einstein in paris t einstein presents and discusses his theory

21stCenturyScience&Technology Summer2011 19

TherecentexpositionbyEinsteinonhiswork,alongwiththediscussionswhichfollowedattheCollègedeFrance,waswithoutdoubtan

unprecedented event. The famous physicist tookpart in itwith inexhaustible patience.One felt inhimthedesirenottoleaveanymisunderstandingsinthe shadows,not to ignore anyof theobjections,but,onthecontrary,toprovoketheminordertobet-tertackleandwrestlewiththemsquarely.

IntheUnitedStates,inLondon,andinItalywhereEinsteinwassuccessivelyreceivedsomemonthsago,helimitedhimselftoexplainingtheTheoryofRelativ-ityinaconferenceformat.IntheUnitedStatesandinLondon,hepreferredtospeakinGermanbecauseofhis imperfectknowledgeofEnglish; in Italy,heex-pressedhimself in Italian,whichpermittedamoreintimatecontactwiththeaudience.Butinallofthosecountrieshelimitedhimselftoa“non-contradictory”monologue—ifImayborrowthisincorrectbutcolor-fulexpressionfromourpoliticallanguage.

InParis,ontheotherhand,Einsteinwasnotsatis-fiedwithspeakingdidacticallyexcathedra.Heres-olutelylaunchedintothecontroversy,replyingpub-liclyinwhatwastobecomeamostcelebratedseriesof discussions, takingonall objections andques-tionsaskedbysomeofthemosteminentrepresenta-tivesofthescientificcommunity.

Ithoughtthatitwouldbeusefultogive,forthesehistoricjoustingsofthought,animageasexactaspossibleandfromwhich,nevertheless,thetoo-eso-tericlanguageofthetechnicianswouldbeexclud-

EDITOR’SNOTEThis is a translation by members of a LaRouche

movementteamofa1922articlebyCharlesNordmanndescribing several lectures byAlbert Einstein duringhisvisittoParisthatyear.Nordmann’sarticle,“EinsteinExposeetDiscutesaThéorie,”appearedinRevuedesDeuxMondes,Vol.IX,pp.129-166.

Charles Nordmann (1881-1941) was an astrono-mer andphysicist,whose research andpublicationswerewellknowninthesciencecommunityandinthepublicatlarge.HewasalaureateoftheFrenchAcad-emyofSciencesandaKnightoftheLegionofHonor.Oneofhisbooks,EinsteinandtheUniverse:APopularExposition of a FamousTheory, was translated andpublishedinEnglishin1922(NewYork:HenryHoltandCompany).

NordmannpublishedfrequentlyonscientifictopicsinRevuedesDeuxMondes(ReviewoftheTwoWorlds),a French-language monthly cultural affairs magazinethathasbeenpublishedinParissince1829.

A translator’s note appears on p.21. Numberedfootnotesarefromtheoriginalarticle,unlessspecifiedasaTranslator’sNote.Illustrationshavebeenadded,ashaveveryoccasionaltranslationsof foreignterms(insquarebrackets).Emphasisisfromtheoriginal.

EINSTEIN IN PARIS

Einstein PresentsAnd Discusses

His TheorybyCharlesNordmann

EinsteininParis,1922.

20 Summer2011 21stCenturyScience&Technology

ed.Thatiswhatguidedmeinthepagesyouwillread.Intimestocome,someyearsfromnow,itisprobablethattheintellec-tualcontroversies,whichEinstein’spresenceinParisprovoked,duringthisfreshspringof1922,willhavegreatlysurpassedinimportancetheaffairsthatpresenttimeshavethrustuponus.Iwouldwagerthatinafewcenturies—andwhatisthatintheastronomicalorevensimplybiologicaltimeoftheplanet?—therecent discussion on relativity in the Collège de France willhavemarkedoffanewstepforwardontheroadofhumanintel-ligence...whiletheConferenceofGenoa[1922]willbelong-forgotten,likesomanyuselesspastarguments,andsomestilltocomeinthefuture.

AttheCollègedeFrance,thefactthatthesessionshadthegoodfortuneofreflectingatightdiscussion,ratherthandidac-ticlectures,originatedfromadesireonthepartofEinsteinhim-self,adesireinspiredinhimbyhismodesty,orbettersaidinhislackofconfidenceinhimself.

Infact,hereiswhathewroteinaletter,afewdaysbeforehearrivedinParis:

IwillcertainlyhavesomedifficultyexpressingmyselfinFrench,butIthinkI’llbeabletopullmyselfthrough,for

examplebyreadingapreparedtext.Furthermore,formulasalsohelpalot,1andIhopeawillingcolleaguewillbegoodenoughtoutterandextractthewordsthatwouldgetstuckinmythroat.

Itwouldperhapsbeevenmoreagreeable,andmoreusefulifweweretohaveasortofsmallcongressonRelativity,inwhichIwouldonlyrespondtoquestions.Thedifficultiesofexpressionwouldannoymelessinthiswaythanamoreorlesscompleteexpositionofthetheory.

Asexperiencewouldhaveit,Einstein’sfearswereun-founded.Atleastforustheyhadbeenworthit,forthesewerethemostpassionatecontroversiesonecouldpossi-blyimagine,andtheygaveushoursofintellectualplea-sure,asonetoorarelyhasoccasiontosavorinthepedes-trianmonotonyofthisbriefexistence.

Themeritofhavingbroughtsuccesstothesenowfamoussessionsisnotslight.ItisdueabovealltoMr.Langevin,

professorofexperimentalphysicsattheCollègedeFrance,onwhoserequestEinsteinhadbeeninvitedtoParis,asIhaveal-ready mentioned. It is Mr. Langevin who oversaw the dailyscheduleofthesmallnumberofmeetings,wheresomanysub-jectshadtobecovered.Itwashewho,withafirmanddiscretehandmanagedtoprovokethediscussions,preventthedebatefromleadingastray,andrestricted,whenevernecessarybutal-wayswithawell-chosenword,theexactpositionsoftheadver-saries.Inrarebutdecisivemoments,healsoparticipatedinthebattlebyhelpingtheslightlywoundedparticipants,orbygivingthecoupdegrâcetothosewhowereinsuchadesperatestatethatitwasnecessarytocutshorttheirunnecessarysuffering.Fi-nally,itishewhoplayedforEinsteintheindispensableanddif-ficultrolethatEinsteinhadaskedforinhisletter,theroleoftheintellectualPylades,theinformedcue-giverwhosevocabularyandacuteknowledgeofthesubjectareneverwanting.

ThefirstsessiontookplaceattheCollègedeFrance,Friday

1. We must understand that Einstein speaks here of the language of mathe-matics which assuredly, with the aid of a blackboard, is the most international language . . . at least for the initiates, and the only one that dispenses with being multi-lingual.

Astronomer Charles Nordmann,with the titlepage fromthebookhewrote in1922, the sameyearthisarticleappeared.

ThecourtyardoftheCollègedeFrance,withastatueofGuillaumeBudé,whowasacontemporaryofErasmusandThomasMore.

AmodernviewoftheauditoriumwhereEinsteinspokeattheCollègedeFrance.


Here,presentedforthefirsttimeinEnglish,isafirsthandaccountofEinstein’shistorictriptoParis,afterWorld

WarI.Notonlyisitofinteresttothehistorianofscienceorresearcherofinternationalrelations,butthissnapshotfromaturningpointintimeprovidesanythinkerwithanexam-pleofhowagenuineideacanbepresentedandhonestlydiscussed.

Beingasocialcreaturemightnotbeexclusivetothehu-manspecies,butcomingtoknowpersonalitiesthatarelongdead,isdefinitelyuniquetousandisaveryspecialtoolinhelpingusliveuptoouruniqueness.Becomingfriendswithoneofhumanity’sgeniusesofthepastprovidesafunstudyindiscoveringanexpressionof thepotentialofmankind,andprovidesaclearexampleofwhatthenatureofanindi-vidualmanis,asopposedtoamonkey.

IhavespecificallypickedEinsteinasmy“buddy.”AsEin-stein’sfuture,weareabletoreaptheideasandmethodthathesowed(ifwebothertoknowhimandourhistory),inor-dertoprovideanewplatformofcultureandideasforourfuture.Ihopethatthispeekintothepastwillhelpfosterthatforyou.

In distilling the significance of the human individual’screativecapability,youquicklyrealizetheeffecttheinterac-tionofthehighestlevelofmindcanhaveonthedevelop-mentofsocietyatlarge;youseethegranderimpactalifecanhaveon theworld, rather thananexistenceofbeingconsumedbythedailysoapoperaofpersonalsituationsthatare inconsequential in the scheme of things (unless, ofcourse,theyhelpyoudevelopyourindividualcreativitytobeaneffectiveworldcitizen.)

Originalsourcesaretheonlywaytogetalivingsenseofadebate.Notonlythepapersapersonwrote,buthisletters,lecturesgivenbycontemporariesonthetopic,newspaperarticles,andsoon.Theseshadowsofaprocessgiveyouachancetoimmerseyourselfinanenvironmenttoappreciateandrediscoverforyourselftheculturaleffectanideahas.

InsearchforsuchacontextofEinstein’sdevelopmentofhypotheses, I reached a road-block in my research. ThePrincetonUniversityPresshadbeenputtingoutthecollect-edworksofEinstein,articlesandletters,butatthispointhadonlyreachedtheyear1920-1921.Justwhenthingsstarttogetgood!Einstein’stheoryofgravityhadjustbeenpubliclyvalidatedandthereforepopularized,hewasplungingintoGeneralRelativity’s implicationson the shapeof theuni-verseanditsinteractionwithotherprinciples,suchaselec-tromagnetism.

InreadingbiographiesofEinstein,theeventtheyspeakofasmostimportantintheseyears—theearly1920s—isnotsomescientificpaperbeingpublished,butEinstein’striptoParis.OneoftheintendeddestructiveeffectsofWorldWarIwastocutoffinternationalintellectualrelations.Einstein’stripwouldbethefirststepinmendingFrenchandGermanrelations.Thiscreatedquiteastirandmanypeoplewerenothappyonbothsides.

Withsuchanimportantinstanceinscientificandpoliti-cal history, I was surprised that I couldn’t find Einstein’sspeechesfromthisconference,butonlythirdhandshortref-

erencestowhatwastalkedabout.IncontactingtheEinsteinarchives,IwastoldthatEinsteinspokeinformally,sotherewerenowrittennotesfromhimpersonally,butthearchivistgavemeadateandthetitleofajournalforwhichaCharlesNordmann was commissioned to report on the event. ItrackeditdownandassembledateamtotranslateitfromtheFrench.

For more on the context of the political environment,pleaseseeMichelBiezunski’sarticle“Einstein’sReceptioninParis in1922” in thebookTheComparativeReceptionofRelativity,*andanarticlebyNordmanninEnglishonvisitingbattlefieldswithEinstein.**Botharepricelessaccountsthathelp you appreciate the actual struggle intellectuals wentthroughtomakehumanitystrongerthroughadvancementinthought;andthefactthatsciencecannotbeseparatedfrompolitics,andshouldtakealeadingroleinculture.

