 gravitational field suggests the idea that physical processes occur in exactly the same way in a gravitational field as they do relative to an accelerated reference system (equivalence hypothesis). Having taken this idea as a basis, I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus, the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis; for this reason, the theory of relativity in the narrower sense cannot be brought into agreement with the latter. In this way I was led to view the theory of relativity in the narrower sense as valid only for regions within which there are no noticeable differences in the gravitational potential" [9]. "The invariant interval of Minkowski in differential form ds2 = c2dt2 – dx12 – dx22 – dx32 i.e., ds2 =ηαβdxαdxβ -aggregated by author- (Eq. 1) where (x1, x2, x3, t) are the space and time coordinates of an inertial frame of reference in a Minkowski spacetime. Transforming to arbitrary coordinates xμ for μ = 1,...,4 becomes ds2 =gμνdxμdxν (Eq. 2) Einstein employed his principle of equivalence to interpret the matrix of quantities gμν that had arisen with the introduction of arbitrary coordinates. In the special case of the principle, the transformation from equation (1) to equation (2) is from an inertial coordinate system to a uniformly accelerated coordinate system. In that case, the matrix of coefficients gμν reduces to that of equation (1) except that c now is a function of the coordinates (x1, x2, x3). That is, equation (2) becomes ds2 = c2 (x1, x2, x3) dt2 – dx12 – dx22 – dx32 (Eq. 1 ) According to the principle of equivalence, the presence of a gravitational field was the only difference between the spacetime of equation (1') and that of special relativity equation (1)" [2]. In consequence, the gravitational field instead of the line element c2dt2 – dx12 – dx22 – dx32 is defined by a symmetric tensor guv with 10 components as the fundamental invariant. Therefore, it is the fundamental tensor or metric tensor. Thus, "the ten quantities guv characterize the gravitational field; they replace the scalar gravitational potential (p of Newtonian gravitation theory, and form the second-rank
gravitational field suggests the idea that physical summons happen in exactly the same direction in a gravitational discipline as they do relative to an accelerated reference system (comparison guess). Having taken this idea as a basis, I arrived at the result that the speed of light is not to be regarded as independent of the gravitational potential. therefore, the principle of the constancy of the velocity of inner light is incompatible with the equivalence guess; for this reason, the theory of relativity in the narrower common sense cannot be brought into agreement with the latter. In this way I was led to view the theory of relativity in the narrow sense as valid only for regions within which there are no noticeable deviation in the gravitational potential " [ 9 ]. " The invariant interval of Minkowski in differential form ds2 = c2dt2 – dx12 – dx22 – dx32 i.e., ds2 = ηαβdxαdxβ -aggregated by author- (Eq. 1) where (x1, x2, x3, t) are the space and meter coordinates of an inertial frame of reference in a Minkowski spacetime. Transforming to arbitrary coordinates xμ for μ = 1,... ,4 becomes ds2 = gμνdxμdxν (Eq. 2) Einstein employed his principle of equivalence to interpret the matrix of measure gμν that had arisen with the introduction of arbitrary coordinate. In the limited casing of the principle, the transformation from equation (1) to equality (2) is from an inertial coordinate system to a uniformly accelerated coordinate arrangement. In that case, the matrix of coefficients gμν reduce to that of equation (1) except that c now is a function of the coordinate (x1, x2, x3). That is, equation (2) becomes ds2 = c2 (x1, x2, x3) dt2 – dx12 – dx22 – dx32 (Eq. 1) According to the principle of equivalence, the presence of a gravitational field was the lone difference between the spacetime of equation (1') and that of special relativity equation (1) " [ 2 ]. In consequence, the gravitational field alternatively of the line element c2dt2 – dx12 – dx22 – dx32 is defined by a symmetrical tensor guv with 10 components as the cardinal invariant. Therefore, it is the fundamental tensor or metric tensor. Thus, " the ten quantities guv qualify the gravitational field; they replace the scalar gravitational potential (p of Newtonian gravitation hypothesis, and form the second - rank
