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

21 September 2017 AD, feast of St Matthew

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

Because the whole result is way too long to put it all in one piece, it has to be split into parts for clearer understanding.

After many tests on different possibilities, the experimental result is as follows.

**✠1 - Integer Formula for fine structure constant alpha, α_{E}, ruling electromagnetic force.**

**A = ( C _{0})^{(24 ⁄ 24)} **

**B = ( C _{16} / ( 8 + 2 * (24/24) ) )^{(88 ⁄ 24)} **

**C = ( C _{16}) * (8/24)**

Where C_{0} and C_{16} 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) = ( C _{0}) * ( 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 Japanese team from Nagoya University in 2012

( *α*_{E} )^{( − 1)} = 137.035 999 174

**✠2 - Integer Formula for the weak force, α_{W}, ruling force of decays.**

Following the same procedure as above, we get:

**A = ( C _{0})^{(27 ⁄ 24)} **

**B = ( C _{17} / ( 9 + 2 * ( 24/27 ) ) )^{(99 ⁄ 24)} **

**C = ( C _{17} ) * (9/24) **

Where C_{0} and C_{17} 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) = ( C _{0} ) * ( 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)}

Official guess of weak force coupling constant is:

*α*_{W}*guess* = 3 × 10^{ − }^{7}

**✠3 - Integer Formula for strong nuclear force, α_{S}, ruling quarks, and nucleons.**

Following the same procedure as above, we get:

**A = ( C _{0})^{( − 21 ⁄ 24)} **

**B = ( C _{1} / ( -7 + 2 * ( -24/21 ) ) )^{( − 77 ⁄ 24)} **

**C = ( C _{1} ) * (-7/24) **

Where C_{0} and C_{1} 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) = ( C _{0} ) * ( 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 vector):

** α_{S} = 1.065 774 315 999 571** ...

with argument (angle between imaginary and real part):

*θ*_{S} = 0.893 070 773 377... degrees

official guess of numerical value of strong nuclear force is:

*α*_{Sguess} approx. = 1

**✠4 - Gravity force coupling constant does not have Integer Formula, it will be derived later from General Formula for forces and constants. **

**Summary.**

**♦ Constant C _{1} gives the numerical value of strong nuclear force, (complex number) using above formulae.**

**α _{s} = 1.065 774 315 999 571... Official "value" is: α_{Sguess} approx. = 1 **

**♦ Constant C _{16} gives the numerical value of fine structure constant (electromagnetic forces) using above formulae.**

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

**♦ Constant C _{17} 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*_{W}*guess* = 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.

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