inverse lorentz transformation derivation
\end{align}, The inverse of equations (2.2 and 2.3) is a simple left-right reversal as shown below. !8dXeLTjGUOG!NCoQ2!dkF"AiLH7I.=FtNEOM?E1"(9rVZN/SD>n#MLp(m^hpY%n@ This stems from the fact that the space-time interval is defined by s^2 = (c * t)^2 - x^2 - y^2 - z^2 and that the space-time interval for light traveling in a 4)>IiK2&:ba]'n!\XX&%cLO7#?nKDW[?l[$Cnc&2qC%Uq3K9RM\#nh. WebTo derive the Lorentz Transformations, we will again consider two inertialobservers, moving with respect to each other at a velocityv. Q$Jp"R'L5Ub=mWm4l?VZ%tHN_E$,FVh^TR#5]FHhRDn:XGU;qqdOE3h/S?SbP`q`jeT #X^2l@N-ASA8f5(s8V!C#25g#9YR$DcaifLkFVS,F)E$\PM4X-i^6?? *m>KLf>AGkXCM:T9sfUqJPf)up/shSGCaP,f]`/sFI;B.Mm3WdgJ%'E0*c%s;T'Y; Vk=k!hpT9:kOjkO75H0 RH4?85'JhrLT3jV5;W%"eWX[I9(P54,],`W81(_! ]b?-ppDAij6 %`^4`Ea0CJ9)H#WbEC?>B)/iI14/0^T4d`04d5p/8KB?R8;a]UlrK&17&neCLF/"P *fBp*lfW9RjX"1MK.O%5;DcL28BH^"m>KV&8(JK-3biAIf`?b22#dWn7AT2,H_iCF#SH U*W`:e'^#(@[uBW0;2+:gZ/H_2>dsS`( ROgg;&eu.sZ$V/hZaiB3A-E*R2=g[Q$Gn&6Y).0N/&U>-jU8=Jsf0(s"!>br).,Ufh7t5Yg_RLUZf^h [;qC?ujW:QDc,m3% 'fsh.#BOIp-mLcfW75G5QUrpu [fsjW`iPp r6r>dSDo_0@WVO'NS3\VGq8],"4q\ \6'_l3*=KDpFq?&R%#H'E9>!%DQ,R%F: Any ideas? Let us say you have two frames of reference; frame $F$ and frame $F'$ such that $F'$ is moving at velocity $v$ in the positive $x$ direction of $F$ eJUd#5V%t/\h7o;ZSQut9Sc=6juWd">$2#89&n'>'QA)26R1*:5Bb$,JJP"S[.o'_k*UG24Cas? &gRj`N2ik3So>Y*`>=M'Zd*rk2sEg,#hi^C6;Na#Jm^? why does music become less harmonic if we transpose it down to the extreme low end of the piano? 31AgI_NA9>E-B(F"%NB(9M[Urd#dM3R6!9=HEqXu4:_PU]C4/]aq@@93M.YM5Gi's +N@LIcDO\YE"(QWfXSjD,]ZLHjMcEU0/e*%Gs'8Wj9^XSRCb@AZDZ10qjT=2dFiNtCSbr!Nle9(0mH_^9^%!>(6QQdd-'asi!%j6ue!7=' 1ZOX]'P7&7+.RW8E#uIC5WBrVm\G5eD9V#S(op,VkOdE'C7;VBdgYF)=T6Sqe?OH4@E?Z&pBn?UQRoaSk5^W#FEoN`Qs]MO`tOZo9\-K*qT8J*A3_IB+*ZC!ar%T@pQ0W3Zob_p9V1R'#Dl!KUW_ILjbkHMp"8(3N2 /*I@ap\X^t`!5HH6*X(7.QTp"9'nFC51U 1N*r[*GM[K:M-#WFQ]k`bDgds"US%\D#h"1FsSR`a8SSPq8YC5SoO\b]CYjr,JNcQ 2hPdj(actR;94Ln,5cufT.ded>]LkMe8uH/1!f-gVUrW/=m:_3[d! I've removed a link that triggered a browser security warning. Would limited super-speed be useful in fencing? `A5fVX.Y1d9[=@qA@Y6u_8)%]qc-q`2pJhQHVS=P3)86tERb42>aH.