The fine structure constant does not vary with time, of course. If it varied with time QED would be dead, but actually QED is an extraordinary theory with an extremely high precision. In their book Gauge Theory in Particle Physics, I. J. R. Aitchison and A. J. G. Hey name part II of their book as THE BEST THEORY WE HAVE: QUANTUM ELECTRODYNAMICS. The supposed variation of the fine structure constant is just a sign of new Physics on the horizon with respect to the evolution of quasars and galaxies.
A paper with the above title, was published in Physics Essays which is not an open journal (An alternative to the variation of the fine structure constant, M. E. de Souza, Phys. Essays 24, 472 (2011)) but the interested reader can take a look at the main ideas and the simple calculations in this article by means of arXiv:astro-ph/0301085.
The basic idea can be grasped from the abstract:
It is considered that quasars evolve into normal galaxies by means of expansion of matter. The order of magnitude of the expansion velocity can be estimated. The Doppler shift caused by such expansion explains the supposed variation of the fine structure constant. This variation has been based on observations of absorption lines of gas clouds seen against background quasars. These ideas maintain the constancy of the fine structure constant.
At the Rencontres de Moriond 2014 (http://moriond.in2p3.fr/QCD/2014/) in La Thuile, Italy, I presented the talk The Higgs Boson and Quark Compositeness in which I show that the recently found Higgs boson is just one of the bosons of a large multiplet. To see the talk, please click on the link http://moriond.in2p3.fr/QCD/2014/SundayAfternoon/Everaldo.pdf
The corresponding paper related to the talk has been published on line in the conference proceedings. To see the paper, please click here.
Please, take also a look at the paper BIASED NUCLEON STRUCTURE.