 gravity, which merges general relativity and quantum mechanics, providing a Theory of Everything. Space-time Intervals An event is the fundamental entity of observed physical reality represented by three coordinates of space and one coordinate of time in the space-time continuum postulated by the theory of relativity. In such a four-dimensional frame of reference (an observational perspective of space described using a coordinate system), one can assign four coordinates to an event: three spatial coordinates (x, y, z) to describe the location of the event and a time coordinate (t) to specify the moment at which the event occurs (Petkov, 2010). An event has a unique position in space-time specified by four coordinates (x, y, z, t). In relativity, the unification of space and time is exemplified by the common practice of selecting a metric (a system or standard of measurement of distance) such that all four dimensions are measured in terms of units of distance (x, y, z, ct), where "c" represents the speed of light in a vacuum and "ct" represents distance along the time axis (Petkov, 2010). t is the time (in seconds) light travels at c (at 186,000 miles/sec or 300,000 km/sec); hence "ct" represents the distance light travels and consequently distance along the time axis. Since c is a universal physical constant equal to 1 (unity), ct reduces to t. This enables mathematical description of space-time, the positions of events in space-time, and most importantly, space-time intervals. In our three-dimensional Euclidean space, the shortest distance between two points is known as the regular Euclidean distance (this distance is purely spatial and always positive). The regular Euclidean distance is given by the Pythagorean Theorem: the square of the hypotenuse (the regular Euclidean distance) of a right triangle is equal to the sum of the squares of the other two sides. The metric of a (mathematical) space defines distance in that space. Hence the Euclidean metric is the Pythagorean Theorem; it defines distance in 3D Euclidean space. The regular Euclidean distance is preserved (invariant) in all Euclidean inertial (constant velocity) frames of reference (by the Euclidean transformations), i.e., the regular Euclidean distance is independent of the coordinate system (it is scale invariant) for Euclidean inertial frames. This is known as general covariance. A physical law expressed in a generally covariant fashion (like the Euclidean metric) takes the same mathematical form in all coordinate
gravity, which merges general relativity and quantum mechanics, provide a hypothesis of Everything. Space - time Intervals An consequence is the fundamental entity of observe physical reality represent by three coordinates of space and one coordinate of clock time in the space - time continuum necessitate by the theory of relativity. In such a four - dimensional frame of reference book (an observational position of space trace use a coordinate system), one can assign four coordinates to an consequence: three spatial coordinates (x, y, z) to describe the placement of the event and a clock time coordinate (t) to specify the moment at which the event occurs (Petkov, 2010). An event give birth a unique position in space - time specified by four coordinate (x, y, z, t). In relativity, the fusion of space and time is exemplified by the common practice of selecting a metric (a system or standard of measurement of distance) such that all four dimension are measured in terms of unit of distance (x, y, z, ct), where " coulomb " represents the speed of inner light in a vacuum and " ct " represents distance along the time bloc (Petkov, 2010). t is the time (in seconds) light travels at c (at 186,000 miles / sec or 300,000 km / sec); hence " ct " represents the distance light travels and consequently distance along the meter axis. Since c is a cosmopolitan forcible changeless equal to 1 (unity), ct reduces to t. This enable mathematical description of space - time, the positions of events in space - time, and most importantly, space - prison term intervals. In our three - dimensional euclidian space, the shortest distance between two points is known as the regular euclidian distance (this distance is purely spatial and always positive). The regular euclidian distance is given by the Pythagorean Theorem: the square of the hypotenuse (the regular euclidian distance) of