpointofview,ifnotfromthatofpurelyobjectivebiology.Moreover,itwillgreatlyfacilitateourtasktochooseforinvestigationtheprocesswhichiscloselyaccompaniedbysubjectiveevents,eventhoughweareignorantofthetruenatureofthiscloseparall
39、elism.Indeed,inmyview,itliesoutsidetherangeofnaturalscienceandveryprobablyofhumanunderstandingaltogether.Wearethusfacedwiththefollowingquestion:Whyshouldanorganlikeourbrain,withthesensorialsystemattachedtoit,ofnecessityconsistofanenormousnumberofatoms,inorderthatitsphysicallychangingstateshouldbeinc
40、loseandintimatecorrespondencewithahighlydevelopedthought?Onwhatgroundsisthelattertaskofthesaidorganincompatiblewithbeing,asawholeorinsomeofitsperipheralpartswhichinteractdirectlywiththeenvironment,amechanismsufficientlyrefinedandsensitivetorespondtoandregistertheimpactofasingleatomfromoutside?Therea
41、sonforthisis,thatwhatwecallthought(1)isitselfanorderlything,and(2)canonlybeappliedtomaterial,i.e.toperceptionsorexperiences,whichhaveacertaindegreeoforderliness.Thishastwoconsequences.First,aphysicalorganization,tobeinclosecorrespondencewiththought(asmybrainiswithmythought)mustbeaverywell-orderedorg
42、anization,andthatmeansthattheeventsthathappenwithinitmustobeystrictphysicallaws,atleasttoaveryhighdegreeofaccuracy.Secondly,thephysicalimpressionsmadeuponthatphysicallywell-organizedsystembyotherbodiesfromoutside,obviouslycorrespondtotheperceptionandexperienceofthecorrespondingthought,formingitsmate
43、rial,asIhavecalledit.Therefore,thephysicalinteractionsbetweenoursystemandothersmust,asarule,themselvespossessacertaindegreeofphysicalorderliness,thatistosay,theytoomustobeystrictphysicallawstoacertaindegreeofaccuracy.PHYSICALLAWSRESTONATOMICSTATISTICSANDARETHEREFOREONLYAPPROXIMATEAndwhycouldallthisn
44、otbefulfilledinthecaseofanorganismcomposedofamoderatenumberofatomsonlyandsensitivealreadytotheimpactofoneorafewatomsonly?Becauseweknowallatomstoperformallthetimeacompletelydisorderlyheatmotion,which,sotospeak,opposesitselftotheirorderlybehaviouranddoesnotallowtheeventsthathappenbetweenasmallnumberof
45、atomstoenrolthemselvesaccordingtoanyrecognizablelaws.Onlyinthecooperationofanenormouslylargenumberofatomsdostatisticallawsbegintooperateandcontrolthebehaviouroftheseassemblieswithanaccuracyincreasingasthenumberofatomsinvolvedincreases.Itisinthatwaythattheeventsacquiretrulyorderlyfeatures.Allthephysi
46、calandchemicallawsthatareknowntoplayanimportantpartinthelifeoforganismsareofthisstatisticalkind;anyotherkindoflawfulnessandorderlinessthatonemightthinkofisbeingperpetuallydisturbedandmadeinoperativebytheunceasingheatmotionoftheatoms.THEIRPRECISIONISBASEDONTHELARGEOFNUMBEROFATOMSINTERVENINGFIRSTEXAMP
47、LE(PARAMAGNETISM)Letmetrytoillustratethisbyafewexamples,pickedsomewhatatrandomoutofthousands,andpossiblynotjustthebestonestoappealtoareaderwhoislearningforthefirsttimeaboutthisconditionofthings-aconditionwhichinmodernphysicsandchemistryisasfundamentalas,say,thefactthatorganismsarecomposedofcellsisin
48、biology,orasNewtonsLawinastronomy,orevenastheseriesofintegers,1,2,3,4,5,.inmathematics.Anentirenewcomershouldnotexpecttoobtainfromthefollowingfewpagesafullunderstandingandappreciationofthesubject,whichisassociatedwiththeillustriousnamesofLudwigBoltzmannandWillardGibbsandtreatedintextbooksunderthenam
49、eofstatisticalthermodynamics.Ifyoufillanoblongquartztubewithoxygengasandputitintoamagneticfield,youfindthatthegasismagnetized.Themagnetizationisduetothefactthattheoxygenmoleculesarelittlemagnetsandtendtoorientatethemselvesparalleltothefield,likeacompassneedle.Butyoumustnotthinkthattheyactuallyalltur
