17 July 2019 AD; St Alexis the Beggar; Bl Martyrs of Compiegne

 

Again, I use the same transformation of the angles:

The transformation is as follows:

 

first quadrant: theta final = theta

second quadrant: theta final = 180 degrees - absolute value |theta|

third quadrant: theta final = 180 degrees + absolute value |theta|

fourth quadrant: theta final = 360 degrees - absolute value |theta|

 

This is a boring part - just calculations but it has to be done so you know where the Final Angles come from.

There will be three different angles, with the same quantum numbers as before - for "regular"  neutrino mixing angles.

First final angle:

These printouts are the results of substituting for Real value X constant C_M_1, C_M_2 and C_M_3 in the main program (more about it later):

 

The first Neutrino Final Angle is:

These printouts are the results of substituting for Real value X constant C_M_1 in the main program (more about it later):

 

ALFA C_M_1 INVISIBLE
A + Bi
0.26742070244365181431D+01 -0.88456206796555758576D+00
MAGNITUDE & THETA IN RADIANS
0.28167061013938110570D+01 -0.31944670772500965983D+00
MAGNITUDE & THETA IN DEGREES
0.28167061013938110570D+01 -0.18302948131992206271D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.28167061013938110570D+01 0.59637385994545768497D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.28167061013938110570D+01 0.34169705186800780439D+03

ALFA C_M_1 VISIBLE
C + Di
0.10921287997995738905D+01 -0.48723746885506363791D+00
MAGNITUDE & THETA IN RADIANS
0.11958869789440584874D+01 -0.41963559257214483322D+00
MAGNITUDE & THETA IN DEGREES
0.11958869789440584874D+01 -0.24043348387855257187D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.11958869789440584874D+01 0.58635497146074415653D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11958869789440584874D+01 0.33595665161214475347D+03

PRODUCT
( A + Bi ) * ( C + Di )
0.24895867249727050563D+01 -0.22690295714163339902D+01
MAGNITUDE & THETA IN RADIANS
0.33684621501691416334D+01 -0.73908230029715449305D+00
MAGNITUDE & THETA IN DEGREES
0.33684621501691416334D+01 -0.42346296519847463458D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.33684621501691416334D+01 0.55441030068824312949D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.33684621501691416334D+01 0.31765370348015250102D+03

DIVISION
( A + Bi ) / ( C + Di )
0.23435167268465875168D+01 0.23558310181902933356D+00
MAGNITUDE & THETA IN RADIANS
0.23553280125860216465D+01 0.10018888484713517339D+00
MAGNITUDE & THETA IN DEGREES
0.23553280125860216465D+01 0.57404002558630518038D+01
MAGNITUDE & THETA FINAL IN RADIANS
0.23553280125860216465D+01 0.10018888484713517339D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.23553280125860216465D+01 0.57404002558630518038D+01

SUM
( A + Bi ) + ( C + Di )
0.37663358242360920336D+01 -0.13717995368206212792D+01
MAGNITUDE & THETA IN RADIANS
0.40083811582913915217D+01 -0.34929217207386531463D+00
MAGNITUDE & THETA IN DEGREES
0.40083811582913915217D+01 -0.20012967276789797921D+02 This is angle θ₁₃  from before the transformation
MAGNITUDE & THETA FINAL IN RADIANS
0.40083811582913915217D+01 0.59338931351057206953D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.40083811582913915217D+01 0.33998703272321017721D+03 This is angle θ₁₃ after the transformation

 

θ₁₃  = ( - 0.20012967276789797921D+02 ) * [(1 / 3.5) * (3 / 2)] = - 8.5770 degrees 

θ₁₃ Final = (0.33998703272321017721D+03) * [(1 / 3.5) * (3 / 2)] = 145.7087 degrees

i.e ("ordinary" angle) * (quantum number) = final angle

 

The second final angle for neutrino is:

These printouts are the results of substituting for Real value X constant C_M_2 and in the main program (more about it later):

 

ALFA C_M_2 INVISIBLE
A + Bi
-0.16469643196137670316D+03 -0.42300580114651573638D+02
MAGNITUDE & THETA IN RADIANS
0.17004191771102927078D+03 -0.28901870692595768020D+01
MAGNITUDE & THETA IN DEGREES
0.17004191771102927078D+03 -0.16559552107185831460D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.17004191771102927078D+03 0.60317797228493699180D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.17004191771102927078D+03 0.34559552107185828618D+03

ALFA C_M_2 VISIBLE
C + Di
0.14778769334016466086D+01 -0.23635598565384036140D+00
MAGNITUDE & THETA IN RADIANS
0.14966577371714127054D+01 -0.15858643318941822997D+00
MAGNITUDE & THETA IN DEGREES
0.14966577371714127054D+01 -0.90863333097870668809D+01
MAGNITUDE & THETA FINAL IN RADIANS
0.14966577371714127054D+01 0.61245988739901680020D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.14966577371714127054D+01 0.35091366669021294911D+03

