25 November 2019 AD; St Catherine of Alexandria (307)

This is an updated version of how to compute the CP Violation Phase Angle of Graviton.

To get the results we need a couple of things:

0. Approximate/exact (guessed/measured) value of CP Violation Phase Angle of Graviton.

(more in this article: 68. Getting CP Violation Phase Angles of Neutrino, Boson, Quark, and Graviton )

1. Quantum Fraction from which we get factors to calculate the angles.

2. Spherical correction angles for each combination of the four fundamental elements - consisting of Neutrino, Boson, Quark, and Graviton.

3. The sum of the Mixing (Oscillation) Angles of Neutrino, Boson, Quark, and Graviton from before and after transformation into the positive part of the Real Plane (we used the sum of two complex vectors).

0 - We need some approximation of a CP Violation Phase Angle of Graviton or a measured value (see article 68, with the link above) or an official estimate which is now about

δ CP VIOLATION PHASE ANGLE GRAVITON = approx. 171.9200 degrees = 3.000571 radians

Having this angle will speed up the computations.

1 - Quantum Fraction which is a fraction different for each of the four fundamental elements, but nevertheless forming two pairs.

For Graviton the Quantum Fraction is:

( 21 / 10 ) / ( ( 3 / 2 ) - ( 3 / 5 ) ) = 7 / 3

The reciprocal of each part will be used for calculation of the CP Violation Phase Angle of Quark,  in the following way:

( 10 / 21 ) for calculation CP Violation Phase Angle of the following combinations:

Quark, Graviton, Quark + Graviton, Boson + Neutrino, Quark + Boson + Neutrino, Graviton + Boson + Neutrino, and Quark + Graviton + Boson + Neutrino.

( 2 / 3 ) for the following combinations:

Neutrino, Quark + Neutrino, Graviton + Neutrino, Quark + Graviton + Neutrino.

( 5 / 3 ) for the following combinations:

Boson, Quark + Boson, Graviton + Boson, Quark + Graviton + Boson.

2 - Spherical Correction Angles. Those are just the sums of the angles of different elements and reduced to multiplications of 90+ deg (or if you prefer multiplications of 22.5+ deg).

Correction Angles for combinations of the elements:

Quark + Graviton = ( 1 / 2 ) x + (1 / 2 ) y = 90.50998 deg

Boson + Neutrino = ( x + y ) / 4 = 90.1793 deg

(Quark + Graviton) + Boson = ( 1 / 2 ) x + ( 1 / 2 ) y = 90.34464 deg

(Quark + Graviton) + Neutrino = as above

Quark + ( Boson + Neutrino )  = ( 1 / 5  )x + ( 4 / 5 ) y = 90.245436 deg

Graviton + ( Boson + Neutrino ) = as above

( Quark + Graviton ) + ( Boson + Neutrino ) = ( 1 / 3 ) x + ( 2 / 3 ) y = 90.289527 deg

Quark + Boson = ( 1 / 3 ) x + ( 2 / 3 ) y = 90.289527 deg

Quark + Neutrino = as above

Graviton + Boson = as above

Graviton + Neutrino = as above

These values are necessary to get Arithmetic Mean of the CP Violation Angle for any element.

3 - The sum of Mixing (Oscillation) Angles of Graviton from before and after the transformation:

θ 13 = 6.1879 deg, and after the transformation θ 13 = 6.1879 deg

θ 23 = 0.5154 deg, and after the transformation θ 23 = 0.5154 deg

θ 12 = - 69.9459 deg, and after the transformation θ 12 = 147.0887 deg

It will be necessary to go back to the article "57. Graviton mixing angles final - after the transformation": [ 57. Graviton mixing angles final - after the transformation ]

( I did some small changes to this article, so it is easier to read. It will be useful later now, in the main article about Graviton ).

Angles before the transformation are calculated using the built-in Fortran function [ ATAN2 (Im, Re) ]. This function gives Polar coordinates: Length of the vector and the Angle of this vector with X-axis. The Angle depends on the location of the initial vector ( i.e. in which quadrant the vector is located in Cartesian coordinates ).

Here is the description from Fortran Wiki: ATAN2

Important note: The angles above θ13 ; θ23 ; θ12 ; from before the transformation and after the transformation are different than the original angles since the Quantum Numbers were applied to them, so that the Mixing (Oscillation) Angles may be calculated.

