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 θ_{13} ; θ_{23} ; θ_{12} ; 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:**

**Θ _{13} = 36.0964 deg. When multiplied by Quantum Number [ ( 1 / 3.5 ) X ( 3 / 5 ) ] then equals to the θ_{13 } = 6.1879 deg**

**Θ _{23} = 6.3141 deg. When multiplied by Quantum Number [ ( 1 / ( 3.5 )^{2} ) ] then equals to the θ_{23} = 0.5154 deg**

**Θ _{12} = - 163.2070 deg. When multiplied by Quantum Number [ ( 1 / 3.5 ) X ( 3 / 2 ) ] then equals to the θ_{12} = - 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 < Θ _{FINAL} < 90.0 deg and**

**270.0 deg < Θ _{FINAL} < 360.0 deg**

This is how it is done:

1: If the original angle Θ is located in the first quadrant: Θ_{FINAL} = Θ

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

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

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

After that transform, the Θ_{FINAL} angles are multiplied by the same Quantum Numbers as in the case of Θ_{BEFORE THE TRANSFORM} ; (which was computed right before), giving the angles θ_{FINAL} .

**Here are the angles after the transformation:**

**θ _{13 FINAL }= ( 36.0964 degrees = angle after the transformation ). When multiplied by a Quantum Number [ ( 1 / 3.5 ) X ( 3 / 5 ) ] then equals to θ_{13 FINAL }= 6.1879 degrees**

**θ _{2}_{3 FINAL }= ( 6.3141 degrees = angle after the transformation ). When multiplied by a Quantum Number [ ( 1 / ( ( 3.5 )^{2} ) ) ] then equals to θ_{23 FINAL }= 0.5154 degrees**

**θ _{12 FINAL }= ( 343.2070 degrees = angle after the transformation ). When multiplied by a Quantum Number [ ( 1 / ( 3.5 ) ) X ( 3 / 2 ) ] then equals to θ_{12 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 }= [ ( θ_{13} = 6.1879 deg X 2 ) + ( θ_{23 }= 0.5154 deg X 2 ) + ( θ_{12 }= - 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 }= [ ( θ_{13} = - 0.20134 deg + 59.7987 deg ) + ( θ_{23 }= 2.3781 deg X 2 ) + ( θ_{12 }= 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 }= [ ( θ_{13} = - 28.1209 deg + 60.2637 deg ) + ( θ_{23 }= 13.3623 deg + 1.3316 deg ) + ( θ_{12 }= 28.0002 deg X 2 ) ] = 102.8371 degrees**

**θ _{TOTAL NEUTRINO}_{ MIXING (OSCILLATION) ANGLE }= 257.8371 deg**

**θ _{TOTAL NEUTRINO}_{ MIXING (OSCILLATION) ANGLE }= [ ( θ_{13} = - 8.5770 deg + 145.7087 deg ) + ( θ_{23 }= - 47.2551 deg + 98.6837 deg ) + ( θ_{12 }= 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 ) = δ _{CP 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 = δ _{GRAVITON}_{ 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 ).

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