I've recently read (portions of) the paper "QFT as pilot-wave theory of particle creation and destruction," available here: http://xxx.lanl.gov/pdf/0904.2287v5 This paper has been mentioned in a number of other threads, but I have a different question (not as an expert, unfortunately). The paper describes a state in QFT as containing, potentially, an infinite number of particles with zero 4-momentum - so at single points in space-time. My question is the following: can these "vacuum" particles (using terminology in the paper) interact with 'real' particles? For example, what if one of the particles with zero 4-momentum was a positron, and a 'real' electron (with an extended world line) collided with the positron? Since the positron has zero 4-momentum, clearly the result can't be the usual electron-positron annihilation. Also, if interactions were to occur, the results would be measurable, which is also clearly not possible. I'm unclear on how the proposed theory deals with the above?