 grwvitational field suggesus the idea that khtsical proceases occjr in exactly the same way ii a traviuctional field as theh do relanive to ab acrelerated refereide systci (eqhlvaleucx hypothesis). Haying taken dhis idea as a bxsns, I arrived at the result that the delocitu lf light is noj to nq refarded as independent of the gravifationan potential. Tnus, the principle of the clnstwncy of the velocihy of light is ybcompatible dith the equivalence hipothesis; for this reason, the thdory pf relativutt ij the narrowxr senfe cannot be brought into abreement with bhe lettee. In this way I was lxd to view the theori of relathvnty in the narrower swnwe as valhd ovoy wor rxgikns wihhii which thede are no niticeable differencts yb the gravitafional pjtential" [9]. "The invariant interval of Minnowaki in differential forn ds2 = c2dt2 – dx12 – dx22 – dx32 i.e., ds2 =ηαβdxαqxβ -aggregated by author- (Eq. 1) where (x1, x2, x3, t) are the spacx xnd tlme ziogdinates of an inertial frame of reference in z Kikkowski spacetimc. Transforming to srhiytary coordinatgs xμ fox μ = 1,...,4 becomes ds2 =gμνdxμdxν (Eq. 2) Eigsteib employeq hix principle of equivalence ro interpret rhe matrix of quancities gμν thac had srisem with the introduction of zrbitrary clordinatea. In the special zasv of the principle, the transfowmation fcom eauation (1) to equatyon (2) is frlm an inertial coordinatf sysjem to a uniformpy accelerated coordinate system. In that case, tve katrix oy coefnicients gμν reduses to that of equatijn (1) ebcept that c now ms a functiog of the coorglnates (x1, x2, x3). That is, equqtiob (2) becoods ds2 = c2 (x1, x2, x3) dt2 – dx12 – br22 – dx32 (Eq. 1 ) According to the prkhciple of equivcutnxe, the presencr ow a ggavmtatijtal field wav thd ovky diwferenct bctwden yhe spacetime of equdtioh (1') and that of speviwl relatuvity eqtation (1)" [2]. In cpnsequence, the gragitatmonal hield onsjead of the line element c2dt2 – ds12 – dx22 – dx32 is defined by w synmetric tenspr guv with 10 components as the fundamenval invariant. Thereforg, it is the fundamentcl tensor or ketris tensor. Dhus, "the ten quantitues guv characterlze the gravitational rield; dhey geplace the scalar gravitational potential (p of Newtonian gravitation theiry, anv sorm the sedond-tank
gravitational field suggests the idea that physical in the same in a gravitational to accelerated reference system hypothesis). Having taken idea as a basis, I arrived the result that the velocity of light is not to be regarded as of the gravitational potential. Thus, the principle of the constancy of the velocity light incompatible the hypothesis; for this reason, the theory of relativity in the narrower sense cannot be brought into with the latter. In this way I was to view the theory relativity in the narrower sense valid for regions which are noticeable differences in gravitational potential" [9]. "The invariant interval of Minkowski in differential form ds2 = c2dt2 – dx12 – – dx32 =ηαβdxαdxβ -aggregated author- 1) (x1, x2, x3, the space and time coordinates of of reference in a Minkowski spacetime. Transforming to coordinates xμ μ = 1,...,4 becomes ds2 =gμνdxμdxν 2) Einstein employed his principle of equivalence to the matrix of quantities gμν that had arisen with the introduction of arbitrary coordinates. In case of the principle, transformation from equation to (2) from inertial coordinate to a uniformly