 a more general theory that contains the former as a limiting case" [9]. But the extended theory of relativity, constructed by Einstein, could not embrace the general case of extended gravity. However, with the geometric power of Absolute Differential Calculus Einstein reached in the equations the general covariance that he presented to the final as the realization of the general principle of relativity supposedly encompassing the general case of extended gravity. Einstein highlights the independence of the guv of the choice of the spacetime coordinates xv although in function of the xv but which are determined by the physical process happenings in all of the rest of the universe according to named principle of Mach (principle of Einstein really because Mach said he was not his author), the relativity of the accelerated motion, the double relation, in both directions, between physical process and gravitational field and the fundamental law of conservation of energy and momentum taken together. "The equation of motion of a mass point in a gravitational field that follows from the equivalence hypothesis can easily be written down in a form in which this law is totally independent of the choice of the variables that determine place and time. By leaving the choice of these variables a priori totally arbitrary, and thus not privileging any specific space-temporal systems, one avoids the epistemological objection explained above. In that law of motion there appears a quantity ds2 = gμνdxμdxν which is an invariant, i.e., a quantity independent of the choice of the reference system (i.e., of the choice of the four space-time coordinates). The quantities guv are functions of x1.. x4 and serve to represent the gravitational field. With the help of the absolute differential calculus, which was developed by Ricci and Levi-Civita on the basis of Christoffel's mathematical investigations, it is possible, based on the existence of the above invariant, to replace the familiar systems of equations of theoretical physics by such equivalent systems (in the case of constancy of all of the guv) that hold totally independently of the choice of the space-time coordinates xv. All such systems of equations contain the quantities guv, i.e., the quantities that determine the gravitational field. The latter therefore have an influence on all physical processes. Conversely, the physical processes must also determine the gravitational field, i.e., the quantities guv. One arrives at the differential equations that determine these quantities by means of the hypothesis that the momentum and energy conservation laws must hold for the material processes and the gravitational field taken together. This hypothesis also restricts,
a more general theory that contains the former as a specify subject " [ 9 ]. But the extended theory of relativity, constructed by Einstein, could not espouse the general case of extended graveness. However, with the geometric might of Absolute Differential Calculus Einstein reached in the equation the general covariance that he presented to the concluding as the realization of the general principle of relativity supposedly encompassing the cosmopolitan case of extended graveness. Einstein highlights the independence of the guv of the option of the spacetime align xv although in function of the xv but which are determined by the physical summons happenings in all of the rest of the population according to name principle of Mach (principle of Einstein really because Mach said he was not his author), the relativity of the accelerated apparent motion, the double relation, in both directions, between physical process and gravitational field and the fundamental law of conservation of energy and momentum taken together. " The equation of motion of a mass point in a gravitational field that follows from the equality hypothesis can easily be write down in a human body in which this law is totally independent of the option of the variables that settle place and time. By leave the choice of these variables a priori totally arbitrary, and thus not privileging any specific space - worldly systems, one avoids the epistemological objection explained above. In that law of motion there appear a quantity ds2 = gμνdxμdxν which is an invariant, i.e., a quantity independent of the choice of the character system (i.e., of the choice of the four space - time coordinates). The quantities guv are functions of x1.. x4 and serve to defend the gravitational field. With the assistant of the absolute differential calculus, which was developed by Ricci and Levi - Civita on the footing of Christoffel's mathematical investigations, it is possible, based on the being of the above invariant, to replace the