Planck charge

The Planck charge is times greater than the elementary charge e carried by an electron.

The Planck charge is defined as:

This is so because a charged elementary particle has approximately one Planck charge, but a mass many orders of magnitude smaller than the Planck mass.

The Planck current is that current which, in a conductor, carries a Planck charge in Planck time.

In physics, the Planck charge, denoted by , is one of the base units in the system of natural units called Planck units.

If the Planck charge were instead defined to normalize the permittivity of free space, ε, rather than the Coulomb constant, 1/(4πε), then the Planck impedance would be identical to the characteristic impedance of free space.

Thus, the planck mass is an attempt to absorb the gravitational coupling constant into the unit of mass (and those of distance/time as well), as the planck charge does for the fine-structure constant; naturally it is impossible to truly set either of these dimensionless numbers to zero.

Note in the second equation that if instead of planck masses the electron mass were used, the equation would no longer be unitary and instead equal a gravitational coupling constant, analogous to how the equation of the fine-structure constant operates with respect to the elementary charge and the Planck charge.