Fine Structure Constant

Fine Structure Constant — A Fundamental Number in Physics

The fine structure constant (α) is a key dimensionless number in physics, measuring the strength of
electromagnetic interactions between charged particles like electrons and light.

Its recent value approximation α ≈ 0.0072973525643(59), or as 1/α ≈ 137.035999206(11).

It appears in the formula α = e² / (4πε₀ ħ c), where:

• e is the elementary charge,
• ε₀ is the permittivity of free space,
• ħ is the reduced Planck's constant,
• c is the speed of light.

Unlike π or e, α is not derived from pure mathematics — it is measured experimentally and remains one
of physics' deepest mysteries.

Its reciprocal being very close to the prime number 137 has puzzled scientists for decades, leading some
to wonder if it hints at deeper patterns in nature.

How to mathematically acquire the fine-structure constant by means of pi and phi:

This constant ties together electricity, magnetism, and quantum effects — a quiet but essential thread
in the fabric of the universe.

Exploratory ideas only — the exact origin of α's value is still unknown

The fine-structure recomended value 1/α ≈ 137.035999206(11)² = 18778.86507838683263

Efforts to match this mathematically began with constant π (π⁸ x 2) 18977.06203214114801

π¹  x π⁴ = π⁵
π²  x π⁴ = π⁶
π⁴  x π⁴ = π⁸ (x 2) = 18977.06203214114801
π⁸  x π⁴ = π¹²
π¹⁶ x π⁴ = π²⁰
etc.

A more detailed explanation:

3.141592653589793238462 = 1 / 0.318309886183790671537 (1 / π)
3.141592653589793238462 x 2 = 6.283185307179586476925
0.020531964509368670378    /    6.283185307179586476925 =
0.003267763643053385472 = 1 / 306.0196847852814533215 (π⁵)

9.869604401089358618834 = 1 / 0.101321183642337771443 (1 / π²)
9.869604401089358618834 x 2 = 19.73920880217871723766
0.020531964509368670378    /    19.73920880217871723766 =
0.001040161473295852296 = 1 / 961.3891935753044371132 (π⁶)

97.40909103400243723644 = 1 / 0.010265982254684335189 (1 / π⁴)
97.40909103400243723644 x 2 = 194.8181820680048744728
0.020531964509368670378    /    194.8181820680048744728 =
0.000105390391653493666 = 1 / 9488.531016070574007128 (π⁸)

1 -------------------------------   X   ------------------------------ (Base line and reversal point)

9488.531016070574007128 = 1 / 0.000105390391653493666 (1 / π⁸)
9488.531016070574007128 x 2 = 18977.06203214114801425
0.020531964509368670378    /    18977.06203214114801425 =
0.000001081935890528998 = 1 / 924269.1815234579471175 (π¹²)

90032220.84293327956713 = 1 / 0.000000011107134652876 (1 / π¹⁶)
90032220.84293327956713 x 2 = 180064441.6858665591342
0.020531964509368670378    /    180064441.6858665591342 =
0.000000000114025647246 = 1 / 8769956796.145963794865 (π²⁰)

etc.

0.020531964509368670378 / 18977.06203214114801425 = 0.0000010819358905289
(2 / π⁴) / (π⁸ x 2) = 1 / π¹²

0.0000010819358905289… / π⁴ (97.40909...) and continue:

0.0000010819358905289 / π⁴ =
0.0000000111071346528 / π⁴ =
0.0000000001140256472 / π⁴ =
etc.
Adding up all of the layers to infinity = 0.0000010931582335562 =  

A visual explanation:

(Spectral lines perhaps?)

0.020531964509368670378… / 18977.06203214114801425… = 0.0000010819358905289…
0.020531964509368670378… / 18784.22352674753383243… = 0.0000010930430251818…
0.020531964509368670378… / 18782.24385007314313978… = 0.0000010931582335562…

18977.06203214114801425… - 192.83850539361418182… =
18784.22352674753383243… - 001.97967667439069265… =
18782.24385007314313978… - 000.02053196450936867… =
18782.22331810863377111…

Dividing by π⁴:

192.83850539361418182… / π⁴ =
...1.97967667439069265… / π⁴ =
etc. to:
...0.02053196450936867… (2 / π⁴)

Adding up the layers: =

194.8387140325142431432… (π⁴ / .5) + (2 / π⁴)

Next step acquiring the end (bottom) number:

194.8387140325142431432… / √(π⁸ / π) =
3.545281301022101405403… +
0.082127858037474681513… (8 / π⁴) =
3.627409159059576086916…

18782.22331810863377… - 3.627409159059576086916… = 18778.59590894957419502…  

18977.06203214114801425… Start # -
18778.59590894957419502… End # =
198.4661231915738192301… -
0.269134858448657890432… (explanation follows) = 198.1969883331251613…

18977.06203214114801425… - 198.1969883331251613… = 18778.86504380802285291…
or
18778.59590894957419502… + 0.269134858448657890… = 18778.86504380802285291…

While working on possibilities a major clue presented itself:

When I subtracted the following two numbers,

18778.865043837324229… original number from the top of the page -
18778.59590894957419502… end # =
0.26913488775003398… -
0.020531964509368670378… (2 / π⁴) =
0.248602923240665309622… 1 / x =
4.022478846847383539716…² =
16.18033607333465644263…

and noticing phi numbers, I reasonably deduced that phi is part of the solution!
I decided to run with it and reverse the process starting with (√1.25 + .5) x 10 =

16.18033988749894848204… √ =
4.022479320953551960229… 1 / x =
0.248602893939289220053… +
0.020531964509368670378… (2 / π⁴) =
0.269134858448657890432… +
18778.59590894957419502… =
18778.86504380802285291… (original number now adjusted, and locked in by ɸ and π) √ =

137.035999079833116867867985771960524751261126710956764394872128728819663336…
1/x
0.0072973525695056931682062262973500731680835106878962634963700448348384385…

I do not believe that these two special numbers 3168 and 31680 are random numbers, especially
so close together, but were placed deliberately. If so, perhaps all those numbers are a language!
Wouldn't it be amazing if it says, "In the beginning God created the heaven and the earth." ?

Three interesting facts:

1. The value for the name “Lord Jesus Christ” in Greek numeric is 3168, the number of his name.

2. Earth's dimensions fitted into a square has a perimeter of 31680 miles (7920 x 4).

3. He was born southeast of Bethlehem, at latitude 31.68 degrees North.

Inserting the final section to complete the formula:

137.035999206157399222318479001000262689537834609473995213691525285349733120…
1/x
0.00729735256277875402980213640259738753519520968347474978298633008561682393…

Observe the interesting number pattern in that 7th formula section: 1, 2, 4, 8, 16

The first 3 sections span the distance between (π⁸ x 2) and the bottom line or end number.
From there the last 3 sections bounce back up to the alpha line, like a fold as in a curtain!

Speed of light in miles per second:

18778.8650438… - = 18628.2396760… x 10 = 186282.396760…

18778.8650784… - = 18628.2397106… x 10 = 186282.397106…

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