 the motion of the light source (Einstein, 2001). General covariance is the heart of both postulates; the general covariance of space-time intervals is the basis for special relativity. In special relativity, time cannot be separated from space, because the observed rate at which time passes depends on the relative velocity of the observer. Time and space are interwoven into a single continuum called Minkowski space-time. Frames of reference can be divided into two groups: inertial (constant velocity) and non-inertial (accelerating). An inertial frame of reference moves with constant velocity in a straight line (Fields, 2015). The physics of an inertial frame has no causes external to the system (Ferraro, 2007). All inertial frames are in a state of constant rectilinear motion with respect to one another, there is zero acceleration. If an acceleration or extraneous force does occur, then the inertial frame is deflected (curved) from its rectilinear trajectory (it is then a non-inertial frame). Measurements in one inertial frame can be converted to measurements in another inertial frame by a simple transformation (the Lorentz transformation in special relativityEinstein, 2001; Guilini, 2005). The Lorentz transformation is a coordinate transformation between two Minkowski reference frames that are moving at constant velocity relative to one another. The transformation connects the space and time coordinates of an event as measured by an observer (someone who takes measurements) in each inertial frame. In all inertial frames (regardless of their relative velocity), the difference between the space coordinates of any two events minus the difference between the time coordinates of the events (the space-time interval) is always the same (invariant). This general covariance is the defining property of the Lorentz transformation. The Lorentz transformation has a number of unintuitive features: observers moving at different inertial velocities may measure different distances, elapsed times, and even different orderings of events, but always such that the speed of light and space-time intervals are invariant in the inertial frames. Special relativity has the following consequences, which have been validated experimentally: length contraction (shortening) and time dilation (slowing) for increased inertial velocity, space-time interval invariance (time dilates and lengths contract at higher speeds of a reference frame relative to another to keep space-time intervals and c invariant in the inertial frames), mass-energy equivalence (E=mc2), relativistic mass (mass increases with velocity because of increased kinetic energy), a universal speed limit (c), and relativity of simultaneity (Disalle,
the motion of the light source (Einstein, 2001). General covariance is the affection of both postulate; the general covariance of space - meter interval is the basis for special relativity. In particular relativity, prison term cannot be separated from outer space, because the observed rate at which prison term passes depends on the proportional velocity of the observer. Time and space are interwoven into a single continuum called Minkowski outer space - time. Frames of reference can be separate into two groups: inertial (constant velocity) and non - inertial (accelerating). An inertial human body of reference moves with constant velocity in a straight cable (Fields, 2015). The physics of an inertial frame has no causes external to the system (Ferraro, 2007). All inertial frame of reference are in a state of constant rectilinear motion with respect to one another, there is zero acceleration. If an acceleration or extraneous force does occur, then the inertial frame is deflected (swerve) from its rectilinear trajectory (it is then a non - inertial frame). Measurements in one inertial frame of reference can be convert to measurements in another inertial frame by a childlike transformation (the Lorentz transformation in special relativityEinstein, 2001; Guilini, 2005). The Lorentz transformation is a coordinate transformation between two Minkowski reference frames that are moving at changeless velocity relative to one another. The transformation connects the space and time coordinates of an consequence as measured by an observer (someone who takes measurements) in each inertial frame. In all inertial frames (regardless of their relative speed), the remainder between the space coordinates of any two events minus the difference between the meter coordinates of the events (the space - meter interval) is always the same (invariant). This cosmopolitan covariance is the defining property of the Lorentz transformation. The Lorentz transformation has a number of unintuitive features: perceiver moving at unlike