Here are the original angles from before the transform:

Θ13 = 36.0964 deg. When multiplied by Quantum Number  [ ( 1 / 3.5 ) X ( 3 / 5 ) ] then equals to the θ13  = 6.1879 deg

Θ23 = 6.3141 deg. When multiplied by Quantum Number [  ( 1 / ( 3.5 )2 ) ] then equals to the θ23 = 0.5154 deg

Θ12 = - 163.2070 deg. When multiplied by Quantum Number [ ( 1 / 3.5 )  X ( 3 / 2 ) ] then equals to the θ12 = - 69.9459 deg

The transformation:

The Transformation computes "Final Angle" - this is a set of rules to get all the angles Θ from previous calculations and transform them into a set of angles with the following values:

0.0 deg < ΘFINAL < 90.0 deg and

270.0 deg < ΘFINAL < 360.0 deg

This is how it is done:

1: If the original angle Θ is located in the first quadrant: ΘFINAL = Θ

2: If the original angle Θ is located in the second quadrant: ΘFINAL = ( 180 deg = π ) - | Θ |; i.e. 180 deg - absolute value of theta.

3: If the original angle Θ is located in the third quadrant: ΘFINAL = ( 180 deg = π ) + | Θ |; i.e. 180 deg + absolute value of theta.

4: If the original angle Θ is located in the fourth quadrant: ΘFINAL = ( 360 deg = 2π ) - | Θ |; i.e. 360 deg - absolute value of theta.

After that transform, the ΘFINAL angles are multiplied by the same Quantum Numbers as in the case of ΘBEFORE THE TRANSFORM ; (which was computed right before), giving the angles θFINAL .

Here are the angles after the transformation:

θ13 FINAL = ( 36.0964 degrees = angle after the transformation ). When multiplied by a Quantum Number [ ( 1 / 3.5 ) X ( 3 / 5 ) ] then equals to θ13 FINAL = 6.1879 degrees

θ23 FINAL = ( 6.3141 degrees = angle after the transformation ). When multiplied by a Quantum Number [ ( 1 /  ( ( 3.5 )2 ) ) ] then equals to θ23 FINAL = 0.5154 degrees

θ12 FINAL = ( 343.2070 degrees = angle after the transformation ). When multiplied by a Quantum Number [ ( 1 / ( 3.5 ) ) X ( 3 / 2 ) ] then equals to θ12 FINAL = 147.0887 degrees

The sum of all these Mixing ( Oscillation ) Angles from before and after the transformation is the Total Graviton Mixing (Oscillation) Angle and equal to:

θ TOTAL GRAVITON MIXING ANGLE = 90.5494 deg

θ TOTAL GRAVITON MIXING ANGLE = [ ( θ13 = 6.1879 deg X 2 ) + ( θ23 = 0.5154 deg X 2 ) + ( θ12 = - 69.9459 deg + 147.0887 deg ) ] = 90.5494 degrees

The sum of all these Mixing ( Oscillation ) Angles from before and after the transformation is the Total Quark Mixing (Oscillation) Angle and equal to:

θ TOTAL QUARK MIXING (OSCILLATION ) ANGLE = 90.4706 deg

θ TOTAL QUARK MIXING (OSCILLATION ) ANGLE = [ ( θ13 = - 0.20134 deg + 59.7987 deg ) + ( θ23 = 2.3781 deg X 2 ) + ( θ12 = 13.0585 deg X 2 ) ] = 90.4706 degrees

In a similar manner we get mixing angles of the other elements:

θ TOTAL BOSON MIXING (OSCILLATION) ANGLE = 102.8371 deg

θ TOTAL BOSON MIXING (OSCILLATION) ANGLE = [ ( θ13 = - 28.1209 deg + 60.2637 deg ) + ( θ23 = 13.3623 deg + 1.3316 deg ) + ( θ12 = 28.0002 deg X 2 ) ] = 102.8371 degrees

θ TOTAL NEUTRINO MIXING (OSCILLATION) ANGLE = 257.8371 deg

θ TOTAL NEUTRINO MIXING (OSCILLATION) ANGLE = [ ( θ13 = - 8.5770 deg + 145.7087 deg ) + ( θ23 = - 47.2551 deg + 98.6837 deg ) + ( θ12 = 34.6599 deg X 2 ) ] = 257.8801 degrees

Now, we can proceed with getting the Cp Violation Phase Angle of Graviton.

