  Much work has been done after the possibility of a fine structure constant
being time-varying. It has been taken as an indication of a time-varying speed
of light. Here we prove that this is not the case. We prove that the speed of
light may or may not vary with time, independently of the fine structure
constant being constant or not. Time variations of the speed of light, if
present, have to be derived by some other means and not from the fine structure
constant. No implications based on the possible variations of the fine
structure constant can be imposed on the speed of light.
