OriginalPaperUDC115:53/EinsteinReceivedApril21st,2006

Ivica PicekSveučilišteuZagrebu,Prirodnoslovno-matematičkifakultet,Fizičkiodsjek,Bijeničkacesta32,HR-10000Zagreb

picek@phy.hr

Absolute and Everlasting in Einstein’s Relativity

Abstractpointing to the importance of invariance principles (symmetry laws) has been ranked as one of Einstein’s greatest merits. the symmetries represent an additional category used in a description of the physical world, additional to initial conditions and the very laws of Nature, as distinguished by Newton. Some invariances related to space and time are easy to describe: that the laws of nature are the same everywhere, that they are time independent, and that they do not change if some physical system is subjected to a rotation around an axis in space. the relativistic invariance, which Einstein re-established in his special relativity, was based on giving a full physical meaning to the transformations which lorentz used to relate observers moving uniformly with respect to each other. He realized that there is no absolute “at rest”, and no sensible “simultaneous” events. What is absolute in his relativity is the constant speed of light, and a well defined proper-time interval.the relativity entered physics as the first great creative principle on Einstein’s list. Sub-sequently, its marriage to the quantum principle established in atomic physics, brought out the quantum field theory as a mighty tool for the future investigation of the subatomic world. the newly discovered fundamental interactions (weak and strong) urged to look for a principle explaining them. It has been found in the form of the gauge principle underly-ing the present day standard model of elementary particle interactions. It is remarkable that Einstein gave his magical touch also to quantum and gauge principles. Still, the most important Einstein’s idea is that the whole of physics has to be expressed in Minkowski’s space, subject to lorentz transformations.today we are aware that, like other symmetries with their restrictions, lorentz symmetry would be restricted to the non-cosmological scale. New ideas in conjunction with the forth-coming cosmological measurements may lead to astonishing results.

Key Wordstheabsolute,everlasting, relativity, invarianceprinciples,quantum principle,AlbertEin-stein

1. A historical prelude

EinsteinwasobsessedwithdiscoveringtheuniversalatributesofNaturethatholdsforeveryonewhoinhabitsourUniverse.Hesaughtfortrulyuniversallaws,whosevalidityextendsbeyondspecialobservers.IfsuchtrulyuniversallawsareaccompaniedbyuniversalconstantsofNature,thenwearepreparedtobeginadialoguewithextraterrestrialinteligences.Inthiswayhegeneral-izedtheCopernicanview,byextendingCopernicanextraterrestrialitytotheconstantsofNatureandthelawsofNature.Einstein’s desire to rely on absolute is somethinghehad in commonwithPlanck,whoseveralyearsearlierintroducedthefirstsuchuniversalconstant,thequantumofaction.WhenEinsteinproposedinhisspecialrelativitythespeedoflightasanotheruniversalconstant,itwasimmediatelyacceptedbyPlanck.Moreover,PlancksupportedEinstein’sfurtherattemptstogeneralise

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity210

thespecialrelativity.Thefinaloutcomeofthisstrugglewasononesidetheformulationofthegeneralrelativity,andontheotherhandariseofinvarianceprinciple(symmetrylaws).Inadditiontotheexistingcategories,theinitialconditionsandtheverylawsofNatureasalreadydistinguishedbyNewton,therecomesthethird,thesym-metryprinciple,asanessentialcategoryusedindescriptionofthephysicalworld.ItsintroductionhasbeenrankedasoneofEinstein’sgreatestmerits.Itisunfortunatethatsomebody’sintellectualcuriosityoftenstopsbecauserel-ativityhasaccumulatedanauraofimpenetrability.Iamawarethatthepeopleintheaudience(andeventualreaders)areadiversegroup,theirprofessionalgoalspanningphilosophy,scienceandarts,sothatIshouldavoidwritingtheequations.Althoughhighschoolalgebraisenoughforspecialrelativity,thegeneralrelativitywouldbemathematicallymoredemanding.Therefore,Iamtryingmerelytoconveythestoryofthebirthofthetheoryofrelativity.Itisastoryonhowtheobservationsonthespeedoflightinourfamiliarworldofspaceandtimeleadtothenotionofspace-time.Itmaygivesomesatisfactiontothosehavingincommonasenseofwonderabouttheworldaroundus.Itisoftenbelievedthattheearlyperiodofamandetermineshislaterperform-ance.Einsteininhislatestascribedhissuccessinscienceto“continuingtoaskquestionsthatchildreneventuallyaretaughtnottoask,combinedwithstub-bornpersistence”.Letus thereforerecall theyearsduringwhichEinstein’scharacterwasshapedtofaceinacertainmomentinhistorythepreconditionsdevelopedforcreatingthespecialrelativity.

