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Lapidus
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How do (e^2)/(4Pi x epsilon x Planck constant x speed of light) cancel to give one and make the fine structure constant dimensionless?
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The fine structure constant, denoted by the Greek letter alpha (α), is a dimensionless physical constant that characterizes the strength of the electromagnetic interaction between elementary particles.
The accepted numerical value of the fine structure constant is approximately 1/137 or 0.0072973525664, which is a dimensionless quantity with no units.
The fine structure constant is related to the speed of light through the equation α = e^2/4πε0ħc, where e is the elementary charge, ε0 is the vacuum permittivity, ħ is the reduced Planck's constant, and c is the speed of light in a vacuum.
The fine structure constant is considered to be a fundamental constant because it describes the strength of the fundamental force of electromagnetism, which governs the interactions between charged particles.
The fine structure constant is not directly related to the strength of other fundamental forces, but it does play a role in determining the strength of the strong nuclear force and weak nuclear force through the concept of coupling constants. However, the exact relationship between these forces and the fine structure constant is still an area of active research in theoretical physics.