ࡱ> ?<=>`!^)9Th٬2jh @xڕRKQ7o5wZ4",jЭ(]5hBСK.]:G*h{],@ /B>BB"@dAEy1jV,jxd0o1- MYʉnzmD i,ֈ=QD̼!";]욵_v%8lvkEV:nʞDheft 3{PqJ fsg+F}gHi->Bo)ޠ˔m]>/}Y~rr ^較t> Wr;[Ƀ34hDT8]Ԇe'i'Kp^ExSP;i R˄^ b:U MXE EO0{qHE?.M`!O'meG="PYN)xtxڥKQ7cS6a Ԓ$BHm1͛]#B"t@Qh{o*gy}f1(`%K#IhsLgcan(CBbp8h2*S J,C2Q&Ku6״,pFj>nkUb9GWջz<<)\L=~"w#8Z=τl>hn_lڲ>MXf)u"Vґ,W~!z-}dq#.(ž-5Aa)7t5̟ތto9Bo/|yd/L3pBœb::1'[?g6? w/YѬND|/kw29-]otP_ r~ǹ:G=仐չ)JoKN}!^FP6qE C=5D/[K`!RkAuXKu @xcdd``~ @c112BYL%bpuvAa3tdcdl'$,Ey u]q8H"諬G"BJӔx>8Tde .@!PU Gd1>tv$xU=Pժ`:ShjE|h댲67+7UCa}o}^]kCajl!"+2ZFpvMvV_ӿxkAV]J h|#/0fb/?^~s|͚.1X~VxlO\eឍ:^<l~;?y'ǙW2x{|zx:n[_$-"##R`.k5c*,p.+Wнzfak#u!_Oxl4[2<>CdTM*<+~@\G. x 7Š`!`AC͸}~ xڥSMK@ݤ_I+{ЖRyPЛzhbli %=gO =Kxn?Qłqg7 V0a̛y]1iLV=J.6᭩A\Su歅`\ U>W8*Srel7 ⑙eN=Ґ[d>SD^OA+WmiXmX+p~dfω$F^Ѵ3ݿQK!aH;荌8:)gZQzG(26|Kqe8 _HPf̉W+9Q `PW}n}Rd"|A1ωCw=Rdg'*O)ͯC8\-Ż! E8A'P,9͖eCX+HiM`!M/(27 @|xڝK@ǿwI%CNqઈ-8hp.@'?Y[ƻ5X}»{AІR|8 dLlΌt"_RzD2,}7.f<6k*;vmY:l]Q:Umxnr}gՎp{rVfuWY\52"Kꑩ1e"N邫ꃨ>I1'\6tiSQ¼z8[{үke|ȷk%Md DR m=mг'bpms!4ٟEwiKFeM.Șܘkr[y{2lr&ww&ڞ! ƪ?hs%x)[{rjSn:Q֣gF8?|(y*.%OEAD?v6-98?zTm$FA+r~ռNuRR^ ?kn~Z-Qj%!>~nT[ .cJ߷vp Z\9s4 pI|yy)e=Cz}=.I>+wtH8Bn|svQ=p DG;A u9Oð `7ª`! Io'dx:@@xcdd``eb``baV d,FYzP1n:&>! KA?H110|dꁪaM,,He`x7&,e`abM-VK-WMcXsF V0Z^"T T0i51\6 a%L.dW}P3Q |{^F&_+a|&6Fb#ܞ< J(_ױa|=l[aɬob `:xڝSJA3C( "mM$$$HP+Q-R 6b#*M ad{9@PV0 9Yb+†ah͹:)$Ģy!pEơsz1W5xly@61$'q(<`ѱӚpYsM7UCf !-QmWjBejܲƿDUrR.>tsK܈XYGQ'vhHݒwUk~ssKx8EZxՋ :U$]u;߷dVM4<~6p[/R 9QGtꔘ+5Zp t/;x65 Q ,cD_C`_`!qRjpe[gxڕ?K@Ɵ{4FXM)c;~VT0Vl!,NEp*~X{hi/{r <`pOPWVKb:^2Zja4 wn_5'\^)}=w*Tc3EĞ"=)5T9?+rd\]?V:mW} S͈)^։7TiEF<7w|ݨ!>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> tl(    6\  `} \ PKliknij, aby edytowa styl wzorca tytuBu) )  0\  ` \ Kliknij, aby edytowa style wzorca tekstu Drugi poziom Trzeci poziom Czwarty poziom Pity poziom*   a  0(\ ^ ` \ >*  0\ ^  \ @*  0\ ^ ` \ @*H  0޽h ? 3380___PPT10.0[  Projekt domy[lny}  $(  r  S X:S> S r  S $?S `   S H  0޽h ? 33___PPT10i.0[+D=' = @B +     8 (  x  0C"?   <${Sn ]Prof. Robert d'E Atkinson, General Relativity in Euclidean Terms (Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 272, Issue 1348, pp. 60-78, 02-1963). >%3        0A  6S  oHans Montanus, Jose Almeida, Alexander Gersten , Carl Brannen, Giorgio Fontana, Anthony Crabbe, Phillips V. Bradford, Richard D. Stafford, Rob van Linden, W.Nawrot  +  0S   ,http://www.euclideanrelativity.com/links.htm--3, H  0@S @Probably the first publication concerning Euclidean Relativity:AAl      s *S xOther authors:" 2 $  BS h  QYahoo's discussion group on Euclidean Relativity (Founded by Prof. J. Almeida). RRZ   00  B)  9 ,$D0B  s *D>) T 9 ,$@0H  0޽h ? 33___PPT10.@X+| Dp' = @B D+' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* D2' =%(D' =%(Dw' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* D' =A@BBB B0B%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* Dw' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* ++0+ [ ++0+ [ ++0+ [ ++0+ [ ++0+ [ +L0 (  8  08 Let us forget for a while about the current state of knowledge and try to construct a new hypothetical model of reality from the beginning 23      0o[X x  )The model should be as simple as possible*(2*3HH  0޽h ? 