Nordmann’s article gives a good picture of the circlewhichexisted,bothassupportersandcritics,aroundEin-steininthedebateonTheRelativityTheory.Howrefreshingitistoseehowanideacanbehonestlyfoughtover,insteadofsimplydecidingtoagreetodisagree,ordecidingthatany-body who dissents from the prevailing opinion is crazy.What’sunusualinwitnessingthebackandforth,isthattheoppositionsideiscompetent,forthemostpart,andisgenu-inelyseekingthetruth.ThisprovidesafoiltothelackoftruescientificdebatetodayinaBoomerera.

IfyoucanbecomeaccustomedtotheflowerydescriptivenatureofNordmann’swriting,you’llfindthisarticleuseful,notonlyfortheon-the-groundreportinginthemiddleofthedevelopmentofEinstein’sthoughts,butalsobecauseitpro-vides a good overview of the fundamental principles onwhichEinstein’s theoryisbased,andthemanyparadoxesthat seem tocomeupaccording tocommonsensewhenfacedwithrelativity.AlsoitpresentsafairapproximationforalaymanofEinstein’sbasicmethodofapproach.

Forexample,onethreadthatcomesuprepeatedlyinthearticleisthesubjectofmath.Nordmann,onbehalfofEin-stein,issuretomakethepointthatmathisnotusefulinandofitself,andisoutofreality,unlessitistheservantofphys-ics.Anothercontinuousthreadisthediscussionofthemeta-physicalvs.positivism. ItseemsthatNordmannissure toqualifybothsidesandimplythatthere’sabalanceneeded;butfromtheworkofEinsteinandmycomingtoknowhisdiscoveryprocess,itisclearthatEinsteinissimplyabovethemysticorthedatacollector,whichcomesupwhenEinsteindiscussesErnstMach.

Aswithall secondhand (orevenfirsthand) sources, thevaluecomesfromwhatyouareableonyourowntoputto-getheroftheprocessofmindoftheindividualcharactersonstage,andwhat’spushingtheoveralldramaasawhole,asopposed to having a perfect map of what was discussedwhen.

Therefore,Ihumblysubmittoyouthistranslation.—ShawnaHalevy

Footnotes _________________________________________________* Michel Biezunski on Einstein’s reception in Paris, 1922.** Charles Nordmann on visiting battlefields with Einstein.

Translator’s Note

http://books.google.com/books?id= GTSftplc2jYC&pg=PA169&lpg=PA169&dq =%22Einstein%27s+Reception+in+Paris+in+1922%22 &source=bl&ots=xW_x4N-hIR&sig=ZufswNBpaB2OI0VAX9Whwr4Ld9M&hl=en&ei=5SDvSppPj-aUB_nmiIAF&sa=X&oi=book_result&ct =result&resnum=1&ved=0CAsQ6AEwAA#v=onepage&q=%22Einstein%27 s%20Reception%20in%20Paris%20in%201922%22&f=false

http://books.google.com/books?id=GTSftplc2jYC&pg=PA185&lpg=PA185&dq=Michel+Biezunski+on+Einstein%E2%80%99s+reception+in+Paris,+1922&source=bl&ots=xXXq8J1eNR&sig=9-9Ig1DFCRR8rVtuix6q2lrBVIU&hl=en&ei=u_O1TojrE4TO2AWnz7XVBQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCwQ6AEwAg#v=onepage&q=Michel%20Biezunski%20on%20Einstein%E2%80%99s%20reception%20in%20Paris%2C%201922&f=false

http://books.google.com/books?id=mHIkAQAAIAAJ&pg=PA586&lpg=PA586&dq=Charles+Nordmann+on+visiting+battlefields+with+Einstein&source=bl&ots=SCjz_Ko4KQ&sig=UpLw1i-49Ff_vLUzM0yFQUHFWx0&hl=en&ei=HPS1Tov6FsfM2AXErfDODQ&sa=X&oi=book_result&ct=result&resnum=2&sqi=2&ved=0CB0Q6AEwAQ#v=onepage&q&f=false


March31st at 5p.m., in thisAmphitheatreVIIIwhich, eventhoughitisthelargestroomofourfineinstitution,isnonethe-lessridiculouslysmall.Longbeforethissessionbegan,thefor-tunately privileged crowd that was admitted to this uniqueeventhadfilledalloftheseatsandwasspillingoverintothenarrow passageways of this all-too-modest room where Ein-steinwasgoingtospeak.Andallthosewhowereinattendancehadtoagreeonthecertaintyofatleastonething,that,atleastfor this place, thenon-existenceof spacewasquite certain.Therewerestudents,professors,scientists,alltheeliteofFrenchscienceandofFrenchculture,allthegreatnameswhichhonorthiscountry.Fromthedensityofattendees,onemightbelieveoneselftobeatafamoussession,whererecentlytheidolizingpublicwouldbeflockingtoalessonofaCarooraBergson.Butinregardingthecrowdalittlemoreclosely,thecomparisonisnotquitejustified.Thereweretrulyveryfewfamousactressesor high-society ladies, in this gathering of dignitaries whosecompressibilitywasputtosuchharshtrial.Hereagain,Mr.Lan-gevin’sextremehonestywasmanifested.Totheextentthatwehadbeengenerousinthedistributionofticketstopeopleinsci-enceandresearch,eventoyoungstudentswhoseattendancewasconsideredlegitimate,inthesamedegree,weweremerci-lessinrejectingallwhocouldrepresentsnobbery,hamactors,or simple idle curiosity.Also, all things considered, I’m notquitesureonecouldhavebeenabletoenumerateamongthiscenter of tasteful intellectuals a half dozen of truly elegantwomen.Withinthedecayingwallsofthisjewelbox,wherethepurestdiamondsofthemindwereabouttorevealtheirluster,notevenaningeniousthiefwouldhavebeenabletostealsuf-ficientjewelstomerittheleastnewsworthycommentforthenewspapers.

ThiswasalsoverymuchinharmonywiththetastesofEin-stein.

But,allofasudden,onthelowerplatformoftheamphithe-atrewherealittledesksurroundedbysomechairsisarranged,herecomesEinsteinaccompaniedbyMr.MauriceCroiset,ad-ministratoroftheCollègeofFrance,andMr.Langevin,followedbytheprofessorsoftheCollège.Thewholeroomrosetoitsfeetinonemovementandgreetedthewiseonewithaterrificac-clamation.Einsteinseemedmovedandanxious.Insomeper-fectly succinct and chosen words, Mr. Maurice Croiset wel-comedhimandtoldhimhowproudtheCollègewastohavehimhere.WhatMr.Croisetdoesnotsay,butwhichalltheide-alistsofthecountryarethankfulfor,istherolethatheperson-allyplayed,andnotwithoutcourage, inbringingEinstein tothisvenerablehouse,andwhichshoweditself,onemoretime,tobedeservingofitshigh,andfreetradition.

Inafewphrases,Einstein,standingthewholetime,thanksuswith his soft and singing voice, initially not very confident-sounding.Inacautiousmanner,heremarksthathispresenceinthisplaceisthehappysignthatscienceisnolongerthreatenedbypolitics.Then,hesitsdown:Therespectfulroom,whichwasalsostanding,doesthesame.Immediately,andwithouttransi-tion,—Einsteinhasnotastefororatory—hebeginstospeaktousabouttheTheoryofRelativity.

Hisdictionisslow.Youfeelthatthewordsarenotgoingfastenoughtofollowtherapidlyadvancingandwell-orderedtroopsofhisideas.Thevoiceiscaressing,andofaratherlowandvi-branttone.HenriPoincaréhadalsoanextremelylowvoice,

butitstonewasstilllowerthanthatofEinstein.Einsteindoesn’tignoreanyofthenuancesofourlanguagewhichhepronounc-eswithaslightaccent.Hesays“lesékations,”“larélativité,”“lakinématique.”2Whilehespeaks,hiseyes,withvery inclinedeyebrowsabovetheeye-sockets,converginguponan“accentcirconflex”[^] towards themiddleof theforehead,seemdi-rectedveryfaraway,muchfartherthantheardentlooksofthepublicforwhomhehadbecomethegeometriccenter.Thoseeyes,whichtheycontemplate,arethesereneregionswherethemindofthescientistsynthesizesthemarvelsofmatteranden-ergy.Thisidealcontemplationisnotatallthatofadream:thatwhichhescrutinizesarelivelyrealities,whichareimpression-ablethings;because,forEinstein—andhewillnotstopinsistingontheseideaswhichseparatehimfromcertaincontemporariesofhis—themathematicalabstractionisnotatallsomewingedthingusedtoleadthemindwildlyastray,itisanddoesnotneedtobeotherthan,thehumbleservantofthings,suchastheyexistin reality.From time to time,he leans towardsMr.Langevinwhoisseatedtohisleftandalittlebitsetback,togettheneces-saryword,theFrenchwordwhichheishavingdifficulty,fol-lowinghisownexpression,in“extractingfromhisthroat.”

Sometimes,it’sanEnglishwordthatcomestohislips,andIhearhimmurmuring“assumption”whileMr.Langevinsoftlywhispers “hypothesis.” But these short pauses, which some-times slowdownhisdelivery, arenotdisagreeable,becausetheygivetheaudiencemembertimetobetterpiecetogetherthereasoning;whoseextraordinarilydensesuccessionofargu-mentsmakesthispresentationtherichestmeltingpotofideasthatcanbeimagined.Andthen,asiftolightentheheavyideasof his presentation, each time that the desired word doesn’t

2. [Translator’s note] This may not be clear to non-French speakers. The ac-tual French spellings of these words, with accents, are les équations, la relativité, la cinématique. It would be as if a German speaker said in English “He sait dat fery vell.”

AlbertEinsteinandProf.PaulLangevinin1922.


comeeasily,Einsteinsmiles,whilewaitingforMr.Langevintodelivertohimthedesiredterm.AndthissmilethatwassowellcapturedbytheartistChoumoff,hassomethingextremelyse-ductivetoit.Itseemstomethatithassomethingofacourteousreluctance,likeaprayertonotbecomeangryatthesesmall,purelyphilologicalhesitations.

Moreover,Einsteinspeakswithoutanynotes,withhissightaimedhigh.Hisusualgestureistoslowlyraisehistwohandswiththethumbandindexfingertouchingsoftlyasifhewereextendingandslackeningsuccessivelyaninvisiblethread,thesuppleandsilkythreadforthedemonstration.

In thisfirstmeeting,Einsteindeclaredat thebeginninghisdesiretolimithimselftoasortofgeneralexpositionoftheprin-cipleofrelativity,orratherofthemethodemployedintheelab-orationofthetheory.Thefollowingmeetings,headdedrightaway,willbeentirelysetasidefordiscussion.

Totellyouthetruth,eversincethisinitialmeeting,Einsteinhad,byhisownpresentation,launchedthecontroversyandde-batedwiththesharpestprecisionsomeofthecriticismswhichwereleveledathim,andsomeofthemisunderstandingsthatthecontroversyhadcreatedaroundthenewdoctrine.

