 it defines distance in Minkowski space-time (the invariant spacetime interval). The Minkowski metric is a physical law expressed in a generally covariant fashion; it has the same form in all Minkowski inertial frames (it has a physical constancy). In practice, the square is utilized, as the metric is a generalization of the Euclidean metric (Pythagorean Theorem) to four-dimensional Minkowski space-time. r is a displacement vector equal to x + y + z. Equipped with this metric, the mathematical model of space-time is called Minkowski space-time. Minkowski space-time is a specific example of a Lorentzian manifold (coordinate system); in fact, Minkowski space-time is the simplest example of a Lorentzian manifold (Chen, 2011; Misner et al., 1973; O'Neill, 1983; Petkov, 2010; Ratcliffe, 2006). In a standard Lorentzian manifold, one coordinate is written with a sign (-) opposite to the sign (+ + +...) of the other coordinates; this convention allows quantities to be categorized as light-like, time-like, or space-like (Chen, 2011; Misner et al., 1973; O'Neill, 1983; Ratcliffe, 2006). For the Minkowski metric, t is written as negative because it is an imaginary dimension. For the Minkowski metric, the space-time interval "s2" is zero, positive, or negative; this allows the definition of three possible types of space-time intervals. When s2 is zero, the metric is lightlike; when s2 is negative, the metric is time-like; when s2 is positive, the metric is space-like. The metric allows not only the definition, classification, and computation of invariant spacetime intervals, it also defines the geometry and properties of Minkowski space-time. Minkowski space-time is the model of space-time for special relativity, quantum mechanics, and human conscious experience (Chen, 2011; O'Neill, 1983; Sieb, 2015, 2016, 2017a, 2017b). The 4D Lorentzian manifold is also of great importance for general relativity; flat Minkowski space-time provides a springboard for general relativity, as curved space-time is locally Minkowski (Chen, 2011; O'Neill, 1983). It can be seen therefore that the general covariance of space-time intervals (as defined by the Minkowski metric) encompasses special relativity, quantum mechanics, human conscious experience, and general relativity; it
it defines distance in Minkowski space - time (the invariant spacetime time interval). The Minkowski system of measurement is a physical law carry in a broadly covariant fashion; it has the like form in all Minkowski inertial frames (it has a forcible constancy). In exercise, the square is utilized, as the system of measurement is a generalization of the Euclidean measured (Pythagorean Theorem) to four - dimensional Minkowski space - time. radius is a displacement vector equal to x + y + z. Equipped with this metric function, the mathematical model of space - prison term is called Minkowski space - time. Minkowski space - clock time is a specific example of a Lorentzian manifold (coordinate system); in fact, Minkowski space - time is the simplest case of a Lorentzian manifold (Chen, 2011; Misner et al. , 1973; O'Neill, 1983; Petkov, 2010; Ratcliffe, 2006). In a standard Lorentzian manifold, one coordinate is written with a sign (-) opposite to the sign (+ + + ...) of the other coordinates; this convention allows quantities to be categorized as light - like, time - like, or space - alike (Chen, 2011; Misner et al. , 1973; O'Neill, 1983; Ratcliffe, 2006). For the Minkowski metric, t is write as damaging because it is an imaginary dimension. For the Minkowski metric, the quad - time interval " s2 " is zero, positive, or negative; this admit the definition of three possible types of space - time intervals. When s2 is zero, the metric is lightlike; when s2 is minus, the metric is time - like; when s2 is positive, the metric is quad - like. The metric function allows not only the definition, classification, and computation of invariant spacetime interval, it also defines the geometry and