izations of the corresponding equations of the original theory of relativity. Second, we established a system of equations that determines the gravitational field insofar as the quantities that determine the material processes are given; and this system can be considered a generalization of the Poisson equation of Newton's theory of gravitation. In the original theory of relativity, there is no corresponding system of equations for this. In contrast to the equations mentioned above, we could not demonstrate general covariance for those gravitational equations. The reason is that their derivation was based (besides the conservation theorems) only upon the covariance with respect to linear transformations, and thus left it an open question as to whether or not there exist other substitutions that would transform the equations into themselves. There are two reasons why the resolution of this question is of particular importance to the theory. The answer to this question gives, first, information on how far the basic idea of relativity theory can be developed; and this is of great import to the philosophy of space and time. And second, the judgment about the value of the theory from the point of view of physics depends to a high degree upon the answer to this question, as is shown by the following consideration. The entire theory evolved from the conviction that all physical processes in a gravitational field occur just in the same way as they would without it, if an appropriately accelerated (three-dimensional) coordinate system would be introduced (hypothesis of equivalence). This hypothesis, which is based upon the experimental fact of the equality between gravitational and inertial mass, gains additional convincing force if the apparent gravitational field-which exists relative to the accelerated threedimensional coordinate system-can be viewed as a real gravitational field; in other words, if acceleration-transformations (i.e., nonlinear transformations) become permissible transformations in the theory. At first glance it appears desirable to look for gravitational equations that are covariant toward arbitrary transformations. However, in §2 of the present paper we will show by a simple consideration that the quantities guv which characterize the gravitational field cannot completely be determined by generally-covariant equations. In the following we shall demonstrate that the gravitational equations established by us are generally covariant just to the degree imaginable under the condition that the fundamental tensor guv must be completely determined. It follows in particular that the gravitational equations are covariant with respect to quite varied acceleration transformations (i.e., nonlinear transformations)". "§2. Remarks on the Choice of the Coordinate System We want to show now that, completely independent of the gravitational equations we established, a complete determination of the fundamental tensor γ
izations of the corresponding equations of the original theory of relativity. Second, we established a arrangement of equation that determines the gravitational field insofar as the quantities that decide the material processes are give; and this system can be considered a abstraction of the Poisson equality of Newton's theory of gravitation. In the original hypothesis of relativity, there is no corresponding organization of equation for this. In contrast to the equations mentioned above, we could not demonstrate general covariance for those gravitational equation. The reason is that their derivation was based (besides the conservation theorem) only upon the covariance with respect to linear transformations, and therefore left it an receptive question as to whether or not there exist other substitutions that would translate the equations into themselves. There are two reasons why the resolution of this question is of particular importance to the hypothesis. The solution to this motion gives, first, information on how far the basic idea of relativity theory can be developed; and this is of great import to the doctrine of outer space and time. And second, the sagacity about the value of the hypothesis from the item of view of physics depends to a high degree upon the answer to this question, as is indicate by the following consideration. The entire theory evolved from the conviction that all physical processes in a gravitational airfield occur just in the same way as they would without it, if an appropriately accelerate (three - dimensional) coordinate system would be insert (guess of equivalence). This hypothesis, which is based upon the experimental fact of the equality between gravitational and inertial mass, gains additional convincing force if the apparent gravitational field - which exist relative to the accelerated threedimensional coordinate system - can be viewed as a real gravitational playing field; in other son, if acceleration - transformations (i.e., nonlinear transformation) become permissible transformations in the hypothesis. At first glance it appears desirable to look for gravitational equations that are covariant toward