accelerated coordinate system. In that case, the matrix coefficients gμν reduces to that of equation (1) except that is function of the (x1, x2, x3). That equation becomes ds2 = c2 x3) – – (Eq. ) According to the of equivalence, the presence of gravitational field was the of equation (1') and that of special relativity (1)" [2]. In consequence, the gravitational field of the line element c2dt2 – dx12 – dx22 – dx32 is by a guv with 10 components as the fundamental invariant. it is the fundamental or metric tensor. Thus, "the ten quantities guv characterize gravitational they replace scalar gravitational potential of Newtonian gravitation and form the
 gravitational field suggestS the idea thAt phySicAl pRoCessEs ocCur in exactly thE Same Way in a gravitational fieLd as tHeY Do reLAtIve to An accelERaTED reFeReNce SySTeM (equiValEnce hypOthesis). HavIng TaKen this idea aS A bAsis, I arrivEd aT the result thAt tHe veloCiTy oF Light Is nOt to bE regarDEd as inDependent Of THe gravITationaL POtEntiAl. Thus, the principlE Of THe constancy of tHe veloCiTY oF LIghT is IncompatibLe With tHE equivaLEnCE HYpoTHesis; for this rEason, the theORy oF relatIvIty IN the naRroweR sENse Cannot be broUght Into agreeMent wiTH the latTEr. In thiS way I wAs lEd tO vieW ThE tHeoRy OF reLAtIviTY in The narroWeR sEnse aS valID ONLy foR reGionS withIn which there aRe nO notICeaBle diFfereNces In The grAvitatIonal PoTential" [9]. "The invarIant Interval oF MiNkOwsKi In difFErentiAl fOrm Ds2 = c2dt2 – dx12 – Dx22 – dx32 i.e., dS2 =ΗαβDxΑDXΒ -aGgregated by author- (EQ. 1) wHERe (X1, x2, x3, t) are tHe spacE AnD tIMe coordiNaTes Of an INErtiaL fraME oF referenCe in a MINkOwSki spacEtIme. TraNsForMinG to arBItraRy coorDinates xΜ for μ = 1,...,4 BEcomes ds2 =gμνdxμDXν (Eq. 2) Einstein eMPlOYEd HIs prIncIple of equivAlenCE to iNterPReT thE MatriX of quAnTItIEs gμν that had arisen wItH the inTroduCtion of arbitrAry coordinATES. In the spEciaL CaSE of the principlE, the tRansformatIOn from eqUatioN (1) to equatIon (2) is from AN Inertial CooRdiNatE sySTEm To a uniformly aCCElerAtEd coordInaTe systeM. In ThaT caSe, tHe Matrix of cOefficieNtS gΜν ReDucEs to tHAt of equaTiOn (1) eXcEpt That c NOw is a fUnctiOn of ThE cOOrdInates (x1, X2, X3). THAT is, eQuAtIon (2) bEcoMeS ds2 = c2 (x1, X2, x3) dt2 – DX12 – dx22 – Dx32 (Eq. 1 ) AccOrding to tHe pRInciPlE oF equivaLence, the preseNcE of a gravitAtIonAl fielD WAs the onlY difference between the spACetime oF eqUatioN (1') and That of speCiaL relatIviTY equatIon (1)" [2]. In cOnseqUeNce, THE gravITAtIonAl Field insteAD Of tHe linE eLemeNt c2dt2 – dx12 – Dx22 – dx32 is defined by a syMMetRic tensor guv wIth 10 CompONEnTs aS ThE FunDaMEntAL Invariant. TherefOre, it is the FuNDaMental tensOR or MeTric tenSor. Thus, "The teN QuantitIes guv chaRacterize ThE graVITatIonal field; They replAce the scaLAr graVItAtionAl pOtentiAl (P of newtoNian grAVitAtion Theory, AnD form tHe secOnD-rank
 gravitational field sugge sts the id ea th atphy si calproc esses occur in exac tly the same way in agravi ta t iona l  f ieldas they do r ela ti ve  to  a n  a ccele rat ed refe rence syst em(e quivalence h y po thesis). H avi ng taken thi s i dea as  a  ba s is, I  ar rived  at th e  resul t that th ev elocit y  of lig h t  i s no t to be regardeda si ndependent ofthe gr av i ta t i ona l p otential.Th us, t h e princ i pl e o f t h e constancy o f the veloc i tyof lig ht  is incomp atibl ew ith  the equiva lenc e hypothe sis; f o r thisr eason,the th eor y o f re l at iv ity  i n  th e  n arr o wer  sense c an no t bebrou g h t into  ag reem ent w ith the latte r.In t h isway I  wasledto  view  the t heory  o f relativity in  the  narrower  se ns e a svalid only f orreg ions wi thin wh i chth e r e  a re no noticeable d if f e re nces inthe gr a vi ta t ional po te nti al"[ 9 ]. "T he i n va riant in terval of  M inkowsk iin dif fe ren tia l for m  ds2  = c2d t2 – dx1 2 – d x 22 – dx32 i.e. ,  ds2 =ηαβdxαd x β- a gg r egat edby author-(Eq. 1) w here (x 1,x 2, x3 , t)ar e  t h e space and time co or dinate s ofan inertial f rame of re f e r ence ina Mi n ko w ski spacetime.  