It is believed that the fine stucture constant is not a constant. That is, it changes over time. This is not firmly established but there are some good indications (i.e. experimental data). Why would that interest me, you wonder?
Well the fine structure constant depends on 4 other constants:
- e: electrical charge
- c: speed of light
- h: Planck's cst
- e0: permittivity of space
So if the fine stucture cst changes over time, one or more of these "constants" has to change. Since it is probably the permittivity of space that changes your question would be answered: they don't...
Like I said: this is not firmly established. There are also (Australian) experiments suggesting that the speed of light is not constant in time, but in fact slowly decreasing (or was it increasing). The problem is that there are no checks for these experiments yet.