arbitrary transformation. However, in § 2 of the present paper we will show by a dim-witted consideration that the measure guv which characterize the gravitational discipline cannot completely be determined by generally - covariant equations. In the following we shall show that the gravitational equations established by us are broadly covariant just to the degree conceivable under the condition that the fundamental tensor guv must be completely determined. It follows in particular that the gravitational equations are covariant with respect to quite varied acceleration transformations (i.e., nonlinear transformations) ". " § 2. Remarks on the Choice of the Coordinate System We desire to show now that, wholly autonomous of the gravitational equations we established, a accomplished determination of the fundamental tensor γ
izahions of the correspondikg equations of jhw origmnal thsory of felativity. Second, we establidhwd a wystem of equations thxt determpnes the travmtational field mhsofar as the euancivies that deterkine the mdterial procesver cre given; and this system can be confidered a generalizatiog of ehe Loisson equation of Newton's theory of granitation. In the otiginal theory of relativihy, tjere is no corresplnding systgj os equations fur this. In contrast to the equations mentioned above, de cobld not deminwtrwje general civariwnce for those gravidationak equations. Thc reavon is that their derivavion was based (besidgs the convexvation theorems) only upon tve cmvarkqncd wjti rsspect to linear trznsformatiobs, and thus left it ag open questioh as tj rhether or not there exist other substiuutiohs that would transform the equations into tjemselves. There are two reasons why the resolution of this quesviun nw of oqrhicular importance to the theory. The answer tj tnix question givcs, first, informatipn om how far the casic nsez of relativity thfory cag be eeveloped; and this is of great import to the philosoihy if space and time. Cnd second, tke judbment about the value of the thekry from thf point or view of physics deiendv to a high degree upon thq answer vo thns questkon, ss is fhown by tje following consideratiln. Thg entise theory fvolved from the conviction thav all physicak [robesses in a grsvitational fyeld occur jusj in the fame day as thej would wmthout it, if an appropriadgly acceleratxd (three-dymenwionql) cooraknate system wpuld be iuuroduced (htpothesis of equivelenzs). This hypothesnr, which is based upun ehv eeperiiantal fact ox thd edialith betwetu gvavktatoonal and inertial mdss, fains additional cpnyincing firce if ehe apparent bravitational fielf-whici exisvs relstide to the accelerated threedimsnsional foovdinate systei-can be viewed ax a real gravitational field; in other wirds, if acceleratiin-transformations (i.g., npnlinear trensforiations) bacome permissible trqnsformations in uhe theory. At first glahce it appewrs desirable to look for gravitational equations that are covariant towaed arbmtwary transfkrmayions. Hjcever, ig §2 oh vhe present paper we will show by a simple consiveration tvac the quantities guv which chsrxcterize the eravitational field cannkt complrtely be determined by generallu-covariant equations. In bhe folloqing se shall dxmonstrate that the bravitctionao equatuons established cy is are genegallb ckvariant just to the degree imagunable ujder the conditimn that the nundamgntal tegsor guv must be comlpeteli determined. Iy follows in psrticular that the ggavytational equauions are covaroant winh respect to quite variad acceleration transformations (i.e., nonlinear transfkrmations)". "§2. Remarks on the Choicg lf the Coordinate Systcm We want to show now thdt, completely independent of the gravitatioisl eqjatpons ws established, a complete determluation of the wundanental tensir γ
izations of the corresponding equations of the of Second, we a system of field as the quantities determine the material are given; and this system can considered a generalization of the Poisson equation of Newton's theory of gravitation. In original theory of relativity, there is no corresponding system of equations for this. contrast the mentioned we could not demonstrate general covariance for those gravitational equations. The reason is that their derivation based (besides the conservation theorems) only upon the with respect to linear and thus left it an question to whether not exist substitutions that would the equations into themselves. There are two reasons why the resolution of this question is of particular to the answer to question first, on how far idea of relativity theory can be is of great import to the philosophy of and time. second, the judgment about the value the theory from the point of view of depends to a high degree upon the answer to this question, as is shown by consideration. The entire theory from the conviction all processes a field occur in the same way as they would without it, if an accelerated (three-dimensional) coordinate system would be introduced (hypothesis of equivalence). which based upon the fact of the equality gravitational inertial mass, gains additional if apparent relative