A period preceding Einstein’s year 1905

AlbertEinsteinwasbornonMarch14,1879,asthesonofHermannEinsteinandPauline(bornKoch).Alreadythenextyearhisfamilymovedfromhisbirthplace(UlminGermany)toMunich,whereAlbertlaterpassedthroughaCatholicgroundschool.TheextraclassesontheJudaismhetookthereattheageofelevenwerefollowedbyaperiodofhisintensereligiousfeelings,whenhewrotethesongsinpriseofGod.Onthebasisofadevotionexperi-encedinthisperiod,heremainedadeeplyreligiousmanfortherestofhislife.Hisothermostwellknownpassionwastheviolin,butsomeotherexperiencesfromhischildhoodactuallydeterminedhisfutureasascientist.Thefirstwasafascinationathisageoffivebythemagneticneedle,i.e.byahiddenforcegoverning itsbehaviour.The secondwashisdiscoveryof simpleprovablegeometricalstatements,hefoundinabookletattheageoftwelve.Hekept ahabit of an independent reading also after entering the studyoftheoreticalphysicsatETHinZurich,in1896.ThenotestakenbyhisfriendMarcelGrossmannhelpedhimtopasstheexams,andthefatherofthesamefriendhelpedhimafterhisdiplomain1900tofindajobinthepatentofficeinBern,andtoacquiretheSwisscitizenshipin1901.HismarriagewithMi-levaMarićcameaftertheygotachildLieserlin1902.Theirmarriagelasteduntilyear1914,theperiodinwhichtheygotalsotwosons,Hans-AlbertandEduard.ThejobinBernallowedEinsteintodevotehimselftotheoreticalphysics,sothatinthenextfouryearshepublishedfourarticlesinAnnalen der physik,atthattimetheleadingGermanjournal.Intheseworksheconsideredtherealityoftheatomsandmolecules,somethingthatwasthenfarfrombeingaccepted.Withoutdoubt,theworkfromthisperiodhasbeennoticedbyMaxPlanck,whowasadmiredbyanexplosionofEinstein’screativityinyear1905,his

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity211

annus mirabilis. Mostofdataandquotationsweputinitalicaretaken(ifnotstateddifferently)fromPais’biographyofEinstein.1

Einstein’s annus mirabilis 1905

Einstein’screativityproducedfiveremarkablepapersinAnnalen der physik inyear1905.Thefollowingdatesarerememberedbythepapersthatshooktheworld:March17,1905isknownasadateonwhichEinsteinsubmittedapaperinwhich he introduced the light quanta in order to explain the photoelectric effect.Thepaperwastitled“Aheuristicpointofviewconcerningtheproduc-tionandtransformationoflight”.2

April30,1905isthedateonwhichhecompletedapaperinwhichheshowedhow tocalculateAvogadro’snumber.Thispaperwasaccepted (in July)asEinstein’sthesisonmoleculardimensions,thatwaspublishedlaterinamodi-fiedform.3Itwasfollowedbyanother paperonthesubjectofBrownian mo-tion, “On themovementof smallparticles, suspended in stationary liquidsrequiredbythemolecular-kinetictheoryofheat”.4

June30,1905isknownforhissubmissionofapapertitled“Ontheelectro-dynamicsofmovingbodies”.5InthispaperheintroducedtheSpecial theory of relativity(STR).September27,1905 is thedateofasubmissionofhis finalpaperof1905,titled“Doestheinertiaofabodydependonitsenergycontent”.6

InthesepapersEinstein’sinterestcentredpartlyonratherspecialandpartlyonvery general problems.We realise that the problemshe had addressed,establishedthealphabet(“A,BandC”)ofthephysicsrelatedtoatomicandsubatomiclayers.Notably,thishappenedasearlyasintheyear1905,wheneventheexistenceofatomswasnotgenerallyaccepted:A)Brownian motionservedtoproveonceandforallthattheatomsdoexist.Themotionof theparticle floating ina liqiud isdeterminedby thepushesfromthemoleculesoftheliquid,andisessentiallyarandomwalkcalculatedbyEinstein.Thisworkstartedarevolutioninstatisticalphysicsthatisstillgoingon today.Brownianmotion theory enterednanotechnology,molecu-larmotorsinbiology,modelingthefluctuationofshareprizesonthestockmarket,trafficflowandchemicaltransportincells.Accordingly,Einstein’spapersonBrownianmotionarethemostcitedamonghisworkfrom1905.b)Einstein’s light quantainitiatedtheparticle-waveduality.Theattemptstoresolve this“particleorwave”dilemmamarked thebeginningofquantum

1

AbrahamPais,Subtle is the lord. Scientific Biography of Albert Einstein,OxfordUniver-sityPress,Oxford1982.

2

Albert Einstein, “Über einen dieErzeugungund Verwandlung des Lichtes betreffendenheuristischenGesichtspunkt”,Ann. phys.17,Leipzig1905,pp.132–148.

3

AlbertEinstein,“EineneueBestimmungderMoleküldimensionen”,Ann. phys. 19,Leip-zig1906,pp.289–306.