33___PPT10i.r$+D=' = @B +L c[P'@(  XB  0D)-- XB  0DԔ -  XB  0D> - XB   0D> - vXB   0D>/-3 2   6Ԇ[C"? Y  ,32   6[C"?y Y  ,32  6[C"?R Y  ,32  6,[C"?Yo ,32  6\[C"?YH ,32  6[C"?Y  ,32  6[C"?   ,32  6̞[C"? s  ,32  6[C"? &  ,32  6[C"? d  ,32  6[C"?  ,32 # 6[C"?  ,32 $ 6İ[C"?y  ,32 % 6|[C"?R  ,32 & 6[C"? o ,32 ' 6ȹ[C"? H ,3RB * s *D- RB , s *D 2 ( 6[C"?  ,3 - 0[c  9t 2 3 . 0[zJ  9s 2  / 08[ e  5y 2  0 0[ `  5x 2  1 0@[(- 95 2 3 4 0[(   93 2  5 0[ W c$  54 2 9 7 <[ ds2=dt2-(dx2+dy2+dz2)            ^r 9 6PH : 0P[Xh? ( 2 ; 0[ 8 Dimensions creating the reality 2 6   < 0[ cMRT: The time describes the fourth dimension The time IS the fourth dimensionHN 22333     = 0[@ In Hitherto Lorentzian Model: 2 3, p2 @ HФ>H  0޽h ?@ 33___PPT10i.B+D=' = @B + %)$q(  $XB $ 0D)-- XB $ 0DԔ -  XB $ 0D> - XB $ 0D> - vXB $ 0D>-: 2 $ 6C"? Y  ,32 $ 6C"? IK  ,32  $ 6C"?3 ?  ,32  $ 6C"? 8  ,32  $ 6C"? : "  ,32  $ 6`"C"?j `  ,32 $ 6 &C"?I [  ,32 $ 6$+C"? &  ,32 $ 6,C"? d  ,32 $ 6C"?  ,32 $ 63C"?  ,32 $ 67C"?y  ,32 $ 6;C"?R  ,3RB $ s *DK? KRB $ s *DN 2 $ 6>C"? [z ,3 $ 0$CKc 9t 2 3 $ 0GZ  9s 2  $ 0K e  5y 2  $ 0DO `  5x 2  $ 0R' e - 95 2 3 $ 0U=M 93 2   $ 0(Y W c$  54 2 2  $ 6t\C"?  q ,39 #$ <4_\ dt2=ds2+(dx2+dy2+dz2)            ^r $$ 6H %$ 0pmXh? ( 2 &$ 0s 8 Dimensions creating the reality 2 6   '$ 0x oYNew model: The time describes the fourth dimension The time IS NOT the fourth dimensionHZ 2 2333     ($ 0 In the New Euclidean Model: 2 3, p2 )$ HФ>H $ 0޽h ?)$ 33___PPT10i.B+D=' = @B +f }u((  (~ ( 6fC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&      ( <X @Postulate 1. FER is the four-dimensional Euclidean space. None of the dimensions of this space has the meaning of the time- or the space-dimension assigned in advance.V .3   _P%?+  (s *@AB`TC`T c"$67t  ( c $X?C"?_P%?+BB  ( 3 oE)BB  ( 3 on( (hB  ( C jJC"?{%bB ( 3 oC"?&bB ( 3 oC"?6%@i& ( 3 \@' Ka ,  ( 3 (,!) Kb ,  ( 3 ৤$rz& St 4  ( 3  3q Sx 4  ( 3 : Xt 4  ( 3 ط& ) Dimensions of the FER ,  $ 6B (   &(6B (   (( ( 3 輤T#  Trajectory of an observed body 4!  $  ( 3 4ä[$$>' Trajectory of an observer 4  $ 0 ( 3 Ȥ: FSpace axis of an observer s frame 4$"  H 2 ( B7rENG`HA?I)Q T~ 7r;)T~ 7r;))`T 7r;))`TC"? h2 ( C C"?] ( C TФ(_!:# Dx B  ( C L֤(x#% Dt B  ( C hܤ(% 0p"  Dt B H ( 0޽h ?( 33___PPT10i. 'UG+D=' = @B + @=(  @~ @ 6fC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&     [ @ <T Postulate 2. In the four-dimensional reality there exist bodies. The bodies move along certain trajectories, and all trajectories are allowed.   w  _P%?+ @s *@AB`TC`T c"$67 @ c $X?_P%?+ *BB @ 3 oE)BB @ 3 on( (BB @ 3 jJ{%bB  @ 3 oC"?&<B  @ # o6%@i&  @ 3 ' Ka ,   @ 3 8(,!) Kb ,   @ 3 $rz& St 4  @ 3 D3q Sx 4  @ 3 t: Xt 4  @ 3 & ) Dimensions of the FER ,  $ 6B @   &(6B @   (( @ 3 T# xTrajectory of a body ,     @ 3 D[$$>' uTrajectory of a body (   0 @ 3 %: FSpace axis of an observer s frame 4$"  H 2 @ B7rENG`HA?I)Q T~ 7r;)T~ 7r;))`T 7r;))`TC"? h2 @ C C"?] @ C |,@_!:# Dx B  @ C ,2@C"?x#% Dt B  @ C 07@% 0p"  Dt B H @ 0޽h ?@ 33___PPT10i. 