25 July 2019 AD; St James the Greater; St Christopher

*More about "Quantum Fractions" in future articles.

As shown in the previous article there have to be certain fractions ("Quantum Fractions") in place to obtain CP VIolation Phase Angles for all the subatomic particles.

These fractions give exact values of the CP Violation Phase for quark, angle delta.

**For Quark and for Graviton the fraction is ( 4 / 21 )**

**For Boson the fraction is ( 2 / 3 )**

**For Neutrino, the fraction is ( 4 / 15 )**

Those Quantum Fractions are not just any numbers, they follow certain rules:

**Rule One:**

**The absolute value of the largest reciprocal equals to the sum of the absolute values of two remaining reciprocals**. i.e. in this example:

**|21 / 4 | = | 15 / 4 | + | 3 / 2 |**

|21 / 4 | = | 15 / 4 | + | 6 / 4 | = | 21 / 4 |

This is the main rule.

Thre is also another property which might be of interest.

The quotient of the Largest Reciprocal and the difference of the remaining reciprocals gives the same value to the first power and to the second power. i.e. in this example:

First power:

**( 21 / 4 ) / [ ( 15 / 4 ) - ( 3 / 2 ) ]** = ( 21 / 4 ) / [ 15 / 4 - 6 / 4 ] = 21 / 9 = **7 / 3**

Second power:

**[ ( 21 / 4 ) ^{2} ] / [ ( 15 / 4 )^{2} - ( 3 / 2 )^{2} ]** = [ 441 / 16 ] / [ 225 16 - 36 / 16 ] = 441 / 189 =

**7 / 3**

Mathematically this is the same expression, but is it the same in the realm of quantum mechanics?

**Is it possible that these expressions represent force/matter duality ( or wave/particle duality )?**

First power:

( x + y ) / ( x - y ) = x+y / x-y

Second power:

(x+y)^{2} / [ (x)^{2} - (y)^{2} ] = (x+y)(x+y) / (x+y)(x-y) = x+y / x-y

Next articles will deal with pairs, triplets, and quadruplets of the group of angles. And then CP VioaltionPhase Angle for Neutrino.

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