4

AlbertEinstein,“Überdievonmolekularki-netischen Theorie der Wärm geforderte be-wegung von in ruhenden Flüssigkeiten sus-pendiertenTeilchen”,Ann. phys.17,Leipzig1905,pp.549–560.

5

Albert Einstein, “Zur Electrodynamik be-wegterKörper”,Ann. phys.17,Leipzig1905,pp.891–921.

6

AlbertEinstein,“IstdieTrägheiteinesKörpersvon seinem Energieinhalt abhängig?”, Ann. phys.18,Leipzig1905,pp.639–641.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity212

mechanics.Still,bothfoundersofquantummechanics,PlanckandEinstein,werereluctanttopursueonit.ThatPlanckwasnotenthusiasticaboutthelightquantumhypothesisbecomesevidentfromtherecommendationthatPlanck,Nernst,RubensandWarburgwrotein1913,proposingEinsteinforamem-bershipinthePrussianacademy:

“Insum,onecansaythatthereishardlyoneamongthegreatproblemsinwhichmodernphysicsissorichtowhichEinsteinhasnotmadearemarkablecontribution.Thathemaysometimeshavemissedthetargetinhisspeculations,as,forexample, inhishypothesisoflight-quanta,cannotreallybeheldtoomuchagainsthim,foritisnotpossibletointroducereallynewideaseveninthemostexactscienceswithoutsometimestakingarisk.”

Einsteinconsideredhimselfthehypothesisoflightquantaashisonlyrevolu-tionaryone.InhisfamousSalzburglecturein1909,thatregardedPauliasaturningpointinthedevelopmentoftheoreticalphysics,EinsteinpropheticallyannouncedwhatwasachievedbyDiracalmosttwentyyearslater:

“…thenextstageinthedevelopmentoftheoreticalphysicswillbringusatheoryoflightthatcanbeunderstoodasakindoffusionofthewaveandemissiontheoryoflight”.

Muchlateritwasrecognizedthatatthesubatomicscalequantummechanicshadtobesupplementedbyspecialrelativity, thefusionthatresultedin thequantumfieldtheory.C)Special relativity theory represents the most general among these issues.It generalizesNewton’s laws ofmotion to encompass particlesmoving atclosetothespeedoflight.AtlowvelocitiesitreducestoNewton’stheory,providingagooddescriptionformotionsateverydayspeeds.Sometimeswecancomeuptotherealizationthatsomeoftheknownphysi-calprinciplescouldn’tallbetrue.ExactlythishappenedtoMaxwellequa-tionsconfrontedwithGalileanRelativity,i.e.theclassicalvelocityadditiontheorem.ThelatterisrelatedtotwounprovenassumptionsstatedalreadybyNewton,attheoutsetofhisprincipia:the absolute space, and the absolute time.EinsteinmusthavebeingfascinatedbyimpressivepredictionsproducedbyMaxwellequations,notablytheexistenceofelectromagneticwaves.Whatheinparticularlyreliedonwasthefactthattheseequationspredictthespeedwithwhichelectromagneticwavespropagatethroughspace.bydecidingtoretainallconsequencesofMaxwellequations,andtoabandonclassicalveloc-ityaddition,Einsteinenteredintorethinkingthenatureofspaceandtime.

2. Einstein’s Special Relativity

A period preceding the formulation of Special Relativity

Maxwell’selectomagnetismofferssomebestexamplesforthe“relativity“oftheappearance:Whileastationaryobserverwillseeonlyanelectricfieldofacharge,anobserverinmotionwithrespecttoitwillseeamagneticfieldinaddition.Infact,itwasFaraday’sinductionthatoriginallyinspiredEinsteintogointhedirectionofformulatingSpecialRelativity.Atthebeginning,Ein-stein’sapproachdidnotdiffermuchfromwhatNewtonhavehadwithhisfirstlaw(thelawthatwasfoundtobetrueonlybysocalled“inertial”observers).Einsteintemporarilyacceptedthingsthatareabsoluteforacertainclassofobservers, that are in uniform relativemotion.Therefore the (unfortunate)nameof“SpecialRelativity”forthetheorythatfollowedfromthisapproach.ThisverynamewasforthesamereasoninventedbyHenriPoincaréoneyear

