User:Tom Allen/ta/AddendumX02P01

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GX02P0100C.jpg


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   mtA=:(vZ0([Ocndc       yRef@hkyX02A)])                                 ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0(0|:])@([:(vZ0([(0{])@Ocn       yRef@hkyX02A),:@])D.1])"_ 1]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_14)qteq[;])"2 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(vZ0([Ocndcdc     yRef@hkyX02A)])                                 ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0(0|:])@([:(vZ0([(0{])@Ocndc     yRef@hkyX02A),:@])D.1])"_ 1]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_12)qteq[;])"3 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(vZ0([Ocndcdcdc   yRef@hkyX02A)])                                 ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0(0|:])@([:(vZ0([(0{])@Ocndcdc   yRef@hkyX02A),:@])D.1])"_ 1]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_11)qteq[;])"4 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(vZ0([Ocndcdcdcdc yRef@hkyX02A)])                                 ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0(0|:])@([:(vZ0([(0{])@Ocndcdcdc yRef@hkyX02A),:@])D.1])"_ 1]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''

   mtA (((2^_44);2^_07)qteq[;])"5 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0101C.jpg


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 51,_ 0.4p1 0.6p1 51,_ 0 2p1 51,:_ 0 2p1 51"_

   mtA=:(vZ0([Ocndc       zRef@hkyX02A)])                                                         ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0([(0|:])@([:(vZ0([(0{])@Ocn       zRef@([hkyX02A vZyc"_ 1)),:@])D.1])"_ 1 vZzc"_ 1)]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
  
   mtA (((2^_44);2^_12)qteq[;])"2 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(vZ0([Ocndcdc     zRef@hkyX02A)])                                                         ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0([(0|:])@([:(vZ0([(0{])@Ocndc     zRef@([hkyX02A vZyc"_ 1)),:@])D.1])"_ 1 vZzc"_ 1)]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   
   mtA (((2^_44);2^_10)qteq[;])"3 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(vZ0([Ocndcdcdc   zRef@hkyX02A)])                                                         ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0([(0|:])@([:(vZ0([(0{])@Ocndcdc   zRef@([hkyX02A vZyc"_ 1)),:@])D.1])"_ 1 vZzc"_ 1)]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   
   mtA (((2^_44);2^_07)qteq[;])"4 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   mtA=:(vZ0([Ocndcdcdcdc zRef@hkyX02A)])                                                         ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   mtB=:(vZ0([(0|:])@([:(vZ0([(0{])@Ocndcdcdc zRef@([hkyX02A vZyc"_ 1)),:@])D.1])"_ 1 vZzc"_ 1)]) ((2^_44)qtsz])@:(zfyc"1)@((0;50"_)pTRandom xCpts)''
   
   mtA (((2^_44);2^_07)qteq[;])"5 mtB
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0102D.jpg


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_

   *./^:3"3 (0=]) (vZ0([ch2k       zRef@hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   *./^:4"4 (0=]) (vZ0([ch2kdc     zRef@hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   *./^:5"5 (0=]) (vZ0([ch2kdcdc   zRef@hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   *./^:6"6 (0=]) (vZ0([ch2kdcdcdc zRef@hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0103C.jpg


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_

   (vZ0([(([Ocn zRef)(((2^_44);2^_44)qteq[;])"1 zdy smx"2 1[Ocn yRef)hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
   
   (vZ0([(([Ocn yRef)(((2^_44);2^_44)qteq[;])"1 ydz smx"2 1[Ocn zRef)hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0104D.jpg


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_
   
NB. ... R is a tensor ...

   vA =:[R zRef
   vB0=:((0|:[)smx])"2 5
   vB1=:((0|:[)smx])"2 5
   vB2=:((0|:[)smx])"2 5
   vB3=:((0|:[)smx])"2 5
   vB4=:((   [)smx])"2 5
   vB =:[(zdy vB4 ydz vB3 ydz vB2 ydz vB1 ydz vB0 R)yRef

   (vZ0([(vA(((2^_44);2^_36)qteq[;])"5 vB)hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


GX02P0105C.jpg


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_

NB. ... conservation of energy (y-coordinates) ...

   (0=]) ((2^_44)qtsz]) +/@((<0 1)|:])"2 (vZ0([Ocndc yRef@hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

NB. ... conservation (z-coordinates) ...
NB. ... (noting also that the Christoffel symbols are zero) ...

   (0=]) ((2^_44)qtsz]) +/@((<0 1)|:])"2 (vZ0([Ocndc zRef@hkyX02A)]) zfyc"1@((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


... BUT ...
...
... in y-coordinates the tensors for lowering and raising indices on tensors ...
... are ...
... those for Cartesian coordinates in an inertial reference frame ...


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_

   (vZ0([(mcv,mcn)yRef@hkyX02A)]) zfyc"1@((0;1"_)pTRandom xCpts)''
1 0 0  0
0 1 0  0
0 0 1  0
0 0 0 _1

1 0 0  0
0 1 0  0
0 0 1  0
0 0 0 _1


... and ...
...
... in z-coordinates the tensors for lowering and raising indices on tensors ...
... are not ...
... those for Cartesian coordinates in an inertial reference frame ...


NB. ... execute (ijx) ...

   vZ0=:1 1 2 8 1 1 8 _8 0 0,:_0.2 1"_

   xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_

   (vZ0([(mcv,mcn)zRef@hkyX02A)]) zfyc"1@((0;1"_)pTRandom xCpts)''
   1 0 0  _0.2
   0 1 0     0
   0 0 1     0
_0.2 0 0 _0.96

0.96 0 0  _0.2
   0 1 0     0
   0 0 1     0
_0.2 0 0    _1


... so ...
...
... y-coordinates must be used for the energy packet in motion along the y0-axis (special relativity) ...
...
... the energy flow along the y0-axis takes into account the change in energy with motion along the y0-axis (motion is energy/mass) ...
... (so that energy is conserved the rate of change of the energy density matches the energy flow) ...



... resume AddendumW01/AddendumX01 ...



GX02P0106D.jpg



Download: File:LX02P0100C.txt
Download: File:LX02P0101C.txt
Download: File:LX02P0102D.txt
Download: File:LX02P0103C.txt
Download: File:LX02P0104D.txt
Download: File:LX02P0105C.txt
Download: File:LX02P0106D.txt