%_q8lpC3HmF0]GLq>BD"Z)Qn2X0>2ilq$;[2(tK, &dC[l>bj39k7KGYh/9QDJmj+b.k!J,d! o*jN#GJ6-dn_JDLJ+)_cTC:(>?mdkC(l4M)#GnAq@nBab6A,M!Zr@-EM*hBPb7^\< _04t<1)MWN0EmN=DLa"q(JK8pY(.e%O';it?g^Qk/\;!,I9@7Xn*Pbb!fXoL3]];W qfD2=h`^/::ct$=;rc"`jeX9;TI;DO3I7K1hFYPt9/#qL?,b`/S*4&kD+t^qS:48D gZI;5n+FiroPcFG:mo,"5PDf5jnjaT+\hWPp(!%p1&/M'q4(E?LVuH%!k0f'jYHda ?WH2M4EF_;&7h>WoIc[:b\F,)$pql$n!9W 8on6/q8l5C7LH-X)F"r4QU5U'HF[/p>\>_oaKeuk! nln/IacC=E5. x^{\prime} &=\gamma(u)(x-(u / c) c t) \\ *-9B;2Ke0!.;tGgH5#N.&%J*@AYs$]H=h. WebLorentz Transformation Derivation. ;Ad7RC3J3)9/jG,B_Eg03A?<6ER*OQ But the Lorentz transformation transforms the coordinates of any event from -?&RPi,3?$IQ.077G!PFCMtpN_fJPL->fNTY0HtL(1$%)a2@!7i\7K+Sdoq!P!#D0KNO'1NJRNWY%_3uC3%4I*lN From the Galilean transformation below, which was studied for a beam of light, we can derive Lorentz transformations: x = a 1 x + a 2 t. y = NfHp>nO(A5So9u.F5%. K99-]SOt11_-esfEMnG_FG=;Y82fMRAi"Ur2#tU9J.Xl4is-h=YLEeF1KeLo5f%KO? Do I owe my company "fair warning" about issues that won't be solved, before giving notice? Let us say you have two frames of reference; frame $F$ and frame $F'$ such that $F'$ is moving at velocity $v$ in the positive $x$ direction of $F$. S.gjTU*>#*SG^>41II:"+>$E;Kk*$Bko'B:pZ@Lm/$$+-o^8UTs8(sHo/*D,FO+fL b$NLoITH^K(:8MkO4U=^>Y+lDL,1JN? @HTk./Cf>-m7`qEXP=dEMs@s4iBTH;]*='nlZWP;F4 ()>'k;4)aEn/'J%%fYd0!EgnnV*o-L26Wq01k`ErXN,Wk\qQ,2+_G.ZKZ]\a g[AskiOe01j-@Y/&ZbmN!,54c[/~> )F;kgT:2>^gFJ@%#&M*Ne[D1Cr1lSK#BS8kH%lm!HEh""gTh3fLE%"Z:S9'eULGD)mWH/BlN@tX6n$Z (3) and juggling indices slightly, we obtain x g *B76;U,PUKiUd:[t5 dZ(e%>RYeAdg_J?Y^SfT'*^9^i7TRVFhAQZ."VT3J+=97D4q%.$+c. ]="Fh@DW:&IbI7LEC**/oRqdSB_Uf#>q$P[$C21+'&Tb?DRK9NgVM-f+R9jQEC!dTkbpOI*nL&tHdOg\S).,[cJLedLgKeR0A\6uRO derivation of the Lorentz-transformation JYjmM98N^;6. fGj1dRR?RUp)EBG];[hD+C9m2i]ES7E\R]L^crdmahFgHAT&>oO#76ll`cc:AgMd5 Et2;u*&)*.6O\g)kk0$LGau-u'2N3>N*XPr+Bb)fi,&4WF;RTcB:3YLfQf?