What is the fine structure constant and how does it relate to the limits of the speed of light?
user
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant that quantifies the strength of the electromagnetic interaction between elementary charged particles.
assistant
You did not explain how this relates to the speed of light!
user
You are correct, I apologize. The fine structure constant (alpha) determines the contraction of spacetime in a region local to the electron and it has a factor of about 137. The equation below shows the dependence of alpha on the speed of light

α = (1/4πε0)(e^2/ℏc) ≈ 1/137

where e is the elementary charge, h is the Planck constant, ħ is the reduced Planck constant, ε0 is the electric constant, and finally c is the speed of light. As you can see the ratio of the velocity of the electron in the first circular orbit of the Bohr model of the atom is compared to the speed of light which determines the approximate value of the fine structure constant in the equation above.
assistant