Iwouldnotbeable,here,tofollowEinsteinstepbystepinhispresentation,whichlastedtwohours.Itwouldtakemesev-eralhundredpagestotranslateitentirelyintoalanguagewherethetechnicalexpressionswouldbemadeaccessibletothenon-specializedreader,sincethewordsandthephraseswithwhichwecanexpressthesethingsunfortunatelydon’thaveanyofthedense and concise brevity of mathematical formulas. Thatwhichcanbesaidinfiveminutes,whenwecantalkfreelyofcoordinateaxes,quadratic forms,geodesics,andtransforma-tionformulas,wouldrequiremuchmoretimetoexpresswhenwehavetofirsttranslatetheseesoterictermsintoordinarylan-guage.Inhispurelydidacticpart,thepresentationofEinsteinhadmoreoversimplyconsistedinrecallingtheessentialbasesofhistheory,andthenotionsalreadyknownbythosewhodomethehonorofreadingmyownwritings.3Thisleavesoutthe

3. I may be permitted here to refer my readers to the articles where I have ex-plained the experimental and theoretical foundations of the Special Theory of

specifically critical and meth-odologicalpartofthepresenta-tionwhichgivesititsoriginality,andofwhichInowproposetoexpress, in the simplest waypossible, the profound interestandconvincingconclusions.

ThetheoryofEinsteinisgen-eratedfromproblemsthatcomefrom “experimentation.” It isbased on facts, and its authorinsistswithmuchvigoronthispointwhichhasoftenbeenmis-understood.Itiscompletelytheoppositeofametaphysicalsys-tem—and my readers remem-ber that I have already devel-opedthisideaatlength.

Whatare,therefore,thefactson which the new theory was

built,andwhichseemed,insomeway, tocompel itsaccep-tance?Thepointisthis:Thereis,inclassicalscience,orinthestudyofmechanics,whichwaslaidoutbyGalileoandNew-ton, a principle which is called the “principle of relativity,”whichcomesmoreorlesstothefollowing:Intheinteriorofamaterialsystem,wecannotinanywayshowitsmotion,viaex-perimentsdonewithinavehicleinuniformtranslation.Forex-ample, ina trainmovinguniformly, (andnot taking intoac-count the vibrations, which are precisely alterations in theuniformity of the motion) we cannot by any known processshowtherealityandthemagnitudeofthemotion.Whentwotrainspassoneanother(nottakingintoconsiderationtheseal-terations),thepassengerscannotknowwhichisactuallyinmo-tion, that is tosay,eachonebelieves that it is theotheronewhichisinmotion.Allclassicalmechanics,alltraditionalsci-ence,isfoundeduponthisverysimpleprinciple.Ithasbeenverifiedthroughoutcenturies.Notonlyisittheresultoffacts,butithasinitajenesaisquoiofevidencewhichsatisfiesthecourseofourreason.Thelatterinfact,repudiatestheideathattherecouldexistinnature,amongalluniformmotions,thatistosayamongsimilarmotions,somewhichcouldberealmo-tions,thatwouldexcludeotherones.

Thegoodintuitivesenseandthefactscombined,havethere-forecometoagreementincementingonsolidfoundationstheclassicalprincipleofrelativity,asfarasuniformmotionsareconcerned.But,notethatsincethe19thCentury,anotheredi-ficewaserectedinscience,whichisnotconcernedwiththedisplacementsofmaterialbodies,butratherwiththesubtlemotionsoflightandelectricity.Ontheothersideofmechan-icswaserectedelectromagnetismwhichnotonlycombinesinasuperbtheoreticalsynthesis,opticsandelectricity,butwhichhasledtomagnificentexperimentallyverifiablepre-dictions;among themostbeautifulare thediscoveryof thewirelesstelegraphandtheproofthatHertzianwavestravelat

Relativity, and, for General Relativity, I refer the reader to my recent little book Einstein and the Universe, where the conclusions are found to be (as one would judge) entirely in agreement with those found in the controversies which pro-vide the occasion for the present article.

OneofthemanyarticlesinthepopularpressreportingonEinstein’svisittoFrance.L’IllustrationalsocoveredEinstein’s1922visittoaFrenchvillagenearDormans(above),whichhadbeendestroyedinWorldWarI.


thespeedoflight.Electromagnetism rees-

tablishesasafoundationthisprinciple that the speed oflightisconstantineverydi-rection.

But, observe that certainrecent facts, certain experi-mentswereshowntobein-compatible,eitherwithelec-tromagnetism, or classicalmechanics, or better still,with the two principleswhich serve as foundationsrespectively for these twodisciplines, which are theprincipleofrelativityandtheprincipleoftheconstancyofthespeedoflight.Theexper-imentofMichelson,amongothers,appearedtobelead-ingtothenecessityofabandoningeitheroneortheotherofthese principles.This is when Einstein, through a profoundanalysisofthenotionsservingasfoundationsforclassicalme-chanics,showedthatthisisdeducedrigorouslyfromtheprin-cipleofrelativityonlyifweallowforcertainhypotheticalenti-tieswhichwecallabsolutespaceandabsolutetime.

Ifweeliminatethesetwohypothesesandifwedefinetimeandspace,thatistosay,extensionsanddurationsasweob-servethem,bytakingintoaccountthenon-instantaneousprop-agationoflight,wethenelaborateanewscienceofmechanics,themechanicsofEinstein,whichisfounded,liketheclassicalone,ontheprincipleofrelativity,butwhichconstitutesanap-plicationofthisprinciplethatisextricatedfrommetaphysicalhypothesesandfromtheapriorinotionsofabsolutespaceandabsolutetime.

Inaword,Einsteinmaintains the twoprinciples thathavebeentestedexperimentallyandwhichareatthebasisofclassi-calmechanicsandelectromagnetism.Solelybyapplicationofthese classical principles, but whichhe purifies of their metaphysical re-fuse,heconstructsanewscienceofmechanics without any special as-sumption.Then, it turns out: 1. thatEinstein’s science of mechanics ac-countsforboththefactsexplainedbytheoldscienceofmechanicsaswellasthisnewone;2.thatitimmediatelysolves the incompatibilities that theMichelsonexperimenthadshownbe-tweenmechanicsandoptics;3.thatitexplains and predicts a number ofphenomena, of facts pertaining toelectronsandwhichescapethegraspof classical mechanics; that it ac-countsforcertainoldresultsthatrep-resented enigmas for traditional sci-ence,suchastheFizeauexperiment.

Asmyreaderswillremember,Ihave

explainedallofthisextensivelyinthisreview.Iwill,therefore,onlyretainthis:TheontogeneticexaminationthatwehavejustmadeofthistheoreticalbodycalledSpecialRelativityprovesclearlythatthisfirstaspectofEinstein’sworkhasbeenelabo-ratedonthebasisofdatagivenbyexperimentation.

TheTheoryofRelativityaccountsforalloftheresultsofthetraditionaldoctrineandonlydiffersfromitbythefactthatithaseliminatedfromitallremainingmetaphysicalresidues.Noonewilldisputethatthismakesitasuperiorscience.Thereisnoth-inginsciencebutthatwhichcanbemeasured,anditissurelybetter tobasescienceonthis, thanonthatwhichcannotbemeasured.

Therefore,whenthenewspapersannounced,withatouch-ingtoneofunanimity,thearrivalinParisofthecelebratedmeta-physicianEinstein,theywerecertainlydeliveringthemostfalsi-fied of all possible inexact news that ever came out of thewhiningprintingpresses.Obviouslywe are allmoreor lessmetaphysicians,startingwiththehousewifewhoisconcernedaboutwhatshewill feedherhusbandforsupper tonightbe-causeshemakestheassumptionthatherhusbandexists,andtherefore,sheismakingadaringmetaphysicalassumptionfrombeyond theoutsideworld.However, thisbeing thecase,wecanascertainthatEinsteinistrulytheleastmetaphysicianofallphysicists.Hismeritandthecauseforscandaltothemisoneistscomespreciselyfromthefactthathehas,betterthananyonebeforehim,de-metaphysicizedthedomainofscience.

Oneofhisconstantpreoccupationsistomakeclearlyunder-stoodhisparticularconcerninthisrespect.InhispresentationofMarch31st,andwiththefinesse-filledimplicationsthatchar-acterizehim,heexplainedthispointextensivelybyaddressingaparticular speciesofmetaphysiciansknownasmathemati-cians, that is, thepuremathematicianswho, lost in theirab-stractdreamsandcarriedonthepowerfulwingoftheirimagi-nationstowardsomeunrealbeauties,neverputtheirfootdownontherigidsoilofwhatexists.

Einsteincertainlydoesnotholdmathematiciansincontempt.Withouttheircollaboration,heprobablywouldnothavebeenabletobringhisworktofruition.ItistheabsolutedifferentialcalculusofRicci,theequationsofLevi-CivittaandofChristof-

FrenchphysicistPaulLangevin(1872-1946) worked closelywith Einstein in science andpolitics.

ForafurtherexplanationofEinstein’smechanics,seethevideo“TheGeniusofAlbertEin-stein.”

www.larouchepac.com/node/15482?page=2




fel,andthegeometriesofGaussandRiemannwhich,whenused

judiciously,allowedhimtocompletehiswork.But,herefusestoconsiderthatcalculatingisanythingelsebutaninstrument,thatis,merelyabridgebetweenhisexperimentalpremisesandthe lawfulconclusionsofexperimentation.Hewantsmathe-maticstobetheservantofthefacts.Alwaysandaboveall,heispreoccupied with the physical significance of mathematicalsymbols.ThosewhohaveseenintheRelativityTheorymerelythemathematicalapparatus,arelikethepassers-bywhowouldmistakeTrinityChurchforthegiganticscaffoldingthathidesitsharmonic lines, and which might otherwise even somewhatcontributetoitsstrength.

Thisisoneofthemostfrequentmisunderstandingsthathasarisen between those who consider the Einstein theory as apurelyphysicaltheory,andthereareafewofuswhoforalong

timehaveheldthatpointofview,andanumberofthosewhoarehismathe-maticaladversaries.

Einstein stoodupwithforce against the often-expressed opinion thattheTheoryofRelativityisnothingbutapurely for-mal construction. It is aphysical theory, a theoryof the outside world, atheoryofthephenomena,oftheeventsoccurringintheuniverse.Hesaidthefollowing in his ownwords:

ManymathematiciansdonotunderstandtheTheoryofRelativityalthoughtheymayapprehenditsanalyticaldevelopments.Theyarewronginseeingsimplyformalrelationsandofnotmeditatingonthephysicalrealitiestowhichcorrespondthemathematicalsymbolsinuse.

Hereisanexamplewhich,Ithink,willhelpusunderstandthis conception. If a man who has learned nothing else butmathematicsweretolivehisentirelifeinsideofaclosedroom,hewouldbeperfectlycapableofreadingandunderstandingthelogicalsequenceoftheformulasofatreatyofcelestialme-chanics.But,hewouldotherwiseunderstandnothingof thecelestialmechanics,becausehewouldfailtounderstandthattheseformulasapplytotherelativemotionsofrealexternalob-jectsthatwecallthestars.Itistothissortofman—dueallow-

Nimitz Library, U.S. Naval Academy, Special Collections and Archives

PhysicistAlbertMichelson(1852-1931).