'UG+D=' = @B +  DX(  D~ D 6GfC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&      D <$<V |rPostulate 3. The length of trajectory of an observer is the measure of his proper time i.e. the body s clock indicates the length of the trajectory already passed by the body in FER. V!` ,        M   _P%?+ Ds *@AB`TC`T c"$67H D C X?_P%?+BB D 3 oE)BB D 3 on( (BB D 3 jJ{%bB  D 3 oC"?&<B  D # o6%@i&  D 3 <' Ka ,   D 3 ,`(,!) Kb ,   D 3 \$rz& Gt (  D 3 ll3q Sx 4  D 3 p: Pt ,  D 3  u& ) Dimensions of the FER ,  $ 6B D   &(6B D   (( D 3 LnT# xTrajectory of a body ,     D 3 h{[$$>' uTrajectory of a body (   0 D 3 : FSpace axis of an observer s frame 4$"  H 2 D B7rENG`HA?I)Q T~ 7r;)T~ 7r;))`T 7r;))`TC"? h2 D C C"?] D C 䉡D_!:# Dx B  D C <Dx#% Dt B  D C D% 0p"  Dt B H D 0޽h ?D 33___PPT10i. 'UG+D=' = @B +  0H(  H~ H 6hsfC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&     Z H < Conclusion 1 In the FER directions interpreted by an observer as the space-dimensions  xyz  must be perpendicular to the trajectory of the observed body. The trajectory of the observed body is interpreted as the time axis of the observed body s frame  t F 4 , FL  6 u _  _P%?+ Hs *@AB`TC`T c"$67H H C X?_P%?+BB H 3 oE)BB H 3 on( (BB H 3 jJ{%<B  H # o&<B  H # o6%@i&  H 3 X' Ka ,   H 3 p(,!) Kb ,   H 3 @$rz& Gt (  H 3 ¡3q Gx (  H 3  ȡ: Pt ,  H 3 <& ) Dimensions of the FER ,  $ 6B H   &(6B H   (( H 3 8ҡT# !Trajectory of the observed body ,"   6  H 3 $ء[$$>' Trajectory of the observer (  6 8 H 3 |ޡ: HSpace axis of the observer s frame (%#  Z 2 H B7rENG`HA?I)Q T~ 7r;)T~ 7r;))`T 7r;))`T <2 H # ] H C TH_!:# pDx 2  H C (Hx#% pDt 2  H C H% 0p" z Dt :  H 0, (-  Dt 2= Dt2- Dx2n 2 3f 3f     H H 0޽h ?H 33___PPT10i. 'UG+D=' = @B + PPJ(  P~ P 6fC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&      P <Pr` Conclusion 2 The time axis of an observer is his trajectory in the FER. The directions interpreted as the space dimensions are perpendicular to the trajectory of the observed body.  $ 4     _  _P%?+ Ps *@AB`TC`T c"$67H P C X?_P%?+BB P 3 oE)BB P 3 on( (BB P 3 jJ{%<B  P # o&<B  P # o6%@i&  P 3 P' Ka ,   P 3 p(,!) Kb ,   P 3  #$rz& Gt (  P 3 '3q Gx (  P 3 ,: Pt ,  P 3 1& ) Dimensions of the FER ,  $ 6B P   &(6B P   (( P 3 t7T# !Trajectory of the observed body ,"   6  P 3 >[$$>' Trajectory of the observer (  6 8 P 3 F: HSpace axis of the observer s frame (%#  Z 2 P B7rENG`HA?I)Q T~ 7r;)T~ 7r;))`T 7r;))`T <2 P # ] P C MP_!:# pDx 2  P C QPx#% pDt 2  P C  XP% 0p" z Dt :  P 0\^ (-  Dt 2= Dt2- Dx2n 2 3f 3f     H P 0޽h ?P 33___PPT10i. 'UG+D=' = @B +     A (  ~  6xhfC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&       0n= <SUMMARY: (2    0q(. ZThe FER is an absolute space  the dimensions of FER are not observable.I 2I    0LP"  xDimensions of space and time which we are able to observe are certain directions in the FER and these directions are not stable. They are different for every pair  observer-observed body.