I meant “Particles interact with other particles SIMULTANEOUSLY over, in theory, indefinite distances”, as in non-local/Belle’s Theorem/EPR Experiment (Einstein, Podolsky, Rosen)
http://en.wikipedia.org/wiki/EPR_paradox
This is, strictly speaking in terms of QM itself, not true. All particle interactions occur at spacetime points. They are "events" in relativistic terms.
Nonlocality is an interpretive description of the implications of the theory itself, and in my opinion, it is not aptly made. The requirement of nonlocality is on a presumed "hidden" reality consisting of discreet classical objects required to mimic, or reproduce, QM behavior, but such particles are in no way part of QM, and again IMO, represent the tenacious hold that classical Newtonian reality retains on our thinking.