Figure1FIRSTMICHELSON-MORLEY

INTERFEROMETER(1881)A.A.Michelson’sinstrument,construct-ed inBerlin in1881, fordetecting therelativemotionoftheEarththroughthepresumedstationaryether.Thetwoper-pendiculararmsarerotatedsothatonepointsinthedirectionoftheEarth’srota-tion.Half-silveredmirrorsatthecentercreate equal path lengths for the lightrayinthetwoorthogonaldirections.Itisexpected that the light ray movingagainsttheetherstreamwilltakeslightlylongerthantheraywhichtraversestheotherperpendiculararm.Thiswillbeevidentasashiftinthefringepatternintheinterferometerpositionedate.

Insetshowsthefringepatternsinnarrowandbroadmag-nificationfromalaterinterferometer.Sources: A.A. Michelson, 1881 “The Relative Motion of the Earth and the Luminiferous Ether,” Am. J. Sci., Vol. 3, No. 22, pp. 122, 12�. D.C. Miller, 1933, “The Ether-Drift and the Determination of the Absolute Motion of the Earth,” Rev. Modern Phys., Vol. 5, p. 211 (July).


ancebeingrespectfullymadetosavetheirreverence—thatEin-steinwilltendtocomparethoseindividualswhocriticizehistheorieswithouthavingstudieddeeplyenoughtheirphysicalcontent.

Wellthen,thephysicalcontent,whichisthebasisfortheen-tireTheoryofRelativity,istheexistenceandtheinvarianceofaquantitymeasurablewithrulersandclocks,aquantitythatwecalltheintervalbetweenthingsandwhichisneithertheirdis-tanceintime,northeirdistanceinspace,but—myreaderswillremember—asortofconglomerationbetweenspaceandtime.

TheentireEinsteinsynthesisisfoundedonthebeliefoftherealexistenceofthisphysicalconcept.Ifthisconceptdoesnotexist—andthisisconditionalonexperimentationandontheinstrumentsofthephysicist—theentiretheorybecomesnoth-ingmorethanaplayofmathematicalformulasandvanishes.But,Einsteinseemstobeuntroubledinthisregardandwehavetorecognizethathistranquilityisbuttressedbysoliddemon-strations.AsidefromalltheverificationsofclassicalmechanicsthatalsoverifyEinstein’smechanics,itistheadmirableexperi-mentalverificationsofphysicaldiscoveries(distortionoflightbygravitationexplainingtheanomalyoftheplanetMercury)thathaveledtothenewtheory.

Ashewasspeakingonthesethings,andbecauseofhisim-perfectmasteryoftheFrenchlanguage,Einsteinhadafewver-balhesitationsandhetreatedustosomeinspiringflavorfulne-ologisms. For instance, when speaking about classicalmechanics,whichdiffersfromhisownasdoesthestaticchrys-alisfromthefastmovingbutterfly,Einsteincameupwiththenewexpressionof“‘antique’mechanics.”Iaskedmyselfiftheuseofthisimproperqualificationdidnotmaskalittlebitofde-liberateirony.

ItisnotonlySpecialRelativitywhichisbasedontheneces-sityofresolvingproblemsposedbyexperimentation;itisalsothecaseforGeneralRelativity,whichrepresentstheadmirablecrownofhis theory. Inparticular,almost theentiresynthesiswastriggeredbythefollowingfactthatclassicalsciencehadnoticed,butwasincapableofexplaining,andinwhichNewton

hadonlyseenacoincidence:Thenumberswhichexpress theweightsofdifferentbodies (that is tosay,theirreactiontogravity)areidenticaltothosethatexpresstheirinertia(thatistosay,theirreac-tiontosomemechanicaldisplacement).Whenwefindsimilartypesofidentitiesinnature,suchsin-gularfacts,itisnaturalthatweseektoelucidatethematterdifferentlythanbysimplysayingthatitisanunbelievableandfortuitouscoincidence.ThatwasnonethelesswhatNewtonresignedhimselftoac-cept.This is something that Einstein was not re-signedtoacceptatall,andhisstunningpenetra-tionfoundthesolutiontotheenigmainthetheoryofGeneralRelativity,whichbroughttogetherintoagrandioseanduniquesynthesisthesetwodomainsof gravitationand mechanicsbetween whichclassical sci-encehaderect-ed an unjustifi-ablebarrier.The

facts, and nothing but thefacts,areattheoriginofEin-stein’sdoctrine.

Again, itwasbymeditat-ingmoreprofoundlyonper-ceived realities and on theexperimental foundation ofgeometrywhichwascarriedoutbeforehim,thatEinstein

Nimitz Library, U.S. Naval Academy, Special Collections and Archives

TheMichelson-Morleyexperimentof1887,setupinthebasementofAdel-bertHall,WesternReserveUniversity.Resultsweresmallerthanexpected,thoughnotcompletelynull—anenigmatothisday.

(Formoreonthistopic,see“OpticalTheoryinthe19thCenturyandtheTruthaboutMichelson-Morley-Miller,”byLaurenceHecht,21stCentury,Spring1998.)

French physicist HippolyteFizeau(1819-1896)

Figure2SCHEMATICOFAFIZEAUINTERFEROMETER

Fizeauusedhis interferometer tomeasure theeffectofmovement of a medium upon the speed of light. Hepassedlightintwodirectionsthroughmovingwater,andmeasuredtheinterferencepattern.Bothbeamstravelthesamedistance,butonegoesinthedirectionofthewaterflow and the other goes in the direction opposing theflow.An interferencepattern is formed (causedby thetimedifferencesofthebeams)whenthetwobeamsarerecombinedatthedetector.


arrivedat theconclusion that theworld inwhichwe live isbarelyapproximatedbyEuclideangeometry.Thisconclusionhasalsobeenconfirmedbythefacts:suchasthebendingoflightraysbyamassivebody,etc.Ihavealreadyexplainedthesethings,andIwanttostressonlythis:TheTheoryofRelativitystartsfromsense-perceptionrealitiesinordertoleadtoothersense-perceptionrealities.Mathematics,howeverconsiderableitsimportance,itslogicalrigor,anditsuniquemodeofexpres-sionsmaybe,onlyplaysarolethatisanalogoustothatoftrans-missionbeltsinmachine-tools.ThatisthereasonwhyEinsteinneverstoppedrivetinghimself to therealworld, to thedata.BetterthanNewtonhimself,hehasappliedthehypothesesnonfingo.

TheTheoryofRelativityisthemostprofoundandthemostsuccessfulofallattemptsbythehumanmindtobanfromsci-encewhatisnotmeasurable,andtochaseoutofphysicsallthatismetaphysical.

SuchwastheimpressionmadeuponusbyEinsteinonMarch31st after he had ended with a few cosmological consider-ations,onwhichIshallreturnlater.Hemadeapenetratingex-posédivestedofanypretense,whosesoleeloquencestreamedfromfactsandfromreason.Then,thegreatphysiciststoodupinthemidstofapplause.

***

ThefirstdiscussionsessiontookplaceonApril3rdinthephys-icsamphitheateroftheCollègedeFrance,whichisevenmorecrampedthanthe“large”amphitheaterinwhichEinsteinspokethepreviousFriday.Theaudiencewascomposedalmostexclu-sivelyofscientists,ofphilosophers,ofresearchers—andinthefirstamongtheirrankswasDoctorRoux,hispaleasceticfacecappedwithhissmalltraditionalskullcap,Mr.Bergson,Mme.Curie,andagreatmanymembersoftheAcademyofSciences.

The session was to be dedicated exclusively to questionsraisedbytheSpecialTheoryofRelativity.EinsteinwasseatednexttoMr.Langevininfrontofasmalltable,tothesideofagi-ganticblackboardwhichwouldsoonrevealthedialecticalpas-sionoftheplayers.

Thefirstquestionwasonthe Michelson experiment.Myreadershavenotforgot-ten that, according to theSpecialTheoryofRelativity,thelengthofagivenobjectandthetimeseparatingtwoeventsarecharacterizedbyquantities which vary withspeed, and which vary insuchawaythat thelengthsandthedurations(expressedinseconds)areshorterforagivenobserverwhentheob-jects under considerationmove very quickly with re-gardtotheobserver.Asfaraslengthsareconcerned,Ihaveeven given an elementaryexplanationhere.Asforthetimes, an analogous expla-

nationcanbeproduced;butduringthispresentation,Einsteingaveanotherdemonstrationofthisfact,whichwassosimplethatIsimplycannotrestrainmyselffromreportingithere.

Itisknownthatlightplaysafundamentalroleintheregula-tionoftimepiecesandtheverydefinitionoftime;thatthereisnobetterdefinitionforthedurationofonesecondthanthetimenecessaryforlighttotraverse300,000kilometers,andthatitislightor electricity (whichhasanequal speed)whichare thepracticalagentsforthesynchronizationofclocks.Letusthere-foreassumethattheidentityoftimebedefinedbythetimetakenbyalightraytomakearoundtripalongthedistancebetweentwoparallelmirrorsuponwhichtherayreflectsnormally.Thisgoingandcomingoftheraysituatedbetweenthetwomirrorsisanexampleofthetypeofperiodicphenomenonbywhichtimeismeasuredout.Itwould,forexample,defineathree-hundred-millionthofasecond,ifthedistancebetweenthetwomirrorsis50centimeters.Suchwouldbethevalueofthedurationascon-sideredbyanobserversituatedbetweenthetwomirrors.

Nowletusassumethatthesystemcontainingthetwomirrorspassesbeforemeataverygreatspeed,carriedbyarapidtrans-lation,paralleltothetwomirrors.I,whoseeitpassby,remarkthat the light ray,which leaves the centerof thefirstmirror,must,inordertoruntothecenterofthesecond,andfromtherebacktothefirst,traverseapathslightlyinclinedinthedirectionofthetranslationandnotnormaltothemirrors.Itfollowsthatthistrajectory,whichdefinestheunitoftimefortheobserverconnectedtothemirrors,definesforimmobilemeatimelon-gerthanmyownunitoftime.Inotherwords,thedurationsofphenomena,thetickingofclocks,likeallthegesturesmadeinavehicle invery rapidmovement,willappear tobesloweddown,andconsequentlyappearprolongedtoanobserverinmotion,andviceversa.Q.E.D.

Inthecourseofhisexplanations,EinsteinwasledtospecifythatalthoughtheapparentcontractionsofobjectsbyspeedisdeduceddirectlyfromtheMichelsonexperimentbythetheory,theapparentslowingoftimefollowsfromthisexperimentonlyindirectly. Experiments will perhaps someday permit time-contraction to bededuced from theobservations of positive

Henri-Louis Bergson (1859-1941)inaportraitpaintedbyJ.E.Blanchein1891.

Polish-French physicist andchemist Marie SklodowskaCurie (1867-1934), in aphototakenaround1920.

Emile Roux (1853-1933)wasaFrenchphysician,bac-teriologist, and immunolo-gistwhocollaboratedclose-lywithLouisPasteur.


rays[ions]orfromtheobservationoftheeclipsesofJupiter’ssatellites.Buttheprecisionofastronomicalobservationsseemsinsufficientatthepresenttimetoestablishthelatter.

Theprincipleandmostcertaindemonstrationoftime-con-tractioncausedbyspeedisfound,asfordistance-contraction,inthemanyindirectyetmutuallyagreeingverifications,whichconstitutetheapplicationsofthisnotiontothenewmechanicsandtheverifiableconsequencesthatitentails.

