8 March 2024 AD; St. John of God (1550 AD)

The third step is to do two scans of the universal equation at each integral point of the complex plane. One scan is done with a Real Vector (Real part positive, Imaginary part equals 0), and another scan with an Imaginary Vector (Imaginary part negative and Real part equals 0). These two vectors are substituted separately into the main equation, giving real and imaginary scans. Then the results are added together to form a sum that contains vector magnitude (i.e., magnetic moment vector) and mixing (oscillation angle) among other things (in polar and rectangular form).

Here are two examples of how this is done for Quark θ₁₃.

Quark θ₁₃ is located at Constant C₀ (sometimes written as C_{M_0}) – when I describe the graph of the equation, you will see the connection between various elementary particles and the numbers of constants.

And now we have the examples from the FORTRAN programs.

First, Real Vector, Real Unit Vector.

      PROGRAM ALFA C_M_0     

      IMPLICIT NONE

      COMPLEX*16  F, EXPM, FT, EXPP, ALFA, J, L, R, S, Q, T, U

      COMPLEX*16 EXPM1, EXPM2, EXPM3, C_M_0, C_0, C_87

      COMPLEX*16 ALFA_MINUS_HALF, ALFA_SQUARE

      REAL*8 X, Y, Z, POL, THETA, THETA_DEG, C_8

      REAL*8 A, C, B, D, G, K, O, P

     

      C_M_0 = ( 0.986976350384356956D+00, 0.0D+00 )     

      C_0 = ( 0.986976350384356956D+00, 0.0D+00 )     

      C_87 = ( 1.1557273497909217D+00, 0.0D+00 )     

      C_8 = 0.314159265358979312D+01

The highlighted line is a complex vector with values (π/e, 0.0). Running this value through the Universal Equation will produce the real values for Quark θ₁₃.

Second, imaginary vector, imaginary unit vector.

      PROGRAM ALFA C_M_0     

      IMPLICIT NONE

      COMPLEX*16  F, EXPM, FT, EXPP, ALFA, J, L, R, S, Q, T, U

      COMPLEX*16 EXPM1, EXPM2, EXPM3, C_M_0, C_0, C_87

      COMPLEX*16 ALFA_MINUS_HALF, ALFA_SQUARE

      REAL*8 X, Y, Z, POL, THETA, THETA_DEG, C_8

      REAL*8 A, C, B, D, G, K, O, P

     

      C_M_0 = ( 0.986976350384356956D+00, 0.0D+00 )     

      C_0 = ( 0.986976350384356956D+00, 0.0D+00 )     

      C_87 = ( 0.0D+00, -1.1557273497909217D+00 )     

      C_8 = 0.314159265358979312D+01

The yellow line is an imaginary unit vector (0.0, (-π/e)). Running this value through the universal equation will produce the imaginary values for Quark θ₁₃.

The third sub-step is to add two previous values, Real and Imaginary, giving the final results.

If you run programs described above for each constant representing a different one in three particles (i.e., three neutrinos, three quarks, etc.) then you get sort of M-shape as in the following picture /please disregard inscriptions about the neutrinos and so on – this is still the work in progress/.

 

 

 

 

This is the graph of all the particles (three in each set) starting with C₀ (Quark θ₁₃) to the right and Neutrino θ₁₃ to the left, starting at the transcendental constant C_{MINUS 1}.

Then to the right are three bosons and to the left might be three gravitons, etc., but there is not enough data right now to be sure of this order.

Finally, there is the output of the two previous programs and the third one – sum on Real and Imaginary parts, which contains mixing angles and among other things the magnetic moments of the quark in this example, etc.

 

 

 

Printout from the sum of the Real and Imaginary parts.

Quark theta13

ALFA C_M_0 INVISIBLE

 A + Bi     0.31543485581699715059D+00   -0.26183391631054520055D+00

 MAGNITUDE & THETA IN RADIANS    0.40994651845674623392D+00   -0.69281098073758540234D+00

 MAGNITUDE & THETA IN DEGREES    0.40994651845674623392D+00   -0.39695145196583020208D+02

 MAGNITUDE & THETA FINAL IN RADIANS    0.40994651845674623392D+00    0.55903743264420011627D+01

 MAGNITUDE & THETA FINAL IN DEGREES    0.40994651845674623392D+00    0.32030485480341701532D+03

 

 ALFA C_M_0 VISIBLE

 C + Di     0.86487560717547162792D+00    0.23694398624611551218D+00

 MAGNITUDE & THETA IN RADIANS    0.89674537551377431210D+00    0.26740194047193616145D+00

 MAGNITUDE & THETA IN DEGREES    0.89674537551377431210D+00    0.15321002622650418346D+02

 MAGNITUDE & THETA FINAL IN RADIANS    0.89674537551377431210D+00    0.26740194047193616145D+00

 MAGNITUDE & THETA FINAL IN DEGREES    0.89674537551377431210D+00    0.15321002622650418346D+02

SUM

  ( A + Bi ) + ( C + Di )    0.11803104629924687785D+01   -0.24889930064429688361D-01

 MAGNITUDE & THETA IN RADIANS     0.11805728684279122032D+01   -0.21084487866453137384D-01

 MAGNITUDE & THETA IN DEGREES     0.11805728684279122032D+01   -0.12080521679425584303D+01

 MAGNITUDE & THETA FINAL IN RADIANS    0.11805728684279122032D+01    0.62621008193131331154D+01

 MAGNITUDE & THETA FINAL IN DEGREES    0.11805728684279122032D+01    0.35879194783205741714D+00

 

For example, the vector magnitude is 1.180572868…

And the angle in radians is 0.02108448…

The vector magnitude is dimensionless as well as the angle.

 

This much for the introduction. As you can see, the process is rather complicated but attainable.

The next articles will be about mixing angles of quarks /exact value plus nice approximation/, and then the g-factor and magnetic moments of quarks, and finally the inside works of quarks in the proton and neutron regarding electromagnetic force.