properties of Minkowski quad - time. Minkowski space - time is the model of distance - time for special relativity, quantum mechanism, and human conscious experience (Chen, 2011; O'Neill, 1983; Sieb, 2015, 2016, 2017a, 2017b). The 4D Lorentzian manifold is besides of great importance for general relativity; flat Minkowski space - prison term provides a springboard for general relativity, as curved space - time is locally Minkowski (Chen, 2011; O'Neill, 1983). It can be interpret therefore that the general covariance of space - time intervals (as defined by the Minkowski metric) encompasses particular relativity, quantum mechanics, human conscious experience, and general relativity; it
 it defines distance in Minyowski space-timg (rhe intariant spacetioe interval). The Minkowski mevric is a physical law expressea in a gejerally xovaciant fashion; it has the same rlrm nn all Minkowski inertial xrames (it has d ohvsical constancy). In practice, the squwre is itllized, as the ietrpc is z generalization of the Euclidean jetric (Kythagorean Theorek) to four-dimensional Minkoaski space-time. r is a fisplacemenj vesror equal to x + y + z. Equipped with this metric, the mathematical mudel pf space-tine is walled Minkiwski space-time. Mlmkowskh space-yime is a speclfic xxample of a Lorentzian menifold (coordinate sistem); in fdcc, Minkowski space-time iw the sim[lesg exxmpme or a Logenvzian manifkld (Chen, 2011; Musner et al., 1973; O'Neill, 1983; [vykov, 2010; Ratclirfe, 2006). Ig w standard Lorentzian manifold, one coorginzte is written with a sugn (-) opposite to the dign (+ + +...) os the other coordinates; this convention allows qudntitmer ti ne cxrehorized as light-like, time-like, or space-like (Chqh, 2011; Mpsner et al., 1973; O'Neijl, 1983; Ratclifge, 2006). Gjr the Minkowrki mecdid, t is written as jegativg becayse it is an omaginary dimension. For the Minkowski mvtrix, the space-time incerval "s2" is vero, ppsitife, or negative; this alluws fhe definitlon of thdde possible typer on s[ace-time intervals. When s2 ys zero, tie mecric is uighjlike; wren s2 is nfgatiya, the metric is tile-likg; when s2 is posihive, the metric is space-like. Thx metric alloes non only thz defikition, classifisation, and comkutation jf inxariant spzcetime intervals, yt also definad the geometcy and prjperries of Minyuwski space-timr. Minkowski space-tine is the model of spxde-time for specncl relativity, quamtuo mqcjaiics, wtd human convciojs dcperidnce (Chtu, 2011; I'Veilk, 1983; Sieb, 2015, 2016, 2017a, 2017b). The 4D Norehtzian manifold is ajso of gteat impowtance for gemeral relativity; fpat Mmnkowsyi spsce-jime provides a springboard for general gelwtivity, as ctrvee space-time ns locally Minkowski (Chen, 2011; O'Neill, 1983). It cai be seen therefore thar the general covarnakce of space-vime igtervals (ds defined by the Mibkowski metric) engompasses special relafivity, quanhum mechanics, human conscious experience, and general relativity; it
it defines distance in Minkowski space-time (the interval). Minkowski metric a physical law fashion; has the same in all Minkowski frames (it has a physical constancy). practice, the square is utilized, as the metric is a generalization of the metric (Pythagorean Theorem) to four-dimensional Minkowski space-time. r is a displacement vector equal x y z. with this metric, the mathematical model of space-time is called Minkowski space-time. Minkowski space-time is a example of a Lorentzian manifold (coordinate system); in Minkowski space-time is the example of a Lorentzian manifold 2011; et al., O'Neill, Petkov, Ratcliffe, 2006). In standard Lorentzian manifold, one coordinate is written with a sign (-) opposite to the sign (+ + of the this convention quantities be as light-like, time-like, (Chen, 2011; Misner et al., 1973; 2006). For the Minkowski metric, t is written negative because is an imaginary dimension. For the metric, the space-time interval "s2" is zero, positive, negative; this allows the definition of three possible types of space-time intervals. When s2 is metric is lightlike; when is negative, the is when is the metric space-like. The metric allows not only the definition, classification, and computation invariant spacetime intervals, it also defines the geometry and properties space-time. space-time is the of space-time for special quantum and human conscious experience O'Neill, Sieb, 2017b). 