InregardstotheMichelsonexperiment,Einsteinhassincerecountedtome,thatthefamousAmericanphysicisttoldhimoneday:“‘IfIhadbeenabletoforeseealltheresultsthathavesince been derived from my experiment, I tend to believe Iwouldneverhaveperformedit.’”Itisincidentallysomethingrathersingularandvery interesting fromahistoricalpointofviewtoconsiderthisattitudeoftheprincipalprecursorsofRel-ativitywhenpresentedwiththetheoryofEinstein.Duringthecourseofarecentconversation,Einsteingavemesomecuriousclarificationsonthissubject,theessentialelementsofwhichIfindusefultosummarizeforthereaderhere.

HenriPoincaréhasdied,anditcertainlywouldhavebeen a profoundly movingthingtoseeEinsteindiscusswith this powerful mind,whohadonsomanypointsshown the way. Would hehavebeenapartisanoftheGeneralTheoryofRelativity?Itisprobable,butnotabso-lutely certain. Studying themany famouspageson theorigins and foundations ofgeometry, Henri Poincaréhad arrived at the conclu-sion that, if it is not moreideallytruethantheothers,Euclidean geometry is thatwhich corresponds to thenatureoftheexternalworldand to our sensations. On

thispointEinsteinmadeacleanbreakwiththeideasof Poincaré, starting fromthe day he forecast thecurvingof raysof lightbygravity,whichwasrecentlyverified,asweknow,andasPoincaréhadnotimag-ined.

ThatisthekeystoneofallRelativity,thecentralpointfrom which Einstein wasabletodeducethattherealgeometryoftheworldisin-deed a non-Euclidean ge-ometry.ItisquitedifficulttoknowwhatPoincaréwouldhave thought about this.Surely under this form orperhapsanother,hewouldhavebeen,inkeepingwithhisownideas,afullrelativ-ist;andhewouldcertainlyhave accepted with totalsympathy anything whichwouldhavepermittedhimtolivewithoutthesemysti-calcreatureswhichhefoundsingularlyrepulsive:thenotionsofabsolutespaceandofabsolutetimeofNewton.

Perhaps even more than Poincaré, Einstein admits havingbeeninfluencedbythefamousViennesephysicistMach(whohadfirstdiscoveredandstudiedtheshockwavethatrapidpro-jectilesproduce in theatmosphere.)Mach formerly strove toreduceallofmechanicstoobservablephenomena,allmotionstomaterialreferencesandsupports.Althoughhewasnotabletobringhisideastomaturityduetohislackofmathematicalandphilosophicaltools,theyareincompleteharmonywiththeveryprinciples of Einstein. However, just before his recent death,MachdeclaredhishostilitytowardtheGeneralTheoryofRela-tivity.“Butitisbecausehewasold,”Einsteintoldme,smiling.

AsforLorentz,whoisincontestablythemostcertainprecur-sorofEinstein,itappearsthatheadmitsthefoundationofGen-eralRelativity,whileat thesame time refusing toaccept theprinciples which established the basis of Special Relativity.Howeverillogicalthisattitudemayseemtobe,itisnotshock-ingifonerecallsthatLorentzalwaysdefendedthethesisoftheabsoluteandimmobileether,andtheactualspeed-contractionofbodies.Hisoverall attitude regardingRelativity is, asonecouldjudge,similarenoughtothatofMr.Painlevé.But,asofnow,itisimportanttonotethattoadmitGeneralRelativityisthe sameas admitting theessentials andmajorityof SpecialRelativity,sincetheformerwasonlycreatedbyEinsteintorem-edy theshortcomingsof the latter;which today,moreover, itsubsumesinamoregeneralsynthesis.Ifyoutakethegreater,yougetthesmalleraswell.

Theconclusionofthisfirstcontroversialsession,andthebe-ginning of the following session (which took place onApril5th),werealmostentirelytakenupbyapassionatediscussionprovokedbyMr.Painlevé,who,tothedelightofhisfriends,had

TheinterferencepatternproducedwithaMichelsoninterfer-ometerusingaredlaser.

French mathematician, physi-cist,engineer,andphilosopherHenriPoincaré(1854-1912).

Thisbustof theViennesephysi-cist and positivist Ernst Mach(1838-1916),sculptedbyHeinzPeter,standsintheCityHallParkofVienna.


abandonedpoliticsforafewhours.Thisdiscussiongreatlycon-tributedindefinitelyclarifyingoneofthemostdelicatepointsoftheTheoryofSpecialRelativity.

Thisanimatedandalwayscourteousdiscussionwasamostcuriousandinterestingspectacletowatchinitsperfectobjectiv-ity.Intruth,Mr.Painlevéneverceasedtopubliclypraise,onalloccasions,hisadmirationforEinstein’sgenius.ItwaswithinafewweeksthatapositionofcorrespondingmembershipfortheMechanicsDepartmenthadbecomevacantattheAcademyofScience,andforwhichafewvoicescalledforEinstein,whowasneitheracandidate,norevenpresentedhimself.Mr.Painlevéwaspleasedtodeclarethathisvoicewasamongthem.ItwasatthisoccasionthatahighlyesteemedmemberoftheAcademyproclaimedthesedeliciouswords:“HowcanyounominateEin-steinasamemberoftheDepartmentofMechanicswhenitisEinstein,himself,whohasdestroyedthescienceofmechanics?”Ifitistruethatallprogress,allchange,constitutes,insomeway,adestructionofthatwhichismodified,itisanaturaltendencyformanymentoconsiderthisdestructionasnecessarilybad.ThesamethingoccurredwhentheCopernicansystemdestroyedthePtolemaicsystem,whenLavoisier’schemistrydestroyedtheolddoctrineofPhlogiston.Butitis,alas,theverynatureoflife’sprogress that itonlygrowsand thrivesupondestruction.The

butterflydoesn’tleaveitscocoon;thebirddoesn’thatchfromtheeggwithoutdestruction.Mandoesn’tbecomeanadultwith-outthedeathofthatwhichmadehimachild.Noflowerwouldblossomthatdidn’tfirstrupturethefragileenvelopeofitsbulb.ThisisalsothehistoryoftheEinsteindoctrine.Unlessyouwishtoseetheuniverseseizedwithinamonstrouslethargy,andideascrystallized forever into rigidforms,whoseimmobilitywouldbetheequivalentofdeath,onemustberesignedtoaccept,es-pecially with science, that theonlyraisond’êtreistostriveal-waysfurther.

Thus, Mr. Painlevé neverceasedtopraiseEinsteinasoneofthegreatestgeniuseshumanhistoryhadever seen. I know,that for his part, Einstein pro-fessedthemostsincereadmira-tionfortheworkofthisfamousFrench geometer. In these cir-cumstances,theatmosphereinwhich the conversation be-tweenthesetwoscientistsopened,wasinfinitelypropitioustothehappyshocksthatconfrontedandanimatedthesesincereintellectsandfromwhichmorelightwasshed.

NothingwasmoreamusingthanseeingEinsteinandMr.Pain-levésidebysideinfrontoftheblackboard:thefirstalwayscalm,armedwiththesoftpatiencewhichcomeswithabsolutesecuri-ty;thesecond,impetuousandlively,boilingwiththeefferves-cenceof ideasandarguments; thefirst immobile, the secondneverremaininginoneplaceandalwaysgoingbackandforthwithinthenarrowarenainfrontoftheboard.Einsteinwaspaleandhisattitudeandmannerofspeakingseemedtoresembletheinflexiblesolidityofanimmovablerock,resistingovercenturiestheforcesoferosion;Painlevéwasallflushedbythefluxofhisboilingblood,passionateinhisgesturesandarguments,attack-ingwiththesuddenoutburstsofunpredictableandbrilliantfitsandstartsthatweusuallywitnessinassaultsagainstoldandshakythings,withtheideaofturningacceptedorderupsidedown.

Justbyjudgingtheappearanceofthesetwomen,who,armedeachwithapieceofchalk,coveredthevastblackboardwithbattalionsoftheiropposedequations,ittrulyseemedasthoughitwereEinstein,whowastheconservative,andMr.Painlevé,the“revolutionary.”Andyet,oddlyenough,theoppositewastrue.Itwasthefirstwhohadcompletelyoverturnedtheentireedificeofthetraditionalstructure,wherethehumanspirithaddozedwithafalsesenseofsecurity,wherebythesecondactedasarampartinfrontofthefortressofNewtoniansciencethatwasunderattack.

ThediscussionwasfocussedonanimportantpointabouttheTheoryofSpecialRelativity.Itended—asweshallsee—withacompleteagreementbetweenthetwochallengers,andservedtocompletelyeliminateamisunderstandingwhichthisfirstlev-eloftheEinsteinmonumentcouldhaveborninsomeminds.

Hereishow,Ibelievewecanpresent,withouttheuseofasingleformulaandwithoutanyesotericcalculation,theques-tionthatwasraisedandtheresponsethatwasgiventoit:

Weknow,asIhaveexplainedinthepast,thatbecauseoftheparticularpropagationoflight,thereexistsnouniversalorab-

Museum Boerhaave, Leiden

DutchphysicistHendrikAntoonLorentz (1853-1928)photo-graphedwithEinsteininLeidenin1921.

French mathematician andPrimeMinisterPaulPainlevé(1863-1933).


solutetime,andthattheworkingsoftwoidenticalclockswouldnotappearidenti-caltoanobserverattachedtooneoftheseclocks,andwhoseestheotherpassingbyhimataveryfastspeed.AsIshowedear-lier,theclockwhichisnotmovingwithrespecttomeseemstogofasterthanthatonewhichwasmovingspeedilybyme.In a general manner, the duration ofevents,suchasthevibrationsofadiapa-son,thebeatsofaheartorallothergivenphenomena, will appear shorter, morehurried, to a non-moving observer ofthesephenomena,thantoanobserver,infrontofwhomthevehicleonwhichthosephenomenon are located, passes byquickly.Forthislastobserver,thesephe-nomena will appear to be slower. In aword,foragivenobserver,eachvehicleinmotioninspacehasitsownparticulartime,itsparticularspeedinwhichflowthephenomena.Thistime,thisdurationofagivenphenomena(e.g.,theburningofacigarette),wouldseemalwaysgreater,whenthephenomenaaremovingatagreaterspeed,inrelationtome.Consequently,thistime,thisduration,hasforme,itssmallestvalue,whenthespeedisnull,thatistosaywhenIamattachedtothevehicleinwhichtheobservedphenomenonisoccurring.Thisminimumvalueoftime,weshallcallthepropertimeofthevehicle,andthisexpressionislegitimatesinceitdesignatesthetimeindi-catedbytheproperclockswhichareinthevehicle.

Allofthisisthenecessaryconsequenceofthestatedlawsofthepropagationoflight,andconstitutesoneofthefoundationsoftheTheoryofSpecialRelativity.

Thissaid,wehavehere,reducedtoitsessentialelements,thequestionraisedbyMr.Painlevéandwhichatfirstsight,seemedtodrivetowardacontradiction,aparadox.

Considerarapidtrainwhichpassesthroughastationatfullspeedandcontinuesitsroutewiththesameprodigiousanduni-formspeed.Thistrainhaswithinitanidenticalclocktotheonewhichisinthestation.Attheprecisemomentwhenitpassesthestation,theconductorofthetrain,whowemaysuppose(harm-lesshypothesescostsolittle)isaskillfulphysicistequippedwithalloftheperfectionsoftechnique,whohadmanagedtosetthetrain’sclockinsyncwiththestation’sclockattheinstantthathesawthisclockpassing,thatis,bytheintermediationoflightrays.