~ 2>33  33z        0|0 6  @BWhat we perceive as a time dimension is our trajectory in the FER.JC 23 3   y  0ܗ n {What we perceive as space dimensions are directions perpendicular to the trajectory of currently observed object in the FER~| 23 3 33      H  0޽h ? 33___PPT10i. 'UG+D=' = @B + L0   < (  <~ < 6fC"?| How is the Four-dimensional Euclidean Reality (FER) constructed and why the observed picture of the FER is the four-dimensional Lorentzian space-time.&      < < @Postulate 1. FER is the four-dimensional Euclidean space. None of the dimensions of this space has the meaning of the time- or the space-dimension assigned in advance.V .3   < <໨E,    < <t   ppPostulate 3. The length of trajectory of an observer is the measure of his proper time i.e. the body s clock indicates the length of the trajectory already passed by the body in FER. L!` ,        L Z < <`ɨ  Conclusion 1 In the FER directions interpreted by an observer as the space-dimensions  xyz  must be perpendicular to the trajectory of the observed body. The trajectory of the observed body is interpreted as the time axis of the observed body s frame  t F 4 , FL  4 u [ < <ר` Postulate 2. In the four-dimensional reality there exist bodies. The bodies move along certain trajectories, and all trajectories are allowed.   w H < 0޽h ? 33___PPT10i. 'UG+D=' = @B +.  E=L4(  4 4 s ߨ0e0e #" 0ex(H   F 4 S X?n@B 4 C o@B  4 C o 6 FB !4 S jJ94 @B "4 C >  :B #4 3 >   $4 C O Ka ,  %4 C p d|5 Kb ,  &4 C  '  Gt (  '4 S   Kx ,  (4 C h  ~ t A >  )4 C \ m zFER dimensions ,   4B *4 #   4B +4 #  |  ,4 C L }8J !Trajectory of body A - observed ,"   $  K -4 C 0 LX  KTrajectory of the observer and the axis of time of his coordinate system (LJ  l   FB .4 S 3fok   /4 C   RTrajectory of body B  not observed now ,*( 3f 6  04 C Kx&  ~ t B >3f3f % 14 S #14 D -Space axis of the observer observing body A ,.,  Z   24 C *QO F ( 2 34 BnENGHI#Q q1xn-q1xn-#`Tn-#`Tv  >:2 44 3 b a H 4 0޽h ?34 33___PPT10i. +D=' = @B +  48)(  8F 8 S X?c@B 8 C o@B 8 C o 6 FB 8 S jJ9) :B  8 3 >   !8 C \D Ka ,  "8 C > d|* Kb ,  #8 C Dt '  Gt (  $8 C I8 O  Kx ,3f  %8 C N  ~ t A >  &8 C $U& m zFER dimensions ,   4B '8 #   4B (8 #  | " )8 C 8rTd TTrajectory of body A  not observed now ,+)  6 J *8 C a% LM  JTrajectory of the observer and the axis of time of his coordinate system (KI  l   FB +8 S 3fo4V  ,8 C k"  !Trajectory of body B - observed ,"  3f $   -8 C o@x&  ~ t B >3f3f % .8 S x.8q -Space axis of the observer observing body B ,., 3f Z  @B /8@ C 3f>Ah =   08 C tyK  F ( 2 18 C$^ENG}H JPQ3f }`T=SS$^}`T=SS$^PSS$^P  :2 28 3 3f3f }o 38 < 0P The direction in FER interpreted as the space dimension depends on the currently observed body (example- one observer, two bodies): Observation of body B$       H 8 0޽h ?18 33___PPT10i. +D=' = @B +  (  r  S 쏩ph     6 H@ ueIf we are observing different bodies, we perceive different directions in the FER as space dimensionsff(     H  0޽h ? 33___PPT10i.Q`(+D=' = @B +z  `$&T(  Tr T S  `}      !, Ts *@AB`TC`T c"$$D H T C X? !,HB T C 3Ԕ##6B T  #+6B T  #'6B  T  #+6B  T  L#MH)6B  TB  J&LJ&6B  TB  >)L>)  T 3 %t9' Vt1 6   T 3 )t`+ Vt2 6   T 3 T!]