# Does electromagnetism have no free parameters?

In SI units, Maxwell's equations (in vacuo) seem to have two free "parameters" or "constants". The vacuum permittivity, however, can be eliminated by properly redefining the electric charge, leaving just one parameter, which can be taken to be the speed of electromagnetic waves (as is done in cgs units). Of course, that's the speed of light, $$c$$, which is the only constant in special relativity. I find this quite fascinating, as EM, as a physical theory, has no free parameters if it is assumed to be consistent with relativity. Alternatively, one can think of EM+SR as having one single parameter, $$c$$. (Of course, you can also eliminate $$c$$ by making it equal to 1, but you still have it in your new time/space conversion definition, so it's not really "gone", unlike the electric charge unit redefinition that can eliminate the vaccum permittivity.) This is unlike Newtonian gravity or GR, for which a constant $$G$$ is needed (plus potentially $$\Lambda$$ in GR), not to mention the Standard Model of particle physics.

I would be really grateful if you could comment on this reflection. Should I really be amazed at the fact that EM has no free parameter, whereas gravity (Newtonian or GR) or the SM do? Does this mean anything deep about EM, or EM+SR, or am I missing something?

Thanks!

EM theory has also elementary charge $$1.6\text{e}-19$$ C, characteristic length of electrons $$1\text{e}-15$$ m where things go weird regarding EM mass of composite systems. If we include material media into EM theory, many more constants and properties have to be included.
• If you think gravity has "fundamental parameter" $G$, why don't you think electromagnetic force has similar "fundamental parameter" $\epsilon_0$? Both $G$ and $\epsilon_0$ can be hidden via change of units of mass and charge, but then the "fundamental parameter" is in those units, no? Commented Oct 22, 2021 at 12:27