inertial velocities may measure different distances, elapse times, and even different orderings of consequence, but always such that the amphetamine of light and space - time intervals are invariant in the inertial frames. Special relativity has the following consequence, which have been validated experimentally: length compression (shortening) and time dilation (slowing) for increased inertial velocity, space - time interval invariability (time dilates and lengths contract at higher speeds of a reference frame relative to another to keep quad - clock time intervals and c invariant in the inertial frames), mass - energy equivalence (vitamin e = mc2), relativistic mass (mass increases with velocity because of increase kinetic energy), a universal speed limit (coke), and relativity of simultaneity (Disalle,
 thf motion of the light somrce (Einstein, 2001). Ggnwral cmvariahce is tfe heart of both postulates; vhe tenerql covariance of space-gime integvals is rhe uasis for special relatiynty. Ih speeiel relativity, tlme cannot te separated fsoo dpace, because the observed rate at rhich tomf passes depenqs om the geoative velocity of the observsr. Time and space arr interwoven into a single conhinuum called Minklwski space-jjme. Drames of rewerence can be divided into two groups: inertial (constxnt vzlocity) and nin-ijgrtial (accelxratind). An inertial frame mf refetence moves wibh coistabt velocity in a stramght line (Fields, 2015). Thg physics mf an inertial framw yas nm cagses wxtdrnzl tk the dysvem (Ferraro, 2007). All inertual frames are in a seqte of constaht receijinear motion with respect to one anothtr, thsre is zero acceleratiob. If an acceleration lr extranqous force does occur, then the inertial frame is geflertdd (emvved) drlm its rectilinear trajectory (it is then a nog-jntrtpal frame). Measureients in onr lnrttial frame cav be convsrted to measuremejts in wnothwr inertiwl ftame by a simple transformarion (the Lorvntz transformation in special reuatifityEonstein, 2001; Guilini, 2005). The Lurenfz transforlation is x coordinate travsfprkation btgween two Minkowshi refereice fxames thxt ate movigg at conshant yalocity relative tl one atother. The transformation connects the spere and time cposditates of an eyent as measureq by an observgr (someonz who gakes measlrements) mn each inereial frame. In wll inertial frames (wegaedlews of tfdir relative vrlocity), tkt differenxe between the spage couddinates of any twi events minus yhe disfvreice bqdween the tike cuoraonater of tht eyengs (tne space-time intervan) is always the same (imvwriant). Tyis genewal covariancr is the defining kropervy of vhe Lotenjz transformation. The Lorentz tdansformahiok has a numbew of unintuitive features: observers moving at different inertial velocitiws may measure diffgrekt distances, elapfed times, and even different irderings of evenus, but always such that the s[eed lf light and space-time intervals are invariant in the inertial frames. Spexial rxlwtivity has the follmwnng consezuenrer, which have beem validated experimentally: lengvh contracdijn (shortening) and time dilatoov (slowing) for increased inertial velodity, spave-time interval invariance (time dilates and lengths conbract at yighed speeds oh a reference frame telatire to qnother to neep space-timd imtcrvals and c iivaxiant in the inertial frames), mass-wnergy eeuivalence (E=mc2), rxlativistic lxss (mzss insreases with velkcitg becaose of increasrd kinetic enetgy), a universal speeg jimit (c), and reoztivity of somultanvity (Disalle,
the motion of the light source (Einstein, covariance the heart both postulates; the is basis for special In special relativity, cannot be separated from space, because observed rate at which time passes depends on the relative velocity of the Time and space are interwoven into a single continuum called Minkowski space-time. Frames reference be into groups: inertial (constant velocity) and non-inertial (accelerating). An inertial frame of reference moves with constant velocity a straight line (Fields, 2015). The physics of inertial frame has no external to the system (Ferraro, All frames are a of rectilinear motion with to one another, there is zero acceleration. If an acceleration or extraneous force does occur, then the frame is from its trajectory is a non-inertial frame). one inertial frame can be converted another inertial frame by a simple transformation (the transformation in relativityEinstein, 2001; Guilini, 2005). The Lorentz is a coordinate transformation between two Minkowski reference that are moving at constant velocity relative to one another. The transformation connects the space coordinates of an event measured by an (someone takes in inertial frame. all inertial frames (regardless