User:Tom Allen/ta/AddendumX01P05

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zS0=:,:@(0.23 1 2 8 1 1 12 _12 0"_)

vSgDd2=:zS0([-@([(0{])@E1cn yRef@hkyX01B),:@(S03yH{]))]

Initx =:  0.960 , 0.5p1 , (0.25p1%12"_) , 0p1  "_
Initdx=: (0     , 0     ,  0.001        , 0.038"_)*%@InitInt=:1"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,120000"_)*InitInt
pdD0960  =:vSgD@vS''

pdD0960 arrayPut   'pdD0960'
        arrayClose 'pdD0960'


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

                    arrayOpen  'pdD0960'
pdD0960=:120001 8 4 arrayGet   'pdD0960'   NB. ... shape required ...
                    arrayClose 'pdD0960'


load 'plot'

pd 'reset'

pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((105000+i.@(10260"_)){]) pdD0960    NB. ... for this geodesic cy2 is zero ...

pd 'show'


... see also JX00P0304C.jpg (the same geodesic) ...


JX01P0500D.jpg


...
...
...


zS0=:,:@(0.23 1 2 8 1 1 12 _12 0"_)

vSgDd2=:zS0([-@([(0{])@E1cn yRef@hkyX01B),:@(S03yH{]))]

Initx =:  0.965 , 0.5p1 , (0.25p1%12"_) , 0p1  "_
Initdx=: (0     , 0     ,  0.001        , 0.038"_)*%@InitInt=:128"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,10000"_)*InitInt
pdDJ     =:vSgD@vS''

pdDJ arrayPut   'pdDJ'
     arrayClose 'pdDJ'

Initx =:  0.960 , 0.5p1 , (0.25p1%12"_) , 0p1  "_
Initdx=: (0     , 0     ,  0.001        , 0.038"_)*%@InitInt=:128"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,10000"_)*InitInt
pdDK     =:vSgD@vS''

pdDK arrayPut   'pdDK'
     arrayClose 'pdDK'


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

                  arrayOpen  'pdDJ'
pdDJ=:1280001 8 4 arrayGet   'pdDJ'   NB. ... shape required ...
                  arrayClose 'pdDJ'

                  arrayOpen  'pdDK'
pdDK=:1280001 8 4 arrayGet   'pdDK'   NB. ... shape required ...
                  arrayClose 'pdDK'


load 'plot'

pd 'reset'

pd ((0.965*cos@]"0);0.965*sin@]"0) pTsteps _ 0p1 0.03125p1 160
pd ((0.960*cos@]"0);0.960*sin@]"0) pTsteps _ 0p1 0.03125p1 160

pd (cy0"1;cy1"1) (S00yL{])"2 pdDJ    NB. ... for this geodesic cy2 is zero ...
pd (cy0"1;cy1"1) (S00yL{])"2 pdDK    NB. ... for this geodesic cy2 is zero ...

pd 'pdf'


JX01P0501F.jpg


... points on these geodesics come into close proximity to each other in spacetime ...


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

NB. ... points on geodesics when the time is the same ...

   9!:11 [8

   {.@{: ((1276613+i.@(778"_)){]) ((2^_44)qtsz]) pdDJ
0.94199028 0.062191526 0 430.59437
   {.@{: ((1272500+i.@(774"_)){]) ((2^_44)qtsz]) pdDK
0.94975104 0.065169016 0 430.59445
   
   {.@{: ((1277390+i.@(423"_)){]) ((2^_44)qtsz]) pdDJ
0.94620582 0.065273637 0 430.7254
   {.@{: ((1273273+i.@(421"_)){]) ((2^_44)qtsz]) pdDK
0.94715929 0.062160414 0 430.72556


load 'plot'

pd 'reset'

pd (cy0"1;cy1"1) (S00yL{])"2 ((1276613+i.@(778"_)){]) pdDJ    NB. ... blue  ...
pd (cy0"1;cy1"1) (S00yL{])"2 ((1277390+i.@(423"_)){]) pdDJ    NB. ... red   ...
pd (cy0"1;cy1"1) (S00yL{])"2 ((1277812+i.@(777"_)){]) pdDJ    NB. ... green ...

pd (cy0"1;cy1"1) (S00yL{])"2 ((1272500+i.@(774"_)){]) pdDK    NB. ... purple     ...
pd (cy0"1;cy1"1) (S00yL{])"2 ((1273273+i.@(421"_)){]) pdDK    NB. ... pink       ...
pd (cy0"1;cy1"1) (S00yL{])"2 ((1273693+i.@(775"_)){]) pdDK    NB. ... dark green ...

pd 'pdf'


... pdDJ moves from blue -> red -> green ...
... pdDK moves from purple -> pink -> dark green ...


JX01P0502G.jpg
... geodesics ...


load 'plot'

pd 'reset'

incy0=:(2-~/\])@:(cy0"1)
incy1=:(2-~/\])@:(cy1"1)
incy2=:(2-~/\])@:(cy2"1)
incy3=:(2-~/\])@:(cy3"1)
veloc=:(((incy0^2:)+incy1^2:)^0.5"_)%incy3

pd (}:@:(cy3"1);veloc) (S00yL{])"2 ((1276613+i.@(778"_)){]) pdDJ
pd (}:@:(cy3"1);veloc) (S00yL{])"2 ((1277390+i.@(423"_)){]) pdDJ
pd (}:@:(cy3"1);veloc) (S00yL{])"2 ((1277812+i.@(777"_)){]) pdDJ

pd (}:@:(cy3"1);veloc) (S00yL{])"2 ((1272500+i.@(774"_)){]) pdDK
pd (}:@:(cy3"1);veloc) (S00yL{])"2 ((1273273+i.@(421"_)){]) pdDK
pd (}:@:(cy3"1);veloc) (S00yL{])"2 ((1273693+i.@(775"_)){]) pdDK

pd 'pdf'


JX01P0503D.jpg
... velocity along geodesics as a fraction of the velocity of electromagnetic waves ...


... for this model ...
...
... neutral particles and particles charged positive and particles charged negative ...
... are ...
... in an ionized plasma ...
... affected by the gravitational field in the same way ...


... in addition ...
...
... particles charged positive and particles charged negative ...
... move to establish ...
... at every point in spacetime ...
... the charge distribution and the rate of change of the charge distribution ...


load 'plot'

pd 'reset'

zS0=:,:@(0.23 1 2 8 1 1 12 _12 0"_)

pd (zS0(cy3"_ 1;[-@((   3){])"1@JEMcn   yRef@hkyX01B)]) (S00yL{])"2 ((1276613+i.@(1976"_)){]) pdDJ
pd (zS0(cy3"_ 1;[-@((<3 3){])"2@JEMcndn yRef@hkyX01B)]) (S00yL{])"2 ((1276613+i.@(1976"_)){]) pdDJ

pd 'pdf'


JX01P0504D.jpg
... charge and rate of change of charge along geodesic (pdDJ) ...


load 'plot'

pd 'reset'

zS0=:,:@(0.23 1 2 8 1 1 12 _12 0"_)

pd (zS0(cy3"_ 1;[-@((   3){])"1@JEMcn   yRef@hkyX01B)]) (S00yL{])"2 ((1272500+i.@(1968"_)){]) pdDK
pd (zS0(cy3"_ 1;[-@((<3 3){])"2@JEMcndn yRef@hkyX01B)]) (S00yL{])"2 ((1272500+i.@(1968"_)){]) pdDK

pd 'pdf'


JX01P0505D.jpg
... charge and rate of change of charge along geodesic (pdDK) ...