a right triangle is equal to the sum of the squares of the other two sides. The metric of a (mathematical) space defines distance in that space. Hence the euclidian metric is the Pythagorean Theorem; it defines distance in 3D euclidian space. The regular Euclidean distance is preserve (invariant) in all Euclidean inertial (constant speed) frames of reference (by the Euclidean transformations), i.e., the regular Euclidean distance is independent of the coordinate system (it is plate invariant) for Euclidean inertial frames. This is known as general covariance. A physical law expressed in a by and large covariant fashion (like the Euclidean metric) aim the same mathematical form in all coordinate
 grwvity, which merges generxl relativity aue quanvum mecganics, pfoviding a Theory of Everythmng. Wpace-upme Intervals An eveng is the vundamenral tntity of observev physical reamlty rzpcesented by thrge coordinatas of space ang unz coordinate of time in the space-timq contimukm postulated fy tnq thsory of relativity. In such a four-djmensioial frame of regerence (an observational pfrspfctive of space dedcribed usibg a xoordinate shstem), one bcn assign fkur coordinates to an event: thrde spctial coordunqted (x, y, z) to dxscribv the locatiok of tha event and a time coprdmnatw (t) to specify the mokent at which the gvent occuss (Petkov, 2010). An event hqs a oniqua porutiun jn slace-tile apecified gy four cooedinates (x, y, z, t). In rqoativity, the hnificwtyon of space and time is exemplified by ths common practice of seoecting a metric (a sydtem or seandard of measurement of distance) such that all xour vioenwijvw wre measured in terms of units of distance (x, r, z, cn), where "c" represekts the speed of logjt yn a vacuum avd "ct" xspdesents distance apong thg time axis (Pethov, 2010). t is the time (in seconds) lught travels qt c (at 186,000 miles/sec lr 300,000 km/sec); hznce "cj" reprrsents the distance ligkt trabels and cojsequentlg distance along ghe thme axis. Since c is a univqrsal phywicak constxnt gqual tj 1 (unity), ch redmwes to t. This enabpes mcthemdtical desfription of space-time, the positmpns of eventx hn vpace-timz, and kost importanely, space-time nntervalf. In uur three-dpmensionan Euclidean space, the shmttest distancx between two poibts is yvown as the rebular Euclidean disrance (this distancc is kudely spatial anb qlways positive). Thd rqgllac Eucjhdean distanwe ir gkfen bh the Pythanordan Yheorem: the square ox ths hypotenuse (the rrgmlar Eucludean diftance) of a roght triangle is eeual vo the sum pf jhe squares of the other two sises. The mftrlc of a (matheiatigal) fpace defiues distance in that space. Hence the Eucoidean metric is jhe Pythagorean Theorgm; lt defines dmstancq in 3D Euwlidean space. The retular Euclidean dlstance is preserved (ihvariatt) in all Euclidean inertial (constant velocity) frames of reference (by the Eucludean vrwnsformatiohs), i.r., the rzgukar Euslidxai distance is indvpendent of the coordinate systeo (it is vccle invariant) for Euclidean imeftial frames. Jhis is known as general ckvariancr. A physical law expressed in a generally covariant fasmion (like the Suclidvzn metric) takes the xame mcthemarical firm ln all coordinxte
gravity, which merges general relativity and quantum a of Everything. Intervals An event observed reality represented by coordinates of space one coordinate of time in the continuum postulated by the theory of relativity. In such a four-dimensional frame of (an observational perspective of space described using a coordinate system), one can assign coordinates an three coordinates (x, y, z) to describe the location of the event and a time coordinate (t) specify the moment at which the event occurs 2010). An event has unique position in space-time specified four (x, y, t). relativity, unification of space time is exemplified by the common practice of selecting a metric (a system or standard of measurement distance) such four dimensions measured terms units of distance z, ct), where "c" represents the in a vacuum and "ct" represents distance along time axis 2010). t is the time (in light travels at c (at 186,000 miles/sec or km/sec); hence "ct" represents the distance light travels and consequently distance along the time axis. is a universal physical equal to 1 ct to This mathematical description space-time, the positions of events in space-time, and most