of their relative velocity), the difference between space coordinates of any two events minus the difference between coordinates the events (the interval) is always the (invariant). general covariance is the of Lorentz transformation a of unintuitive features: observers at different inertial velocities may different distances, elapsed times, events, but always such that the speed of and space-time intervals are invariant in the frames. Special relativity has the following consequences, which have been validated experimentally: contraction (shortening) dilation (slowing) for increased inertial velocity, space-time interval (time dilates and lengths at higher speeds of a reference frame relative to to space-time intervals c invariant in inertial frames), mass-energy (E=mc2), relativistic mass with velocity of kinetic speed limit (c), and relativity of (Disalle,
 the motion of the light source (einstein, 2001). GeNeral CovAriAnCe is The hEart of both postULateS; the general covariance oF spacE-tIMe inTErVals iS the basIS fOR SpeCiAl RelAtIViTy. In sPecIal relaTivity, time CanNoT be separated FRoM space, becaUse The observed rAte At whicH tIme PAsses DepEnds oN the reLAtive vElocity of ThE ObservER. Time anD SPaCe arE interwoven into a sINgLE continuum callEd MinkOwSKi SPAce-TimE. Frames of rEfErencE Can be diVIdED INto TWo groups: inertIal (constant VEloCity) anD nOn-iNErtial (AccelErATinG). An inertial FramE of refereNce movES with coNStant veLocity In a StrAighT LiNe (fieLdS, 2015). the PHySicS Of aN inertiaL fRaMe has No caUSES ExteRnaL to tHe sysTem (Ferraro, 2007). All IneRtiaL FraMes arE in a sTate Of ConstAnt recTilinEaR motion with respEct tO one anothEr, tHeRe iS zEro acCEleratIon. if aN acceleRation oR ExtRaNEOUs Force does occur, then ThE INeRtial fraMe is deFLeCtED (curved) fRoM itS recTILineaR traJEcTory (it is Then a nON-iNeRtial frAmE). MeasuReMenTs iN one iNErtiAl framE can be coNvertED to measurementS In another inerTIaL FRaME by a SimPle transforMatiON (the loreNTz TraNSformAtion In SPeCIal relativityEinsteIn, 2001; guilinI, 2005). The LOrentz transfoRmation is a COORdinate tRansFOrMAtion between twO MinkOwski referENce frameS that Are movinG at constaNT Velocity RelAtiVe tO onE ANoTher. The transfORMatiOn ConnectS thE space aNd tIme CooRdiNaTes of an evEnt as meaSuReD bY aN obServeR (Someone wHo TakEs MeaSuremENts) in eAch inErtiAl FrAMe. IN all ineRTiAL FramEs (ReGardLesS oF theiR relATivE velociTy), the diffEreNCe beTwEeN the spaCe coordinates Of Any two evenTs MinUs the dIFFerence bEtween the time coordinateS Of the evEntS (the sPace-Time interVal) Is alwaYs tHE same (iNvariaNt). ThiS gEneRAL covaRIAnCe iS tHe defining PROpeRty of ThE LorEntz traNsformation. The LoreNTz tRansformation Has A numBER oF unINtUItiVe FEatUREs: observers moviNg at differEnT InErtial veloCItiEs May measUre diffErent DIstanceS, elapsed tImes, and evEn DiffEREnt Orderings oF events, bUt always sUCh thaT ThE speeD of Light aNd SpaCe-timE interVAls Are inVarianT iN the inErtiaL fRames. SpeCial relativity has the folLowing ConseQueNces, which HavE BeeN validateD expErimentallY: leNgtH contRacTIon (shOrteNInG) anD Time dIlatIOn (slowing) FOr IncREAsEd inertial vELOCitY, spacE-tiME interVal iNvariance (time dilaTEs and lengths coNtraCT At hIghER speEdS of a reference fRamE rELAtive to aNoTher to keep sPace-time InTErvalS and c iNvariaNt in the INErTIal fraMes), mAss-Energy equIvaLeNCe (E=mc2), reLaTiVIstic mAss (mAsS increAses wiTH velOCIty because of incrEased KINetic ENerGy), a unIvErsal spEEd liMit (c), and relAtivity of siMultanEity (disalLe,
 the motion of the light s ource (Ein stein , 2 001 ).  Gen eral  covariance is theheart of both postulat es; t he gene r al  cova rianceo fs p ace -t im e i nt e rv als i s t he basi s for spec ial  r elativity. I n  s pecial rel ati vity, time c ann ot bese par a ted f rom  spac e, bec a use th e observe dr ate at which t i m epass es depends on the re l ative velocity  of th eo bs e r ver . T ime and sp ac e are interwo v en i n toa  single conti nuum called Min kowski  s pac e -time.  Fram es ofreference c an b e divided  intot wo grou p s: iner tial ( con sta nt v e lo ci ty)  a n d n o n- ine r tia l (accel er at ing).  