Afterhavingrunthetrainforasmanykilometersaswewishatthesameprodigiousanduniformspeed,withhisclockthusreg-ulated,Mr.Painlevésupposedthatthetrainsuddenlystopped,and,suddenly,ranbackwards,thatistosay,returnedtowardsthestation,alwayswiththesamespeed,butnowdriveninre-verse.Now,wecancalculateintheseconditions(knowingthenumber of kilometers traversed by the train) the exact timemarkedontheclock[onthetrain]asitre-passesthestationandtheexacttimemarkedoffonthestation’sclock.Inmakingthiscalculation,wefindthatatthepreciseinstantwhenthetrainre-passesthroughthestation,theclockinthetrainmarkedashort-ertimethanthestation’sclock,asthiscanbenotedattheinstantofpassingby thestationchiefand theconductor,as the twoclockscrosspathsandarevisiblesimultaneously.

Inotherwords,if,atthemomentthetraincrossedthestationforthefirsttime,thestation’sclockandthetrain’sclockbothin-dicatedthetimeofnoonsharp,ortwelvehours,zerominutes,zeroseconds,zeromillionthsofasecond,thissynchronizationwouldnolongerexistuponthetrain’sreturntothestation.Iftheclockonthetrainindicated,say,1p.m.andzeromillionthsofasecond,theclockinthestationwouldindicateatthesamemo-ment(definedbythepassageofthetrainthroughthestation),1p.m.andsomemillionthsofasecond.Weindeedassume,Ire-peat,twoclocksofidenticalconstruction.Inotherwords,thepropertimeelapsedbetweenthetrain’stwosuccessivepassesbythestationwouldbeshorteronthetrain’sclockthanthesta-tion’sclock.Thestationchiefwouldhavealsogrownolderthanthetrainconductorduringthisinterval.Thus,ifwecouldsuffi-cientlyprolongthelengthandthespeedofthetrain’svoyage,itcouldhappenthat,assoonasitre-passedthestation,thestationchiefwouldhavegrownolderbytenyears,whereasthetrainconductorwouldhaveonlyagedbyoneyear.Thechronometersandcalendarsofthetwomen,nottomentiontheirstateofageoftheirorgans,orthenumberoftheirheartbeats,supposingthattheywerecounted,wouldtestifyaswitnesses.

Thesewere the fantasticunsuspectedconsequencesof thelogic of theTheory of Special Relativity. But what appearedshockingandmysterioustoMr.Painlevéinitsconsequences,wasnotthatitoffendscommonsense;itwasn’tthatsomemenagedreallymuchless thanothers,simplybecause theyvoy-agedso;no.Whatshockedhimwasnotthat,ifIcouldsay,voy-agesnotonlyformedbutprolongedyouth;hisanalyticalimag-inationhadalready,doubtless,madedreamsmoreastonishingthanthat,andheknewthataworldinwhichmencouldtravelatspeedsoftensofthousandsofkilometerspersecond,relativetooneanother,wouldbeaworldverydifferentfromours.

No,onceagain,whatshocksMr.Painlevéabouttheseconse-quences,issomethingelse;itissomethingthat,atfirstglance,seemstohimtogoagainstlogic;itisthefollowing:WhenintheTheoryofSpecialRelativityoneconsiderstwoobserversinrel-ativemotion,onealwaysmakessuretospecifythattheappear-ancesobservedbyeachsubjectarereciprocal.If,forexample,observerAseesthenumberofmeterstravelledandtheclock

FurtherexplanationofEinstein’sclockonthemovingtrainappearsinthevideo“TheGeniusofAlbertEinstein.



heldbyobserverBrespectivelyshrunkandsloweddownbyhisspeed,itwillfollowthatobserverBwillseeA’smetersandheldclockshrunkandsloweddownbythesameproportions.ThisresultsfromthefactthatthespeedsofAinrelationtoB,andBinrelationtoA,arenecessarilyidentical,andthisreciprocityisinconformitywiththeclassicalprincipleofRelativity.

Istherenot,asksMr.Painlevé,anessentialcontradictioninallofthis,inthefactthat,inthechosenexample,thestationmasterseesthattheexpressclockhassloweddowncomparedtohisown,whilethetrainconductorsees,inagreementwiththestationmaster,thatthestation’sclockrunsearlycomparedtohisown?Shouldn’tthereciprocity,whichiscommandedbytheprincipleofRelativity,demandonthecontrarythatthetrainconductorseestheclockofthestationrunlaterelativetohis?Besides,ifthatwerethecase,wewouldfindourselveswithanabsurdity,animpossibility,becauseit iscontrarytocommonsensethatiftwomenseeclocksH1andH2atthesamemo-mentandatthesameplace,onecanseeH1earlyrelativetoH2,andtheotherseesH2earlyrelativetoH1.

Howcanwegetoutofall this,howcanweescape fromthose difficulties, those contradictions that some might betemptedtoconsiderasimpossible?

Einstein’sanswercompletelydissipatedthemisunderstand-ingbecauseitis,asweshallsee,onlyamisunderstanding,and,followinghisownexpression,“broughttolighttheparadox.”Here,reducedtoitsmostimportantelementsandfreedfromitstechnicalterminology,isthewayonecouldsummarizetheex-planationofthegreatphysicist,whosedemonstrativeevidencewas—althoughabithidden—implicitlycontainedintheTheo-ryofRelativity:

TheTheoryofSpecialRelativityexclusivelyconcerns—myreadersdidn’tforgetit—systemsinrelativeuniformmotionstooneanother, that is, those systemswhich, in traditionalme-chanics,playaprivilegedrole,andaretheonlyonestowhichcanbeappliedtheprincipleofGalileo’sandNewton’sclassicalrelativity.But,itisconvenienttorecall,thattheTheoryofSpe-cialRelativitywasfirstelaboratedbyEinsteinforthepurposeofenlargingandconsolidating,ifIdaresay,thisprincipleofGali-leanrelativity,withtheintentionofsubjugatingtoittheopticalandelectromagneticphenomenathatseemedtorebelagainstit.Therefore,theequationsofEinsteinianSpecialRelativitycanonlybeappliedtouniformmotions,thatis,tospeedsconstantinvalueanddirection.

Thus,intheexamplewhichistheobjectofthedebate,wecouldnot consider the train,which goes to a certainplace,stops,andthengoesback,asinuniformmotion.Thesuddenstopand return inanoppositedirectionconstituteaccelera-tionsandperturbationsofthetrain’smovement,whichmomen-tarilyceasestobeuniform,andthenbecomesuniformagain,butintheoppositedirection.Thus,evenwhenconsideringthetrainonlyduringmomentswhen the speed is constant, it isclearthatthesametrainonitsoutboundandreturnjourneysdoesnotconstitute in reality thesamereferencesystem,buttwodifferentreferencesystems.Asaresult,theexpresstrain’sclock,startingatthemomentwhenthetrainreversesdirection,mustbeadjustedanewtoindicatethenewpropertimeofthetrain,andtheoldadjustmentmustbemodifiedtotakeintocon-siderationthechangeofspeed,becauseitisachangeofspeedwhensomeone,relativetoanobserver,reversesthedirectionof

themovingobject.Inaword,thetrainstation,thedepartingtrain,andthere-

turningtrain,reallyconstitute,notjusttwo,butthreedifferentsystems,eachhavingitspropertime.Itisnotvalidtosupposethattheclockonthereturningtraincouldindicatetherealtimeofthevehicle,ifitdidnotreceiveotheradjustmentsthanthosemadewhenitdepartsthestation.Iproposetodemonstratethis,withthefollowingsimpleexample:Let’ssupposethatanotherexpresstrain(let’scallitExpress2)movestowardthetrainsta-tion,while Express1,whichwehaveconsidereduntil now,movesawayfromitwiththesameuniformspeed.Let’ssupposethat the station’s clockproducesa light signal atpreciselyaquarterpastnoon,asignalfromwhichExpress2andExpress1willsynchronizetheirclocks.Eachofthetwotraindriverssetshisclockbyconsideringthetimetakenbythesignaltoreachhimfromthestation,whichtheyconsiderasthedistancefromthisstationdividedby300,000kilometers.But traindriver2recognizesthathiscolleaguefromExpress1madeamistakeinthisoperation,becausetraindriver2observes,whilepassingbyExpress1,thatthelatterdrivesawayfromthelightwhich,con-sequently, reaches him at a speed inferior and not equal to300,000kilometers.Inconsequence,traindriver2,ifhehadtofixhiscolleague’sclockwhilepassingby,wouldmakeacorrec-tion,whichthelatterdidnottakeintoconsideration.Thissuf-ficestodemonstratethattheclockonExpress1wouldnotbeable to give indications comparable to the preceding ones,whilehemakeshisreturntrip.Q.E.D.

Butthisonlysolvesonepartofthedifficulty,andleavesun-touched the one concerning the reciprocity of the vehicles’hourlyindications.Respectingthispoint,thequestioninfinalanalysisisposedthus:Sinceallmotionsarerelative,shouldn’ttheresultbethesame,whetherourexpressgoesbackandforthandthetrainstationstaysunmoved,orifwesupposeourex-press stationaryand the stationgoing thedistancebackandforth?And,thereforewhyisitthattheclockinthestation,atthemomentofthesecondintersection,runsearlyrelativetothatoftheexpress,andnottheotherwayaround?

Theansweristhefollowing:InSpecialRelativity,onlysys-temsinuniformmotion,intheGalileansenseoftheterm,showareciprocity,fromthestandpointofthemeasureofspaceandtime,butitisnotthesameforsystemsinacceleratedmotion.Thishasbeenshownclearlysince1911(atatimewhenEin-steinhadnotyetdevelopedGeneralRelativity)byMr.LangevininaremarkablememoironTheEvolutionofSpaceandTime.

InSpecialRelativity,allchangesofspeed,allaccelerationsrelativetotheenvironmentinwhichlightpropagates,haveanabsolutedirection.Thisiswhy,inthisfirsttheory,wecannotsubstitutetheaccelerationofourtrainwhenitchangesspeed,foranaccelerationofthestationintheoppositedirection.Fi-nally, this is why, between the indications from the station’sclockandtheoneonthetrain,thereisthedissymmetrythatMr.Painlevéhassoappropriatelybroughttoourattention.

AtatimewhenweonlyknewoftheTheoryofSpecialRela-tivity,whichgaveanabsolutevaluetoaccelerationsintheUni-verse,asclassicalmechanicsdid,wehadforamomenthopedtobeabletodemonstrate,throughcertainnewelectromagneticexperiments,theexistenceofamedium(let’scallitetherifyouwish)relativetowhichthoseaccelerationswereconsideredtoexist.


ButtherewassomethinginthisthatwasshockingtothemindofEinstein.Hisideasmadehimrejectapriorithepossibilityofeverattaininganabsolutespace.Thisiswhyhecalledthe“The-oryofSpecialRelativity”thefirststepofhiswork,whichap-pliedonlytouniformmotions,wantingtoindicatethatitwasonlyafirststeptowardstotalrelativismofallmotions.

