“Seems like the physical mechanics of our universe depends on a 1:137 ratio, especially on an atomic level” -NATURE

The number 137 is viewed as a boundary between the physical and spiritual realms.

There are mad universal ratios that involve the number 137:

Fine‑structure constant ALPHA (α) – a dimensionless coupling constant that measures the strength of the electromagnetic interaction. Its measured value is ≈ 1/137.036, so the reciprocal is about 137. This ratio links the electron charge, Planck’s constant, the speed of light, and the vacuum permittivity, and appears in many atomic‑physics formulas. 

Golden angle – the angle that divides a circle according to the golden ratio. It is ≈ 137.508° (often rounded to 137°) and governs the spiral patterns of seeds, leaves, and galaxies. Wikipedia

Electron orbital speed in the Bohr model – the speed of an electron in the ground state of hydrogen is about 1/137 times the speed of light, i.e., the electron moves 137 times slower than light. PBS

Energy ratios in the Bohr atom – the binding energy of the ground‑state electron is smaller than the electron’s rest‑mass energy by a factor of 1/137².

Role in the universe – α determines the size of the fine‑structure splitting of atomic spectra and thus influences chemistry, atomic stability and the formation of elements. Because 1/α is small, electromagnetism is weak enough for atoms to form, yet large enough that stars can synthesize carbon; a significantly different value would make life as we know it impossible. [Quanta Magazine]

Quantum vacuum fluctuations – Even “empty” space is filled with virtual particle‑antiparticle pairs that constantly appear and vanish. These fluctuations affect the effective electromagnetic coupling, causing α to run with energy. Thus the vacuum is not truly empty; its properties are directly tied to the value of α. [Big Think ]

-NATURE