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The White Knight is Talking Backwards - A Bayesian Hot Gas Crystallization Model for QM

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Abstract and Figures

Presents a Baysian Network based 'reality crystallization' model for physical phenomena. This model turns out to have attributes in common with QM. The model produces dual slit results, delayed choice, and explains multiple realities. Ignore the introduction. All computational models can be interpreted as programs. I started to write the paper on that subject and ended up with a paper with a different focus.
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The White Knight Is Talking Backwards
A Computational Interpretation of QM
by 

Introduction
 !"!#" $ !
%   # ! % "   &" # " 
% "'() *  +"   !"!" ,
! !% +"% ! "" "
    "% "# " )
-!.%#%! #" % "   %""
"  '()
! /!" "!!  ! 0 %  
"" "  % # ""#   
% " "+   "  %  "
"+!  ##%!!+ 
"!!)1 "% ! 0/!"2 0+"
% "!"  %!,% "'3()
"!!"!""# " "%4 '5()
#  % "%""!% 
"+ "%""   %""% "" %
% )6" " "  !"!2!0#
"#!#"  "  "%  %") 2"
 "% + 1"!%0% !  7" 
"!2!)8!"" " % "%
9 % !  ""!"%")
6+ +# " &""% "" "%
":* " "*#" %"" !#
   "" # " 0
"!"" #!# #";<)9 """ 
# ;<" "  %%  "%%")
1/20
Moving a Piece
8  ""  " "   "  % "!  
!+   ! "!7!"# i+! % j+ #" 
 "!7 " %+) %"!
4% "" !+"#" " )
*"  "" " "#" " " ! '(+  " +#
,!%)"" "!! =% !"
!")>   '("   )*"#"  %
  " "+% 7  " 
%!"% " 7 " ")7 " " "
" "!  %    " "%   !)
  "'(  ! #" # 
"   "7 " " "   !+  '(
'()
#"%%!"   # "
#"   "7 ) " " # #  " % 
")*  " " !"!?
(
[
1 0 1
1 0 2
0 0 1
][
1 0 2
1 0 1
0 0 1
][
1 0 1
1 0 2
0 0 1
][
1 0 2
1 0 1
0 0 1
][
1 0 1
1 0 2
0 0 1
][
1 0 2
1 0 1
0 0 1
][
1 0 1
1 0 2
0 0 1
][
1 0 2
1 0 1
0 0 1
]
)
[
i0
j0
1
]
=
[
i10 i11 i12 i13 i14 i15 i16 i17
j10 j11 j12 j13 j14 j15 j16 j17
11111111
]
Equation 1: Next Move Calculation
 % "" "#  % " " 'i
j ( "   "7  " %+ #  %  
  "7 " ") "" "%  "7!
%  !  !  " "  !)
" "  !   ",   #"  % 
%! !"  %) * % 7 %  %! % 
 "  )
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Zero Knowledge Strategy
8" # "    , #!
%   ) "#" %" "" ")8!"
#!   7 % " %"!
) @% " ! " "  #  " 
" " "" $!"%"   " "k"  
% %)
! "7 kA " "" "!" ") "" " 
$!" "  '(+!,  " ")* ,
"" " ") kA! "7# "" 
$!"  "  " "    + !  "! !
#  #+ )
1" "  % "  ! "7   kB#
" ! "7 k?
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Figure 1: Probability of Finding the Knight on a Square k Moves into the Future
 " /"% %7#   "!
kA)* # kA "7,)* #
"! kA! " " C#+  " "+
 '(+,%+" %D" 4% %   )
$!   #   " 7 " "+  ' ( ! ' (+
 nA)  "" " ""  " +  # !! "    
" "+'(!'( kA "7+ %E)
  "  " "  kA ! 
%  "" " kA!)#! "+##"$!
 p " E+ !  A+  #  !!" " E3  7
" ")8  kB!" "'(##"!!"E3 # "+
 A" "'(+! kA" "'(+ 
" % ""  "" F#" '(+!   
!!% E)
*" #  ! !+n#%!#G)"" 
%% )"" ""n  ""
* !" "   "
 "% ""  " k)#"  " "" n 
% "" " " " !" 
k#"#)    "" " %""
F%"!F#"" !%"! "#"  "k)
4/20
 ! "7B  "%,)"#" 
%% )
"! ! "7 )/!" "+'"4(+! #"?
2.1 !  ""   "" "p)
)%=% "! !"""  %  7
!" " "7kB)8 ""    #"
n" """)
)5 n" " "7kB?
)5)!!" %
pk
n
Figure 2: Probability Flow Calculation
> "    %"=% " " !+ #   
% ! ", "  " #  % % " )""
%"  ! "" " 7   "
"!!   %  "  ""   "   =%+ !