_# Lt (  T 3 * , sx1=x2 P    T 3 ("# v Dt 6  T 3 Hũh$-% j Dt1 D   T 3 ˩&V8( j Dt2 D  BB T 3 3>#L#<B T # >#4)<B T # >#LU&<B T # >#E4) T 3 ϩ, #z% j Dx1 D   T 3 ֩^ b% & j Dx2 D  (r T #rG&(r T 8 r# )2 T c C1ENGєHs#JQ >`TT_TD1>`TT_TD1_TD1# &2 T c CENGNH JQ `TeU^TO`TeU^TO^TO#Ut$ T 3 +#7$ \j1 8   T 3 p$Dw& \j2 8  ^ !T 6j  T S A J??"?( R J "T 0 x  wSpeed definition/limit: 2$  #T 0 dTime dilation: 2 $T0 NA ? ?d   &T 0   ;C=1 2 3H T 0޽h ?/ TT 33___PPT10i. 3F +D=' = @B +v  0(  r  S 0`%   k  6  } Since the time- and the space-dimensions are observable aspects of the same dimensions in the FER, it is natural to assume C=1 .{((3(4 R  H  0޽h ? 33___PPT10i.Rr+D=' = @B +  L0   p XY (  Xr X S  `}    X <\*  frPostulate 4: The trajectory* of photon is perpendicular to the trajectory of the body which emitted this photon. `s &3"c"&   @    U 0^ X 6m! X <) * Notions  to move along trajectory or  trajectory are, in relation to photon, conventional notions only; they are introduced temporarily in order to simplify the description of certain phenomena. They will be explained in detail in the further part of this paper2 " "   0= X <*   YPostulate 5: The trajectory* of photon is carried along the trajectory of the observer. 4Z3J  L  X <0   ~Postulate 6: In vacuum and in absence of gravitational field Dxi=Dti xG 32V  0       X <7 nPropagation of EM waves differs, in FER, from the motion of bodies. At first we have to accept the postulates:"on"   H X 0޽h ? 33___PPT10i. 3m+D=' <= @B + L0 "$\(  \x \ c $M `    \ <LSJ6 rPostulate 4: The trajectory* of photon is perpendicular to the trajectory of the body which emitted this photon. Vs &33c"&   l     C  0^ \ 6m!4 \ <b * Notions  to move along trajectory or  trajectory are, in relation to photon, conventional notions only; they are introduced temporarily in order to simplify the description of certain phenomena. They will be explained in detail in the further part of this paper2 " ". H  0- P #T \s *@AB`TC`T c"$ -t  \ c $XjJ?C"?P #T<B  \ # op<B  \ # o2!k<B  \ # o HB  \ C jJOHB \ C jJOTB \ c $f>  62 \  T.62 \  U62 \  t 62 \  4P  \ C Hgo^!  1Trajectory of a body emitting photon - observed 21H   \ C hoo'-! Xt 4   \ C to x1=x2 ^      \ C |~o} "y bt1 B    \ C  o*j 0 bt2 B    \ C ؍on#\ 'Trajectories of the observers A and B 2(%  6   6B \  g &6B \B  g  \ C XoG$;G "Resultant trajectories of photon #"6  6B \B  g ^} 6B \B  g ^} \ 3    Dx1=Dx2    6B  \  >6B !\  >H6B "\  >I #\ 3 , v Dt1 P   $\ 3 (> v Dt2 P  H \ 0޽h ? 33___PPT10i. 3m+D=' = @B + L0  ""`(  `x ` c $Ƚ `   + ` < °J6 YPostulate 5: The trajectory* of photon is carried along the trajectory of the observer. "ZX  L ^ ` 6m! ` < ˰ * Notions  to move along trajectory or  trajectory are, in relation to photon, conventional notions only; they are introduced temporarily in order to simplify the description of certain phenomena. They will be explained in detail in the further part of this paper2 " "   0- P #T `s *@AB`TC`T c"$ -t ` c $XjJ?C"?P #T<B ` # op<B  ` # o2!k<B  ` # o HB  ` C jJOHB  ` C jJOTB  ` c $f>  62 `  T.62 `  U62 `  t 62 `  4P  ` C հo^!  