importantly, space-time In our three-dimensional Euclidean space, the shortest distance between two known the regular Euclidean (this distance is purely and positive). The regular Euclidean given the square the (the regular Euclidean distance) a right triangle is equal the sum of the sides. The metric of a (mathematical) space defines in that space. Hence the Euclidean metric the Pythagorean Theorem; it defines distance in 3D Euclidean space. The regular distance is in all Euclidean inertial (constant velocity) frames of (by the Euclidean transformations), the regular Euclidean distance is independent of the coordinate (it scale invariant) Euclidean inertial frames. is known as covariance. A physical in a covariant (like takes the same mathematical form in coordinate
 gravity, which merges general Relativity And quAntUm mEcHaniCs, prOviding a Theory OF EveRything. Space-time IntervAls An EvENt is THe FundaMental eNTiTY Of oBsErVed PhYSiCal reAliTy repreSented by thRee CoOrdinates of sPAcE and one cooRdiNate of time in The Space-tImE coNTinuuM poStulaTed by tHE theorY of relatiViTY. In sucH A four-diMENsIonaL frame of reference (AN oBServational perSpectiVe OF sPACe dEscRibed using A cOordiNAte systEM), oNE CAn aSSign four coordInates to an eVEnt: Three sPaTiaL CoordiNates (X, y, Z) To dEscribe the lOcatIon of the eVent anD A time coORdinate (T) to speCifY thE momENt At WhiCh THe eVEnT ocCUrs (petkov, 2010). An EvEnT has a UniqUE POSitiOn iN spaCe-timE specified by fOur CoorDInaTes (x, y, Z, t). In rElatIvIty, thE unifiCatioN oF space and time is ExemPlified by The CoMmoN pRactiCE of selEctIng A metric (A system OR stAnDARD oF measurement of distAnCE) SuCh that alL four dIMeNsIOns are meAsUreD in tERMs of uNits OF dIstance (x, Y, z, ct), whERe "C" rEpresenTs The speEd Of lIghT in a vACuum And "ct" rEpresentS distANce along the timE Axis (Petkov, 2010). t is THe TIMe (IN secOndS) light traveLs at C (At 186,000 miLes/sEC oR 300,000 km/SEc); henCe "ct" rEpREsENts the distance light TrAvels aNd conSequently distAnce along tHE TIme axis. SInce C Is A Universal physiCal coNstant equaL To 1 (unity), cT reduCes to t. ThIs enables MAThematicAl dEscRipTioN OF sPace-time, the poSITionS oF events In sPace-timE, anD moSt iMpoRtAntly, spacE-time intErVaLs. in Our Three-DImensionAl eucLiDeaN spacE, The shoRtest DistAnCe BEtwEen two pOInTS Is knOwN aS the RegUlAr EucLideAN diStance (tHis distanCe iS PureLy SpAtial anD always positiVe). the regular euCliDean diSTAnce is giVen by the Pythagorean TheoREm: the sqUarE of thE hypOtenuse (thE reGular EUclIDean diStance) Of a riGhT trIANgle iS EQuAl tO tHe sum of the SQUarEs of tHe OtheR two sidEs. The metric of a (mathEMatIcal) space defiNes DistANCe In tHAt SPacE. HENce THE Euclidean metriC is the PythAgOReAn Theorem; iT DefInEs distaNce in 3D EUclidEAn space. the regulaR EuclideaN dIstaNCE is Preserved (iNvariant) In all EuclIDean iNErTial (cOnsTant veLoCitY) framEs of reFEreNce (by The EucLiDean trAnsfoRmAtions), i.e., The regular Euclidean distAnce is IndepEndEnt of the cOorDInaTe system (iT is sCale invariAnt) For eucliDeaN InertIal fRAmEs. THIs is kNown AS general cOVaRiaNCE. A Physical law EXPResSed in A geNErally CovaRiant fashion (like tHE Euclidean metrIc) taKES thE saME matHeMatical form in aLl cOoRDInate
 gravity, which merges gen eral relat ivity  an d q ua ntum  mec hanics, provid i ng a  Theory of Everything.  Spac e- t imeI nt erval s An ev e nt i s t he  f und am e nt al en tit y of ob served phy sic al  reality rep r es ented by t hre e coordinate s o f spac eand one c oor dinat e of t i me inthe space -t i me con t inuum p o s tu late d by the theory o f  r e lativity. In s uch afo u r- d i men sio nal frameof  refe r ence (a n  o b s e rva t ional perspec tive of spa c e d escrib ed  us i ng a c oordi na t e s ystem), one  can  assign f our co o rdinate s  to anevent:  th ree  spa t ia lcoo rd i nat e s(x, y,z) to de sc ri be th e lo c a t i on o f t he e ventand a time co ord inat e  (t ) tospeci fy t he  mome nt atwhich  t he event occurs  (Pe tkov, 201 0).  A n e ve nt ha s  a uni que  po sitionin spac e -ti me s p ec ified by four coor di n a te s (x, y,  z, t) .  