the threedimensional coordinate system-can be as a real gravitational field; other words, if acceleration-transformations transformations in the theory. At first glance it desirable to look for gravitational equations that covariant toward arbitrary transformations. However, in §2 of the present paper we show by consideration that the quantities guv which characterize the field cannot completely be by generally-covariant equations. In the following we shall demonstrate the equations established us are generally just to the imaginable under the the fundamental guv be follows in particular that the gravitational are with respect to quite varied transformations transformations)". "§2. Remarks on the Choice of the Coordinate System We want to show now independent of the gravitational we a complete determination of the fundamental tensor γ
izations of the correspondinG equations Of the OriGinAl TheoRy of Relativity. SecoND, we eStablished a system of equAtionS tHAt deTErMines The gravITaTIOnaL fIeLd iNsOFaR as thE quAntitieS that deterMinE tHe material prOCeSses are givEn; aNd this system Can Be consIdEreD A geneRalIzatiOn of thE poissoN equation Of nEwton's THeory of GRAvItatIon. In the original tHEoRY of relativity, tHere is No COrRESpoNdiNg system of EqUatioNS for thiS. in CONTraST to the equatioNs mentioned ABovE, we couLd Not DEmonstRate gEnERal Covariance fOr thOse gravitAtionaL EquatioNS. The reaSon is tHat TheIr deRIvAtIon WaS BasED (bEsiDEs tHe conserVaTiOn theOremS) ONLY upoN thE covArianCe with respect To lIneaR TraNsforMatioNs, anD tHus leFt it an Open qUeStion as to whetheR or nOt there exIst OtHer SuBstitUTions tHat WouLd transForm the EQuaTiONS InTo themselves. There aRe TWO rEasons whY the reSOlUtIOn of this QuEstIon iS OF partIculAR iMportancE to the THeOrY. The ansWeR to thiS qUesTioN giveS, FirsT, inforMation on How faR The basic idea of RElativity theoRY cAN Be DEvelOpeD; and this is oF greAT impOrt tO ThE phILosopHy of sPaCE aND time. And second, the juDgMent abOut thE value of the thEory from thE POInt of vieW of pHYsICs depends to a hiGh degRee upon the ANswer to tHis quEstion, as Is shown by THE followiNg cOnsIdeRatION. THe entire theorY EVolvEd From the ConViction ThaT alL phYsiCaL processeS in a gravItAtIoNaL fiEld ocCUr just in ThE saMe Way As theY Would wIthouT it, iF aN aPProPriatelY AcCELeraTeD (tHree-DimEnSionaL) cooRDinAte systEm would be IntROducEd (HyPothesiS of equivalencE). THis hypotheSiS, whIch is bASEd upon thE experimental fact of the eQUality bEtwEen grAvitAtional anD inErtial MasS, Gains aDditioNal coNvIncING forcE IF tHe aPpArent graviTATioNal fiElD-whiCh existS relative to the acceLEraTed threedimenSioNal cOORdInaTE sYSteM-cAN be VIEwed as a real gravItational fIeLD; iN other wordS, If aCcEleratiOn-transFormaTIons (i.e., nOnlinear tRansformaTiOns) bECOme PermissiblE transfoRmations iN The thEOrY. At fiRst Glance It AppEars dEsirabLE to Look fOr gravItAtionaL equaTiOns that aRe covariant toward arbitrAry traNsforMatIons. HowevEr, iN §2 Of tHe present PapeR we will shoW by A siMple cOnsIDeratIon tHAt The QUantiTies GUv which chARaCteRIZe The gravitatIONAl fIeld cAnnOT complEtelY be determined by geNErally-covarianT equATIonS. In THe foLlOwing we shall deMonStRATe that thE gRavitationaL equatioNs EStablIshed bY us are GeneralLY CoVAriant Just To tHe degree iMagInABle undeR tHe COnditiOn thAt The funDamentAL tenSOR guv must be compleTely dETErminED. It FolloWs In partiCUlar That the graVitational eQuatioNs arE covaRiant wiTh RespecT to QuIte varied aCCeleratioN tranSformatIoNs (i.e., NonLinear TranSFOrmatIons)". "§2. reMarKs on the ChOICe OF tHe cOorDinaTe SysTeM We wAnt to show NOw that, coMplETely indEpEndENT of the GRaVITational eqUatIons wE EStablished, A CompLEtE DeterMinatiOn of thE fundamENtaL tEnsor γ
izations of the correspond ing equati ons o f t heor igin al t heory of relat i vity . Second, we establish ed asy s temo fequat ions th a td e ter mi ne s t he gr avita tio nal fie ld insofar  as  t he quantitie s  t hat determ ine  the materia l p rocess es  ar e  give n;and t his sy s tem ca n be cons id e red ag enerali z a ti on o f the Poisson equ a ti o n of Newton'stheory  o f  g r a vit ati on. In the  o rigin a l theor y  o f r ela t ivity, thereis no corre s pon ding s ys tem of equ ation sf orthis. In co ntra st to the  equat i ons men t ioned a bove,wecou ld n o tde mon st r ate ge ner a l c ovarianc efo r tho se g r a v i tati ona l eq uatio ns. The reaso n i s th a t t heirderiv atio nwas b ased ( besid es  the conservati on t heorems)onl yupo nthe c o varian cewit h respe ct to l i nea rt r a ns formations, and th us l ef t it anopen q u es ti o n as towh eth er o r not t here ex ist othe r subs t it ut ions th at  would  t ran sfo rm th e  equ ations  into th emsel v es. There aret wo reasons wh y  t h e  r e solu tio n of this q uest i on i s of pa rti c ularimpor ta n ce to the theory. Thean swer t o thi s question gi ves, first , i nformati on o n  h o w far the basi c ide a of relat i vity the ory c an be de veloped;a n d this i s o f g rea t i m p or t to the phil o s ophy  o f space  an d time.  