Singles:

Quark = (90.4706 deg + 3 X 90.4706 deg) X ( 10 / 21 ) = 362.0005 deg X ( 10 / 21 ) = 172.3812 deg

Graviton = (90.5494 deg + 3 X 90.5494 deg ) X ( 10 / 21 ) = 362.0794 deg X ( 10 / 21 ) = 172.4188 deg

Boson = (102.8371 deg + 0 X 90.1793 deg ) X ( 5 / 3 ) = 102.8371 deg X ( 5 / 3 ) = 171.3952 deg

Neutrino = (257.8801 deg + 0 X 90.1793 deg ) X ( 2 / 3 ) = 257.8801 deg X ( 2 / 3 ) = 171.9201 deg

Arithmetic Mean of the Singles = 688.1153 deg / 4 = 172.0288 deg

Pairs:

Quark + Neutrino = (90.4706 deg + 257.8801 deg - 1 X 90+ deg) X ( 2 / 3 ) = 258.0611 deg X ( 2 / 3 ) = 172.0408 deg

Graviton + Neutrino = (90.5494 deg + 257.8801 deg - 1 X 90+ deg) X ( 2 / 3 ) = 258.1400 deg X ( 2 / 3 ) = 172.0933 deg

Quark + Boson = (90.4706 deg + 102.8371 deg - 1 X 90+ deg) X ( 5 / 3 ) = 103.0181 deg X ( 5 / 3 ) = 171.6969 deg

Graviton + Boson = 90.5494 deg + 102.8371 deg - 1 X 90+ deg) X ( 5 / 3 ) = 103.3097 deg X ( 5 / 3 ) = 171.8283 deg

Quark + Graviton = (90.4706 deg + 90.5494 deg + 2 X 90.5100 deg ) X ( 10 / 21/ ) = 362.0399 deg X ( 10 / 21 ) = 172.4000 deg

Boson + Neutrino = (102.8371 deg + 257.8801 deg + 0 X 90.1793 deg ) X ( 10 / 21 ) = 360.7172 deg X ( 10 / 21 ) = 171.7701 deg

The arithmetic mean of the Pairs = 1031.1829 deg / 6 = 171.9716 deg

Triplets:

Quark + Graviton + Boson = (90.4706 deg + 90.5494 deg + 102.8371 deg - 2 X 90.34464 deg) X ( 5 / 3 ) = 103.1679 deg X ( 5 / 3 ) = 171.9463 deg

Quark + Graviton + Neutrino = (90.4706 deg + 90.5494 deg + 257.8801 deg - 2 X 90.34464 deg ) X ( 2 / 3 ) = 258.2108 X ( 2 / 3 ) = 172.1405 deg

Quark + Boson + Neutrino = (90.4706 deg + 102.8371 deg + 257.8801 deg - 1 X 90.2454 ) X ( 10 / 21 ) = 360.9423 deg X ( 10 / 21 ) = 171.8773 deg

Graviton + Boson + Neutrino = (90.5494 deg + 102.8371 deg + 257.8801 deg - 1 X 90.2454 deg) X ( 10 / 21 ) = 360.0212 deg X ( 10 / 21 ) = 171.9148 deg

The Arithmetic Mean of the Triplets = 687.8789 deg / 4 = 171.9697 deg

Quadruplet (the sum of the angles = 540 deg i.e. Pentagon shape):

Quark + Graviton + Boson + Neutrino = (90.4706 deg + 90.5494 deg +102.8371 deg + 257.8801 deg - 2 X 90.28953 deg) X ( 10 / 21 ) = 361.15811 deg X ( 10 / 21 ) = δCP VIOLATION PHASE ANGLE GRAVITON  = 171.98005 deg = 3.00161813 radians

The arithmetic mean of Singles, Pairs, Triplets, and Quadruplet = ( 172.0288 deg X 4 + 171.9716 deg X 6 + 171.9697 deg X 4 + 171.9801 deg X 1) / 15 = 2579.80384 deg / 15 = δGRAVITON CP VIOLATION PHASE ANGLE = 171.9869 deg = 3.00173807 radians

Again, the result from the quadruplet seems to be better and a lot simpler to compute, than the arithmetic mean.

Next articles - Aether ( probably Space and Time ).