1Trajectory of a body emitting photon - observed 21H   ` C ڰo'-! Xt 4   ` C o x1=x2 ^      ` C o} "y bt1 B    ` C Lo*j 0 bt2 B    ` C xon#\ 'Trajectories of the observers A and B 2(%  6   6B `  g &6B `B  g  ` C $oG$;G "Resultant trajectories of photon #"6  6B `B  g ^} 6B `B  g ^} ` 3    Dx1=Dx2    6B `  >6B `  >H6B  `  >I !` 3 , v Dt1 P   "` 3 (> v Dt2 P  H ` 0޽h ? 33___PPT10i. 3m+D=' = @B + L0 !#d$(  dx d c $* `    d <-J6 Postulate 6: In vacuum and in absence of gravitational field Dxi=Dti therefore V= Dxi / Dti =1a>  0         - P #T ds *@AB`TC`T c"$ -t d c $XjJ?C"?P #T<B d # op<B  d # o2!k<B  d # o HB  d C jJOHB  d C jJOTB  d c $f>  62 d  T.62 d  U62 d  t 62 d  4P  d C @o^!  1Trajectory of a body emitting photon - observed 21H   d C Fo'-! Xt 4   d C Lo x1=x2 ^      d C So} "y bt1 B    d C Zo*j 0 bt2 B    d C `on#\ 'Trajectories of the observers A and B 2(%  6   6B d  g &6B dB  g  d C hoG$;G "Resultant trajectories of photon #"6  6B dB  g ^} 6B dB  g ^} d 3 n   Dx1=Dx2    6B d  >6B d  >H6B  d  >I !d 3  x, v Dt1 P   "d 3 t> v Dt2 P  5 #d 6Ȍ kLimits of speed of the bodies and speed of the light are equal to 1. These are two different phenomena now.2lS   H d 0޽h ? 33___PPT10i. 3m+D=' = @B +2 p h  h (  h h <x9  "From the previous slides one can see that: Already in the moment of emission, the photon must  know by which body it will be received. 0+\3 V 8X h 6Ԯ\@ ),$0 tHence:   8X1 h 6,$0 )The emission of photon must be a result of a certain interaction between two specific particles. The character of this interaction is not known yet. The photon cannot be therefore emitted somewhere into empty space and move like a particle until it reaches any random body and is absorbed by it. (*=T * 8X h 6T< ,$0 gThe idea of trajectory and motion of a photon must be a conventional notion, because we are only able to know the points of emission and absorption of the photon. We are not able to examine the route of the photon or what happens with it between the emission and absorption, because the photon can interact only with the body towards which it has been sent. (h2 % A 8XX  h 6ڲ ,$0 All particles of the Universe must be somehow informed about the existence of other particles, because already in the moment of the photon s emission, the place and the particle which the photon will hit is known, regardless of the time needed for it. b /*   8XH h 0޽h ? 33jb___PPT10B.`nq+^,mDD6 ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-6B'blinds(horizontal)*<3<*hD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-6B'blinds(horizontal)*<3<*hD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-6B'blinds(horizontal)*<3<*hD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =-6B'blinds(horizontal)*<3<* h++0+h ++0+h ++0+h ++0+ h +  P(  r  S 5   H  0޽h ? 33___PPT10i.R!+D=' = @B +  @y(  r  S } `}     <Ԣ  [We were talking about the motion of the bodies in FER. If we are talking about motion we should define a time according to which this motion will be described. In FER, the time will be called the SUPERTIME The SUPERTIME differs from the time known from SRT   3 3.  