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alpha (α)

alpha ($\alpha$), commonly referred to as the fine-structure constant, is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, approximately equal to $1/137$ ($0.0072973525693$).

Definition & Formula

$\alpha$ is defined by the relation:

$\alpha =\frac{e^2}{4\pi {\epsilon }_0\hslash c}$

Where:

• $e$: elementary charge
• ${\epsilon }_0$: vacuum electric permittivity
• $\hslash$: reduced Planck constant
• $c`: speed of light in vacuum

Because it is dimensionless, its value is independent of the system of units used. It governs the scale of Fine Structure splitting in atomic spectra and determines the coupling strength in Quantum Electrodynamics.

Significance & Enigma

The precise origin and theoretical derivation of $\alpha$‘s numerical value remain one of the greatest unsolved problems in physics. Unlike constants that can be derived from deeper symmetries, $\alpha$ appears to be an input parameter to the Standard Model.

• Electromagnetic Strength: It dictates the probability of photons interacting with charged particles.
• Universal Constant: Appears universally in electromagnetic phenomena across all scales.
• The 1/137 Mystery: The specific value approximates $1/137$, a number that has intrigued physicists (including Richard Feynman) for its lack of obvious theoretical justification.

Related Notes & Sources

• 137): Derivation, Significance, and Quantum Enigma
  • Summary of PBS Space Time analysis on the derivation and quantum enigma of $\text{[}[concepts/fine-structure-constant|alpha]]$.
  • Fine Structure Constant (1/137): Derivation, Significance, and Quantum Enigma

References

• PBS Space Time. “Why Is 1/137 One of the Greatest Unsolved Problems In Physics?” YouTube video, https://www.youtube.com/watch?v=RCSSgxV9qNw