User:Tom Allen/ta/AddendumX00P04

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GX00P0400D.jpg


NB. ... (1) ...

gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)

vSgDd2=:''([-@([(0{])@E1cn yRef@([hkxX00B zfxc"_ 1)),:@(S03yH{]))]

Initx =:  1.03 , 0.5p1 , 0.25p1 , 0p1   "_
Initdx=: (0    , 0     , 0.01   , 0.0106"_)*%@InitInt=:8"_

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

NB. 'ds' is defined by the first interval of the integration as in flat spacetime.

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=:(0,600"_)*InitInt
pdDQ     =:vSgD@vS''

NB. ... (2) continuation ...

vSgDd2=:''([-@([(0 0 0"_,(<0 3){])@E1cn yRef@([hkxX00B zfxc"_ 1)),:@(S03yH{]))]

vS00yL   =:((0 1 2{])@(S00yL{]),0:)@(4634{])@(pdDQ"_)
vS01dyL  =:0,0,0,0:
vS02d1L  =:0 0 0 1"_
vS06ds   =:Initds
vS07count=:(0,600"_)*InitInt
pdDF     =:vSgD@vS''

NB. ... (3) continuation ...

vSgDd2=:''([-@([(0 0 0"_,(<0 3){])@E1cn yRef@([hkxX00B zfxc"_ 1)),:@(S03yH{]))]

vS00yL   =:((0 1 2{])@(S00yL{]),0:)@(4634{])@(pdDQ"_)
vS01dyL  =:0,0,0,0:
vS02d1L  =:0 0 0 1"_
vS06ds   =:Initds
vS07count=:(0,3000"_)*InitInt
pdDT     =:vSgD@vS''

pdDQ arrayPut   'pdDQ'
     arrayClose 'pdDQ'

pdDF arrayPut   'pdDF'
     arrayClose 'pdDF'

pdDT arrayPut   'pdDT'
     arrayClose 'pdDT'


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

                arrayOpen  'pdDQ'
pdDQ=:04801 8 4 arrayGet   'pdDQ'   NB. ... shape required ...
                arrayClose 'pdDQ'

                arrayOpen  'pdDF'
pdDF=:04801 8 4 arrayGet   'pdDF'   NB. ... shape required ...
                arrayClose 'pdDF'

                arrayOpen  'pdDT'
pdDT=:24001 8 4 arrayGet   'pdDT'   NB. ... shape required ...
                arrayClose 'pdDT'


load 'plot'

pd 'reset'

pd ((1.03*cos@]"0);1.03*sin@]"0) pTsteps _ 0p1 2p1 160

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(4635"_){]) pdDQ

pd 'aspect 1'
pd 'pdf'
pd 'show'


... path of electromagnetic wave (blue) ...
... a geodesic once around from fixed point (red) ...


JX00P0400G.jpg


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

NB. ... space coordinates start/end geodesic (fixed point) ...
   
   9!:11 [4

   ((2^_44)qtsz]) (0 1 2{]) {.    (0{]) pdDQ
0.7283 0.7283 0
   ((2^_44)qtsz]) (0 1 2{]) {. (4634{]) pdDQ
0.7285 0.7286 0

   9!:11 [6


... (2) continuation ...


load 'plot'

pd 'reset'

pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(0{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDQ
pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(1{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDQ
pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(2{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDQ
pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(3{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDQ

pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(0{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDF
pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(1{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDF
pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(2{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDF
pd (((S06ds{])*i.@>:@(S0700nmbr{]))@{:;(3{])@(0|:])@:((S00yL{])"2)) (i.@(4635"_){]) pdDF

pd 'aspect 1'
pd 'pdf'
pd 'show'


... spacetime coordinates of geodesic ...
... and ...
... spacetime coordinates of fixed point ...


JX00P0401G.jpg
... plotted against length ...


... (3) continuation ...


load 'plot'

pd 'reset'

gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)

Initx =:  1.03 , 0.5p1 , 0.25p1 , 0p1   "_
Initdx=: (0    , 0     , 0.01   , 0.0106"_)*%@InitInt=:8"_

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

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

pdPrds =:(Initds*i.@>:@(S0700nmbr{]))@{:
pdPrtim=:(3{])@(S00yL{])"2
pdPrdiv=:''([-@(3{])"1@E1cn yRef@([hkxX00B zfxc"_ 1))(S00yL{])"2

pd (}:@pdPrds;      }:@(pdPrtim-pdPrds)       ) (i.@(21851"_){]) pdDT
pd (}:@pdPrds;(2-~/\])@(pdPrtim-pdPrds)%Initds) (i.@(21851"_){]) pdDT
pd (}:@pdPrds;      }:@(pdPrdiv       )       ) (i.@(21851"_){]) pdDT

pd 'aspect 1'
pd 'pdf'
pd 'show'


... for 2 cycles at fixed point ...
...
... 'elapsed time minus flat time' (blue) ...
... derivative of 'elapsed time minus flat time' (red) ...
... divergence of time (green) ...


JX00P0402G.jpg
... plotted against length ...


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

NB. ... NOTE: for this energy distribution ...

   9!:11 [5

   4p1
12.566
   (3{])@{.@(21849{])@(pdDT"_)''    NB. ... 2 cycles ...
12.566

   9!:11 [6


load 'plot'

pd 'reset'

gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)

Initx =:  1.03 , 0.5p1 , 0.25p1 , 0p1   "_
Initdx=: (0    , 0     , 0.01   , 0.0106"_)*%@InitInt=:8"_

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

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

pdPrds =:(Initds*i.@>:@(S0700nmbr{]))@{:
pdPrtim=:(3{])@(S00yL{])"2
pdPrdiv=:''([-@(3{])"1@E1cn yRef@([hkxX00B zfxc"_ 1))(S00yL{])"2

pd (}:@pdPrds;      }:@(pdPrtim-pdPrds)       ) (i.@(22907"_){]) pdDT
pd (}:@pdPrds;(2-~/\])@(pdPrtim-pdPrds)%Initds) (i.@(22907"_){]) pdDT
pd (}:@pdPrds;      }:@(pdPrdiv       )       ) (i.@(22907"_){]) pdDT

pd 'aspect 1'
pd 'pdf'
pd 'show'


... at fixed point ...
...
... 'elapsed time minus flat time' (blue) ...
... derivative of 'elapsed time minus flat time' (red) ...
... divergence of time (green) ...


JX00P0403F.jpg
... plotted against length ...


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

NB. ... NOTE: for this energy distribution ...

   9!:11 [6

NB. ... the length of the path around for electromagnetic wave in 3-dimensional space ...

   4p1*1.03
12.9434

NB. ... the time of the path around for electromagnetic wave measured at fixed point ...

   (3{])@{.@(22905{])@(pdDT"_)''
12.9434

   9!:11 [4

NB. ... the velocity of electromagnetic wave measured at fixed point ...
NB. ... (the length in 4-dimensional spacetime is zero) ...

   ((4p1*1.03"_)%(3{])@{.@(22905{])@(pdDT"_))''
1

   9!:11 [6



Download: File:LX00P0400D.txt