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, αE, 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
( αE )( − 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, αE with numerical value:
( αE )( − 1) = 137.035 999 181 727 13
This result is consistent with alpha calculated by a Japanese team from Nagoya University in 2012
( αE )( − 1) = 137.035 999 174
✠2 - Integer Formula for the weak force, αW, 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
( αW )( − 1 ⁄ 2) = ( FT(x) / ( 9 + 2 * (24/27))) ExpP
and numerical value of weak force constant, αW, is:
αW = 4.365 962 559 083 515 × 10( − 7)
The official guess of the weak force coupling constant is:
αWguess = 3 × 10 − 7
✠3 - Integer Formula for the strong nuclear force, αS, 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:
( αS )( − 1 ⁄ 2) = ( FT(x) / ( -7 + 2 * (-24/21))) ExpP
and numerical value of strong force coupling constant in rectangular coordinates is:
αS = 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):
αS = 1.065 774 315 999 571 ...
with the argument (angle between imaginary and real part):
θS = 0.893 070 773 377... degrees
The official guess of the numerical value of strong nuclear force is:
αSguess 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.
αs = 1.065 774 315 999 571... The official "value" is αSguess approx. = 1
♦ Constant C16 gives the numerical value of fine structure constant (electromagnetic forces) using the above formulae.
( αE )( − 1) = 137.035 999 181 727 13... Official value is approximate: ( αE )( − 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).
αW = 4.365 962 559 083 515... × 10( − 7) Official guess is: αWguess = 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
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