conversant systems of equations of theoretical physics by such equivalent system (in the case of constancy of all of the guv) that hold totally independently of the choice of the space - time coordinates xv. All such systems of equations contain the quantities guv, i.e., the measure that determine the gravitational field. The latter consequently have an influence on all physical processes. Conversely, the physical processes must also determine the gravitational sphere, i.e., the quantities guv. One arrives at the differential equations that determine these quantities by means of the hypothesis that the momentum and department of energy conservation laws must hold for the material processes and the gravitational field taken together. This hypothesis besides restricts,
 a lore general theory that contains the former av a lijiting cxse" [9]. But the extended theory od relqtivity, constructed by Einstein, could nit envrace the jsneral gcse or extznved gravity. Howgver, with tha geometric pofef lf Absolute Differential Calculus Eynstein rfached in the gquatpogs tgv neneral covariance that he presehted to the final as the realization of the gejerap principle of relwtivity supkkseqoy encompasskng the general case or extended gravity. Einstein higflighcs the indekzbdejwe of the gnv of nhe choice of the spawetime voordinates xv alvhouth in function of the xv but which are qetermineg yy the physical procews happgningv in qll of tie dest ov tie universe according ro named principle pf Nach (principls of Eynftein really because Mach said he was nmt gis author), the relativiry of the accelerated motion, tre double relation, in both directions, between phyvical oroecfr ajd gravitational field and the fundamental lar og bonservation of ekergy and momentum twkrg together. "Thg equatnkn of motion of a mads poinj in a gravitatyonak field that follows from tye equivalenbe htpothesis can easipy be writtzn dowm in s form in which this lac is tktally indeoendent or the choice of tfe naridbles that determine place and time. By keaving the choicq of these variables a priori totaply atbitrasy, and thud not privileging any specific space-temporal xyvteks, one aroids bhe epistemologycal objection explaiued abuve. In than law of kotion therq appears a qgwntity ds2 = gμνvxμdxν whicr is an unvariavg, i.e., a quantitu indepenbtnt of the choice of the refcrencg aystem (i.e., of thz xhoice of the fpur spwcv-tike woordinates). Dhe duavyitier guv are fmncgionx of x1.. x4 and serve tm relresent the gravitstlonal fieod. With ehe help of tne absolute differtntial cauculux, wrich was developed by Ricci ans Levi-Civlta on the basif of Christoffel'x mathematical investigations, it is poswible, based on thg existence of the abpye invariant, to rqplace tha familiar systems od equations of thtoretical physics by sudh equhvalejt systems (in the case of constancy of all of the guv) that hold totally ibdepenvegtly of the chooce ox che space-eime roordinates xv. Alk such systems of equations convain the qgautities guv, i.e., the quantities tfat determine the gravitational field. The latyer therefore have an influence on all physical processcs. Converwely, fhe phjairal processes must akso decerminw the geavibational field, i.e., tme quantitles juv. One arrives at the differential equatuojs that determinx these quanbiuies by means of the hypothesjs tgwt thg momentum and energy conserfation laws must holg sor the materiqm processes snd the gravitationel field takan together. This hypothesis also restricts,
a more general theory that contains the a case" [9]. the extended theory could embrace the general of extended gravity. with the geometric power of Absolute Calculus Einstein reached in the equations the general covariance that he presented to final as the realization of the general principle of relativity supposedly encompassing the case extended Einstein the independence of the guv of the choice of the spacetime coordinates xv although in function the xv but which are determined by the process happenings in all the rest of the universe to principle of (principle Einstein because Mach said was not his author), the relativity of the accelerated motion, the double relation, in both directions, between process and and the law conservation energy and momentum "The equation of motion of a a gravitational field that follows from the equivalence can easily written down in a form in this law is totally independent of the choice the variables that determine place and time. By leaving the choice of these variables a arbitrary, and thus not any specific space-temporal one the objection above. In law of motion there appears a quantity ds2 = gμνdxμdxν which an invariant, i.e., a quantity independent of the choice of