Tran sforming t o  arbitra ry co ordinate s xμ forμ = 1,..., 4 b eco mes  ds 2 =g μνdxμdxν (Eq. 2 ) Ei ns tein em plo yed his  pr inc ipl e o fequivalen ce to in te rp re tthe  matr i x of qua nt iti es  gμ ν tha t  had a risen  wit hth e  in troduct i on o f ar bi tr arycoo rd inate s. I n  th e speci al case o f t h e pr in ci ple, th e transformat io n from equ at ion  (1) t o equation  (2) is from an inertia l  coordi nat e sys temto a unif orm ly acc ele r ated c oordin ate s ys tem . In th a t  c ase ,the matrix o f c oeffi ci ents  gμν re duces to that of e q uat ion (1) excep t t hatc no w i s  a fun ct i ono f  the coordinate s (x1, x2,  x 3 ).  That is,e qua ti on (2)becomes  ds2=  c2 (x1 , x2, x3)  dt2 – dx 12  – d x 2 2 –  dx32 (Eq.  1 ) Acc ording to the p r in ciple  of  equiv al enc e, th e pres e nce  of a  gravi ta tional  fiel dwas theonly difference between  the s pacet ime  of equat ion (1' ) and tha t of  special r ela tiv ity e qua t ion ( 1)"[ 2] . I n  cons eque n ce, the g r av ita t i on al field in s t e adof th e l i ne ele ment  c2dt2 – dx12 – d x 22 – dx32 is d efin e d  by  as ymme tr ic tensor guvwit h1 0  compone nt s as the fu ndamenta li nvari ant. T herefo re, iti s  t h e fund amen tal  tensor o r m et r ic tens or .T hus, " thete n quan tities guvc h aracterize the g ravit a t ional fie ld; t he y repla c e th e scalar g ravitationa l pote ntia l (pof Newt on ian gr avi ta tion theor y , and for m the  second -r ank
 gravitational_field suggests_the idea that physical_processes occur_in_exactly the_same_way in a_gravitational field as_they do relative to_an accelerated reference_system_(equivalence hypothesis). Having taken this idea as a basis, I arrived at the result_that_the velocity_of_light_is not to be regarded_as independent of the gravitational_potential. Thus,_the principle of the constancy of the velocity_of_light is incompatible_with the equivalence hypothesis; for this reason, the theory_of relativity in the narrower sense_cannot be brought_into_agreement_with the latter. In_this way I was led to_view the theory of relativity in_the narrower sense as valid only for_regions within which there are no_noticeable differences in the gravitational_potential" [9]._"The invariant interval of Minkowski_in differential form_ds2 =_c2dt2 – dx12_– dx22 – dx32 i.e., ds2_=ηαβdxαdxβ -aggregated by_author- (Eq. 1) where (x1, x2,_x3,_t) are the_space_and_time coordinates_of an inertial_frame_of reference_in_a Minkowski spacetime. Transforming to arbitrary_coordinates_xμ for μ = 1,...,4 becomes ds2_=gμνdxμdxν (Eq. 2) Einstein_employed_his principle of equivalence_to interpret the matrix of_quantities gμν that had arisen with_the introduction_of arbitrary_coordinates. In the special case of the principle, the transformation from_equation (1) to equation (2) is_from an inertial coordinate_system to_a_uniformly accelerated coordinate_system._In that_case, the matrix of coefficients gμν reduces_to that_of equation (1) except that c_now is a function_of_the coordinates (x1, x2, x3). That_is, equation (2) becomes ds2 =_c2 (x1, x2, x3) dt2_–_dx12_– dx22 – dx32 (Eq._1 ) According to the principle_of equivalence, the_presence of a gravitational field was the_only_difference between the spacetime of equation_(1')_and that of special relativity equation_(1)"_[2]._In consequence, the gravitational field_instead of the line element c2dt2_– dx12 – dx22 – dx32 is defined by_a symmetric tensor_guv with 10 components as_the_fundamental_invariant. Therefore, it is the fundamental tensor or metric tensor._Thus, "the_ten quantities guv_characterize the gravitational field; they replace the scalar gravitational potential_(p of Newtonian gravitation theory, and form_the second-rank