Note the complementarity between the two types of non-local quantum effects: the explicitly homotopical situations require the loop to be uninterrupted, i.e. having no localized interaction along the paths between J and F, whereas EPR by definition requires a "measurement" at A or B. It might be possible to invent an EPR experiment in which the carriers of the information from A or B to F would consist of the same type of particle as those resulting from the disintegration at I (and thus moving along IA and IB). However, this would still not lead to a "combined" effect, because the interaction at A or B would automatically exclude the explicit global result. 4. DiscussionThis FB realization of the EPR situation posits that (non- relativistic) QM is indeed "incomplete", but only in the following sense: (1) there would be no justification, anyhow, to expect a non- relativistic theory to display "Einstein locality" or "separability" (modern "local causality" in axiomatic relativistic quantum field theory); (2) the marriage of QM with Special Relativity has been long (since 1948) known to require Quantum Field Theory, but we now also know (from our acquaintance with the Standard Model of Particle Physics) that these have to be Gauge Field Theories. Such theories are geometrical in their nature and are realized by Fibre Bundle geometries. All EPR situations can therefore be embedded in some bundle geometry deriving from an appropriate combination of the basic geometries of the Standard Model gauges and/or Gravity. (3) Thus, QM is a truncation of the 7?s spatial submanifold of a FB's Minkowski base manifold. As such, it carries a structure allowing it to fit properly into the complete relativistic FB and excluding faster-than-light effects. QM has no formal 'knowledge' of relativity; however, having emerged from studies of electromagnetism, it is endowed with several such "pre-coded" interfaces with Special Relativity. Example: E = hu and p = A/A will yield E2 �(cp)2 = 0. Similarly, the non-local structure does not represent a violation of SR because it is a part of the FB 'heritage', its active aspect being limited to global homotopy. This is the structure behind that situation which has been termed "peaceful coexistence" by Shimony14. In an indirect way, this picture is related to the fact that we have a complex Hilbert space, involving phases, the "basic element" of all gauge groups Q. The complex Hilbert space itself derives directly from the Heisenberg algebra [x,p] = ih, once we require z and p to have real eigenvalues, i.e. to be hermitean. Intuitively, one might have indeed expected quantum nonlocality to reflect the blurring of spacetime, due to the uncertainty relations. Something of the sort is happening in the FB approach, but only in a rather loose sense.47779