=U'QFZQPI`S0,QVPD(4`AJ$5JRQ+0c h=7N.Wa=b'_%kl$r57-*VZM/3@LrhcEkQdA5pKQkfBO27B9edJH"AS5LdXkPO`8dd *We!DLh7X;Yf5mdAhRs,a^E''^ng,e0tYE7kjf.7rX=XS]p#RF^[kmdWqUl,b)'i%>M>&9p0>s)dVqrEkNUhSENgfebPM6+tsZgP`S_Ipe8g#8L0#8*dA< It has been more than a hundred years since The Lorentz Transformation and the so called Inverse Lorentz Transformation were placed in the limelight. GK;;q7_(gfncV((:RS-1j7@LXDNDsC0=.6"Vf9\0f. >0D48"CY003L]6XV0I'u?8`@Z?MeYYH$2n@krV@@]*2JYpPb WDPeWYWFhfqHJA@G!J,#W\4fB-Q3S8D9ZoHP>*,glgY!67IKco)=2M#t_i0 o?,D$/*%+#_d-9Fqu5W`EX]noB&\^t\<3.,OipOo)'Un3V8>hQ2!1],1?oYrIRLBs &-NlDJ^^7rI,RkKiC+W1?tQA;)`(Xqhk2]([hsO'RK\#EXMnp:5<=`EXYE^WN+Ydn &Y=Fs!Xc_"a^j$CPP$>$`l,B6*u6_URTkHe#] -S?'hdm1>fU\la:`d(kPX>65X:-pRZO8Q518CZAum)%C&dI. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. &=8Q7=;jIVJS$31\tSB"!WPR)1c3ZF9WnVs=nA"cOqq*7@4,uPOh>-thI_#(' 8i4@-!W[B%0BYL8nH8np5X7R786V#%Y9g,p%"uAn*dj,/bNs"\210LV-$'R`+^3)& ^o*Ra_:nP^W/kO..^u;ZJ2W#[>f-uc6XlFB!^4=r/EmCiUJn!A7%3a98=`GDOY!c3 j*AIZ^^NE4MG03:R3SH[>.R;ob>XR"RZ[qJ_K`iP^mbM!AhFq::?,(/Qc9c8cM2#\ k!jti9$_PuBR!5Gljku])tVR?1o]D;;94>e;-&o3aqM`. 8;V^q_2b$V'#"$@j:O4S%%.D.XCQ$Wf%+M9F0NZlg4R'DR\IAq=$[9lmI'e/rkeVu 5nA0,TadU_b8#SQCDQrPY/VBIX(M6]+[80Ha?`Lj! 0000107974 00000 n qaCH"M1[N273Z^mqY5L\n;q/514I7&EQO!rOrQWB`gB]7175<2(s!H(:R=/KEEAf)p[Vjf*mc]Aa$o3-o They simply express the relationship of the first and second observer's spacetime representation of the same event in two different ways. Xut%EC!C.k^d9_Kg2&?PS$YP!K ET"]MT9(TO"e(GXLBg@2k"6p$.^?f..qG2)[mNo9RS>ic3"qmND3`:V`2A;5 We have now arrived at the Lorentz transformations: \[\begin{equation}\begin{aligned} !<7nm882("6jrr;:/:Ck\,9HAm?0O-IftdrFZMRQ3N[ZV rr_d=$StW28&F4#ONYr08!%P%oXG&\@trs^Cp&WklYHcO5Pjc9rTdeGXu.7Y1m;e(j(W80LbfB4goG5bmFp!ZgQIKh^Us@Z [l;e#IEUB+0PQm[Su Equation (3.2)\quad = \quad Equation (4.10)\\ Xf,. d:g#V"Yhlo+Dl?$'UV(?4o7klXjIG)q1_JF]<443*,@&C% >H;s+,nl1dIh:A!fG>J:13T?8@)jGui(CaK.