User:Tom Allen/TensorExperimentsZ33

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...

... ADDENDUM ...

...


...

... the scheme for this model ...

...


...

... NOTE 1 ...

...


GTEZ3300C.jpg


...

... NOTE 2 ...

...


GTEZ3301C.jpg


...

... NOTE 3 ...

...


GTEZ3302D.jpg


...

... plot a geodesic with increasing accuracy ...

...


GTEZ3303C.jpg 


NB. ... compare with TensorExperimentsZ31 ...

gXm0All=. 1  _0.02  _  0"_
gXm1All=. 1  _0.02  1  1"_


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(2"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*2"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDA=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(4"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*4"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDB=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(8"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*8"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDC=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(16"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*16"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDD=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(32"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*32"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDE=:vSgD@vS''


pdDA      arrayPut   'pdDA'
          arrayClose 'pdDA'
pdDB      arrayPut   'pdDB'
          arrayClose 'pdDB'
pdDC      arrayPut   'pdDC'
          arrayClose 'pdDC'
pdDD      arrayPut   'pdDD'
          arrayClose 'pdDD'
pdDE      arrayPut   'pdDE'
          arrayClose 'pdDE'



NB. ... establish arrays if necessary ...

                 arrayOpen  'pdDA'
pdDA=: 18001 8 4 arrayGet   'pdDA'   NB. ... shape required ...
                 arrayClose 'pdDA'

                 arrayOpen  'pdDB'
pdDB=: 36001 8 4 arrayGet   'pdDB'   NB. ... shape required ...
                 arrayClose 'pdDB'

                 arrayOpen  'pdDC'
pdDC=: 72001 8 4 arrayGet   'pdDC'   NB. ... shape required ...
                 arrayClose 'pdDC'

                 arrayOpen  'pdDD'
pdDD=:144001 8 4 arrayGet   'pdDD'   NB. ... shape required ...
                 arrayClose 'pdDD'

                 arrayOpen  'pdDE'
pdDE=:288001 8 4 arrayGet   'pdDE'   NB. ... shape required ...
                 arrayClose 'pdDE'



load 'plot'

pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDA
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDB
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDC
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDD
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDE

pd 'pdf'
pd 'show'


Zgraphic3300.jpg
... geodesic ... 


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

NB. ... path in n0/n1 plane ...

   *./ (0=]) cn2"1@:((S00xL{])"2) pdDE
1

NB. ... time increases continually (a real path in spacetime) ...

   *./@(0<])@(2-~/\])@:(cn3@(S00xL{])"2) pdDE
1


...

... additional precision ...

... 


NB. ... compare with TensorExperimentsZ31 ...

gXm0All=. 1  _0.02  _  0"_
gXm1All=. 1  _0.02  1  1"_


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(32"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*32"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDF=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(64"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*64"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDG=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0   "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(128"_)

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

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*128"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDH=:vSgD@vS''


pdDF      arrayPut   'pdDF'
          arrayClose 'pdDF'
pdDG      arrayPut   'pdDG'
          arrayClose 'pdDG'
pdDH      arrayPut   'pdDH'
          arrayClose 'pdDH'



NB. ... establish arrays if necessary ...

                  arrayOpen  'pdDF'
pdDF=: 288001 8 4 arrayGet   'pdDF'   NB. ... shape required ...
                  arrayClose 'pdDF'

                  arrayOpen  'pdDG'
pdDG=: 576001 8 4 arrayGet   'pdDG'   NB. ... shape required ...
                  arrayClose 'pdDG'

                  arrayOpen  'pdDH'
pdDH=:1152001 8 4 arrayGet   'pdDH'   NB. ... shape required ...
                  arrayClose 'pdDH'



load 'plot'

pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDF
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDG
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDH

pd 'pdf'
pd 'show'


Zgraphic3301.jpg
... geodesic ... 


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

NB. ... path in n0/n1 plane ...

   *./ (0=]) cn2"1@:((S00xL{])"2) pdDH
1

NB. ... time increases continually (a real path in spacetime) ...

   *./@(0<])@(2-~/\])@:(cn3@(S00xL{])"2) pdDH
1


...

... plot paths in spacetime ...

...


GTEZ3305D.jpg 


NB. ... compare with TensorExperimentsZ31 ...

gXm0All=. 1  _0.02  _  0"_
gXm1All=. 1  _0.02  1  1"_


Initn =.  1 , 0    , 0 , 0        "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(2"_)

Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*2"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDJ=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0        "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(4"_)

Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*4"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDK=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0        "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(8"_)

Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*8"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDL=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0        "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(16"_)

Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*16"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDM=:vSgD@vS''


Initn =.  1 , 0    , 0 , 0        "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(32"_)

Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn

vS00xL   =.Initn
vS01dxL  =.0,0,0,0:
vS02d1L  =.Initdn%Initds
vS06ds   =.Initds
vS07count=.(0,9000"_)*32"_

vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]

pdDN=:vSgD@vS''


pdDJ      arrayPut   'pdDJ'
          arrayClose 'pdDJ'
pdDK      arrayPut   'pdDK'
          arrayClose 'pdDK'
pdDL      arrayPut   'pdDL'
          arrayClose 'pdDL'
pdDM      arrayPut   'pdDM'
          arrayClose 'pdDM'
pdDN      arrayPut   'pdDN'
          arrayClose 'pdDN'



NB. ... establish arrays if necessary ...

                 arrayOpen  'pdDJ'
pdDJ=: 18001 8 4 arrayGet   'pdDJ'   NB. ... shape required ...
                 arrayClose 'pdDJ'

                 arrayOpen  'pdDK'
pdDK=: 36001 8 4 arrayGet   'pdDK'   NB. ... shape required ...
                 arrayClose 'pdDK'

                 arrayOpen  'pdDL'
pdDL=: 72001 8 4 arrayGet   'pdDL'   NB. ... shape required ...
                 arrayClose 'pdDL'

                 arrayOpen  'pdDM'
pdDM=:144001 8 4 arrayGet   'pdDM'   NB. ... shape required ...
                 arrayClose 'pdDM'

                 arrayOpen  'pdDN'
pdDN=:288001 8 4 arrayGet   'pdDN'   NB. ... shape required ...
                 arrayClose 'pdDN'



load 'plot'

pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDJ
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDK
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDL
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDM
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDN

pd 'pdf'
pd 'show'


Zgraphic3302.jpg
... paths in spacetime ... 


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

NB. ... path in n0/n1 plane ...

   *./ (0=]) cn2"1@:((S00xL{])"2) pdDN
1

NB. ... time increases continually (a real path in spacetime) ...

   *./@(0<])@(2-~/\])@:(cn3@(S00xL{])"2) pdDN
1


...

... NOTE 4 ...

...


...

... energy is manifested in the divergence of space and time ...

...


Download: File:LTEZ3300C.txt
Download: File:LTEZ3301C.txt
Download: File:LTEZ3302D.txt
Download: File:LTEZ3303C.txt
Download: File:LTEZ3305D.txt


Download MoinMoin source: File:TensorExperimentsZ33.ijs

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