50、nparallel.Forifyoudoublethefield,yougetdoublethemagnetizationinyouroxygenbody,andthatproportionalitygoesontoextremelyhighfieldstrengths,themagnetizationincreasingattherateofthefieldyouapply.Thisisaparticularlyclearexampleofapurelystatisticallaw.Theorientationthefieldtendstoproduceiscontinuallycounte
51、ractedbytheheatmotion,whichworksforrandomorientation.Theeffectofthisstrivingis,actually,onlyasmallpreferenceforacuteoverobtuseanglesbetweenthedipoleaxesandthefield.Thoughthesingleatomschangetheirorientationincessantly,theyproduceontheaverage(owingtotheirenormousnumber)aconstantsmallpreponderanceofor
52、ientationinthedirectionofthefieldandproportionaltoit.ThisingeniousexplanationisduetotheFrenchphysicistP.Langevin.Itcanbecheckedinthefollowingway.Iftheobservedweakmagnetizationisreallytheoutcomeofrivaltendencies,namely,themagneticfield,whichaimsatcombingallthemoleculesparallel,andtheheatmotion,whichm
53、akesforrandomorientation,thenitoughttobepossibletoincreasethemagnetizationbyweakeningtheheatmotion,thatistosay,byloweringthetemperature,insteadofreinforcingthefield.Thatisconfirmedbyexperiment,whichgivesthemagnetizationinverselyproportionaltotheabsolutetemperature,inquantitativeagreementwiththeory(C
54、urieslaw).Modernequipmentevenenablesus,byloweringthetemperature,toreducetheheatmotiontosuchinsignificancethattheorientatingtendencyofthemagneticfieldcanassertitself,ifnotcompletely,atleastsufficientlytoproduceasubstantialfractionofcompletemagnetization.Inthiscasewenolongerexpectthatdoublethefieldstr
55、engthwilldoublethemagnetization,butthatthelatterwillincreaselessandlesswithincreasingfield,approachingwhatiscalledsaturation.Thisexpectationtooisquantitativelyconfirmedbyexperiment.Noticethatthisbehaviourentirelydependsonthelargenumbersofmoleculeswhichco-operateinproducingtheobservablemagnetization.
56、Otherwise,thelatterwouldnotbeanconstantatall,butwould,byfluctuatingquiteirregularlyoffromonesecondtothenext,bearwitnesstothevicissitudesofpethecontestbetweenheatmotionandfield.SECONDEXAMPLE(BROWNIANMOVEMENT,DIFFUSION)Ifyoufillthelowerpartofaclosedglassvesselwithfog,ptconsistingofminutedroplets,youwi
57、llfindthattheupperorboundaryofthefoggraduallysinks,withawell-definedvelocity,determinedbytheviscosityoftheairandthesizeandthespecificgravityofthedroplets.Butifyoulookatoneofthedropletsunderthemicroscopeyoufindthatitdoesnotpermanentlysinkwithconstantvelocity,butperformsaveryirregularmovement,theso-ca
58、lledBrownianmovement,whichcorrespondstoaregularsinkingonlyontheaverage.Nowthesedropletsarenotatoms,buttheyaresufficientlysmallandlighttobenotentirelyinsusceptibletotheimpactofonesinglemoleculeofthosewhichhammertheirsurfaceinperpetualimpacts.Theyarethusknockedaboutandcanonlyontheaveragefollowtheinflu
59、enceofgravity.Thisexampleshowswhatfunnyanddisorderlyexperienceweshouldhaveifoursensesweresusceptibletotheimpactofafewmoleculesonly.Therearebacteriaandotherorganismssosmallthattheyarestronglyaffectedbythisphenomenon.Theirmovementsaredeterminedbythethermicwhimsofthesurroundingmedium;theyhavenochoice.I
60、ftheyhadsomelocomotionoftheirowntheymightneverthelesssucceedinongettingfromoneplacetoanother-butwithsomedifficulty,sincetheheatmotiontossesthemlikeasmallboatinaroughsea.AphenomenonverymuchakintoBrownianmovementisthatofdiffusion.Imagineavesselfilledwithafluid,saywater,withasmallamountofsomecolouredsu
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