# When was Coulomb's constant made/established?

Charles-Augustin de Coulomb lived from 14 June 1736 – 23 August 1806. Coulomb's constant is

$$k_{\text e}=\alpha\frac{\hbar c}{e^2},$$

a form of Planck's constant is included, but Max Planck lived 23 April 1858 – 4 October 1947.

• Isn't this just a case of a constant being first empirically determined through measurements, and then explained as physical theory develops? – Anders Sandberg Apr 12 at 4:00

The relationship you've quoted, $$k_e = \alpha \frac{\hbar c}{e^2},$$ does not serve as a definition of $$k_e$$. At best, it serves as a definition of the fine structure constant, $$\alpha$$, which can be thought of in two distinct ways:
• It gives the strength of the electromagnetic interaction in 'natural units' - that is, in the units that are natural once you have established both quantum mechanics and special relativity, so you can set both $$\hbar$$ and $$c$$ to unity.
• It gives (the inverse of) the speed of light in 'atomic' units, which are also quantum mechanical, and in which you set both $$\hbar$$ and the electron-electron interaction constant to unity.
In either case, $$\alpha$$ is an intrinsically quantum-mechanical object, and (unless you're fully committed to an outlook fully encased within quantum field theory) it cannot really be used to define the Coulomb constant.