system of the choice the four space-time coordinates). quantities are functions of x1.. serve represent With help the absolute differential calculus, was developed by Ricci and on the basis of possible, based on the existence of the above to replace the familiar systems of equations theoretical physics by such equivalent systems (in the case of constancy of of the hold totally independently of the choice of the coordinates xv. All such of equations contain the quantities guv, i.e., the quantities determine gravitational field. latter therefore have influence on all processes. Conversely, the must also the field, guv. One arrives at the differential that these quantities by means of hypothesis momentum and energy conservation laws must hold for the material processes and the gravitational field This hypothesis also restricts,
 a more general theory that conTains the foRmer aS a lImiTiNg caSe" [9]. BuT the extended thEOry oF relativity, constructed By EinStEIn, coULd Not emBrace thE GeNERal CaSe Of eXtENdEd graVitY. HoweveR, with the geOmeTrIc power of AbsOLuTe DifferenTiaL Calculus EinSteIn reacHeD in THe equAtiOns thE generAL covarIance that He PResentED to the fINAl As thE realization of the GEnERal principle of RelatiViTY sUPPosEdlY encompassInG the gENeral caSE oF EXTenDEd gravity. EinsTein highligHTs tHe indePeNdeNCe of thE guv oF tHE chOice of the spAcetIme coordiNates xV AlthougH In functIon of tHe xV buT whiCH aRe DetErMIneD By The PHysIcal procEsS hAppenIngs IN ALL of tHe rEst oF the uNiverse accordIng To naMEd pRinciPle of mach (PrIncipLe of EiNsteiN rEally because MacH saiD he was not His AuThoR), tHe relATivity Of tHe aCceleraTed motiON, thE dOUBLe Relation, in both direCtIONs, Between pHysicaL PrOcESs and graViTatIonaL FIeld aNd thE FuNdamentaL law of COnSeRvation Of Energy AnD moMenTum taKEn toGether. "the equatIon of MOtion of a mass poINt in a gravitatIOnAL FiELd thAt fOllows from tHe eqUIvalEnce HYpOthESis caN easiLy BE wRItten down in a form in wHiCh this Law is Totally indepeNdent of the CHOIce of the VariABlES that determine Place And time. By lEAving the ChoicE of these Variables A PRiori totAllY arBitRarY, ANd Thus not privilEGIng aNy SpecifiC spAce-tempOraL sySteMs, oNe Avoids the EpistemoLoGiCaL oBjeCtion EXplained AbOve. in ThaT law oF Motion There AppeArS a QUanTity ds2 = gΜΝdXΜDxν wHiCh Is an InvArIant, i.E., a quANtiTy indepEndent of tHe cHOice Of ThE refereNce system (i.e., of ThE choice of tHe FouR space-TIMe coordiNates). The quantities guv arE FunctioNs oF x1.. x4 anD serVe to repreSenT the grAviTAtionaL field. with tHe HelP OF the aBSOlUte DiFferential CALcuLus, whIcH was DevelopEd by Ricci and Levi-CiVIta On the basis of CHriStofFEL's MatHEmATicAl INveSTIgations, it is posSible, based On THe Existence oF The AbOve invaRiant, to ReplaCE the famIliar systEms of equaTiOns oF THeoRetical phySics by suCh equivalENt sysTEmS (in thE caSe of coNsTanCy of aLl of thE Guv) That hOld totAlLy indePendeNtLy of the cHoice of the space-time coorDinateS xv. AlL suCh systems Of eQUatIons contaIn thE quantitieS guV, i.e., The quAntITies tHat dETeRmiNE the gRaviTAtional fiELd. the LATtEr therefore HAVE an InfluEncE On all pHysiCal processes. ConveRSely, the physicaL proCESseS muST alsO dEtermine the graVitAtIONal field, I.e., The quantitiEs guv. One ArRIves aT the diFferenTial equATIoNS that dEterMinE these quaNtiTiES by meanS oF tHE hypotHesiS tHat the MomentUM and ENErgy conservation Laws mUST hold FOr tHe matErIal procESses And the gravItational fiEld takEn toGetheR. This hyPoThesis AlsO rEstricts,
 a more general theory tha t contains  thefor mer  a s alimi ting case" [9] .  But  the extended theory o f rel at i vity ,  c onstr ucted b y  E i n ste in ,cou ld no t emb rac e the g eneral cas e o fextended gra v it y. However , w ith the geom etr ic pow er  of Absol ute  Diff erenti a l Calc ulus Eins te i n reac h ed in t h e  e quat ions the generalc ov a riance that he  prese nt e dt o  th e f inal as th ereali z ation o f  t h e gen e ral principle  of relativ i tysuppos ed lye ncompa ssing  t h e g eneral case  ofextendedgravit y . Einst e in high lights  th e i ndep e nd en ceof the gu v o f  th e choice  o fthe s pace t i m e  coo rdi nate s xvalthough in f unc tion ofthe x v but  whi ch  aredeterm inedby  the physical p roce ss happen ing sinal l oft he res t o f t he univ erse ac c ord in g t onamed principle of  M a c h(princip le ofE in st e in reall ybec ause M ach s aidh ewas nothis au t ho r) , the r el ativit yofthe  acce l erat ed mot ion, the  doub l e relation, in both directio n s, b et w eenphy sical proce ss a n d gr avit a ti ona l  fiel d and  t h ef undamental law of c on servat ion o f energy andmomentum t a k e n togeth er." Th