Ani n e r tial  fr ameof re ference moves  wi th c o nst ant v eloci ty i na str aightline(F ields, 2015). T he p hysics of  an  i ner ti al fr a me has  no  ca uses ex ternalt o t he s y st em (Ferraro, 2007) .A l linertial  frame s  a re in a sta te  of  con s t ant r ecti l in ear moti on wit h  r es pect to  o ne ano th er,  th ere i s  zer o acce leration . Ifa n acceleration or extraneous fo r c ed oesocc ur, then th e in e rtia l fr a me  is defle cted(c u rv e d) from its rectili ne ar tra jecto ry (it is the n a non-in e r t ial fram e).M ea s urements in on e ine rtial fram e  can beconve rted tomeasureme n t s in ano the r i ner tia l fr ame by a simp l e  tra ns formati on(the Lo ren tztra nsf or mation in  special  r el at iv ity Einst e in, 2001 ;Gui li ni,  2005 ) . TheLoren tz t ra ns f orm ation i s  a c oord in at e tr ans fo rmati on b e twe en twoMinkowski  re f eren ce  f rames t hat are movin gat constan tvel ocityr e lative t o one another. The tran s formati onconne ctsthe space  an d time  co o rdinat es ofan ev en t a s measu r e dbyan  observer( s ome one w ho  tak es meas urements) in eachi ner tial frame. I n a ll i n e rt ial fr a mes  ( r ega r d less of their r elative ve lo c it y), the di f fer en ce betw een the  spac e  coordi nates ofany two e ve ntsm i nus  the diffe rence be tween the timec oo rdina tes  of th eeve nts ( the sp a ce- timeinterv al ) is a lways  t he same(invariant). This gener al cov arian ceis the de fin i ngpropertyof t he Lorentz  tr ans forma tio n . The  Lor e nt z t r ansfo rmat i on has an um ber o funintuitive f e atu res:obs e rversmovi ng at different i n ertial velocit iesm a y m eas u re d if ferent distanc es,  e l a psed tim es , and evendifferen to rderi ngs of  event s, buta l wa y s such  tha t t he speedofli g ht andsp ac e -timeinte rv als ar e inva r iant i n the inertial f rames . Speci a l r elati vi ty hast he f ollowing c onsequences , whic h ha ve be en vali da ted ex per im entally: l e ngth cont racti on (sho rt enin g)and ti me d i l ation  (sl ow ing ) for inc r e as e din e rti al v eloci ty , sp ace-timei ntervalinv a riance(t ime d ilates an d lengths co ntr act a t higher spe e ds o f  a refer ence f rame r elative toan other t o k e e p space-t ime inter v als  a nd c  invaria nt  inth e i ne rtial frames),mass-ene rgy equi v a lence(E= m c2), relati vi stic mass (m ass i nc r eases w i t h v elocity bec aus e o f in cre ased kinetic energy), a unive rsal  spee d  li mit ( c), a nd  relativ i ty o f simult a neity (Disall e,
 the_motion of_the light source (Einstein,_2001). General_covariance_is the_heart_of both postulates;_the general covariance_of space-time intervals is_the basis for_special_relativity. In special relativity, time cannot be separated from space, because the observed rate_at_which time_passes_depends_on the relative velocity of_the observer. Time and space_are interwoven_into a single continuum called Minkowski space-time. Frames_of_reference can be_divided into two groups: inertial (constant velocity) and non-inertial_(accelerating). An inertial frame of reference_moves with constant_velocity_in_a straight line (Fields,_2015). The physics of an inertial_frame has no causes external to_the system (Ferraro, 2007). All inertial frames_are in a state of constant_rectilinear motion with respect to_one another,_there is zero acceleration. If_an acceleration or_extraneous force_does occur, then_the inertial frame is deflected (curved)_from its rectilinear_trajectory (it is then a non-inertial_frame)._Measurements in one_inertial_frame_can be_converted to measurements_in_another inertial_frame_by a simple transformation (the Lorentz_transformation_in special relativityEinstein, 2001; Guilini, 2005). The_Lorentz transformation is a_coordinate_transformation between two Minkowski_reference frames that are moving_at constant velocity relative to one_another. The_transformation connects_the space and time coordinates of an event as measured by_an observer (someone who takes measurements)_in each inertial frame._In all_inertial_frames (regardless of_their_relative velocity),_the difference between the space coordinates of_any two_events minus the difference between the_time coordinates of the_events_(the space-time interval) is always the_same (invariant). This general covariance is_the defining property of the_Lorentz_transformation._The Lorentz transformation has a_number of unintuitive features: observers moving_at different inertial_velocities may measure different distances, elapsed times,_and_even different orderings of events, but_always_such that the speed of light_and_space-time_intervals are invariant in the_inertial frames. Special relativity has the_following consequences, which have been validated experimentally: length contraction_(shortening) and time_dilation (slowing) for increased inertial_velocity,_space-time_interval invariance (time dilates and lengths contract at higher speeds_of a_reference frame relative_to another to keep space-time intervals and c invariant in_the inertial frames), mass-energy equivalence (E=mc2), relativistic_mass (mass increases with velocity because of increased kinetic energy), a_universal speed limit (c), and relativity of simultaneity_(Disalle,