30 July 2024

St. Peter Chrysologus 450 AD; Sts. Abdon & Sennen 303 AD

 

In this article, I will calculate the last anomalous magnetic moment in this series, the anomalous magnetic moment of the electron, the g-2 electron. The calculation will be done using transcendentals but in a slightly different way than in the g-2 muon case. Again, the final result agrees perfectly (12-digit accuracy) with the experimental value.

Before I start, I would like to explain to the reader (if necessary) what this anomalous magnetic moment is. Basically, it is a g-factor of the electron (or muon and tau) less by the value 2.0 and then the result is divided by 2.0, that’s all there is. If one wants to see the explanation from Fermi Labs and Wikipedia, here are the links:

ttps://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment

 

The following are theoretical and experimental values of the g-2 electron:

 

Theoretical value of the g-2 electron = g-2 electron_THEORY = 0.001159652181643(764)

 

And, from 2023,

 

Experimental value of g-2 electron_EXPERIMENT = 0.00115965218059(13)

 

Three transcendental constants will be used:

 

S5Vx④P = 11723.1886417; i.e., from multiplication/division table, 4^th configuration, pairs

 

See   >>>   https://luxdeluce.com/360-148-division-multiplication-cross-product-table-of-transcendental-constants-in-quantum-physics-and-cosmology.html

 

PTx①P = 271.083197567; i.e., from multiplication/division table, 1^st configuration, pairs

 

See   >>>   https://luxdeluce.com/356-144-multiplication-division-table-of-transcendental-constants-in-quantum-physics-and-cosmology.html

 

And,

 

Elementary transcendental constant, C₁₆

C₁₆ = 9.999838797805; this constant will appear many times in calculations

 

See   >>>   https://luxdeluce.com/16-table-of-transcendental-constants-going-up-from-constant-number-8-equal-to.html

 

Let us do the calculations:

 

Step A:

 

A = S5Vx④P = 11723.1886417

 

Step B:

 

B = A – (g-2_{ELECTRON – EXPERIMENT}) X 1E7 = S5Vx④P = 11723.1886417 - 0.00115965218059(13) X1E7

= 11723.1886417 – 11596.5218059 = 126.6668358

 

So,

 

B = 126.6668358

 

Step C:

 

B = 126.6668358;

 

We have to approximate this value with a fraction, which is equal to:

B_APPROX = 126.666666667 = 380/3

 

Now, we have to obtain an exact exponent of C₁₆ /10.0, from the following equation:

(126.6668358) = ( 380/3 )^x  Eqn. 1

And, from the above equation,

x = LN (126.6668358) / LN ( 380/3 )

x = 1.00000027579

x^-1 = 0.999999724208

 

Now, this (1/x) looks almost like a constant

C₁₆ /10.0 = 0.9999838797805

 

Let us use the following equation to obtain the exponent of C₁₆ /10.0

( 1/x = 0.999999724208 ) = ( C₁₆ /10.0 )^y Eqn. 2

 

And, exponent y is equal to

 

y = LN ( 1/x = 0.999999724208 ) / LN ( C₁₆ /10.0 = 0.9999838797805 )

y = 1.71083169452E-2

 

Step D:

 

Notice that constant

PTx①P = 271.083197567

Has a lot in common with exponent y.

 

Let us divide constant PTx by 100, subtract 1.0 from PTx/100, and then divide the result by 100:

D = {(( PTx①P = 271.083197567 ) / 100 ) – 1 } / 100 =

= ( 2.71083197567 – 1 ) /100 = 1.71083197567 / 100 = 0.0171083197567

D = 0.0171083197567

 

This is almost equal to the exponent

y = 1.71083169452E-2

 

Step E:

 

Constant C₁₆ /10.0 to the power of D

E = ( C₁₆ /10.0 = 0.9999838797805 )^{( D = 0.0171083197567 )} = 0.999999724208

 

So, this result is approximated ( 1/x ).

 

Step F:

 

Now we can go back to Step C and calculate ( 380 / 3 )^{( 1 / E )} ( this will be part of Eqn. 1)

F = ( 380 / 3 )^{( 1 / E )} = 126.6668358

 

Final Step G:

 

Now we can obtain the value of the anomalous magnetic moment of an electron:

 

G = A – F = ( g-2 _{ELECTRON EXPERIMENT} ) / 1E7 =

G = (( A = S5Vx④P = 11723.1886417 ) – ( F = ( 380 / 3 )^{( 1 / E )} = 126.6668358 )) / 1E7 =

G = ( 11596.5218059 / 1E7 ) = 0.00115965218059

 

And,

 

Result of ( g-2 _{ELECTRON EXPERIMENT} ) = 0.00115965218059

 

Versus Laboratory Experiment value from 2023,

 

Experimental value of g-2 electron_EXPERIMENT = 0.00115965218059(13)

 

The results are identical, again showing the power of transcendental constants.

 

HP Prime Calculator has only 12-digit accuracy. Once it is done through FORTRAN, the number of significant digits will increase substantially.

 

The next articles will be on the g-factors of the proton, neutron, electron, and muon. Unless, I can see that this is enough heavy calculations, so, I will proceed with Mathematics behind this, and only after some posts I will go back to the calculation of the g-factors again.

 

 

 

 

 

 

The Flemalle Panels -Trinity of the Broken Body Robert Campin, 1430:

 

 

Medieval Bridgettine Chants; St. Birgitta Convent (?)

Summe Trinitati   >>>   https://www.youtube.com/watch?v=KLa1_ddrVwY