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity213

before1905.Inaddition,PoincaréacknowledgesLorentz’spioneeringrole,andallthishasraisedquestionsaboutprioritiesinthediscoveryofrelativity.LaterLorentzwascomplainingthatEinsteinwasjustpostulatingwhatotherstriedtoprove.EinsteindaredtoconsiderLorentz’stransformationsseriously,andtoconcludethatbypassingfromoneinertialobservertoanother,thetimeandspacecoordinatesstarttomix.Theremainingstepwasjoininglighttotime,leadingtospaceandtimebeingfusedtogetherintounitedfour-dimen-sionalspace-timeworld.TheprevailingopiniontodayisthatLorentzhadthemathematics,Poincaréhadthephilosophy,butneitherofthetwohadthephysics.Thetimewasripethatsomebodyspellsoutclearlyalsothephysics ofrelativity.Fromtoday’spointofviewtheessentialdiscoverycamefromtwoAmericanphysicists,A.MichelsonandE.Morley.Non-observationofEarth’smotionthroughthe“ether”clearlyindicatedthattheusualadditionofvelocitieswasnotvalidforlight.LetusquotefromA.Pais’biographyofEinstein,7howEinsteindescribedtheeventsprecedinghispapersontherelativityintheyear1905,yearbeforehisdeath:

“Iwas,forgeneralreasons,firmlyconvincedthattheredoesnotexistabsolutemotionandmyproblemwasonlyhowthiscouldbereconciledwithourknowledgeofelectrodynamics.OnecanthereforeunderstandwhyinmypersonalstruggleMichelson’sexperimentplayednorole,oratleastnodecisiverole”,

andtwomonthsbeforehisdeath:

“Lorentzalreadyrecognizedthatthetransformationnamedafterhimareessentialfortheanal-ysisofMaxwell’sequationsandPoincarédeepenedthisinsightstillfurther…”

ToEinsteinitwasclearthat thesoughttheoryshouldrelyontwoabsoluteingredients:the speed of light c, and the proper time τ.Ontheotherhand,Poincarérequiredthethirdhypothesis,that

“Abodyintranslationmotionsuffersadeformationinthedirectioninwhichitisdisplaced…”

ThisindicatesthatPoincarédidnotrealizethatthecontractionisalreadycon-tainedinthetwoEinstein’spostulates.

Special Relativity

Einstein’sspecialrelativityisbasedontwoinvariant quantities,thatarethesameforallinertialobservers.Thefirstofthem,thespeedoflight c,beingthesameforeverybody,independentofthevelocityofpersonmeasuringit,enablesonetomeasuredistancesinlightseconds.Ithasadeepconsequence,revealedseveralyearslaterbyMinkowski,thatspaceandtimearefusedintoa unified four-dimensional spacetime. Newton’s separate intervals of timeandspacearecombinedintoaspace-time interval s,obeyingageneralizedPythagoreanrule:(space-timeinterval)2=(timeinterval)2–(spaceinterval)2

7

A.Pais,Subtle is the lord…,p.172.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity214

Figure 1.Thelightconeseparatesthecausalyconnected“timelike“regionfromspacelikelocationsunreachabletolight8

Theprecisemathematicalnotationdefinesthefamous“lightcone”displayedonFigure1,theenvelopeofpathsoflightraysforwhichthespacetimedis-tanceiszero.Suchis,forexample,thedistancebetweenoureyeandthestars.Ontheotherhand,eachobserverpossesseshisproperreferenceframe,whereheisatrest,andwherehemeasuresthepropertime.Inthiswaythepropertimeτdefinedbys2=c2τ2

emergesasaninvariantconcept.Itenablesustoattributethelifetimetoanele-mentaryparticle,actingasaclock.Itmightlookasasurprisethatthemuons–unstableparticleslivingatrestonlyamillionthofasecond–traveloverconsiderabledistancesintheatmosphereandintheringsodtheparticleac-celerators.Itisafeatureofthefourdimensionalspace-timethatmovingmu-onslivelonger,orthatthepaththeytravellappearscontractedtoanobserversittingonthemuon.Suchobservationofthetimedilationandtheobservationofthelengthcontractioncontradictsordinarycommonsense.Allthesepecu-liarrelativisticeffectsaregivenbytheLorentzgammafactor

sothattheybecamehugeforvelocitiesapproachingthevelocityoflight.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity215

TheSpecialTheoryofRelativityidentifiestheLorentztransformationsasameanstoconnectdifferentinertialobservers.Itisobviousthattwomanoeu-vresbytherocketareneededtoapproachthespacestationinEarth’sorbit:theboostoftherockettothespeedofthestationshouldbeaccompaniedbytherotation,adjustingtheaxesofthetwobodies.Eachbodyinthefourdi-mensionalspace-timeischaracterizedbyfourcoordinatesor,technically,bythefourvector(ct,x,y,z).Theinvariantlengths2 introducedabove,isjustthesquareofthisfourvector.Theimportanceofthisconceptwasstrenghtenedbyobservationofanotherfourvector,thatcanbeinferredfromthefirstpaperonrelativitypublishedbysomeoneotherthanEinstein.Itwaspublishedbym.PlanckinVerh. Deutsch. phys. Ges.,4(1906),p.136,at timewhenhepresentedspecialrelativityinthephysicscolloquiuminBerlininthewintersemesterof1905–1906.Inhislaterscientificautobiographyin1948PlanckexplainedwhyhewassostronglydrawntoEinstein’stheory:

“FormeitsappeallayinthefactthatIcouldstrivetowarddeducingabsoluteinvariantfeaturesfollowingfromitstheorems.”

