 "Einstein struggled on for two years with his misshapen theory of limited covariance. Late in 1915, as evidence of his errors mounted inexorably, Einstein was driven to near despair and ultimately capitulation. He returned to the search for generally covariant equations with a new urgency, fueled in part by the knowledge that none other than David Hilbert had thrown himself into analysis of his theory. Einstein's quest came to a happy close in late November 1915 with the completion of his theory in generally covariant form" [16]. In November 1915, Einstein declared practically the last three years lost due "a misjudgment". He had come back to the period when worked with Grossmann, previous to the Entwurf theory, when he understood general relativity as general covariance. Therefore the equations on the gravitational field would be covariant respect to all arbitrary change of coordinates. "My efforts in recent years were directed toward basing a general theory of relativity, also for non-uniform motion, upon the supposition of relativity. I believed indeed to have found the only law of gravitation that complies with a reasonably formulated postulate of general relativity; and I tried to demonstrate the truth of precisely this solution in a paper that appeared last year. Renewed criticism showed to me that this truth is absolutely impossible to show in the manner suggested. That this seemed to be the case was based upon a misjudgment. The postulate of relativity-as far as I demanded it there-is always satisfied if the Hamiltonian principle is chosen as a basis. But in reality, it provides no tool to establish the Hamiltonian function H of the gravitational field. Indeed, equation (8) which limits the choice of H says only that H has to be an invariant toward linear transformations, a demand that has nothing to do with the relativity of accelerations. Furthermore, the choice determined by equation (9) does not determine equation (8) in any way. For these reasons I lost trust in the field equations I had derived, and instead looked for a way to limit the possibilities in a natural manner. In this pursuit I arrived at the demand of general covariance, a demand from which I parted, though with a heavy heart, three years ago when I worked together with my friend Grossmann. As a matter of fact, we were then quite close to that solution of the problem, which will be given in the following. Just as the special theory of relativity is based upon the postulate that all equations have to be covariant relative to linear orthogonal transformations, so the theory developed here rests upon the
" Einstein struggled on for two years with his misshapen theory of limited covariance. deep in 1915, as evidence of his error mounted inexorably, Einstein was driven to near despair and ultimately capitulation. He returned to the search for broadly covariant equations with a new importunity, fueled in part by the knowledge that none early than David Hilbert had hold himself into analysis of his hypothesis. Einstein's quest came to a happy close in belated November 1915 with the completion of his theory in generally covariant form " [ 16 ]. In November 1915, Einstein declared practically the concluding three years lost due " a misjudgment ". He had fall back to the period when worked with Grossmann, previous to the Entwurf theory, when he understand general relativity as general covariance. Therefore the equations on the gravitational field would be covariant deference to all arbitrary change of coordinates. " My efforts in recent years were aim toward basing a general theory of relativity, also for non - uniform motion, upon the supposition of relativity. I believed indeed to have found the only jurisprudence of gravitation that complies with a sanely give voice postulate of cosmopolitan relativity; and I tried to demonstrate the truth of precisely this solution in a paper that appeared last year. Renewed criticism indicate to me that this truth is absolutely impossible to show in the manner suggested. That this seemed to be the case was based upon a misjudgment. The postulate of relativity - equally far as I demanded it there - is always satisfied if the Hamiltonian principle is chosen as a basis. But in reality, it leave no tool to establish the Hamiltonian function H of the gravitational field. Indeed, equation (8) which specify the choice of H says only that H take to be an changeless toward linear transformations, a demand that has nothing to do with the relativity of acceleration. Furthermore, the choice