e  equation of m otion  of a mass point in  a gr avitatio nal field t hat foll ows  fr omthe e qu ivalence hypo t h esis  c an easi lybe writ ten  do wninaform in w hich thi sla wis  to tally independ en t o fthe  choi c e of t he va riab le st hat  determ i ne p lace  a nd  tim e.By  leav ingt hechoiceof thesevar i able saprioritotally arbit ra ry, and th us  no t priv i l eging an y specific space-tempor a l syste ms,  oneavoi ds the ep ist emolog ica l  objec tion e xplai ne d a b o ve. I n th atla w of motio n the re ap pe arsa quant ity ds2 = gμνdxμdx ν  wh ich is an inv ari ant, i .e .,a  q u ant it y  in d e pendent of thechoice ofth e  r eference s y ste m(i.e.,of thechoic e  of the  four spa ce-time c oo rdin a t es) . The quan tities g uv are fu n ction s  o f x1. . x 4 andse rve  to r eprese n t t he gr avitat io nal fi eld.Wi th the h elp of the absolute dif ferent ial c alc ulus, whi chw asdeveloped  byRicci andLev i-C ivita  on the b asis of  Ch r istof fel' s  mathemat i ca l i n v es tigations,i t ispossi ble ,  based  onthe existence oft he above invar iant , torep l aceth e familiar sys tem so f  equatio ns  of theoret ical phy si c s bysuch e quival ent sys t e ms (in th e ca seof consta ncy  o f  all of  t he guv) t hatho ld tot ally i n depe n d ently of the cho ice o f the s p ace -time  c oordina t es x v. All suc h systems o f equa tion s con tain th equanti tie sguv, i.e., the quant ities  that d et ermi nethe gr avit a t ional  fie ld . T he latter t he r ef or e  ha ve a n inf lu ence  on all p h ysical p roc e sses. C on ver s e ly, th e  p h y sical proc ess es mu s t  also dete r mine th e  grav itatio nal fi eld, i. e .,th e quant iti e s  guv. One  arrivesa t t he  dif ferentia lequa ti ons  t hat determine t hese qua ntitiesb y  means  of theh ypothe si s that the m oment um and ene r g y c onserva t ion  la wsmust  ho ld f o r the material processes  and  theg rav itati onalfi eld take n  tog ether. T h is hypothesis  also restricts , 
 a_more general_theory that contains the_former as_a_limiting case"_[9]._But the extended_theory of relativity,_constructed by Einstein, could_not embrace the_general_case of extended gravity. However, with the geometric power of Absolute Differential Calculus Einstein_reached_in the_equations_the_general covariance that he presented_to the final as the_realization of_the general principle of relativity supposedly encompassing the_general_case of extended_gravity. Einstein highlights the independence of the guv of_the choice of the spacetime coordinates_xv although in_function_of_the xv but which_are determined by the physical process_happenings in all of the rest_of the universe according to named principle_of Mach (principle of Einstein really_because Mach said he was_not his_author), the relativity of the_accelerated motion, the_double relation,_in both directions,_between physical process and gravitational field_and the fundamental_law of conservation of energy and_momentum_taken together. "The_equation_of_motion of_a mass point_in_a gravitational_field_that follows from the equivalence hypothesis_can_easily be written down in a form_in which this law_is_totally independent of the_choice of the variables that_determine place and time. By leaving_the choice_of these_variables a priori totally arbitrary, and thus not privileging any specific_space-temporal systems, one avoids the epistemological_objection explained above. In_that law_of_motion there appears_a_quantity ds2_= gμνdxμdxν which is an invariant, i.e.,_a quantity_independent of the choice of the_reference system (i.e., of_the_choice of the four space-time coordinates)._The quantities guv are functions of_x1.. x4 and serve to_represent_the_gravitational field. With the help_of the absolute differential calculus, which_was developed by_Ricci and Levi-Civita on the basis of_Christoffel's_mathematical investigations, it is possible, based_on_the existence of the above invariant,_to_replace_the familiar systems of equations_of theoretical physics by such equivalent_systems (in the case of constancy of all of_the guv) that_hold totally independently of the_choice_of_the space-time coordinates xv. All such systems of equations contain_the quantities_guv, i.e., the_quantities that determine the gravitational field. The latter therefore have_an influence on all physical processes. Conversely,_the physical processes must also determine the gravitational field, i.e., the_quantities guv. One arrives at the differential equations_that determine these quantities by means of_the hypothesis that the_momentum_and energy conservation laws must hold for_the_material_processes_and the gravitational_field taken together._This hypothesis also_restricts,