Inhisbookonthe theory of Heat radiationhewrote:

“Allthesystemsunitswhichhavehithertobeingemployed(…)owetheirorigin(…)notaccor-dingtogeneralpointsofviewwhichwouldnecessarilyretaintheirimportanceforallplacesandalltimes,butessentiallywithreferencetothespecialneedsofourterrestrialcivilization.Thustheunitsoflengthandtimewerederivedfromthepresentdimensionsandmotionofourplanet…Incontrastwiththisitmightbeofinteresttonotethat(…)wehavethemeansofesta-blishingunitsoflength,mass,time(…)whichareindependentofspecialbodiesorsubstances,whichnecessarilyretaintheirsignificanceforalltimesandforallenvironments,terrestrialandhumanorotherwise,andwhichmay,therefore,bedescribedas‘naturalunits’.Themeansofdeterminingtheunitsoflength,massandtime(…)aregivenbytheconstanth,togetherwiththemagnitudeofthevelocityofpropagationoflightinavacuumandthatoftheconstantofgravitation,G.Thesequantitiesretaintheirnaturalsignificance(…)whenmeasuredbythemostwidelydifferingintelligencesaccordingtothemostwidelydifferingmethods.”

Figure 2.TheHuman’swithrespecttoNature’schoiceofthebasicunits.

8

Taken over from Matts Roos, Introduction to Cosmology,J.WileyandSons,NewYork21997.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity216

Thus,PlanckproposedtheNewton’sgravitationalconstantGasthethirdNa-ture’schoiceon Figure2. LikePlanckplayedahugeroleinsupportingEin-stein’sworkingravity,hewasamongfirstthatunderstoodandcontributedto special relativity. Expressions that Planck wrote for total energy E andmomentumpofabodywitharbitraryvelocityv

E = γmc2

p = γmv

can be arranged to the relation expressing an equivalence of energy andmass

E2–(pc)2=(mc2)2

InEinstein’swords(recordedishisvoiceonthesoundtrackofthefilm,Atom-ic physics,1948):

“Itfollowedfromthespecial theoryofrelativitythatmassandenergyarebothbutdifferentmanifestationsof the same thing–a somewhatunfamiliarconception for theaveragemind.Furthermore,theequationEisequaltomc-squared,inwhichenergyisputequaltomass,mul-tipliedbythesquareofthevelocityoflight,showedthatverysmallamountsofmassmaybeconvertedintoaverylargeamountofenergyandviceversa.Themassandenergywereinfactequivalent,accordingtotheformulamentionedabove.ThiswasdemonstratedbyCockcroftandWaltonin1932,experimentally.”

Figure 3.Anartist’sviewonthebirthandthemeaningoftheenergyandmassequivalence.

Thisequivalenceofmassandenergycanbederivedbyassumingthatthepairformingthefourvector(E/c,p)transformsinthesamewayasthepairform-ingthefourvector(ct,r).Thenitisevidentthatwhatwasthe proper timeinthesquareofthelaterfourvector,thesameroleplaysthe invariant mass min“Planck’s”fourvector.Thisclarifiessomeconfusionintheliteraturewhenusingalsothetermsof“relativisticmassm”and“restmassm0”.Thisisil-

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity217

lustratedonFigure3,thewarningson“thepedagogicalvirusofrelativisticmass”repeatedlygivenbyLevOkun.9

AllthisbecameobviousonlyafterMinkowskiinhisfamous“spaceandtime”lecturegiveninColognein1908introducedthenotionoffour-dimensionalspace-time:

“Henceforth,spacebyitselfandtimebyitselfaredoomedtofadeawayintomereshadows,andonlythekindofunionofthetwowillpreserveanindependentreality.”

Inhispaperfromthesameyear,MinkowskimadethetranscriptionofEin-stein’stheoryintotensorform,wherethefour-vectorsareoneexampleoftherelativistictensors.Atfirst,Einsteinregardedthisformalsimplificationasasuperfluous learnedness (überflüssige Gelehrsamkeit). Under the influenceofhisfriend,amathematicianMarcelGrossman,Einsteingraduallyrealisedthatthetensorcalculuswouldenablehimtoexpressthelawsofnatureinaformthatwouldlookthesameforallobservers,irrespectivelyofhowtheyweremoving.Thelawsofnaturewrittenastensorequationsgaveapreciseexpressiontohisprinciple of Covariance.In1912healreadyacceptedtensormethodsonhiswaytoformulatethegeneralrelativity.

