  In a recent paper, a model for describing the quantum dynamics of massive
particles in a non-commutative two-sheeted spacetime was proposed. This model
considers a universe made with two spacetime sheets embedded in a 5D bulk where
the fifth dimension is restricted to only two points. It was shown that this
construction has several important consequences for the quantum dynamics of
massive particles. Most notably, it was demonstrated that a coupling arises
between the two sheets allowing matter exchange in presence of intense magnetic
vector potentials. In this paper, we show that non-commutative geometry is not
absolutely necessary to obtain such a result since a more traditional approach
allows one to reach a similar conclusion. The fact that two different
approaches provide similar results suggests that standard matter exchange
between branes might finally occur contrary to conventional belief.
