  The massless fermion limit of QED is discussed. For on-shell renormalisation
the high energy behaviour fixes no lower limit on the mass of the lightest
fermion if the fine structure constant $\alpha$ is allowed to vary. The choice
of an arbitary (space-like) subtraction point does, however, fix a lower limit
on the mass of the lightest fermion, for any subtraction scale $\mu$, if the
effective charge $\aefmu$ respects both quantum mechanical superposition and
renormalisation scale invariance. Limits on the values of $\alpha$ or the
electron mass are obtained within the Standard Electroweak Model by requiring
convergence of $\aefmz$.