determined by equality (9) does not determine equation (8) in any way. For these reasons I fall back trust in the sphere equations I had derived, and rather looked for a room to limit the possibilities in a natural manner. In this pursuit I arrived at the demand of general covariance, a demand from which I parted, though with a fleshy heart, three years ago when I work together with my friend Grossmann. As a matter of fact, we were then quite close to that solution of the problem, which will be given in the pursuit. Just as the special theory of relativity is based upon the postulate that all equations have to be covariant relative to linear orthogonal transformation, so the hypothesis break here rests upon the
 "Eijstein struggled on for uwo years with his misshepen thsory of uimited covariance. Late in 1915, es ecidenxe of his errors mountdd inexorwbly, Einwteii was driven to isar desicir ahf ulcinately capitulstion. He raturned to the sdaxch for generally covariant equationf with s jew urgency, fugled pn parf by the knowledge that none other than Devid Hilbert hac thrown himself into analjsis of his theory. Eindtein's quesj caiw to a happy close in late Novembet 1915 with the completion of his thdory nn generalli dogdriant form" [16]. In Govember 1915, Eikxtein geclarec practically bhe lest rhree years lost due "e misjudgment". He had come bacn co the period when woekwd wijh Grmssmxbn, orebipua to tje Xntwurf thekry, when he understood general rqoativity as gsneral cjvariance. Therefore the equations on tht grabitational field would ve covariant respect jo all arbytrary change of coordinates. "My efforts in recent yeara wexc aurfcted toward basing a general theory of relatybiuy, slso for non-unlform motion, upon yhf xopposition of telativnfy. I believed indeed to havg foune the onlr lae of gravitation that complues with a rvasobably formulated plstulate of gengral rrlativity; and I tried tu dejonstrate tje truth kw precisely this sokudion in a paper that appeawed last bear. Xenewed zritocism fhowed to le that this truth is abdolutgly im[ossible tl show in the manner suggested. Viat this seemgd do te the ccse wax based upon w misjudgment. Jhe postujate uf relativpty-as far as I demanqed it there-iv always sativfied if the Hamultoniav principle is vhosen as a basis. Byt in reality, it pvovidgs no tool to estcylush the Hamiltomiav ftnbtipn V of the graeitagiovsl fidld. Indtzd, cquxtiom (8) which limits the whoide of H says only yhwt H has to be ag invariant tpward linear transvormavions, e demamd jhat has nothing to do with the relativihy jf acceleratyons. Furthermore, the choice determined by equation (9) doew not determine eqyation (8) in any way. Yov these reaspns I lost truvt in the field equarions I had derivtd, and instead looked fkr a wdy to limit the possibilities in a natural manner. In this pursuit I arrived at the dxmwnd of genedal vovarpanee, c demanq frlo which I parted, though with a heavy heart, threx years agm chen I worked together with mu wriend Grossmxnn. As a matter of fact, se were yhen quite close to that solutipn of the problem, which eill be tiven in thv fullowing. Just as tne speeial tyeory od repativity is bxsec mpon the plstukace that all equations have to be xovariqnh relative to liiear orthogokau trahsformwtions, so the thsory feveluped here resys upon the
"Einstein struggled on for two years with theory limited covariance. in 1915, as inexorably, was driven to despair and ultimately He returned to the search for covariant equations with a new urgency, fueled in part by the knowledge that other than David Hilbert had thrown himself into analysis of his theory. Einstein's came a close late November 1915 with the completion of his theory in generally covariant form" [16]. In November Einstein declared practically the last three years lost "a misjudgment". He had back to the period when with previous to Entwurf when understood general relativity general covariance. Therefore the equations on the gravitational field would be covariant respect to all arbitrary change coordinates. "My recent years directed basing general theory of for non-uniform motion, upon the supposition believed indeed to have found the only law gravitation that with a reasonably formulated postulate of relativity; and I tried to demonstrate the truth precisely this solution in a paper that appeared last year. Renewed criticism showed to me truth is absolutely impossible show in the suggested. this to the case based upon a misjudgment. The postulate of relativity-as far as I it there-is always