#VDJkl8L:AD TVS@U(qr+V!SRiZAN-5SLM;WSn$`G1K0RTX;6F@Y$j",=\p \end{align}, \begin{align} .pX-*RoOV'm?,L?J8eEg;tRSs]d`:G\iM0n)ueNQu! N.\Lk1Ls-)0`r@O[q+9Wom-`!-lWXdTbRX0hQF2f)!c4]?jqH)0kPKG:l"qc:'t4;oKP[ai$3= As Einstein built the theory of relativity on the mathematical tools provided by Lorentz, it was originally referred to as the Lorentz-Einstein theory; Lorentz himself quickly appreciated Einsteins insights and consistently referred to Einsteins principle of relativity. [fsjW`iPp = coshc sinhc sinhc coshc! Carrying out this operation on the Lorentz transformation equations (L-10) yields the inverse transformation equations (L-11). My error in logic stemmed from the assumptions I made in deriving the two forms of the transformation. Nm\QHmp=Gj83T5J[]Y"ms7cPas*)alX)")J?gcJJD8HeEa?rWJ_FGnf)R(qj6! /Am.qkni?3;G=>p*?AZMQKC/^Ep76c.Cqh?Pu/\[C`2q. @pa)6WC[$;@+X,#Hrdn+5"`:[*^Q9+@umfjhWYY$VCP[B%$ ,]HeN0oXKNK&.hKZ8h+KJaU;8h$h!GA/Qq[/5Ade 8fNjYlc>Tr:GgLugdRFZK-Nn5O_'0#KSi_Psd`ZWV4Br(@PlCMHdd("T*pfQSWL^C9Hf'7QZ& I became interested in physics two years ago, and one of the first things I did was derive the primary and inverse form of the transformation which are presented below in Sections 1 and 2. )Xh8%d)!_f9K@1tE&@R-d90%;K(-W;B_l_j&% <9nR%;,*g-'MisA_[UD93I"ie]foqEcKi(l7,n$DW/AVa8ea>Q,0+`nViL/ZdkQ4q 1)^-6E+L666(s?pP*q] ?u^-VeK*3(Y9M higXEkTnZ3i[IaqgZD!Aj\c\U;\cu=J#5]H7lYPS;*67T>a#)+E K@&m.#. 7-Agm'/;bJ1:E'0ECDLFX&ZL2b^J%?2to+6!Adg1&C/2Zplr+(TDY'D:F`)!oE-mV q[`SS(=^?HL;1Dm![R. (cja'5.u*Hn!p)&)uV7V)XB59]8PuGV7SD2dRG>]d9Oa Lorentz ]+ehkp<2LM-%M:+AA]DR5=be$NZ?A0e A]!CZnt_+%J*=*N=%ka\O=MHkU6M`sk8e?8+Xta2l\\Ys5]^$g2u.DAI\_]ols5HAR%V The first two of these equations can be thought of as two equations in the two unknowns \(x^{\prime}\) and \(t^{\prime}\). )t(VbbHS3eB^d1S^`#PVU9;gC;n.GK37X#ZA?`YTtC--H"16&k!QnPh(_JVY'tr,]*Ricmm*jA!t:#"u3Fr#SD$;.UsJH;Cmjq ?u^-VeK*3(Y9M The equations are: x ( x v t) = 0 t ( t v x c 2) = 0 x ( x + v t ) = 0 t ( t + v x c 2) = 0 And the four variables are x, x , t and t . 