"!!  % k) """" k "!%  
 %!"  ) %+ " # "!  ! 
   "" " k+ #  % "      
 "7 $!#""   kB)"   "7""
  "  %"=% %   ! " ") 1#+ "
%  "" + %"")
#"%" ++   " """ " ) i+j
! "7 !"    !    "!"
!" ?
*%7 % " "'EE3E3()H%
"" F#" /"% %  !  "7
 "?
Bk+1=F Bk
Equation 3: Probability Flow, Incremental
&" "% %  "" """/"%?
[
1/2
0
1/2
0
0
0
0
0
0
]
=
[
0 0 0 0 0 1/2 0 1/2 0
0 0 0 0 0 0 1/2 0 1/2
0 0 0 1 /2 0 0 0 1/2 0
0 0 1/2 0 0 0 0 0 1/2
0 0 0 0 0 0 0 0 0
1/2 0 0 0 0 0 1/2 0 0
0 1/2 0 0 0 1 /2 0 0 0
1/2 0 1 /2 0 0 0 0 0 0
0 1/2 0 1 /2 0 0 0 0 0
]
[
0
0
0
0
0
0
0
1
0
]
!
5/20
i A5Ii "7Bj "7
Equation 2: Board matrix co-ordinate indexes to Board Vector component index mapping
[
0
0
0
1/4
0
1/4
0
1/2
0
]
=
[
0 0 0 0 0 1 /2 0 1 /2 0
0 0 0 0 0 0 1/2 0 1/2
0 0 0 1 /2 0 0 0 1 /2 0
0 0 1/2 0 0 0 0 0 1 /2
0 0 0 0 0 0 0 0 0
1/2 0 0 0 0 0 1 /2 0 0
0 1/2 0 0 0 1/2 0 0 0
1/2 0 1/2 0 0 0 0 0 0
0 1/2 0 1/2 0 0 0 0 0
]
[
1/2
0
1/2
0
0
0
0
0
0
]
J !" "/"%?
Bk=FkB0
Equation 4: Probability Flow, Absolute
Emergent Properties
 %   "k%"%"  ") 
 !% "  "+  + #"  
)  " !$ 0" " 0   %  " "
 "" "%"  "+ A+K =%
" %L)    % % "" " %  7 !
" " ")
/  k  !""""  ! % + !  " %
" #""#" "!)MA" "" 
"  "  " #" "  !%"   
""" ")*!#" " " !+"  "
   #"   $ #" " )8!"# $
#" "   '" 4( '" 4(  !#"  " 
'"4( '"4()1#+ #"" "
"!" )
 %"=%! 4 "  MA5)8 M A3 
! 4 "  % 5 !" " ! " ")   
"#!%" " MA)/7+  
  ""!+'('('('('(+"#!  "
" '('('(+4%"  '('('
(+ 4%" $" '('()
6/20
   M A G  !   !%" 
 +))'('('('('('('('('()* " 
"   !  ! #"    " #" % "
"" # "   !) *  " "  " "
  % #")H  " " !
  #)
"" "  !"" #)
* "" # " !
 " !" ) % 
  !   + # # 
"!" "" !" ")
1"% 7 "   "
A ! ' (+  " 
#"" ' (  "
% #" " ' () * 
7   "  "
!! '(+ '('
()
@%   " "" " "" % 
"" F# " " " ! "7)" 
""  ! "+!""!"  #+!"
 #     ")  ""  F# #"  
"   " '("#" 7 $%+/"%3)
7/20
Figure 3: Knight Ring Network
#"  " "%  "" F#+$  "  "
""!) 8   "   #  , ""   $!" 
"   "!)6!"#  ,"" "
!#$!"=%)7!'(?
12
4
3
8
10
32
18
64 1
4
Equation 5: Node [0 1] Large k Convergence
"!" "#%  E3
 =%?
6"""#"!!'(?
>!'(" E3!" )
1%"!"!"?
8/20
Figure 4: probability flow over ring network
Figure 5: Ring Modes for Large k
 #  " # "   % " " 7" 
"% %"%" "   +%"#
" "" !+ "!##"$!"  )
> +  " #"   %!   "!!   !)
9 " "" " ) 9" #!% 
  "#"  %%    "" F%"! " "  
" !!"% %%!!") %  "+ % 
" #%! ! "  " !" "  "
+ " #""!#"  %%)
With Constraints
6% % +%!"!!!   
%   #" "#!)  "%"
!"?