3  3  3   3  3  3    3     8XH  0޽h ? 33___PPT10i.z+D=' = @B +y  ` (  x  c $0 `}   h  < D<4___PPT9 The main property of THE SUPERTIME would be the ordering of events along the trajectory in FER  the subsequent positions on the trajectory should correspond to the subsequent values of THE SUPERTIME. THE SUPERTIME should flow identically (i.e. with the same speed) for all photons and bodies, independently of their relative motion. THE SUPERTIME must include the fact that the time in the bodies frames depends on their relative motion and the time in the photon s frame must be equal to zero. x O 5 F <  8XH  0޽h ? 33___PPT10i.z+D=' = @B +1   H @ ` (  X  0o@ x  c $dz `}   ^  6j  S A  ,??"?X ,   <ɳ, 6It means that THE SUPERTIME is not an additional dimension in the sense of the well-known space-time dimensions. It is a value composed of the time- and space dimensions. Such a definition of THE SUPERTIME changes the understanding of the time flow. Up to now, variability of events was related only to the changing of the body s position along the time dimension. Now the variability is determined by the change of its position in FER  along the time dimension (the proper time of the observed body) and along the space dimensions. ! 3- 33 3F3,3^  ]     0x~ tbThe conditions from the previous slide are satisfied by the following formula, where T - SUPERTIMEc 2c   H  0޽h ? 33___PPT10i.z+D=' = @B + p`(  x  <0j fSince the flow of time in the frame of the body  dt  and the change of the distance  dr  treated separately are relative quantities and depend on the choice of the frame, then their composition, equal to dT2=dt 2+dr2 , is an absolute quantity and does not depend on the choice of the frame. Therefore, THE SUPERTIME can characterize the body itself, independently from any observer. We can write the SUPERTINE in a comlex form:    3: O-3  %    S  ^  6  j  S A  U??"?kyK,  U^  6j  S A W??"?   WH  0޽h ? 33___PPT10i.]03+D=' = @B +1  H @ (  X  0oX 0h `  c $A R??/ R`  c $A ??w `   c $A h??l;D  h`   c $A f?? &  f  0L x( ( 2W  0 hn ?If we describe the wave in FER as a function of the SUPERTIME:@ 2@~    0xp RWhere  2`  c $A i??LD  i  0 5And 2  0T֩  cWe will obtain: 2l  0 N    0   SUA simple wawe in FER is described in Lorentzian space-time as an wave function V(2V3   H  0޽h ? 33___PPT10i.^&+D=' = @B +}  $(  r  S K `}   r  S `  H  0޽h ? 33___PPT10i.f+D=' = @B +sxXMlUi\(a)7"'HEAm*4JC@$f#{ۺ>Pzqh%"qB*$B8@۷z7&c=<{o|zi`c ).WxCt%CԇQEqٿ⟫ko,./CH:g nxXA;a94f/{O?܍~?¬<\ǰ볿VĹ=NS, ?J7{go[8w08)0Fy`BICR`x?DŽ2d'ӓqt~1[vvr>+dg}r8;drdNEa4^!w ,u ⑎$3L&~etٚ;#YCU0YѧÆ.mV l_s7=5-ƕq7xٲ-4fHMW <Zbt \ZӔh,Ov|HŠ ,$̝ڥ=XD]kiKCTc~vI^fG|΋iK;^m{ ?}-MŤ V]5Y 2cBX.}t(+rGScm04 *2-%_ /y4>7A9?bA "}L0h Yl$[/ 3m7^oo1NWˎY^|(L!#./O`}&:D@j'?YOа[OڋKmJ_ڕOig)8% xKlEͬk7E2" F I+nU{m[ 9p㄄ԊD^*q .)pBB"TzL>_4y;o{;;bw>ZHkzǪ -ZRQ&( J!(@H@б8bX5_l[yprdVUO={Ly◛x<.ԥUG~Q :ԳǸow1߄ovj@Us-ߎU9ߊ'PFy@|kw}~o[/l%4{)M9 omo Z[Ӆyk7 قK7YEk> GC%* 9dm[~>gOj]9,\]I|9i54]g4c| ۇAZ03fL"Kk4j 6fcQ@2;K}3'qeɒxςAwf8Oѹ2gwCtLn*=lɽS_s݌}}>ʴm++kwϨ==tWO&#Ț z@=!