Prevailing and conventional wisdom holds that intermediate gauge Bosons for long range interactions such as the gravitational and electromagnetic interactions must be massless as is assumed to be the case for the photon which mediates the electromagnetic interaction. We have argued in Nyambuya (2013) that it should in-principle be possible to have massive photons. The problem of whether or not these photons will lead to short or long range interactions has not been answered. Naturally, because these photons are massive, one would without much pondering and excogitation on the matter assume that these photons can only take part in short range interactions. Contrary to this and to conventional wisdom; via a subtlety, we show within the confines of Proca Electrodynamics, that massive photons should be able to take part in long range interactions without any problem. While leaving the speed of light as an invariant fundamental constant, the resulting theory leads to a time variation in the Fundamental Constants of Nature, namely the permittivity and permeability of free space. In-turn, this leads to a plausible explanation as to why the fine structure constant strongly appears to be varying over cosmological times.