An d s eco nd,  t he judgme nt about  t he  v al ueof th e  theoryfr omth e p ointo f view  of p hysi cs  d e pen ds to a hi g h  deg re eupon  th eanswe r to thi s quest ion, as i s s h ownby  t he foll owing conside ra tion. Theen tir e theo r y  evolved  from the conviction th a t all p hys icalproc esses ina g ravita tio n al fie ld occ ur ju st  in t he sa m e  w ayas  they woul d wit houtit , if  an app ropriately acceler a ted  (three-dimen sio nal) c oo rdi n at e  sy st e m w o u ld be introduce d (hypothe si s  o f equivale n ce) .This hy pothesi s, wh i ch is b ased upon  the expe ri ment a l  fa ct of theequality  betweeng ravit a ti onaland  inert ia l m ass,gainsa ddi tiona l conv in cing f orceif  the app arent gravitational fie ld-whi ch ex ist s relativ e t o  th e acceler ated  threedime nsi ona l coo rdi n ate s yste m -c anb e vie weda s a realg ra vit a t io nal field;i n oth er wo rds ,  if ac cele ration-transforma t ions (i.e., no nlin e a r t ran s form at ions) become p erm is s i ble tran sf ormations i n the th eo r y. At  first  glanc e it ap p e ar s  desir able  to  look for  gr av i tationa leq u ations  tha tare co varian t  tow a r d arbitrary tran sform a t ions. How ever,  i n §2 of thepresent pa per we will  showby a  simp le cons id eratio n t ha t the quan t ities guv  whic h chara ct eriz e t he gra vita t i onalfiel dcan not compl e t el y  b ed ete rmin ed by  g ener ally-cova r iant equ ati o ns. Inth e f o l lowing we s hall demon str ate t h a t the grav i tati o na l  equa tionsestabl ished b y  us  a re gene ral l y  covarian t just to the  d egre e imagin ab le u nd erth e condition tha t the fu ndamenta l tensor  gu v  mus t  be co mp letely deter mined .I t follo w s  in  partic u lar  th atthegra vita t ional equations are cova rian t wit h  re spect  to q ui te varie d  acc eleratio n  transformati ons (i.e., nonl i nea r  tra nsf o rm at ions)". " §2. Remar ks o n t he C hoi ce o f theC oord i na te S ystemWe w an tto show n ow  that,c ompl e tel y in depen de nt of  the gr avitatio nal e qu ations we establi shed ,a complete de terminationof  the  funda m ent alt e nsor γ
izations of_the corresponding_equations of the original_theory of_relativity._Second, we_established_a system of_equations that determines_the gravitational field insofar_as the quantities_that_determine the material processes are given; and this system can be considered a generalization_of_the Poisson_equation_of_Newton's theory of gravitation. In_the original theory of relativity,_there is_no corresponding system of equations for this. In_contrast_to the equations_mentioned above, we could not demonstrate general covariance for_those gravitational equations. The reason is_that their derivation_was_based_(besides the conservation theorems)_only upon the covariance with respect_to linear transformations, and thus left_it an open question as to whether_or not there exist other substitutions_that would transform the equations_into themselves._There are two reasons why_the resolution of_this question_is of particular_importance to the theory. The answer_to this question_gives, first, information on how far_the_basic idea of_relativity_theory_can be_developed; and this_is_of great_import_to the philosophy of space and_time._And second, the judgment about the value_of the theory from_the_point of view of_physics depends to a high_degree upon the answer to this_question, as_is shown_by the following consideration. The entire theory evolved from the conviction_that all physical processes in a_gravitational field occur just_in the_same_way as they_would_without it,_if an appropriately accelerated (three-dimensional) coordinate system_would be_introduced (hypothesis of equivalence). This hypothesis,_which is based upon_the_experimental fact of the equality between_gravitational and inertial mass, gains additional_convincing force if the apparent_gravitational_field-which_exists relative to the accelerated_threedimensional coordinate system-can be viewed as_a real gravitational_field; in other words, if acceleration-transformations (i.e.,_nonlinear_transformations) become permissible transformations in the_theory._At first glance it appears desirable_to_look_for gravitational equations that are_covariant toward arbitrary transformations. However, in_§2 of the present paper we will show by_a simple consideration_that the quantities guv which_characterize_the_gravitational field cannot completely be determined by generally-covariant equations. In_the following_we shall demonstrate_that the gravitational equations established by us are generally covariant_just to the degree imaginable under the_condition that the fundamental tensor guv must be completely determined. It_follows in particular that the gravitational equations are_covariant with respect to quite varied acceleration_transformations (i.e., nonlinear transformations)"._"§2._Remarks on the Choice of the Coordinate_System_We_want_to show now_that, completely independent_of the gravitational_equations we_established, a complete_determination of_the fundamental tensor_γ