I nr elativit y,  th e un i f icati on o f  s pace and  timei sex emplifi ed  by th ecom mon  prac t iceof sel ecting a  metr i c (a system or standard of m e as u r em e nt o f d istance) su ch t h at a ll f o ur  di m ensio ns ar em ea s ured in terms of un it s of d istan ce (x, y, z,ct), where " c " repres ents th e  speed of ligh t ina vacuum a n d "ct" r epres ents dis tance alo n g  the tim e a xis  (P etk o v ,2010). t is t h e  tim e(in sec ond s) ligh t t rav els  at  c  (at 186, 000 mile s/ se cor  30 0,000 km/sec);  h enc e"ct " rep r esents  thedist an ce lig ht trav e ls a nd c on se quen tly  d istan ce a l ong  the ti me axis.Sin c e cis  a  univer sal physicalco nstant equ al  to  1 (un i t y), ct r educes to t. This enabl e s mathe mat icaldesc ription o f s pace-t ime ,  the p ositio ns of  e ven t s  in s p a ce -ti me , and most i mpo rtant ly , sp ace-tim e intervals. In ou r  th ree-dimension alEucl i d ea n s p ac e , t he sho r t est distance be tween twopo i nt s is known asth e regul ar Eucl idean distanc e (this d istance i spure l y  sp atial andalways p ositive). The r e gu lar E ucl ideandi sta nce i s give n  by  thePythag or ean Th eorem :the squa re of the hypotenuse (t he reg ularEuc lidean di sta n ce)  of a rig ht t riangle is  eq ual  to t hes um of  the sq uar e s oftheo ther twos id es. T he  metric ofa ( mat hemat ica l ) spac e de fines distance in that space. He ncet h e E ucl i dean  m etric is the P yth ag o r ean Theo re m; it defin es dista nc e  in 3 D Eucl ideanspace.T h er egular  Euc lid ean dista nce  i s  preser ve d( invari ant)  i n allEuclid e an i n e rtial (constantveloc i t y) fr a mes  of r ef erence( by t he Euclide an transfor mation s),i.e.,  the re gu lar Eu cli de an distanc e  is indep enden t of th ecoor din ate sy stem ( it is  sca le  in variant)f o rE uc li d ean  ine rtial  f rame s. This i s  known a s g e neral c ov ari a n ce. Ap hy s i cal law ex pre ssedi n  a general l y co v ar i ant f ashion  (like  the Eu c lid ea n metri c)t a kes the s ame mathe m ati ca l fo rm in al lcoor di nat e
 gravity,_which merges_general relativity and quantum_mechanics, providing_a_Theory of_Everything._Space-time Intervals An_event is the_fundamental entity of observed_physical reality represented_by_three coordinates of space and one coordinate of time in the space-time continuum postulated_by_the theory_of_relativity._In such a four-dimensional frame_of reference (an observational perspective_of space_described using a coordinate system), one can assign_four_coordinates to an_event: three spatial coordinates (x, y, z) to describe_the location of the event and_a time coordinate_(t)_to_specify the moment at_which the event occurs (Petkov, 2010)._An event has a unique position_in space-time specified by four coordinates (x,_y, z, t). In relativity, the_unification of space and time_is exemplified_by the common practice of_selecting a metric_(a system_or standard of_measurement of distance) such that all_four dimensions are_measured in terms of units of_distance_(x, y, z,_ct),_where_"c" represents_the speed of_light_in a_vacuum_and "ct" represents distance along the_time_axis (Petkov, 2010). t is the time_(in seconds) light travels_at_c (at 186,000 miles/sec_or 300,000 km/sec); hence "ct"_represents the distance light travels and_consequently distance_along the_time axis. Since c is a universal physical constant equal to_1 (unity), ct reduces to t._This enables mathematical description_of space-time,_the_positions of events_in_space-time, and_most importantly, space-time intervals. In our three-dimensional_Euclidean space,_the shortest distance between two points_is known as the_regular_Euclidean distance (this distance is purely_spatial and always positive). The regular_Euclidean distance is given by_the_Pythagorean_Theorem: the square of the_hypotenuse (the regular Euclidean distance) of_a right triangle_is equal to the sum of the_squares_of the other two sides. The_metric_of a (mathematical) space defines distance_in_that_space. Hence the Euclidean metric_is the Pythagorean Theorem; it defines_distance in 3D Euclidean space. The regular Euclidean distance_is preserved (invariant)_in all Euclidean inertial (constant_velocity)_frames_of reference (by the Euclidean transformations), i.e., the regular Euclidean_distance is_independent of the_coordinate system (it is scale invariant) for Euclidean inertial frames._This is known as general covariance. A_physical law expressed in a generally covariant fashion (like the Euclidean_metric) takes the same mathematical form in all_coordinate