  The continuity assumption breaks down because of two features of the example: the concentration of the electric charge on a point particle, and the way we have treated (or, more accurately, failed to treat) the point P, the edge of L+ (and L-). We have assumed that a point particle either hits L+, and then emerges from L-, or else it misses L+ and sails on into the region of space-time above it. This means that the charge on the incoming particle only has two possibilities: either it is transported whole back in time or it completely avoids time travel altogether. Let's see how it alters the situation to imagine the charge itself to be continuous divisible.