3. From General Relativity to Unified Field Theory

Einstein’s General Relativity

Einstein’s1907papershowsthatforhimthespecialrelativityisonlyanintro-ductionintoamoregeneraltheorythatwillincludealsothegravitationalforce.Hiscorrespondencefrom1907tohisfriendConradHabicht(withwhom,andanotherfriendMauriceSolovine,hehadmetregularlyinhisBern’spatentofficeperiodtodiscussphilosophical,scientific,andliterarymatters)revealsthathewas“busyworkingonrelativitytheoryinconnectionwiththelawofgravitation”. Einstein was very fortunate that pure mathematicians alreadyinvestigated,intimeforhim,geometriesthatcouldexistoncurvedsurfaces.Therebytheyalsodevelopedthemathematicsoftensors,thatenabledhimtoformulatetheprincipleofcovariance.ForhimitwasobviousthatNewton’stheoryofgravity,withnoreferencetothespeedoflight,violatedevenbasicprinciplesofspecialrelativity.Einsteinlaterwrote

“…thatthebasicdemandofthespecialtheoryofrelativityistoonarrow,i.e.thataninvarianceofthelawsmustbepostulatedalsorelativetonon-lineartransformationsofthecoordinatesinthefourdimensionalcontinuum”.

Fromthisinitialstepmadein1908,eightlongyearsofhardworkwerenec-essarytoexecutetheidea.DuringthatperiodEinsteinhadaveryimportantsupportofMaxPlanck,whocreatedforhimexeptionalworkingconditionsinberlin.IntheGeneralTheoryofRelativityEinsteinproposedafurtherbigleap,tounite space-time and matter-energy. The latter curves a four dimensionalspace-timecontinuum.Warpingofthespace-timebythepresenceofthemat-ter-energywastestedduringatotaleclipseonMay29,1919.Thestarlightwasdeflectedasitpassedbythesun,makingEinsteinafamousperson.

9

LevB.Okun,“Theconceptofmass”,phys-ics today, June 1989, p. 31; “The concept

of mass in the Einstein year“, arXiv:hep-ph/0602037,2006.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity218

AnotherapplicationofEinstein’sGeneralRelativityiscosmology.Therea-sonisthatgravitationalforce,weakonthelaboratoryscale,dominatesovercosmologicaldistances.Byprovidingtheequationsthatcouldbeappliedtotheuniverseasawhole,Einsteinopenedanewchapterincosmology.

Figure 4.ThecubeofphysicaltheoriesconstructedaboveabasisofNewtonmechan-ics (NM),SpecialRelativity (SR),QuantumMechanics (QM) andQuantumFieldTheory(QFT).GeneralizationstothegravityincludeNewtonGravity(NG),GeneralRelativity(GR),NonrelativisticQuantumGravity(NQG)andanultimateTheoryof

Everything(TOE).

Idea of Unified Field Theory

The special relativity entered physics as the first great creative principleonEinstein’slist.Besidesit, thequantum principlehasbeenestablishedinatomicphysics.Thesetwoprinciples,takentogether,correspondtoNature’schoiceoftwobasicunitsdisplayedonFigure2.Thereseemstobeanarbitrarychoiceofthethirdunit,neededtomatchthethreeunitsofeveryday’sexperi-ence.TakingforitPlanck’schoice,theNewton’sgravitationalconstant,pro-videsathirdaxisthatenablesonetodrawthebronshtein-Zelmanov’scube of physical theories displayedonFigure4.WhileEinsteinwasfocusedtounderstandthenatureofforces,thequantummechanicsleadtobreakthroughsinunderstandingofmatter.Inparticular,themarriageofspecialrelativitytothequantum principlebroughtouttheQuan-tumFieldTheory(QFTcornerofthecubeinFigure4)asamightytoolforthefutureinvestigationofthesubatomicworldthatultimatelyrevealednewsubatomicforces.Einsteinwasoutsideofthesenewdevelopmentsand,asheremarkedhimselfin1954:

“Imustseemlikeanostrichwhoforeverburieshisheadintherelativisticsandinordernottofacetheevilquanta”.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity219

SeemsthatEinsteinbelievedthat

“…ultimatelytheweakandstrongforceswouldbeshownjusttobeaspectsoftheelectromag-neticforce”.10