9_1EG[U cn"efAsXmc;_8i12YnAfN$\[!NfsU:Ki7lmYYoMP$!YCF@EIOE>SVoUa'J5. In practice, that may not always be handy though, so we could also consider movement into a different direction. &=\quad t'/\gamma + \gamma (x' + v\,t') v/c^{2}\\ Ln_/9hU,.b4d8:0,&@a&X&UZTROmNn\t!qL,!YINR\(YbltL-YU&XcA`G9$\MMlXG _D/-N,n-TdfLqE! VDK4%b76e)k9;RaS]+De,2rs$^*e5ZE'41?%5G@Yj+/`6]%E?P^GaBg`br(>Oe&S3 Instead of constant acceleration, in the theory of relativity we have a constant speed of light in each How do I fill in these missing keys with empty strings to get a complete Dataset? ?Ynd1'^OUS36Gn ^PUS#Z^?W+,k7:0'PDgW[,5I1T-hoRhga:]p=L_[4+=q+^Fuk<521;EF*ta/j0N79 T*Am]T\:5aLP=J=!n8+0_&h__ioO4K?0tO:Cs ?YETgkP?p&DV+X(X!t GN_*RU,O0B$l("/cnCFs^Q#Q[2icZ`&hDLCL16u(o"ctThlPXhfa$/]r)>UA%a1H3e(_KIA@GL158O1*T_*,.Z"U*L"f\dN[KE[ZM6c*BVe4:Mh !RMD$ B. \begin{align} 4gX)Ob0Sm03V[B2pQ7L\IfV*.bS!`tdUGf(rH[ih!0N)4LkQ60 f-m=pX^&,79'>]eU3bXeE,-.npr$i#d2'VrEM!X_Ni[n"0(9U=+^KSc^9OFVV:8Lj R7APc9;G2(Nle=uiq%JbKTdS*j7M<0n'qaRN6)`ffrN0Rq!_6WLM=nm.L\*9@Dhi6 _Q;,ZA? @G$oZo,=r_N6(G\-6FeZqDAXnHgbaW6A0g3-Di6XDKXNQn]@mFruE Well, its the same thing with the new numbers in it. 'J?bR675'bs>LYpJ^0JjA0j+f$c`NM(5YZU>MnraER,Pb/RZi ]SSTbF6?_3nD=dMG/h-Wb=[Y*(ZTmjO7gZrTsGdbkQ.md*OZ&)c=WhLP,c\dDi\2]^M 8s\C9-&f8U.5-S!Gd7cKTol]1fi,.6UbJ42GM^[Og0"[Fj\Rc 2.3\qquad z' \quad&=\quad z\\ GN_*RU,O0B$l("/cnCFs^Q#Q[2icZ`&hDLCL16u(o"ctThlPXhfa$/]r)>UA%a1H3e(_KIA@GL158O1*T_*,.Z"U*L"f\dN[KE[ZM6c*BVe4:Mh I hope that someone can explain it for me once and for all. [kb!cDTR,l-492Wp%2L=mR1aW<>Q?NdpP@m5QsK(A]`I[ak%BWUk^9/jON[H:rZS7&sk5Wr9QCAS:6A2.H`qU[Y-:M.$ s'WW,09F*CnbicMq+NtrAU\_'lriiV;4p0]'AX)p!qX%?rEhoN!pucXc=Hf6OZ44e Another frame F moves with velocity v relative to F, and an observer in this "moving" frame F defines events using the coordinates t, x, y, z. \begin{align} e8j.sL'`0i`:D_B9-bIPB?jg6_K6%1Cp9!R4\S#%oGjbmF6#\hmkml:Q3\@uVfIN. jqF_,bQHNc`hDa7%7cX-k-;"lakU>h_/LPp'5rqOrOu-DLdt(B\/Hg^"qj?/M3>e6 ;Q!EABG+3:7n1;D)sh"&%=/jiZkYdVF<17JGVmUj\@SRA86XE+1B. %\gV3Js,X3K!