9/20
*   #  "! % " 4  "
# " "  "!   # " "+    @% 6"
7" ""'()*     " + " #"
"    " "+ #    " "  "
"" !%  % "" ) >#" !#+#
" !  % + #" "  # "!  
 " ) #$!  4      %  "
"" !  # "+! "" )
> +# %  " " %/"%N  " +
!  %    "  $ ) " !" % "
""%  ")1#+%"    +
!%" "!7 !%!%"+#! 
  "" " 4 "!"%  " ) 
" " %   " %   #!+ ")) %
10/20
Figure 6: Constraint and Measurement
"  #!) "   ) ! 
"" "+ !    " +   % + "!
!!" "" "+# % "#" " %!  
"" "!"%   " )
 0%   """ ""!"" )
 0""%% "" !%"0"0#
"/"%)
 "  "  4 "" "  %
#" #" ?
11/20
Figure 7 Ring Angle
> + k "=%  % k+ * " , %"
""  "    #"!#%")""" " !!
  " %,)
9" %  "!""%?
12/20
path k0k0+1 k0+2 base with
constraint
with
measurement
0 0 7 6 1/16
1 0 7 0 1/16 1/8
2 0 1 0 1/16 1/8
3 0 1 2 1/16 1/8 1/4
4 2 1 0 1/16 1/8
5 2 1 2 1/16 1/8 1/4
6 2 3 2 1/16 1/8 1/4
7 2 3 4 1/16
8 4 3 2 1/16 1/8 1/4
9 4 3 4 1/16
10 4 5 4 1/16
11 4 5 6 1/16
12 6 5 4 1/16
13 6 5 6 1/16
14 6 7 6 1/16
15 6 7 0 1/16 1/8
Figure 8: Knight Trajectories
1 # k " ! " "+ % %
 " =%     ! % % "" " 
$!" "  "" ")    " #" 
$ #+!   " K% L" !#
"  +  %     " %  " 
 % "  "" ")8 %+ " " %
#%   % %     #"  
! "  !") "  #! "  % "+  
 " !" )
*%"" #" % "  "
  )* % #" "  
  !  "  " "+     ") *
"% " !% %!!" ")
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Figure 9: With Back Propagation
Next Move According to The Reality Wavefront Model
* "    #!"%"%  "!
 " " !) 8     !  #"  
""  F#+ +       " #  
!"%")1  + ""7
" )
8 " #% 7 + #" )
/ "# 7  " "
" ""  ! "7  kA) *   
  7 + % "! )
" "% ! A  #"" "  +!#
!!")>7  "##"A+ )
* % "   7 0! "0%" 
!   ! "" ")
#" 7 "!)%  !
 #%   %  "+     "% #
"  )8 #  
" $!  4 " " "7")
 "" #?
"   " 7  " " ) 9
" "" !7 # 
!" " #" !"    ! 7 " "
"" ")
14/20
 9 "" ")
 8 "   ")
5 "#!! "!%! "" "
3 @ " 7 +#""  " )
 /#! " %! "" ")
N J  +% """ )
Figure 10: Reality Wavefront Model Algorithm
 "## 0" " 0+ 0!" "% #" 0
! " "% "+ %! # ! "!!" 
! "" $! %!% "k) !
 "%!!$ ""% )! " 
! "!  0" 0)! "!!#"  
 %"!0  0)% %7" "k%+
!" "$!#"  "" $!)8   %!% 
"   % #    " 0"  # 0 "
#!)
6  "  "" k "     " " ")
J  " 7 %! #0# "
! "!0 !  ""  $! !$ ") % #  
!" " # )  0" 0 # +  #! "" 
% "# +! "" % "# )
Next Move According to the Reality Crystallization
Model
" # !! "" "  A+
%" 7   +A+A+ ) 4% "% # "
! ! " " ) *  +"% %#!#
!  %   " 0    0) 1 " 
% 7    "%#!$!%! #
! "!K" L! "" $!#%! 
)
* !!$" "   " "#% "!
#" %"=%" %%"#+ # " "%
0 "  "#)  +  !$" "+ " "!  " 
""  $!) " "%!   #! " "
!4%  )
8+" !""!""7  + %%
 #"" "  " +  " "0%!!
 " 0)H"#" "#%!"""" " 
$" % "+  %" #  !" $7! #"! % 
#!) *  " %! ""  ! %+ 
15/20
% !)  ""  F%"! " ""+  # 
"" "%!!%+ #" %!!!#)
"" "%!!  " +%+   
!%  ,)
/7"" !%  " % 
%  k, > 0+   %"    " "  ! 
!"" ""4%  %  " " 
kA+% " " % "  " #"    =%  k,
)># "!   % ")! !