>Ipkmnm!Wq53 f*'*0uq zX|W; ),*EL8D^&;@8_bmC@DѦ]L@ A[#n>E~D╈+λ\B%s >=x5.w#Uyx#Wfiv,:~.A,CreY)"6(ŘUt(9>iR7\8?ƏnJ؍W11=ןNpRxga7t? (QruwQwtmv;rF:Svnz-q^7T}71j}~=F|8r^m8Tyt:z Q?[~AWrɡNqbo K=Sys c~x{WP]?svw&LqV xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH(`V#3HV30d'2b`bDD`;PtGC y'bOzC? rB x}Vh9020-2qR i=yy Ei% z <@)`Ē<n 3fbX03P~p;p5GBqɌ\\B) B! ܂LF@9.6[fYFtP D Ra5f`ejTif,a`jRG5!XgK<`=U*+C9=c'(Sl@C~-z<2<xXkA~3j"-ԋ" U+`l0b6Y-EēR"*I!xѓ"QffvMꦍHK^d{2$3Z^ޜ |4-4BNhSf ;^ɒH 0C)rwS'̠:S4ot]\0$>FT`>Ț5⪯)q' ]56:Ϫ&c%HdyH5OXG%7@U?[ u!F&}0g O RJ;yG0ؐn .&Cp_v8Te1۔;uէL`6yQ;UV -@9HuP#,\{A0y Y/O`- >L<#%R{nu\`7ưh?>7Q4[G bz*kMl_ yJClXrYG9'rEMemw'{,So :8+g^I;kEqk جx^dG1Ct[Nڳ ^?c Jxqޭ:ruʖꤏچ PHB{ltn筃c'!O~F4am{ʜW7fP\oST¶%Ndtܱwu ĜD:%U×wGa6D_cL3 4n_r٠)Ԃ'@[Ek~]hG͐K3h ۂm̑cfE5^iƯ ^r8Xiq&Wm ~Ӹcz@֐폿}^# 9q|5#GMcp:DGqkW_`R/qsN~SRs׵ߋy?ȽWUE].1jA~/ gMf"xXMlWcuۤ  hqJR\CRp*d WΏiZ"NT VRKsUzj7^h3zcAIz7ofv盙o'6?s&:ƘsA`+|ѧE+&!(]*m7 p9>?t}S6?s5b;hp5tl}g`8,? NrO& ĝ=kϖ9|Lñpʦz?C绣8`I5ck0 Oe1ksO4Fۈ펗ވ9|@U~i1xgn{ xܩ:# ./U>KT;t6o{NOj6{"@5"Ftu{::[t8/@sIb+'q[,yZz1c6c!{]3t#{/6Ul'ʿٜ+Oq/x }! RqvE>$G9$p˱ lf?cX>S4kikgAF4?#7Qm8?d}R(+}բݖ/9'QxT[Ih9̖s3l rGl Լ}զqF3/9^BX$@oēg]=5@7L+=&g+:bl?xɼXƾ7#~mTehdeq}0Of`KYi\(mP{[}J:n6r,Ȧf_Hn4ʛ]m24çt.+Ŵu+w JGpV ` yJC;q@ȼ]@ke֋ 8!4q?/}w`@N;Wta/EWq*VUW6;+ۿEg*3vWcnߢ#:םZ>t쿍>Q}ZBzdxKLAlg*Y=EI0zI)m-֍19x7DaLA<\KԘxP5yeu5of{;s_ޙ48dsPczF\Y6\V ~)Pb?Fpm.1R|Z'6ϝ >nI}!Hw>u @O3@Y;ko׋q7 1;gK*9ᏼĘ@'l0wT`o ~/+.3ltҫr>X.ѕd_ \g_PsY o:_,xLs*?`/B-0NVcG?@~(֬sBOV PXC:>v0,%awcnov6_j_ɀ8A NJ: nS[HqD({x҃1k&ѳc'1F5ZD8pzBv}7 ?Ώ\h8j  `|Sz]jǗ-귓=n36 s/QWy*q$$W+iHoC<.ă.ǥS9V'rw`A嵿y_t96i75)gџ"~-:?p/??뗨+3./o|_B"}:5ǝyW$c9D 7b^wF#OO?[(_/o.w}s9IȻ&v |JBHX퉜Lēw#T$@r<2Nw6Cבf>d%}FBǔmJ&t) rQj .D8Eɤ^n'fI?8c7LJkT8 SOQUooTBCGs/a?ʹ?~iY>"xKoEpv?;?a;/dFQZH*8TI@:jPm7W9E) #2R(JQZUxZh@˷mϧwfgv1;;W{z<,(P/C'ibڋUT9>H,LSX9L9}F4?彺0m@8$(AݖRd:Xi>0f>!!!WKUfogeЏ2xw\NRHJbǞNUm3 H#?G 1^lDN9@'wn5u ƙ]&:6ѷz.VR`sSSY;\u)n)i5 "tٲb7msxnCx@h1?À9(!A WsU_5;uk_xfؾbxk#Ex oqVv6*'{c] ,FDu/Ǜ nWqa ~lc&e|mq7wqC%%!<(Ԡ_ >?{@xo/O{?V.c xYMlE~3'_KHJAJ)EOU9ĭS؊Qn6.PSJCʹ\@(h{BVfvƮ֖)I{޼k Tk!w1|bZըJ÷֣EP§ _ l+< \{!|wz: bSarmtϘuiXE h"!poZс|_Nk(ׄshYxJg ~o_c (@;+3 u*[?cFjG0MuSWqZkDaltG1&hRB >J)ѶP,L4 )\WH = cS i;}>𽸱; f,AJ[."=(f(җn/ ɷ"fD)caf8;N8qjD54]gҺ/J4;01~9y ba "_If(MQ10R xxa6]%~)JB#YMYX:"4;$rzb.~7@aaYϫT }3ddrd,_H<XorޛjHw?ur7ؿ!p^~7ޏp߾Ԇ'AcN'ZB/q6Ե?ɓ' {L'Nly~>3ry6gcLνϲ+`j@Ͱn]PucРğ6br=AzVx1"n{o{owM-o{ٳ{fm- CrlT꿡S_hq~"g/8Ξ)|ڙ^V~9S\MzxT~u/۞ya1Ssn^gky3^G",t>di#}le!ߘռ^}XS|OMGQ0ZWk4m]C$eA$ydq~`^*Ly< үIAsʼyE>7ZB34&E+v .بv!Lef1Hih51DV1U]肸˜HMt!.ԍiM.j:=7y f`L.=s=Օ+=dn1Q<ԖfؤжnH_ B@)Wߩއ+_XfxԘwhQ2gV}ie' 0,̻dnQI.qQvsN Uqk~r~*yjEq ?6G/Q*9e7r?b*U7CA:۝0cv~qGV*t*E~9i;7czh`|f}7`~m}ڿH v &FZ!J,qQ?}zu4ʺƘ.k|0g 0M\{3hv^0~ׂKI8^N p§_CEWRӭxݰ&eo2(0*}/D#.}Rd/Z5 cqjyI-T'2,iI.*LipGRaᎻM6}w>6amwFj;&k̶ltkPx&eqPgt"ԝGɧ7'jkWar BN=V|E5_s[vi%d/A9 `4}46^ .Px2eDqOߒw*>Re?uq|ѫH%*% /uޞh*q\8+'߂`IL/*q d5-wD"ECc@*t]"zBᑱH*LHgi2m'>Y=E/Mԟ$&!4G Sci_'|M·&"|ppp]9ӄgx/LyR}Y+=of~[k͓KΛZzr7Ft77-M͸n9P>xWMLA~3[h7I#4M.KZöKo$ 1fL<`@B<<$ h z,mS~mv~{3ڵta2pH$+?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#%&'()*+-./012356789:;@Root EntrydO)PicturesCurrent User4SummaryInformation($PowerPoint Document( 2DocumentSummaryInformation8,