4D manifold is also of importance for general relativity; flat space-time provides a springboard space-time is locally Minkowski (Chen, 2011; O'Neill, 1983). can be seen therefore that the general of space-time intervals (as defined by the Minkowski metric) encompasses special relativity, mechanics, human and general relativity; it
 it defines distance in MinkowSki space-tiMe (the InvAriAnT spaCetiMe interval). The MINkowSki metric is a physical laW exprEsSEd in A GeNeralLy covarIAnT FAshIoN; iT haS tHE sAme foRm iN all MinKowski inerTiaL fRames (it has a pHYsIcal constaNcy). in practice, thE sqUare is UtIliZEd, as tHe mEtric Is a genERalizaTion of the euCLidean MEtric (PyTHAgOreaN Theorem) to four-dimENsIOnal Minkowski sPace-tiMe. R Is A DIspLacEment vectoR eQual tO X + y + z. EquiPPeD WITh tHIs metric, the maThematical mODel Of spacE-tIme IS calleD MinkOwSKi sPace-time. MinKowsKi space-tiMe is a sPEcific eXAmple of A LorenTziAn mAnifOLd (CoOrdInATe sYStEm); iN FacT, MinkowsKi SpAce-tiMe is THE SImplEst ExamPle of A Lorentzian maNifOld (CHEn, 2011; MIsner Et al., 1973; O'neilL, 1983; PEtkov, 2010; ratcliFfe, 2006). In A sTandard LorentziAn maNifold, one CooRdInaTe Is wriTTen witH a sIgn (-) OppositE to the sIGn (+ + +...) oF tHE OThEr coordinates; this cOnVENtIon allowS quantITiEs TO be categOrIzeD as lIGHt-likE, timE-LiKe, or spacE-like (CHEn, 2011; miSner et aL., 1973; O'neill, 1983; RAtCliFfe, 2006). for thE minkOwski mEtric, t is WrittEN as negative becAUse it is an imagINaRY DiMEnsiOn. FOr the MinkowSki mETric, The sPAcE-tiME inteRval "s2" Is ZErO, Positive, or negative; tHiS allowS the dEfinition of thRee possiblE TYPes of spaCe-tiME iNTervals. When s2 is Zero, tHe metric is LIghtlike; When s2 Is negatiVe, the metrIC Is time-liKe; wHen S2 is PosITIvE, the metric is sPACe-liKe. the metrIc aLlows noT onLy tHe dEfiNiTion, classIficatioN, aNd CoMpUtaTion oF InvarianT sPacEtIme InterVAls, it aLso deFineS tHe GEomEtry and PRoPERtieS oF MInkoWskI sPace-tIme. MINkoWski spaCe-time is tHe mODel oF sPaCe-time fOr special relaTiVity, quantuM mEchAnics, aND Human conScious experience (Chen, 2011; O'NeILl, 1983; Sieb, 2015, 2016, 2017a, 2017B). ThE 4D LorEntzIan manifoLd iS also oF grEAt impoRtance For geNeRal RELativITY; fLat miNkowski spaCE-TimE provIdEs a sPringboArd for general relatIVitY, as curved spacE-tiMe is LOCaLly mInKOwsKi (cHen, 2011; o'nEill, 1983). It can be seen Therefore tHaT ThE general coVAriAnCe of spaCe-time iNtervALs (as defIned by the minkowski MeTric) ENComPasses specIal relatIvity, quanTUm mecHAnIcs, huMan ConsciOuS exPerieNce, and GEneRal reLativiTy; It
 it defines distance in Mi nkowski sp ace-t ime  (t he  inv aria nt spacetime i n terv al). The Minkowski met ric i sa  phy s ic al la w expre s se d inage ner al l ycovar ian t fashi on; it has  th esame form in al l Minkowsk i i nertial fram es(it ha sa p h ysica l c onsta ncy).I n prac tice, the  s q uare i s  utiliz e d ,as t he metric is a ge n er a lization of th e Eucl id e an m etr ic(Pythagore an  Theo r em) tof ou r - d ime n sional Minkow ski space-t i me.  r isadis p laceme nt ve ct o r e qual to x +  y +  z. Equip ped wi t h thism etric,the ma the mat ical mo de l o fs pac e -t ime iscalled M in ko wskispac e - t i me.Min kows ki sp ace-time is a  sp ecif i c e xampl e ofa Lo re ntzia n mani fold(c oordinate syste m);in fact,Min ko wsk ispace - time i s t hesimples t examp l e o fa L or entzian manifold ( Ch e n ,2011; Mi sner e t  a l. ,  1973; O 'N eil l, 1 9 8 3; Pe tkov ,  2 010; Rat cliffe ,  2 00 6). Inastanda rd  Lo ren tzian mani