Infact,thesenewlydiscoveredfundamentalinteractions(weakandstrong)urgedtolookforaprincipleexplainingthem.Ithasbeenfoundintheformofthegaugeprincipleunderlyingthepresentdaystandardmodelofelementaryparticleinteractions.ItisremarkablethatEinsteingavehismagicaltouchalsoto the gauge principle.11Although Einstein admired attempt by H.Weyl in1918todescribegravitationandelectromagnetismwithinaunifyinggeomet-ricalframework,hefounditsfailureasaphysicaltheory.Thiscritiquepavedthewayforthecorrectunderstandingofgaugeinvariance,whereWeyl’sex-ponentbecomesa“phase”.AfterEinsteinformulatedgeneralrelativity(GRcorneronthecubeonFigure4)heturnedtoinvestigatethe“unifiedfieldtheory”thatwouldauthomatical-lyaccountforthefeaturesofquantummechanics.12Inthisattempthe,ononeside,followedtheproposalbyTheodoraKaluzafrom1919togotoanotherdimension,whereitwaspossibletocombineEinstein’stheoryofgravitywithMaxwell’stheoryoflight.EinsteinwrotetoKaluzathat“Theformalunityofyourtheoryisstartling”,butaskedwheredidthe5thdimensiongone!AfterOskarKleinin1926discoveredapossiblesolution,thatitcouldbecurledupintoanunobservablesmallcircle,Einsteintriedfortherestofhislifetofigureoutwhythe5thdimensioncurledup.KaluzaandKleinideasreturnedtophysicsinthecontextofthesuperstringsasthecandidatesfortheTOEcorneronthecubeonFigure4.ThetrickofKaluzaandKleinwasusedforgoingfrom26or10dimensionalspace,wheresuperstringscanexist, toourordinary4dimensions.Cosmologically,13thebreakdownof10dimensionalfabricofspace-timecouldgeneratetheinfla-tionaryexpansionof4dimensionaluniversesattheexpenseofthe6dimen-sionaluniversescollapsingdowntothePlancklengthscale.Todayavarietyofstringtheorieshasbeenidentified,obscuringtheideaofan“ultimateTOE”.AwayoutmaybetherecentdiscoverybyE.Witten,14offeringthatsuperficiallydifferentstringtheorieswerejustdifferentlimitingsituationsofasingle,deepertheory.ItisdubbedM(formystery)theory,themathematicsofwhichisasyetunknowntous.Thisattituderesembles theonethatEinsteinhadinhislaterperiod,that“thecreativeprincipleresidesinmathematics”,andthatthepurethoughtcangraspreality.This is incontrast to theway inwhichyoungEinsteinarrivedathismostimportantidea,thatthewholeofphysicshastobeexpressedinMinkowski’sspace, subject to Lorentz transformations.Young physicists should followyoung Einstein.Whatever theTOE and itsmathematics is, it should be atheoryofphysicsateveryscale.Accordingly,oneneedstodevelopthemathe-

10

John D. Barrow, the Constants of Nature,VintageBooks,NewYork1995,p.302.

11

Norbert Straumann, “Gauge principle andQED”,arXiv:hep-ph/0509116,2005.

12

MichioKakuandJenifferThompson,Beyond Einstein,AnchorBooks,NewYork1995,p.32.

13

M.Kaku& J. Thompson,Beyond Einstein,p.142.

14

J.D.Barrow,the Constants of Nature,p.66.

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity220

maticaltoolstogetoutthelowenergyconsequencesthatcanbecheckedinexperiments.Onepossibleclassofexperimentsisthesearchforrelativity(i.e.Lorentz)violations.15

AlthoughLorentzinvarianceisaconceptthatadmitsageneralizationtospace-timeswithadditionaldimensions,Lorentztransformationsin4dimensionalspace-timebearsomespecialfeatures, thatmay“select”4dimensionsasafavourablechoice.Forexample,theequalityofthenumberofboostsandthenumberofrotationsisaspecialfeatureoffour-dimensionalspacetime.16Withfivespatialcoordinates,wehavetenrotations,whichistwicethenumberofboosts.Moregenerally,thealternativesto

“…three-dimensionalworldswithasinglearrowoftime(…)aretosimple,toounstableortoounpredictableforcomplexobserverstoevolveandpersistwithinthem”.17

Todayweareawarethat,likeothersymmetrieswiththeirrestrictions,Lorentzsymmetrywould be restricted to the noncosmological scale.New ideas inconjunctionwith the forthcomingcosmologicalmeasurementsmay lead toastonishingresults.