#  " ) * %   #    "
" "% "! +" "+! )*  "
"# #!)> #"   % "
!+% #"  "% O "nP!% %
%! !")   "! "  "  " "% ! 
""% #"""# % "!#%!
+0 % %0) /   "# %   
&"#!"%")
J%!"  " " % % k " %!!
 ""  " ")1#+" " " %
    ! ! "!) 1+ #   " 
 ",%   "" $!) 8 7+  
%!"  "   "" F###!"/"%3)1
##"   ! E)
16/20
 #" "$%! "" F##"/"%
3) *  ! # "" "  ! E  %!!
 " )*+ ""  E"" "
!  "  A+" 7  %"" "  )*  %%  
 #E"" " "# %!%+!  
%!!# " "  %"" " 
")
%!" % % "   #! % 
"" $!)8# kA#!   % "
+ A" ! ! "!+ % "# #  " k #
#%! ) "% "" " "   k "  
 ")""#" !#)
>#kA" "     !%!"+ 
%!!+! % "  "!# !)
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Figure 11: Reality Crystalization
!#" "  !%   "  % $7!
k %+  ""  $! " " " %! + ! "  
"  " %! ") 1 "  
#""#  " )
#%!  "" %     " J"  
<!) !"D"  #"   !  " "!
 "     kB !)*)) "7  "") *
  + "" "  "" "" "  !
!"%!!%)"% "   #+! 
# "     0 "0) 1+ " "  7 
"!+%  "  !)
% "" "!" ""##+ #" "" 
#  "  " +  # ! " % 7) *  
7  "  #  ""  "   
!+ %  "" kB)8+ " #+!%
 " +%!"  " % "k %" "! 
! "! %   !" !   "" " !" ")
9 # #"!   "" "   " "  "  
"!#"#! )""%",! ""
#"$%?
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Figure 12: Schematic of Reality Crystalization in a Complex System
*7  %! ## ! "!!
#   ! "! #" 4!!  " )
""%% " ")!#"
% "4!%! "!" 7" %!! 
"% "% ")   "##"    "! !
" " "! !0! "!0)
% " 7"  %  " #"  F#!)  " 
"! ! "" !!!" " "!" ) 
 !  "+  +  "   " !
"" "  )6"" " " #"%!
 #% !$ ")6"%+ ! "!
!!0 %! "! 0)
8 F#" 7"  "+ " ""
!# ""!0" !"!%!+"    
"!) * " 0" % %0+  !" ""  
!!! "!)" " % "!
! "" #)
 " " " !%  "" + "
 % "    % "" $!!  
"" "" ")   "  %   " "
  !  %!"  " + % %" 
 % " Q ! "     " K")) A L
""  #  !+ % %"  "  
! "!" )
How Fast are Probability Computing Waves
8  %   #"     " 4 " =% %
" % "    !!!+    
"  % %!   ""  $! #  ! " "
% """!)
>   % ""  $! 7"  " %" ") * % "
7+  G """ " " " " ) 8 
  ""   ") 1 "" $! 
!4% !! %!"%" "  )
19/20
"  "#% " #  "  " /"%)
%!!   #  #4%  %" $!  " )
1 =% """ "+  "+!%" "" 
$!%!    $"#" #%)
9"  C#+"  " "!+ "" 
 !% "  %!" ##  " ! "!
!#  ! "!)  "%!=%" 
"" " %!!  " +% ""   $  
%!!  " +!  %!!  " +  
%!+=%"   "" % "#"!
%)1+ "" #" "" # ")
6% """% %7 ! "7
% " "   /"% + !  " " # !  
" ")8%+"  " #  #" k"!
 "7+!   "7 %  k"B "7)#
 ""+ %  " " )
% " ""   ! #)
"" % "# ""!"D "'"4
(" !"D  % )* "   " ""  %
7"  $!%D )
1#+ "% " "" #! %
% ! " !" "  !"D    "  
!! " 7" 'N(+ % "  %!" " 
7"  " ! "" #  ""! 
#!"k)
Bibliography
1: Charles Babbage Esq., The Ninth Bridgewater Tratise; A Fragment, John Murray, 1837
2: Konrad Zuse, Rechnender Raum, Vieweg+Teubner Verlag, 1969
3: Kevin Kelly, God Is the Machine, Wired, https://www.wired.com/2002/12/holytech/
4: Fredkin gate, https://en.wikipedia.org/wiki/Fredkin_gate
5: Double-slit experiment, https://en.wikipedia.org/wiki/Double-slit_experiment
6: Wheelers delayed choice experiment, https://en.wikipedia.org/wiki/Wheeler
%27s_delayed_choice_experiment
20/20
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