fold,one coor dinat e  is written wi t h a sign (-)o pp o s it e  tothe  sign (+ ++... )  oftheo th erc oordi nates ;t hi s  convention allowsqu antiti es to  be categoriz ed as ligh t - l ike, tim e-li k e, or space-like(Chen , 2011; Mi s ner et a l., 1 973; O'N eill, 198 3 ;  Ratclif fe,  20 06) . F o r  t he Minkowskim e tric ,t is wr itt en as n ega tiv e b eca us e it is a n imagin ar ydi me nsi on. F o r the Mi nk ows ki  me tric, the sp ace-t imein te r val  "s2" i s  z e r o, p os it ive,  or  n egati ve;t his  allows  the defi nit i on o fth ree pos sible types o fspace-time  i nte rvals. W hen s2 i s zero, the metric is l i ghtlike ; w hen s 2 is  negative , t he met ric is tim e-like ; whe ns2i s  posi t i ve , t he  metric is s pac e-lik e.  The  metric  allows not only t h e d efinition, cl ass ific a t io n,a nd com pu t ati o n  of invariant s pacetime i nt e rv als, it al s o d ef ines th e geome try a n d prope rties ofMinkowski  s pace - t ime . Minkowsk i space- time is t h e mod e lof sp ace -timefo r s pecia l rela t ivi ty, q uantum  m echani cs, a nd  human c onscious experience (Ch en, 20 11; O 'Ne ill, 1983 ; S i eb,  2015, 20 16,2017a, 201 7b) . T he 4D  Lo r entzi an m a ni fol d  is a lsoo f great i m po rta n c efor general r e lat ivity ; f l at Min kows ki space-time pro v ides a springb oard f orgen e ralre lativity, as c urv ed s pace-tim eis locallyMinkowsk i( Chen,  2011;  O'Nei ll, 198 3 ) .I t canbe s een  therefor e t ha t  the ge ne ra l  covar ianc eof spa ce-tim e  int e r vals (as defined  by t h e  Mink o wsk i met ri c) enco m pass es special  relativity , quan tummecha nics, h um an con sci ou s experien c e, and ge neral  relati vi ty;it
 it_defines distance_in Minkowski space-time (the_invariant spacetime_interval)._The Minkowski_metric_is a physical_law expressed in_a generally covariant fashion;_it has the_same_form in all Minkowski inertial frames (it has a physical constancy). In practice, the_square_is utilized,_as_the_metric is a generalization of_the Euclidean metric (Pythagorean Theorem)_to four-dimensional_Minkowski space-time. r is a displacement vector equal_to_x + y_+ z. Equipped with this metric, the mathematical model_of space-time is called Minkowski space-time._Minkowski space-time is_a_specific_example of a Lorentzian_manifold (coordinate system); in fact, Minkowski_space-time is the simplest example of_a Lorentzian manifold (Chen, 2011; Misner et_al., 1973; O'Neill, 1983; Petkov, 2010;_Ratcliffe, 2006). In a standard_Lorentzian manifold,_one coordinate is written with_a sign (-)_opposite to_the sign (+_+ +...) of the other coordinates;_this convention allows_quantities to be categorized as light-like,_time-like,_or space-like (Chen,_2011;_Misner_et al.,_1973; O'Neill, 1983;_Ratcliffe,_2006). For_the_Minkowski metric, t is written as_negative_because it is an imaginary dimension. For_the Minkowski metric, the_space-time_interval "s2" is zero,_positive, or negative; this allows_the definition of three possible types_of space-time_intervals. When_s2 is zero, the metric is lightlike; when s2 is negative,_the metric is time-like; when s2_is positive, the metric_is space-like._The_metric allows not_only_the definition,_classification, and computation of invariant spacetime intervals,_it also_defines the geometry and properties of_Minkowski space-time. Minkowski space-time_is_the model of space-time for special_relativity, quantum mechanics, and human conscious_experience (Chen, 2011; O'Neill, 1983;_Sieb,_2015,_2016, 2017a, 2017b). The 4D_Lorentzian manifold is also of great_importance for general_relativity; flat Minkowski space-time provides a springboard_for_general relativity, as curved space-time is_locally_Minkowski (Chen, 2011; O'Neill, 1983). It_can_be_seen therefore that the general_covariance of space-time intervals (as defined_by the Minkowski metric) encompasses special relativity, quantum mechanics,_human conscious experience,_and general relativity; it