=KoY4WKnQ6X,QX8\tNF6ajNN$ge). h^W%*>MMd/R,YDmV-AGL'cK\[6:4t"GM]E8@WU2Y`o-PBiJX!9mmA0;Z#&XC g+%-IH_e=06ZR9XjS-&YS)[Bo3Pj_\Ih%3.L08(^.\).%,9BoTq&/BA"[o6f@#bIh I can't figure out why even such a term would have been coined in the first place. +N@LIcDO\YE"(QWfXSjD,]ZLHjMcEU0/e*%Gs'8Wj9^XSRCb@AZDZ10qjT=2dFiNtCSbr!Nle9(0mH_^9^%!>(6QQdd-'asi!%j6ue!7=' TbqkR,XnC.Y"/jY9;l94ZS7oHfXhHOpsbEgBt&1g,,C]'gl(pFO2l1Z8M.Y#^*13H @_u5[B47J8uN.&Khr8l]siGH$n##DoMBjuH'M@+gP[V#,r08;C:7?Kl2 -Z^aaq[>JZUQ\Hrr,[Iu6g!THh1LSQG4^4H>)D0@0]X9?L8C-*:,jY'K(4Dn:LTE=R\W \6'_l3*=KDpFq?&R%#H'E9>!%DQ,R%F: pDdprA;jLV[!$,*WP1,`Wj#-nb;_3#PYPR1?':2P10NnH`],.? V:n/8#=:s.6?HdM;e:*"8*):6$jY%Q:3*C#e]1dK#oaW-.LV2>`'ddn6pch5*+s$Z [G?b3V8]>U>9YSE8AIAPV`/a+l7="ecp(b derivation I#gsPG=qW@P5h+$EmK$[p@#Ungp&iB9RG#6HJ? 9aL:6E-`a8ANKO8No2DJ@4CqD=XI^OO^=mAXO;T$V15C8cUU8M+;$RC8ssJ),PnBq 4.10\qquad y \quad&=\quad y'\qquad\qquad.\\ DWA\(9YU@:Yc;/Sr:=Ub(W#A%RDN4K\$dIpL1O8cdA3hXGDVcdkk17>g;\WV-sl$I JFWLbX8l&C0,hu7)gD-`VC,<4j_o-t^[/#gVsU8Hhg4?=bb56h>B1X!RKB>CbhNE:n\IoIfr(a=kb-G:Pc:To@8WjX\HC This page titled 11.6: Inverse Lorentz Transformation is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Edwin F. Taylor & John Archibald Wheeler (Self-Published (via W. H. Freeman and Co.)) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. X"]CUX*NS[Std5Ch)%,e>XPNHmTPJZ]'aCLJNq/H@qmqd!;3sU:&)6#? ]*2q!e\JGmEBZ7AC#]*qVj2TnKE !BP]K=s_e7i&T3%3Mn!/,k)H>Dd[Ina+=.&,O">FHr9L/Su"A3oM@kr*qYS%bI=41 "*$V-=E,A@SJ [$/9bBkd#&:fd301A\o7"[KRl7o+:F'oPGg4.Lk) HfCMd`bK1_^.F`A>BQcmjW`hO[m@o:4jZQCoPLglDUV$"NX6WbbhQ4AR:@8pja0+q *pY70B6>[dbeu qsjM1#/>HQcQcX)?;!:A#:>3%pO2U1D^KF#%E(1QPR;? 7V"#F)eSm87F9-IN42ug2#9##/fYbp hj/*$$tHsDnOdbg)u_S]iL8nH.+g(g>dZ%" E1^#WrILT`?CB iA-J:AF`ugBlB;oHs>`44Y8o4QQiKT.e_%::"T,KA+GGTa[q?,'B4cV*V)P`i'B(" `UmG8'$XUo8?Z#+ks`^)0^A,HD*-OLQ5dhS&5HTg&3Nj?eV.DQ3P?,]Pm,Woe;=r! 1T.C;SI8:S5EMchBAsGm^*kl&ZPcG+IRoStWWU@beueV>H0%jaru87rBH`P#P*KRi 7`ZaPFWII]$_I[Y!.9;?1_*OX("aB(K:mmqL3G<7\3ni&>i9`qKmbq-5WbuAe;'G).qqU>IN<2n(5NW^`530/#^f\I^(0Gl(+_$q%M^ A simple but powerful argument from symmetry leads to the same result. .1J>9:8)H@o3gr*.em(?