We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics can be reproduced with this form of behaviour. In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. (...) In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction. (shrink)