# [Physics] the significance of Planck charge

absolute-unitschargephysical constantsquantum-gravityunits

It seems for me that Planck units are somehow connected to limits where our current knowledge breaks down because of (quantum) gravitational effects. Please correct me if I'm wrong.

For example Planck mass is the maximum mass allowed for point particle. Had a particle had mass greater than Planck mass, it would have formed black hole, because its Compton wavelength would have been less than its Schwarzschild radius.

Does similar physical significance exist for Planck charge?

My understanding of the Planck charge is that it is the unit charge necessary to normalize

1. the speed of light (and other "instantaneous" interactions e.g. strong force and gravity), $c=1$
2. reduced Planck constant, $\hbar=1$
3. Coulomb constant, $\frac{1}{4 \pi \epsilon_0}=1$

So it's a natural definition of charge that has no reference to the elementary charge. So you can represent the value of the elementary charge in terms of this Planck charge and it comes out as

$$e = \sqrt{\alpha}$$

where $\alpha$ is the fine-structure constnat.

So the significance of the Planck charge is, like the other Planck units, they are defined in such a way that no object or particle (not even any subatomic particles) are needed nor used to define the base units. Only free space. Then you can go about asking what the properties of these elementary sub-atomic particles are, in terms of these units that only normalize properties of free space. For the charge of an electron, it is $-e = -\sqrt{\alpha} \approx -0.0854245$, in terms of Planck units.

I prefer rationalized units over unrationalized units because I think it is useful to equate the concepts of flux density and field strength and that is done if you normalize the electric constant rather than the Coulomb constant. If you do that, the elementary charge comes out as $e=\sqrt{4 \pi \alpha} \approx 0.302822$. This is done in a few books on QFT or something and makes it more clear that the elementary charge, while not exactly the natural unit of charge, is in the ball park of the natural unit of charge. Well within an order of magnitude.