TheinterestingandsosuggestivediscussionbroughtupbyMr.PainlevéonthisparticularsubjectandwhichrepresentedthehighpointofthediscussionsattheCollègedeFrance,hadthebenefitofdemonstratingbrilliantlythefactthattheTheoryofSpecialRelativitymaintainedcertainprivilegedmotionsinmechanicsandcertainsomewhatabsoluteaxesofreferenceintheGalilean-Newtoniansenseoftheterm.Somepeoplehadassuredlythetendencytoforgetthat,butsuchhadneverbeenthecaseforEinstein.

WhenEinsteindevelopedSpecialRelativity,hisonlypurposewastointroduceelectromagneticphenomenaundertheprin-cipleofclassicalrelativity.Butheknewbetterthananyoneelsethatthiswasonlyafirststep.Itwasforthepurposeofeliminat-ing that last remnant of absolute space which still survivedwithinSpecialRelativitythathetackledthegiganticproblemofGeneralRelativity.Here, therewasno longeranyprivilegedmotion.Bothuniformandacceleratedspeedswereunitedto-getherinagrandsynthesisandwereobedientlysubjugatedtoauniqueconceptionofuniversalphenomena.4

WejustsawthattheparadoxmentionedbyMr.PainlevécanbeexplainedquiteadequatelybySpecialRelativityitself,butonlyontheconditionthatwemaintainanabsolutevalueforchangesinvelocity,whichispreciselyoneoftheresiduesofan-cientmechanics.ItwouldbeeasytodemonstratethatinGen-eralRelativity,theparadoxcanbeexplainedevenmoreeasily,andthistimewithoutpreservinganythingremotelyresembling

�. See chapters V and VI of my little book: Einstein and the Universe.

absolute motion. But this demonstration would requiremorespacethanIhaveavailable,andbesides,theques-tionwasnotevenbroughtupattheCollègedeFrance.

***

When the evening session of Wednesday April 5thopened,Mr.Langevinfirstaskedthatthosewhointendedtointervenenotspeaklongerthantwentyminuteseach.Twentyminutes,timedonmywatch!headdedamongstthelaughs.Weshallneverknowifthisonlyalludedtothepropertimeofeachsystemofreference,orifitwasrathera consequence of the practical necessity of definingthingsbyapossiblyarbitrary,butunivocalunit.Thesec-ondhypothesisislessflatteringforclockmakers,butthefirstisquitedifficulttoadmit.Because,ifeversomeob-serverswererigidlyattachedtooneandthesamesystemofreference,itisobviouslythose,who,thatevening,sit-tingcloselypiledtogetherinacontinuousmassonthesmallstepsoftheamphitheaterofphysics,werecoordi-natingall theirminds’ tensorsonuniqueaxesallcon-vergingintoEinstein’sbrain.

AfterEinsteinandMr.Painlevéhadreachedanagree-ment on the concluding statement by Mr. Langevin; aconcludingstatementthatIreplicatedaboveandwhich

wasnecessarytomakeinordertoclosethedebateofthepre-cedingsession,thewordwasgivenforMr.EdouardGuillaume,aSwissphysicist,tospeak.Inthepreviousdays,mostnewspa-pershadpublishedawireannouncingthat thisphysicisthaddiscoveredblatantcalculatingmistakesinEinstein’stheory,andthatheintendedtorevealthem,corampopulo,[beforethepub-lic]at theCollègedeFrance.Thesemistakeswouldnaturallylead to a complete collapse of Einstein’s synthesis, the totalbankruptcyofthisLawofScience.Tobehonestwithyou,allofthosewhohadfollowed,withfullknowledgeofthefacts,theseriesofanalyticaldevelopmentofEinstein’stheory,thosewhoknewthatafterathoroughstudy,Mr.Hadamard,theprofoundmathematician and successor of Henry Poincaré, had pro-claimed thatmathematically speaking,Einstein’sconstruction

Swiss physicist Charles-ÉdouardGuillaume(1861-1938), who received theNobelPrize inPhysics in1920 for his discovery ofanomalies in nickel steelalloys.

French mathematician Félix Éd-ouard Justin Émile Borel (1871-1956).

AdrawingbyLucien JonasofEinsteinandPainlevédiscussing themovingclockproblem,onMay28,1922.


hadamostperfectandrigorouscohesion,withoutanylogicalflaw,oranyformaldefect;those,Isay,weresomewhatsurprisedbythenewstrumpetedinthepressbytheonewhowould,innotimeflat,makemincemeatoutofthepoorEinstein.

Thus,Mr.Guillaumetookthefloorandstartedwithaloudcalltoattention:“LadiesandGentlemen.”Then,hewenttotheblackboardwherehehadpinnedsomecleverpinkandbluegraphicsaheadoftime,andhebegantolineuphisformulas.Afterafewmoments,itbecamecleartoeveryonethatthiswasnotgoingtobetheday,northeindividual,thatwouldforceEin-steintobitethedust.Whentheoratorwasdone,ithadtakenlessthantwosecondsforthosewhohadunderstood,andalltheassistantsagreed,toshrinkbackthisloudlytrumpetedinter-ventiondowntoitsmodestproportions.ItwasMr.Borelwhointerpretedtheunanimousopinion(sincethethingwassosim-ple,thattherewasnotasingleelementarymathematicsstudentwhowouldnothavebeenabletopassjudgment)anddeclaredthat “the whole argumentdoesn’tholdwater,becauseitisnotpossibletofirststartbywritingequationsonRel-ativity and then introduce,solelybymanipulatingthoseequations,aseriesofforeignpostulates which contradictthesystem.”Theerrorwassoobvious,asitfollowedfromtheprincipleofhomogenei-ty, that it was necessary todismiss it with a one liner.Refuting a scientific con-structionbyfirstintroducingelementswhichitrejects,iseasy, but it proves nothing.Speaking in his turn, Mr.Langevin concluded bythesetextualwords,whichbuttressedademonstrationthatwasasbriefasitwasclear,relativetoasideissue:“Themisunder-standingresultsfromthefactthatMr.Guillaumedoesnotun-derstandwhatalightwaveis.”AsforEinstein,smiling,hetookrefugeinacharitableabstentionbypretendingnottohaveun-derstoodanythinghisopponentwastryingtosay.Thisishowthismorecomicalthanpainfulincidentended.

Wethenreturnedtoseriousmatters.Mr.Langevinfirstex-posedhowhehadcometoestablishtheformulasofthenewdynamicsby simply starting fromGeneralRelativityand theprinciple of the conservation of energy. I have previouslysketchedforthispublicationtheastonishingconsequencesofthenewmechanicswhichshowusthatmass—whichclassicalscience considered constant—increases and decreases withspeed,andthatenergyisendowedwithrealinertia.Ihavein-dicated—you will recall—some of the stunning verificationsthatthephysicsoftheatomandtheelectronhavebroughttotheserevolutionaryconceptions.

EinsteintookthefloortopraisethebeautyoftheworkthatledMr.Langevintothoseresults.Hehimselfcametothemin-dependently,butthroughamuchmorecomplicatedwaythatcalls uponnotions that are still somewhat unreliable and inwhichthefamousquantatheory,thisChinesepuzzleoftoday’s

physics,wasrequired.Inoneofhisusualhumorousandagnos-ticformulations,Einsteinconcluded:“Itisthusthatmechanicsisprofoundlychangedbythenot-yet-existingquantatheory.”

Thus,endedtheexaminationofthequestionraisedconcern-ingSpecialRelativity.

Allthatremainednow,wastodealwiththequestionsraisedbyGeneralRelativity.

ItwasMr.Hadamard,celestialmechanicsprofessorat theCollègedeFrance,whoopenedfirewithaquestionrelatingtotheformulabywhichEinsteinexpressesthenewlawofuniver-salgravitation.

Inthisformula,underthesimpleformthatSchwarzschildgavetoitandthatanswersallthepracticalneedsofastronomy,thereexistsacertaintermthatMr.Hadamardisverymuchconcernedwith;ifthedenominatorofthattermbecomesnull,meaningifthistermbecomesinfinite,theformulanolongermakessense,oratleastonecoulddemandwhatisitsphysicalmeaning.5

Mathematicallythistermcannotbecomeinfinite;butphysi-cally,practically,couldittakeplaceinnature?NotintheSun’scase,butpossiblyinthecaseofastarthatwouldbeinfinitelymoremassivethantheSun.

Einsteindoesnothidethefactthatthisveryprofoundques-tionissomewhatembarrassingtohim.“If,”hesays,“thistermcouldeffectivelybecomenullsomewhereintheuniverse,thenitwouldbeanunimaginabledisasterforthetheory;anditisverydifficulttosayaprioriwhatwouldoccurphysically,be-causetheformulaceasestoapply.”Isthiscatastrophe—whichEinsteinpleasantlycallsthe“Hadamardcatastrophe”—possi-ble,andinthiscasewhatwouldbeitsphysicaleffects?

Ithoughtitwouldbeusefultointerveneatthispointinthediscussion,andInotedthat,althoughweknowofsomestarsmuchlargerthantheSun(suchasBetelgeuse,whosediameterequals300Suns),forthefewstarswhosemasseswehavebeenable todetermine,wefind that theyarenevermuchgreaterthanthesolarmass.

Additionally,itseemedtomefromtheworksoftheEnglishastronomerEddington,thatwhenastar’smasshasatendencytoincreasemoreandmorebygravitationalattractionofoutsidematter,theinternaltemperatureofthismassincreasesgreatlyandtheradiationproducedtendstothrowoutward(accordingto theMaxwell-Bartolipressure)anynewadditionofmatter,andtobalancetheattractiveeffectofgravitation.Therefore,itwouldbeintheverynatureofthingsthataninsurmountablelimitbereachedintheincreaseofmassofastar.SuchastarcouldnevergrowmuchgreaterthanthemassofourownSun.Therefore,theveryphysicsofthingswouldpreventtheHad-amardcatastrophe fromeverhappening,because thecondi-tionsofexistenceofstarsthatwouldhaveincomparablygreatermassesthantheSuncouldnotbeproduced.

Einsteinrepliedtomethathewasnotentirelyreassuredby

5. For the reader who wants more specifics, I allow myself to indicate that Ein-stein’s gravity formula is the following:

ds2 = dt2(1 – a/r) – r2(d2 + sin d2) – dr2/(1 – a/r)where ds is the geodesic element traversed in the universe by a gravitating point. r designates the radius vector of this gravitating point with respect to the mass’s center and a is a length proportional to this mass and which, in the Sun’s case, is equal to about 3 km. We see that when a becomes equal to r, the last term takes on an infinite value, and Mr. Hadamard is then asking what would actually happen in reality.

