16. Book 5 - Integer Formula for Dimensionless Coupling Constants of Fundamental Forces

21 September 2017 AD; Feast of St Matthew

 

Andrew Yanthar-Wasilik

 

 

Before the General Formula is derived in the following books, here is a short description of formulae for particular constants.

Because the whole formula is too long to put in one piece, it must be split into parts for a clearer understanding.

After many tests on different possibilities, the experimental results are as follows:

 

 ✠1 - Integer Formula for the fine structure constant alpha, α_E, ruling electromagnetic force.

 

 

A = ( C₀)^{(24 ⁄ 24)}

B = ( C₁₆ / ( 8 + 2 * (24/24) ) )^{(88 ⁄ 24)}

C = ( C₁₆) * (8/24)

Where C₀ and C₁₆ are calculated constants (see books 4a and 4b for numerical values).

ExpM = ( A / B )^C

ExpM stands for Exponent Main

D = 16 + ExpM

FT(x=D) = ( C₀) * ( π / e )^D

where FT(x) is value of transcendental constant at x = D (see Book 1)

ExpP = ( 16 + (24 / 24) ) / ExpM

where ExpP stands for Exponent Partial

Now, fine structure constant to the power (-1/2) may be calculated

( α_E )^{( − 1 ⁄ 2)} = ( FT(x) / ( 8 + 2 * (24/24))) ^ExpP

This last result to the power (2) will give reciprocal of alpha, and result to the power (-1) finally gives

 the fine structure constant, alpha, α_E with numerical value:

( α_E )^{( − 1)} = 137.035 999 181 727 13

This result is consistent with alpha calculated by a Japanese team from Nagoya University in 2012

( α_E )^{( − 1)} = 137.035 999 174

 

 

✠2 - Integer Formula for the weak force, α_W, the ruling force of decays.

Following the same procedure as above, we get:

 

 

A = ( C₀)^{(27 ⁄ 24)}

B = ( C₁₇ / ( 9 + 2 * ( 24/27 ) ) )^{(99 ⁄ 24)}

C = ( C₁₇ ) * (9/24)

Where C₀ and C₁₇ are calculated constants (see books 4a and 4b for numerical values).

Again

ExpM = ( A / B )^C

ExpM stands for Exponent Main

D = 17 + ExpM

FT(x = D) = ( C₀ ) * ( π / e )^D

where FT(x) is value of transcendental constant at x = D (see Book 1)

ExpP = ( 17 + ( 27/24 ) ) / ExpM

where ExpP stands for Exponent Partial

Now, weak force constant to the power (-1/2) may be calculated

( α_W )^{( − 1 ⁄ 2)} = ( FT(x) / ( 9 + 2 * (24/27))) ^ExpP

and numerical value of weak force constant, α_W, is:

α_W = 4.365 962 559 083 515 × 10^{( − 7)}

The official guess of the weak force coupling constant is:

α_Wguess = 3 × 10 ^− 7

 

 

✠3 - Integer Formula for the strong nuclear force, α_S, ruling quarks, and nucleons.

Following the same procedure as above, we get:

 

 

A = ( C₀)^{( − 21 ⁄ 24)}

B = ( C₁ / ( -7 + 2 * ( -24/21 ) ) )^{( − 77 ⁄ 24)}

C = ( C₁ ) * (-7/24)

Where C₀ and C₁ are calculated constants (see books 4a and 4b for numerical values).

again

ExpM = ( A / B )^C

ExpM stands for Exponent Main

D = 1 + ExpM

FT(x = D) = ( C₀ ) * ( π / e )^D

where FT(x) is value of transcendental constant at x = D (see Book 1)

ExpP = ( 1 + ( -21/24 ) ) / ExpM

where ExpP stands for Exponent Partial

Now, strong force constant to the power (-1/2) may be calculated:

( α_S )^{( − 1 ⁄ 2)} = ( FT(x) / ( -7 + 2 * (-24/21))) ^ExpP

and numerical value of strong force coupling constant in rectangular coordinates is:

α_S = 1.065 644 850 828 233... + 1.661 157 872 169 887...i  x 10^-2

changing to polar coordinates gives modulus (length of the vector):

α_S = 1.065 774 315 999 571 ...

with the argument (angle between imaginary and real part):

θ_S = 0.893 070 773 377... degrees

The official guess of the numerical value of strong nuclear force is:

α_Sguess approx. = 1

 

 

✠4 - Gravity force coupling constant does not have Integer Formula (2 March 2019 - Yes, it does have an integer formula at x=18); it will be derived later from General Formula for forces and constants. The coupling force of gravity is weaker than an official educated guess.

 

Summary.

 

♦ Constant C₁ gives the numerical value of strong nuclear force (complex number) using the above formulae.

α_s = 1.065 774 315 999 571...  The official "value" is α_Sguess approx. = 1 

♦ Constant C₁₆ gives the numerical value of fine structure constant (electromagnetic forces) using the above formulae.

( α_E )^{( − 1)} = 137.035 999 181 727 13...  Official value is approximate: ( α_E )^{( − 1)} = 137.035 999 174 (changes every couple of years once better results are obtained from experiments).

♦ Constant C₁₇ gives the numerical value of weak force responsible for particle decay (using the above formulae).

α_W = 4.365 962 559 083 515... × 10^{( − 7)}  Official guess is: α_Wguess = 3 × 10 ^− 7 

♦ The numerical value of gravity is not connected to Integer Constant, as are the previous ones. It will be calculated later on.

 

The numbers were calculated using Intel Parallel Studio Fortran.

 

Andrew Yanthar-Wasilik