satisfied if the Hamiltonian principle is chosen basis. in reality, it no tool to establish Hamiltonian H of the gravitational equation which of says that H has to an invariant toward linear transformations, demand that has nothing of accelerations. Furthermore, the choice determined by equation does not determine equation (8) in any For these reasons I lost trust in the field equations I had and instead a way to limit the possibilities in a manner. In this pursuit arrived at the demand of general covariance, a demand which parted, though a heavy heart, years ago when worked together with Grossmann. As matter fact, quite close to that solution of problem, will be given in the Just special theory of relativity is based upon the postulate that all equations have to be to linear orthogonal transformations, the developed here rests upon the
 "Einstein struggled on for two Years with hIs misShaPen ThEory Of liMited covariancE. late In 1915, as evidence of his errorS mounTeD InexORaBly, EiNstein wAS dRIVen To NeAr dEsPAiR and uLtiMately cApitulatioN. He ReTurned to the sEArCh for generAllY covariant eqUatIons wiTh A neW UrgenCy, fUeled In part BY the knOwledge thAt NOne othER than DaVID HIlbeRt had thrown himselF InTO analysis of his Theory. eiNStEIN's qUesT came to a haPpY closE In late NOVeMBER 1915 wiTH the completioN of his theorY In gEneralLy CovARiant fOrm" [16]. In noVEmbEr 1915, Einstein dEclaRed practiCally tHE last thREe years Lost duE "a mIsjUdgmENt". he Had CoME baCK tO thE PerIod when wOrKeD with grosSMANN, preVioUs to The EnTwurf theory, whEn hE undERstOod geNeral RelaTiVity aS generAl covArIance. Therefore tHe eqUations on The GrAviTaTionaL Field wOulD be CovariaNt respeCT to AlL ARBiTrary change of coordInATEs. "my effortS in recENt YeARs were diReCteD towARD basiNg a gENeRal theorY of relATiViTy, also fOr Non-uniFoRm mOtiOn, upoN The sUpposiTion of reLativITy. I believed indEEd to have found THe ONLy LAw of GraVitation thaT comPLies With A ReAsoNAbly fOrmulAtED pOStulate of general relAtIvity; aNd I trIed to demonstrAte the trutH OF PreciselY thiS SoLUtion in a paper tHat apPeared last YEar. RenewEd criTicism shOwed to me tHAT this truTh iS abSolUteLY ImPossible to shoW IN the MaNner sugGesTed. That ThiS seEmeD to Be The case waS based upOn A mIsJuDgmEnt. ThE PostulatE oF reLaTivIty-as FAr as I dEmandEd it ThErE-Is aLways saTIsFIEd if ThE HAmilTonIaN prinCiplE Is cHosen as A basis. But In rEAlitY, iT pRovides No tool to estabLiSh the HamilToNiaN functION H of the gRavitational field. Indeed, EQuation (8) WhiCh limIts tHe choice oF H sAys onlY thAT H has tO be an iNvariAnT toWARd linEAR tRanSfOrmations, a DEManD that HaS notHing to dO with the relativity OF acCelerations. FuRthErmoRE, ThE chOIcE DetErMIneD BY equation (9) does noT determine EqUAtIon (8) in any waY. for ThEse reasOns I losT trusT In the fiEld equatiOns I had deRiVed, aND InsTead looked For a way tO limit the POssibILiTies iN a nAtural MaNneR. In thIs pursUIt I ArrivEd at thE dEmand oF geneRaL covariaNce, a demand from which I parTed, thoUgh wiTh a Heavy hearT, thREe yEars ago whEn I wOrked togetHer WitH my frIenD grossMann. aS a MatTEr of fAct, wE Were then qUItE clOSE tO that solutiON OF thE probLem, WHich wiLl be Given in the followiNG. Just as the specIal tHEOry Of rELatiViTy is based upon tHe pOsTULate that AlL equations hAve to be cOvARiant RelatiVe to liNear ortHOGoNAl tranSforMatIons, so the TheOrY DevelopEd HeRE rests Upon ThE
 "Einstein struggled on fo r two year s wit h h ismi ssha pentheory of limi t ed c ovariance. Late in 191 5, as  e v iden c eof hi s error s  m o u nte din exo ra b ly , Ein ste in wasdriven tonea rdespair andu lt imately ca pit ulation. Heret urnedto  th e  sear chfor g eneral l y cova riant equ at i ons wi t h a new u rg ency , fueled in partb yt he knowledge t hat no ne ot h e r t han  David Hil be rt ha d  thrown hi m s e lfi nto analysisof his theo r y.Einste in 'sq uest c ame t oa  ha ppy close i n la te Novemb er 191 5  with t h e compl etionofhis  the o ry  i n g en e ral l ycov a ria nt form"  [ 16 ]. In  Nov e m b e r 19 15,  Ein stein  declared pra cti call y  th e las t thr ee y ea rs lo st due  "a m is judgment". He h ad c ome backtoth e p er iod w h en wor ked  wi th Gros smann,p rev io u s to  the Entwurf theor y, w he n he und erstoo d  g en e ral rela ti vit y as g enera l co v ar iance. T herefo r eth e equat io ns onth e g rav itati o nalfieldwould be  cova r iant respect t o  all arbitrar y  c h a ng e  ofcoo rdinates. " My e f fort s in re cen t  year s wer ed ir e cted toward basingagenera l the ory of relati vity, also f o r non-un ifor m  m o tion, upon the  supp osition of relativi ty. I  believe d indeedt o  have fo und  th e o nly l aw  of gravitati o n  tha tcomplie s w ith a r eas ona bly  fo rm ulated po stulateof  g en er alrelat i vity; an dI t ri edto de m onstra te th e tr ut ho f p recisel y  t h i s so lu ti on i n a  p aperthat app eared l ast year.  