Frenchmathematician JacquesHadamard(1865-1963).


thesecalculations that involve severalhypotheses.Hewouldmuchpreferanothermeanstoescape“themisfortunewhichtheHadamardcatastropherepresentedforthetheory.”Effectively,inthefollowingsessionofApril7th,hebroughtuptheresultofacalculationhehadmadeconcerningthisfinepoint.Hereiswhatthiscalculationshows:Ifthevolumeincreasesindefinitelywithoutincreasingitsdensity(thiswouldbethecaseforasphereof water) it happens, well before the Hadamard catastropheconditionscouldbemet,thatthepressureatthecenterofthemassbecomesinfinite.Intheseconditions,giventheGeneralTheoryofRelativity,theclocksmoveatzerospeed,nothinggoeson,itisdeath;andthereforeanynewchangecapableofbring-ingtheHadamardcatastrophehasbecomeimpossible.Einsteinaskedifitmightnotbethecasethat,followinghisexpression,“theenergyofmatteristransformedintoenergyofspace,”thatistosay,whenmassistransformedintoradiation.“ThatisallIcansay,”heconcluded,“becauseIdon’twanttomakehypoth-eses,”whichsoundedliketheverywordsofNewton.Mr.Had-amard in theseconditionsdeclaredhimself satisfied,andbe-lievedimpossiblethecatastrophesogreatlydreaded.

SuchwasthediscussionsurroundingoneofthemostcuriouspointswhichwereraisedattheCollègedeFrance.Allwouldagreethatitdidnotlacktaste,norinsightfulpenetration.Itwell

characterizedtheidealatmosphere,saturatedwithanenthusi-asm for pure truth and detached from the contingencies inwhichthenoweternallyfamouscontroversies,tookplace.

DuringthelastdiscussionsessiononApril7th,thequestionoftheHadamardcatastrophegaveMr.PainlevétheopportunitytoaskEinsteinsomequestionsregardinghisgravitationalandsimilarformulaswhichnowallowustoexpressnewphenom-ena(theadvanceoftheperihelionofMercury,thedeviationoflightbygravity)observedinthefieldsofcelestialmechanicsandoptics.

Whatfollowedwasanextremelybrilliantandsprightlydis-cussion,attimessoanimatedthateverybodywasspeakingatonce.Atacertainpoint,whileMr.HadamardandMr.Painlevéwere exchanging the mostspirited and contradictoryargumentsabout themean-ing of the stated formulas,we suddenly saw Mr. Brill-ouin(whohadgivenupanyattemptatinsertingasinglewordedgewisebetweentherapidfireofthetwoantago-nists)leaptotheblackboardwithapieceofchalkinhishand,andshout:“Sinceyouarespeaking,Iwillresorttowriting; because the sim-plestwaytomakeaquadra-tureisstilltowriteit!”Inthismanner,hewasabletocap-turetheattentionofabreath-less public without theslightestunsealingofhislips.Itwasreallyaverybeautifulbattleand a rewarding sport event. Moreover, the two adversarieswerevyingincourtesywitheachothersomewhataggressively,andwecouldhear,atacertainpoint,Mr.PainlevéshoutingatMr.Hadamard:“Ican’tseehowthediscussioncanbenefitany-onebybeingconducted in thismanner;butgoon, Ibegofyou”;andthenextmoment,heapologizedbysaying:“Pleaseforgivemefornotmakingmyselfclear,but....”Whileallthewrittenandspokenargumentsdashedandclashedagainstoneanother,quicklyandsharplyfillinguptheroomwithtumult,andtheboardwithelegantintegralswiththeirnecksinclinedlikewhiteswans,Einsteinsatinthemiddleofthetempest,smil-ingandremainingsilent.

Then,suddenlyraisinghishandasaschoolboyrequestingtheteachersattention:“MayIalsobepermittedtosayalittlesomething?”heaskedsoftly.Everybodylaughed.Einsteinspokeinthenowrestoredsilence,andwithinafewminutesevery-thingwasmadeclear.IbelievethisishowonecansummarizetheessentialpointsprovidedbyEinsteinandwhichdefinitelysettledthemainobjectionsraised.

Aboveall,peoplewantedtoknowwhatthequantitiesofEin-stein’sgravitationalformularepresented,andespeciallythera-diusvector,thatistosay,thelinejoiningtheSuntoeachplanet.

Newton’slaw,thefoundationofalltraditionalcelestialme-chanics,expressesarelationlinkingthemassesoftwostars(orcelestial bodies) and their distance. Let’s leave aside, to notoverloadthisexposé,allthatconcernsthemassandlet’scon-

Betelgeuse,intheconstellationOrion,is theeighthbrighteststarinthenightsky.Nordmannpointedoutinthediscussionthatithasthediameterof300Suns,althoughhesaidthatthefewstarswhosemasshadbeendeterminedwerenevermuchlargerthantheSun’smass.

Frenchphysicistandmathema-tician Marcel Brillouin (1854-1948).


sideronlytheirdistance.Inordertomakeexactcalculations,wemustspecifyatwhichmomentweconsiderthedistance.Classicalscience,withitsapriorinotionofauniversalandab-solutetime,ignoredthisdifficultyand,ifconsiderablemistakesdidnot follow, itwasonlybecauseof theslowspeedof theplanetsrelativetothespeedoflight.Moreover,whenclassicalastronomersdeterminebytriangulationtheradiusvectorofaplanet,andtranslatetheirdesignonpaper,theytracearectilin-ear triangle,aEuclidean triangle,because they suppose thattheirlineisrigorouslystraight.Butsincelightisslightlycurvedbygravity,itisnot.Thus,smallbutnecessarycorrectionsaretobemadewhenwewanttodefinethelinelinkingtwocelestialbodies, of which classical science was unaware. Moreover,classically,itwassupposedthattheradialvectorsweremea-suredwithidenticalrulerslinedupfromendtoend,andwhoselengthsweresupposedtobethesame.Thereagain,wedidnotdothenecessarycorrectionthatfollowsfromtheapparentcon-tractionof the rulers causedby speed, due to theparticularpropagationoflightrays.

Inaword,themagnitudeswhichareusedinthenewlawofgravitationareconcretemagnitudes.Forexample, theradiusvectorjoiningaplanetandtheSunmustbeconsideredtobemarkedoutbyidenticalrulers(naturallyassumedtobesubjecttoelasticandthermaldeformations)alignedinthedirectionofthelineofsight,stationarywithrespecttofixedstars,andsub-jectedtothegravitationalactionoftheSun.Whenastoneisthrownintheair,attheinstantwhenitceasestoascendandisabouttobegintofall,itisentirelysubjectedtotheeffectsofgravity.Therulersthatconstitutetheradialvectorunderconsid-erationmustbeconsideredasbeinginananalogoussituation.Totheserulersaresupposedlyattachedidenticalclockswhichare,also,ideallysubjectedtotheactionoftheSun.Undertheseconditions, the astronomical data are defined in a perfectlyconcreteandobjectivemanner.“Thereisnothingleftbutrulersandclocks,therearenolongerobservers,andallthatissubjec-tivehasbeeneliminated.”

Thisis,touseEinstein’sexpression,acertain“absolute”man-nerofdefiningmeasuredmagnitudesinastronomy,sinceitisnolongernecessarytorelateittoaparticularobserver.

Such are the concrete, objective, measurable quantitieswhichenter,withoutambiguity,intoEinstein’sgravitationalfor-mula.Bythismathematicalmetamorphosis,bythesechangesofvariablethatarecalledpointtransformations[mappings],wecancertainlyfindothermoreorlessdifferentformulasforgrav-itation,butthesetransformationschangenothingoftheobserv-ableandobjectivethingsaswehavejustdefinedthem.

Thereis,therefore,forEinstein,onlyoneuniqueformulaes-tablishing an unambiguous relationship between measuredquantities: it is thatwhichMr.Painlevécalledironically“theclassicalformula,thealreadyclassicalEinsteinianformulaofgravitation.”

Inaword,itisalwaysbettertogiveameasurablemeaningtosymbolsthatareintroducedinformulas,andtoneverlosesightofthephysicalsignificanceofthesesymbols:aphysicalsignifi-cancewhichdoesnotobjectivelychangewhen thesymbolshavebeentransformed.

Thesesameremarksareapplicabletotheinterestingobser-vationsthatwerepresented,attheendofthesession,byadis-tinguishedmathematicianMr.Leroux.Here,onceagain,Ein-

stein strongly insistedonunderscoring the fact that theonlygeometricalfiguresthatheconsidersinspacearethosereallytracedoutwithrulers,andnottheidealizedfiguresofthepure-lyformalgeometries.

“Wecanalwaysdefine,”heconcluded,“butwemustdefinephysically.”

Thus,thecycleofthesememorablediscussionswasconclud-ed.Andif,asstatedbyMr.Langevininclosingthem,wehadnottackledallofthequestionsthatcouldhavebeenraised,atleast,allofthequestionsposedreceivedasatisfactoryanswer.

ThetheoryofEinsteinemergedfromthistournamententirelyunscathed,andEinsteinhimselfcameoutofitgreaterthanbe-fore.AsMr.Painlevérelatedtomewithamostappropriateil-lustration, theworkof the famousphysicist stoodfirmlikeaperfectlycoherentandinflexiblegraniteblockthatdidnothaveasingleflaw.Relativityisabrickwhosecohesioncannotbeim-paired,asystemwithoutlogicalcontradiction,freeofallambi-guity,andwithoutanyinternaldefects.

However,eventhoughheconcededonthedetails,Mr.Pain-levéstillrefusedtoacceptthedoctrineasawhole.Hewasin-capable,asheconfessed,oftakingdownsuchamajesticandpracticaledificeasthatofclassicalscience.Forhim,ifIdaresay,thecuberestsonitsvertex;forothers,myselfincluded,itrestedunshakableonitsbase.Everyonecan,dependingonhisinclinations,eitherdistancehimselfwithprudence,asonedoeswhenpassingunderanoverhangingledge,oronthecontrary,makeuseofitasapedestalcapableofsupportinganexactim-ageoftheworld.

***

The discussion session that was held at the Sorbonne, onThursday,April 6th, under the auspices of the FrenchPhilo-sophicalSociety,wasnotinanywaytobedismissedasbeingoflesserimportancethanthephysical-mathematicalcontrover-siesattheCollègedeFrance.

Although the philosophers already had the opportunity todiscusstheTheoryofRelativity,notablywithMr.Langevin,“theapostleofthisnewgospel,”theyneverthelesswerequitenu-merousatthismeeting,wherethediscussionwastotakeplaceinthepresenceofthemonsterhimself.

AfteragoodopeningaddressfromthePresidentoftheSoci-ety,Mr.XavierLéon,thedebategotstartedwithaprofoundandremarkableexposébyMr.Langevinwhichcouldhavebeenen-titled:“WhyphilosophersshouldbeinterestedintheTheoryofRelativity.”Theknowledgeablephysicistdescribedwithmas-terfulclaritythekeyelementsofmethodologyandepistemol-ogythatestablishedthestrengthandappealofEinstein’swork.

Someday,IplantoreturntothispenetratingcommentaryonrelativitygivenbytheFrenchscientistwhobestmasteredit.Itdeservesbetterthanasummaryofafewlines.

The discussion that followed, and in which a number ofmathematiciansparticipated,made itclear that, strictly fromthestandpointoflogic,theentiredoctrineofrelativitywasco-herent,andwas freeofany internalcontradictions.Thishadalreadybeentheimplicitconclusiveassessmentfromthedis-cussionattheCollègedeFrance.

Afterthemathematicians,thephysicistsenteredinturnintothediscussion,introducingdiversequestionsposeddistinctly,whichledEinsteintogivehisopiniononseveralveryinterest-

einstein in paris t einstein presents and discusses his theory

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