Ivica Picek

Das Absolute und das Dauerhafte in Einsteins Relativität

ZusammenfassungDie Hervorhebung der Bedeutung der Invarianzprinzipien (Symmetriegesetze) wird zu den größten Verdiensten Einsteins gezählt. Die Symmetrien stellen eine neue Kategorie zur Be-schreibung der physikalischen Welt dar, zusätzlich zu den Randbedingungenund den Natur-gesetzen, wie sie von Newton aufgestellt wurden. Einige Invarianzen in Bezug auf die Zeit und den raum sind leicht zu verstehen: dass die Naturgesetze überall die gleichen sind, ferner dass sie zeitunabhängig und unveränderlich sind, wenn ein Bezugssystem der Drehung im raum um eine Achse ausgesetzt ist. Die relativistischeInvarianz hingegen, die Einstein in seine re-lativitätstheorie eingebaut hat, bleibt weniger plausibel. Den lorentz-transformationen, mit denen Beobachter bei konstanter Geschwindigkeit in einem gemeinsamen Bezugssystem ma-thematisch beschrieben werden, maß Einstein ihre volle physikalische Bedeutung zu, infolge seiner Erkenntnis, dass es nicht möglich ist, den absoluten Stillstand zu bestimmen oder die Gleichzeitigkeit verschiedener Ereignisse festzustellen. Gleichwohl bestehen in der relativität auch absolute Bestandteile, die für alle Beobachter gelten: die konstante lichtgeschwindigkeit und ein genau definiertes Intervall der Eigenzeit des Beobachters.Die Relativität hielt als eines der ersten „kreativen prinzipien“, die Einstein erkannt hatte, ih-ren Einzug in die physik. In Verbindung mit dem Quantenprinzip, das aus der Erforschung der Atomphysik hervorgeht, kam die Quantentheorie der Felder zustande, eine mächtige Waffe für künftige Erforschungen der subatomaren Welt. Die neuentdeckten fundamentalen Interaktionen (schwache und starke) eröffneten die Frage nach einem neuen prinzip, das sie erklären konnte. Ein solches kreatives prinzip wurde im mathematischen Messprinzip erkannt, auf dem auch das heutige Standardmodell des Zusammenwirkens von Elementarteilchen gründet. Es ist erstaun-lich, dass beide prinzipien, das Quantenprinzip und das Messprinzip, aus Einsteins Arbeit her-vorgehen. Doch vor allem bleibt Einsteins bedeutendste Idee, dass nämlich die gesamte physik im Minkowski-raum zu verorten ist, den lorentz-transformationen unterstellt.Heute ist man sich der tatsache bewusst, dass, wie bei allen anderen Symmetrien mitsamt ihrer Einschränkungen, auch bei der lorentz’schen mit Abweichungen auf der kosmischen Skala zu rechnen ist. Neue Ideen in Zusammenhang mit kosmischen Messungen, deren Zeugen wir schon jetzt sind, könnten zu erstaunlichen Ergebnissen führen.

SchlüsselwörterDasAbsolute,dasDauerhafte,Relativität,Invarianzprinzipien,Quantenprinzip,AlbertEinstein

SYNTHESISPHILOSOPHICA42(2/2006)pp.(209–221)

I. Picek,Absolute andEverlasting inEin-stein’sRelativity221

Ivica Picek

L’absolu et l’éternel dans la relativité d’Einstein

Sommairele fait d’avoir signalé l’importance du principe de l’invariance (les lois de la symétrie) est con-sidéré comme un des plus grands mérites d’Einstein. les symétries sont présentées comme une nouvelle catégorie dans la description du monde physique, laquelle s’ajoute aux catégories des conditions initiales et des lois mêmes de la nature, définies par Newton. Certaines symétries de l’espace et du temps sont faciles à décrire: les lois de la physique doivent être les mêmes partout et indépendantes du temps, de même que ces lois ne changent pas si un système physique subit une rotation autour d’un axe dans l’espace. D’autre part l’invariance relativiste qu’Einstein a incorporé dans sa théorie de la relativité est moins évidente. Einstein a donné une signification physique pleine aux transformations dont se servait lorentz pour relier mathématiquement les observateurs en mouvement relatif uniforme, reconnaissant qu’il n’était pas possible d’établir le repos absolu ou de déterminer la simultanéité des faits différents. pourtant la relativité a des éléments absolus, identiques pour tous les observateurs: la vitesse constante de la lumière et l’intervalle bien défini du temps de l’observateur.la relativité a fait son entrée en physique comme un des principes créatifs d’Einstein. Associée au principe quantique provenant des recherches atomiques, elle a donné naissance à la théorie des champs quantiques qui sera une arme puissante dans les recherches futures sur le monde subatomique. les nouvelles interactions fondamentales, faibles et fortes qui y ont été découver-tes ont posé la question d’un nouveau principe responsable des interactions fondamentales. Un tel « principe créatif » se trouve dans le principe mathématique de jauge sur lequel repose le modèle standard actuel des interactions des particules élémentaires actuelles. Il est remarqua-ble que les deux autres principes, le principe quantique et le principe de jauge sont également attribués à Einstein. pourtant l’idée la plus importante d’Einstein est de faire entrer l’intégralité de la physique dans l’espace de Minkowski soumis aux transformations de lorentz.Aujourd’hui nous sommes conscients du fait que, comme les autres symétries ont leurs restricti-ons, on peut, à l’échelle cosmique, s’attendre à des écarts par rapport à la symétrie de lorentz. les nouvelles idées conjugées avec des mesurages cosmiques dont nous sommes déjà témoins, peuvent nous conduire vers des découvertes surprenantes.

Mots clésL’absolu,l’éternel,larelativité,principedel’invariance,principequantique,AlbertEinstein

15

AlanKostelecký,“TheFrontiersofPhysics”,Scientific American,Vol.15,No.3,2005.

16

Barton Zwiebach, A First Course in String theory, Cambridge University Press, Cam-bridge2004,p.28.

17

J. D. Barrow, the Constants of Nature, p.222.