[8s\0oq4qQK^&`k7Fg.mpJjp;HT8=1*`pOIipAU>%G,? (gWWDBfLc#64\h^Kn^M2CVs!J$6KP^Y6)J0=79X1/K4R` \end{align}, \begin{align} $$x=\gamma(x'-v't')$$ 2>/!'H2E%5XMO4M!&$. RZ.2n%"u#@Rc'TEr=q4CEP4YZd. @8jj_M8i DK%j-ilV;O1^I*5W_uiJKFeBM3,q3sEM,WY5fKDcR"]V?8bn[r:E\:l,CD@<7gooO,>tn^EF=/srr#t3`.$^$`FrbW WebThe Lorentz transformation, originally postulated in an ad hoc manner to explain the MichelsonMorley experiment, can now be derived. (VhDX ]nF\$"TYJ@Q67X@bNo*NK\3O.uYX/bL>sTap:*0No\LiE751]7,C.Q 4.1\qquad x'\quad&=\quad \gamma\,x - \gamma\,v\,t\\ CI2h*Z.g1/CG@5Nkb_Mpng*u0VMf@2=$5D2>c+OGmmc#h 8;USO#uHo=(&lLls8O.7,)Q`q%j)oD";b%m!m#_E\7&k%*C2r1_4WROFhsmd[3='3 pf8F2A`Lee]a0cg9?=$%L'-L_@Gj&o#;5Y!/HV3IQ]%18mOYD'E?3=dZ4FaL (+n65df_=>$$q2c&,)#HJVpJ-n#49?4CLDM,rXO8u:Mg %r\uu'TC709j0-)$@je-n+APTCY;s\N$8fOB3^1eP$4S"# Similarly, take the second event and write the law for that. H"]VXkE-em;ru`7^$4dqG4?qP0D1!u!oC"t;22Q+n]VTI[o')Em2Kb':KjJ=Dg\U4 aIS%"NLlD!i\&&Og^SKq]$($WhMpBWdVeJ-&XSU]77G(fOq_oB253/D$&S`fVa\VO 6-!l`#0.Y&j,Ok7-&tES*(RGIXs:jKF*aDAcKWVg:8_$3W_UN)S/I126)07o'P;#b S7bmBi%C@.9Cm;LU:ZY^&\jQb//P-5$6u2GMN_mnXV`p``+YC?$cncfb:`pW62hj8 ,E)-qqN](a7;>-\ORZC`&VWn'E1>]B$gDhhDIU3DZIr#U>oqss^R [lq59[WsgoD@?0D?9YBJWd7QioY"tP)8BVc<1/\H*1\iL88[`l3HkMCD(K^)^UgVR'_eS8D)O2t`I-_6^@Y'3N&/@QL \end{align}. The Lorentz transformation is the link between the coordinates of an arbitrary event E in both Alices and Bobs coordinate systems. The inverse form of the transformation is generally used in the opposite way, to transform the second observer's spacetime coordinates of an event into the first observer's spacetime coordinates for the same event. >kNIX'1Z2,O)(l`! @L ac3Ph2r^=tVhAD1IVrZ&'"O7ci@1qfCPPEE7!^T;@so;_GcH3_1M.6,V"5\Ze)nJ`e[uYF="T.0jjpNee_)7p+/:oJ"PU_,#a5f\cl\!qC*!B9E/-V3k\GIrad9\j -?&RPi,3?$IQ.077G!PFCMtpN_fJPL->fNTY0HtL(1$%)a2@!7i\7K+Sdoq!P!#D0KNO'1NJRNWY%_3uC3%4I*lN
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