PRODUCT
( A + Bi ) * ( C + Di )
-0.25339905311600006144D+03 -0.23588064111050094596D+02
MAGNITUDE & THETA IN RADIANS
0.25449455178567663438D+03 -0.30487735024489950320D+01
MAGNITUDE & THETA IN DEGREES
0.25449455178567663438D+03 -0.17468185438164536549D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.25449455178567663438D+03 0.61903661560387881480D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.25449455178567663438D+03 0.35468185438164539391D+03

DIVISION
( A + Bi ) / ( C + Di )
-0.10419852225472008911D+03 -0.45286940362340857291D+02
MAGNITUDE & THETA IN RADIANS
0.11361443133444632281D+03 -0.27316006360701585720D+01
MAGNITUDE & THETA IN DEGREES
0.11361443133444632281D+03 -0.15650918776207123528D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.11361443133444632281D+03 0.58731932896599516880D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11361443133444632281D+03 0.33650918776207123528D+03

SUM
( A + Bi ) + ( C + Di )
-0.16321855502797504300D+03 -0.42536936100305410946D+02
MAGNITUDE & THETA IN RADIANS
0.16867035198345195113D+03 -0.28866501582687109639D+01
MAGNITUDE & THETA IN DEGREES
0.16867035198345195113D+03 -0.16539287099956825955D+03 This is angle θ₂₃  from before the transformation
MAGNITUDE & THETA FINAL IN RADIANS
0.16867035198345195113D+03 0.60282428118585045240D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.16867035198345195113D+03 0.34539287099956828797D+03 This is angle θ₂₃ after the transformation

 

θ₂₃ = ( - 0.16539287099956825955D+03 ) * ( 1 / 3.5 ) = - 47.2551 degrees 

θ₂₃ Final = (0.34539287099956828797D+03) * ( 1 / 3.5 ) = 98.6837 degrees

i.e ("ordinary" angle) * (quantum number) = final angle

 

The third and last final angle for neutrino is:

These printouts are the results of substituting for Real value X constant C_M_3 in the main program (more about it later):

 

ALFA C_M_3 INVISIBLE
A + Bi
0.12483662752856212238D-03 -0.14913959339723874536D-02
MAGNITUDE & THETA IN RADIANS
0.14966115111952314493D-02 -0.14872864483626460075D+01
MAGNITUDE & THETA IN DEGREES
0.14966115111952314493D-02 -0.85215236418181461886D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.14966115111952314493D-02 0.47958988588169404466D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.14966115111952314493D-02 0.27478476358181853811D+03

ALFA C_M_3 VISIBLE
C + Di
0.11967254058809253525D+01 0.51215407798285539354D+00
MAGNITUDE & THETA IN RADIANS
0.13017117563713305195D+01 0.40437757327188500467D+00
MAGNITUDE & THETA IN DEGREES
0.13017117563713305195D+01 0.23169128278221215567D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.13017117563713305195D+01 0.40437757327188500467D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.13017117563713305195D+01 0.23169128278221215567D+02

PRODUCT
( A + Bi ) * ( C + Di )
0.91321967321893193510D-03 -0.17208558165418871410D-02
MAGNITUDE & THETA IN RADIANS
0.19481567988434958429D-02 -0.10829088750907609473D+01
MAGNITUDE & THETA IN DEGREES
0.19481567988434958429D-02 -0.62046108139960246319D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.19481567988434958429D-02 0.52002764320888257288D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.19481567988434958429D-02 0.29795389186003978921D+03

DIVISION
( A + Bi ) / ( C + Di )
-0.36261210291615981029D-03 -0.10910461667493448305D-02
MAGNITUDE & THETA IN RADIANS
0.11497257391046434693D-02 -0.18916640216345310677D+01
MAGNITUDE & THETA IN DEGREES
0.11497257391046434693D-02 -0.10838436469640268456D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.11497257391046434693D-02 0.50332566752243241837D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11497257391046434693D-02 0.28838436469640265614D+03

SUM
( A + Bi ) + ( C + Di )
0.11968502425084539542D+01 0.51066268204888298765D+00
MAGNITUDE & THETA IN RADIANS
0.13012405149817243277D+01 0.40328613176847122324D+00
MAGNITUDE & THETA IN DEGREES
0.13012405149817243277D+01 0.23106593286490191730D+02 This is angle θ₁₂ before the transformation
MAGNITUDE & THETA FINAL IN RADIANS
0.13012405149817243277D+01 0.40328613176847122324D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.13012405149817243277D+01 0.23106593286490191730D+02 This is angle θ₁₂ after the transformation

 

θ₁₂ = ( 0.23106593286490191730D+02 ) * ( 3 / 2 ) = 34.6599 degrees 

θ₁₂ Final = (0.23106593286490191730D+02) * ( 3 / 2 ) = 34.6599 degrees

i.e ("ordinary" angle) * (quantum number) = final angle

 

The sum of all six neutrino mixing angles (three "ordinary" and three after the transformation) is:

θ _{SUM OF NEUTRINO ANGLES =} (-8.5770 + 145.7087) + (-47.2551 + 98.6837) + (34.6599 + 34.6599) = 257.8801 degrees 

 

When this sum of Neutrino angles (257.8801 degrees) is added to the sum of Boson angles (102.8371 degrees) we get a spherical quadrangle, with the total angle a bit bigger than 360 degrees.

This fact also implicates a relation between Neutrinos and Bosons - they are one family.