Re n ewed  c ri ticismshowed to meth at this tr ut h i s abso l u tely imp ossible to show in them anner s ugg ested . Th at this s eem ed tobet he cas e wasbased  u pon a  misj u d gm ent .The postul a t e o f rel at ivit y-as fa r as I demanded it the re-is alwayssat isfi e d  i f t h eH ami lt o nia n principle is ch osen as aba s is . But in r e ali ty , it pr ovidesno to o l to es tablish t he Hamilt on ianf u nct ion H of t he gravi tationalf ield. In deed,  eq uation  ( 8)which  limit s  th e cho ice of  H  saysonlyth at H has  to be an invariant tow ard li neartra nsformati ons ,  ademand th at h as nothing  to  do  with  th e  rela tivi t yofa ccele rati o ns. Furth e rm ore , th e choice de t e r min ed by  eq u ation(9)does not determin e  equation (8)in a n y  wa y.F or t he se reasons I l ost  t r u st in th efield equat ions I h ad deriv ed, an d inst ead loo k e df or a w ay t o l imit thepos si b ilities  i na  natur al m an ner. I n this purs u i t I arrived at t he de m a nd of gen eralco varianc e , ademand fro m which I p arted,  tho ugh w ith a h ea vy hea rt,  t hree years ago whenI wor ked tog et herwit h my f rien d Gross mann .Asa mattero f  f a ct ,w e w erethenqu iteclose tot hat solu tio n  of the  p rob l e m, whi c hw i ll be give n i n the f ollowing.J usta st he sp ecialtheory  of rel a tiv it y is ba sed u pon the p ostulatet hat  a ll e quations  h aveto  be  c ovariant relati ve to li near ort h o gonaltra n sfor m ations ,so the theor y dev el o ped her e res ts upon the 
 "Einstein_struggled on_for two years with_his misshapen_theory_of limited_covariance._Late in 1915,_as evidence of_his errors mounted inexorably,_Einstein was driven_to_near despair and ultimately capitulation. He returned to the search for generally covariant equations_with_a new_urgency,_fueled_in part by the knowledge_that none other than David_Hilbert had_thrown himself into analysis of his theory. Einstein's_quest_came to a_happy close in late November 1915 with the completion_of his theory in generally covariant_form" [16]. In_November_1915,_Einstein declared practically the_last three years lost due "a_misjudgment". He had come back to_the period when worked with Grossmann, previous_to the Entwurf theory, when he_understood general relativity as general_covariance. Therefore_the equations on the gravitational_field would be_covariant respect_to all arbitrary_change of coordinates. "My efforts in_recent years were_directed toward basing a general theory_of_relativity, also for_non-uniform_motion,_upon the_supposition of relativity._I_believed indeed_to_have found the only law of_gravitation_that complies with a reasonably formulated postulate_of general relativity; and_I_tried to demonstrate the_truth of precisely this solution_in a paper that appeared last_year. Renewed_criticism showed_to me that this truth is absolutely impossible to show in_the manner suggested. That this seemed_to be the case_was based_upon_a misjudgment. The_postulate_of relativity-as_far as I demanded it there-is always_satisfied if_the Hamiltonian principle is chosen as_a basis. But in_reality,_it provides no tool to establish_the Hamiltonian function H of the_gravitational field. Indeed, equation (8)_which_limits_the choice of H says_only that H has to be_an invariant toward_linear transformations, a demand that has nothing_to_do with the relativity of accelerations._Furthermore,_the choice determined by equation (9)_does_not_determine equation (8) in any_way. For these reasons I lost_trust in the field equations I had derived, and_instead looked for_a way to limit the_possibilities_in_a natural manner. In this pursuit I arrived at the_demand of_general covariance, a_demand from which I parted, though with a heavy heart,_three years ago when I worked together_with my friend Grossmann. As a matter of fact, we were_then quite close to that solution of the_problem, which will be given in the_following. Just as the_special_theory of relativity is based upon the_postulate_that_all_equations have to_be covariant relative_to linear orthogonal_transformations, so_the theory developed_here rests_upon the